G C O P U B L I C A T I O K N o . 1 / 9 0

R E V I E W O F D E S I G N M E T H O D S

F O R E X C A V A T I O N S

G E O T E C H N I C A L C O N T R O L O F F I C E

C i v i l E n g i n e e r i n g S e r v i c e s D e p a r t m e n t

H o n g K o n g

© Government of Hong Kong

First published, March, 1990

Prepared by :

Geotechnical Control Office,Civil Engineering Services Department,6th Floor, Empire Centre,68, Mody Road,Kowloon,Hong Kong*

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FOREWORD

This document presents the results of a review carried outwithin the Geotechnical Control Office of the state of the art inthe design of excavation support systems, and in the predictionof ground movements around excavations. Whilst the document isnot intended to be a design guide, the information given hereshould facilitate the use of modern methods and knowledge in thedesign of excavation support systems. Practitioners areencouraged to comment to the Geotechnical Control Office on thecontents of this publication.

The review has been carried out under the general directionof Mr J.B. Massey as a project in the Geotechnical ControlOffice's Research and Development Theme on Excavations. It wasundertaken by Mr C.Y. Kwan, with checking, editing and productionby Dr P.L.R. Pang. Numerous staff of the Geotechnical ControlOffice and the Housing Department, and several firms ofconsulting engineers, have contributed during the preparation ofthis document. In particular, Dr S. Buttling provided valuablecomments in the final stages. The contributions of all those whohave assisted are gratefully acknowledged.

i f

A.W. MalonePrincipal Government Geotechnical Engineer

March 1990

CONTENTS

PageNo.

TITLE PAGE 1

FOREWORD 3

CONTENTS 5

1. INTRODUCTION 9

2. TYPES OF EXCAVATION SUPPORT SYSTEMS 11

3. CONSTRUCTION ASPECTS OF EXCAVATION SUPPORT SYSTEMS 13

3.1 SHEET PILE WALLS 13

3.2 SOLDIER PILE WALLS 15

3.3 DIAPHRAGM WALLS 16

3.4 CAISSON WALLS 18

3.5 GROUTED PILE WALLS 19

3.6 STRUTTED OR BRACED WALLS 20

3.7 TIED-BACK OR ANCHORED WALLS 21

4. LIMIT STATE METHOD OF DESIGN 23

4.1 GENERAL 23

4.2 ULTIMATE LIMIT STATES 23

4.3 SERVICEABILITY LIMIT STATES 24

5. AN OVERVIEW OF ANALYTICAL METHODS 25

5.1 TYPES OF METHODS 25

5.2 LIMIT ANALYSIS 255.2.1 General 255.2.2 Upper Bound Methods 255.2.3 Lower Bound Methods 26

5.3 ASSOCIATED STRESS AND VELOCITY FIELDS 26

5.4 BEAM ON ELASTIC FOUNDATION 275.4.1 General ,275.4.2 Power Series Method 275.4.3 Finite Difference Method 275.4.4 Distribution Method 275.4.5 Discrete Element Method 285.4.6 Advantages and Limitations 28

5.5 BOUNDARY ELEMENT METHOD 29

5.6 FINITE ELEMENT METHOD 30

6. CAm"ILEVERED OR UNBRACED WALLS 33

6.1 GENERAL 33

PageNo.

6.2 ULTIMATE LIMIT STATES 336.2.1 Types of Limit States 336.2.2 Overall Stability 346.2.3 Foundation Failure 366.2.4 Hydraulic Failure 37

6.3 SERVICEABILITY LIMIT STATES 37

6.4 EARTH PRESSURES FOR STRUCTURAL DESIGN 38

6.5 DESIGN WATER PRESSURES 40

7. STRUTTED OR BRACED WALLS 43

7.1 SINGLE-LEVEL STRUTTED WALLS 437.1.1 General 437.1.2 Ultimate Limit States 437.1.3 Serviceability Limit States 447.1.4 Earth Pressures for Structural Design 447.1.5 Design Water Pressures 48

7.2 MULTI-LEVEL STRUTTED WALLS 487.2.1 General 487.2.2 Ultimate Limit States 487.2.3 Serviceability Limit States 497.2.4 Earth Pressures for Structural Design 507.2.5 Design Water Pressures 53

7.3 TEMPERATURE EFFECTS 53

8. TIED-BACK OR ANCHORED WALLS 55

8.1 SINGLE-LEVEL TIED-BACK WALLS 558.1.1 General 558.1.2 Ultimate Limit States 558.1.3 Serviceability Limit States 588.1.4 Earth Pressures for Structural Design 588.1.5 Design Water Pressures 59

8.2 MULTI-LEVEL TIED-BACK WALLS 598.2.1 General 598.2.2 Ultimate Limit States 608.2.3 Serviceability Limit States 608.2.4 Earth Pressures for Structural Design 618.2.5 Design Water Pressures 63

V9. GROUND MOVEMENTS AROUND EXCAVATIONS j 65

9.1 GENERAL 65

9.2 FACTORS INFLUENCING MOVEMENTS 659.2.1 Effect of Stress Changes 659.2.2 Dimensions of Excavation 659.2.3 Soil Properties 659.2.4 Initial Horizontal Stress / 669.2.5 Groundwater Conditions / 669.2.6 Stiffness of Support System/ 669.2.7 Effect of Preloading / 669.2.8 Effect of Passive Soil Buttresses 67

PageNo.

9.2.9 Associated Site Preparation Works 679.2.10 Influence of Construction Factors 68

9.3 PREDICTIVE METHODS 689.3.1 Types of Methods 689.3.2 Empirical Methods 699.3.3 Semi-empirical Methods 729.3.4 Method of Velocity Fields / 729.3.5 Finite Element Method / 72

10. REVIEW OF LOCAL DESIGN PRACTICE 75

11. GEOTECHNICAL CONTROL OF EXCAVATIONS IN HONG KONG 77

12. CONCLUSIONS AND RECOMMENDATIONS 79

REFERENCES 81

TABLES 99

LIST OF TABLES 101

TABLES 103

FIGURES 109

LIST OF FIGURES 111

FIGURES 117

1. INTRODUCTION

This document presents a review of the state of the art in the designof excavation support systems in soils, and in the prediction of groundmovements around excavations. It is written in the context of the denseurban setting of Hong Kong and its geological and topographicalcharacteristics. While a fair proportion of the literature reviewed isbased on British and North American work, relevant Hong Kong literature isalso cited. A brief review of the design practice and geotechnical controlof excavations in Hong Kong is given in Chapters 10 and 11 respectively.

In this document, the term "excavation" is applied generally to coverall basements, large pits and trenches, while the term "deep excavation" isreserved for excavations which are deeper than about six~lnetres (20'feet),in conformity with the convenient distinction made by Terzaghi & Peck(1967). Descriptive terms used for rocks and soils are as defined inGeoguide 3 : Guide to Rock and Soil Descriptions (GCO9 1988).

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TYPES OF EXCAVATION SUPPORT SYSTEMS

Excavations for urban building development and civil engineering worksare often carried out up to the property boundary and usually requirebatters which are not stable without structural support. Some of thestructural systems which have been used to provide lateral support to theground are illustrated in Figure 1 (Institution of Structural Engineers,1975)5 and their advantages and disadvantages are listed in Table 1.

The following retaining wall types are commonly used in Hong Kong tosupport excavations :

(a) sheet pile wall,(b) soldier pile wall,(c) diaphragm wall,(d) caisson wall, and(e) grouted pile wall.

The above retaining wall types can be further divided into the followingthree categories according to the form of support provided :

(a) cantilevered or unbraced wall,(b) strutted or braced wall, and(c) tied-back or anchored wall.

The factors to be considered in the choice of a support system for a deepexcavation are given in Table 2.

The cantilevered wall depends upon its own strength and embedment tocarry the earth and water loads, while strutted and tied-back wallstransfer much of these loads to additional support elements. Cantileveredwalls are limited to relatively shallow excavations unless designed to bemassive and embedded in stiff soils. However, under such circumstances thestrutted or tied-back wall is likely to be more economic than thecantilevered wall.

In a strutted excavation, there is an economic incentive to thecontractor to excavate as far as possible below the supports. For tlerbacksystems.* the excavation floor at • any given time is a necessary arvEtconvenient platform for the installation of the anchors, which is usuallycarried out at the correct levels due to difficulties in providing accesslater. In this respect, tie-back systems have an advantage over struttedsystems in that they automatically guard against over-excavation. Althoughan open excavation area is created by the tie-back systems, their adoptionis not always possible due to encroachment into adjacent property. In theurban areas of Hong Kong, (the strutted excavation is the most popularsystem. ")A summary of the design considerations for strutted and tied-backwalls is given in Table 3.

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3. CONSTRUCTION ASPECTS OF EXCAVATION SUPPORT SYSTEMS

3A SHEET PILE WALLS

The sheet pile wall is the most common type of temporary retainingwall system used in Hong Kong. When selecting sheet piles to be used, itis important to taken into account the drivability of the piles. Theability of a sheet pile to penetrate the ground depends on the section sizeof the pile and the type of pile hammer used, as well as the groundconditions, Gillespie (1983) considered that it is difficult to drivesheet piles through soils with' Standard Penetration Test (SPT) :':|NI valuesgreater than about 50, and that the penetration through zones with N valuesof 80 or more is very limited. For heavy pile sections, however, thecorresponding SPT values could be up to 80 and 120 respectively. It shouldbe noted that hard driving conditions will necessitate the use of pilesections larger than those required to resist bending moments due tolateral earth pressures.

It is not uncommon in Hong Kong for sheet piles not to reach designpenetration. At an estimated 75% of sites where sheet piles were used(Malone, 1982), this problem was sufficiently extensive to necessitate asignificant design change after the piles were driven. In weathered rocksand colluvium, hard corestones and boulders are the obstacles, whereas infill, the problems are boulders, old foundations and seawalls. Theseobstructions are normally removed in advance of the main excavation bymeans of a local cofferdam, and then the sheet piles are redriven to therequired depth of penetration. In some cases, even the use of a powerfulpile hammer and heavier steel sheet pile sections is unable to either splitor push aside the boulders or corestones. Special measures such as theprovision of grout curtains behind, and driving of H-piles in front of theinadequately penetrating sheet piles may be necessary. Sometimes, part ofa line of sheet piles is replaced by a group of soldier piles installed inpre-drilled holes through the obstruction.

Seepage may be expected to pass through interlocking steel sheetpiling which supports a difference in hydraulic head. In compressiblesoils, the drop in piezometric levels may induce cjyjsol.Tdation. Tearing ofinterlocks under hard driving conditions may cause ground loss due togroundwater infiltration through the torninterlocks. Extraction of steelsheet piles from cohesive soils often results in removal of soil at thesame time, leading to settlement of adjacent ground.

Driving steel sheet piles in loose sandy soils can result in settle-ments in adjacent ground. The effects of noise and vibration caused bysheet piling operations have been discussed by Clough & Chameau (1980) andSarsby (1982). In Hong Kong, legislation was introduced in 1988 to controlnoise from construction and other activities. Under the Noise ControlOrdinance (Government of Hong Kong, 1988), construction noise permits mustnow be obtained from the Environmental Protection Department prior to theuse of percussion piling during specified periods. Information on 'quiet1

construction equipment and working practices, including percussion pilingmethods, is given by Environmental Protection Department (1989).

Malone (1982) reported six sheet pile wall collapses and two cases ofgross movement of sheet pile walls (Figure 2), and listed the factorspresent in these eight cases as follows :

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(a) inadequate toe support to pi les which do notpenetrate below bottom excavation level (Figure2(a)), four known instances,

(b) buckling of struts due to inadequate horizontal orvert ical s t i f fening (Figure 2(b}), three knowninstances,

(c) raking struts too steep and improperly fixed topiles (Figure 2(a)), two known instances,

(d) raking struts inadequately founded (Figure 2(b)),one known instance,

(e) over-excavation in the passive soi l buttress ori t s complete premature removal p r i o r toinstallation of struts (Figure 2(c)) , two knowninstances.

(f) In one case, translationai shear fa i lure appearsto have taken place along a surface at about toelevel in a layer of clay, presumed to be a marinedeposit, the low shear strength of which had notbeen appreciated.

I t should be noted that in seven of these cases lateral support wassupposed to be provided by raking struts, and that in at least f ive of theeight cases the piles involved had not been driven to the design levelbefore excavation commenced.

Other case histories of sheet pi le wall failures have been given bySowers & Sowers (1967), Broms & St i l l e (1976), and Daniel & Olson (1982)•These studies show that failures of anchored bulkheads and excavationsupports are seldom the result of the inadequacies of modern earth pressuretheories. Instead, they are caused by the neglect of surcharge loads,construction operations that produce excessive earth pressures, poorlydesigned support systems, inadequate allowance for de f l ec t i on ,deterioration and corrosion, and poor design and construction deta i ls .

The following comments were given by Beattie (1983) on the practicaldesign of sheet pi l ing under Hong Kong conditions :

(a) Sheet piles are rarely installed in a straightl ine or ve r t i ca l at depth and the design ofshoring and packing may need to be modified onsite to cope with the deviations. The packingdetai ls should be adequate to take the designloads. Otherwise, yielding of the support w i l lallow movement of the piles and retained ground.

(b) Guidance should be given on the drawings ofactions to be taken i f the sheet pi les areprevented from reaching their design depths byboulders or o the r o b s t r u c t i o n s . Otherdifferences between the designer's assumptions andthe actual s i te conditions should be investigated.

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(c) The designer should specify monitoring, theresults of which should be made immediatelyavailable if they are to be of use in gauging theperformance of the works.

(d) The site staff should take time to secure progressby ensuring proper installation of struts andsupport before proceeding with excavation.

(e) Regular site inspections by the designer and closecooperation with the builder are important toensure the works comply with the intent of thedesign at all stages.

3.2 SOLDIER PILE WALLS

Soldier pile walls have two basic components, soldier piles (verticalcomponent) and lagging (horizontal component). Soldier piles provideintermittent vertical support and are installed before excavationcommences. Due to their relative rigidity compared to the lagging, thepiles provide the primary support to the retained soil as a result of thearching effect. Spacing of the piles is chosen to suit the arching abilityof the soil and the proximity of any structures sensitive to settlement. Aspacing of 2 to 3 m is commonly used in strong soils, where no sensitivestructures are present. The spacing is reduced to 1 to 2 m in weaker soilsor near sensitive buildings. It is essential that the soldier piles aremaintained in full contact with the soil. For this reason, they are eitherdriven or placed in pre-drilled holes, which are backfilled to the groundsurface with lean concrete.

The lagging serves as a secondary support to the soil face andprevents progressive deterioration of the soil arching between the piles.It is often installed in lifts of 1 to 1.5 m, depending on the soil beingsupported and on the convenience of working. There are four methods oftransferring earth pressures from the lagging to driven soldier piles, asshown in Figure 3 (Peck, 1969b) :

(a) Lagging is wedged against the inside flanges(Figure 3(a)). In this method, the soil yields asit is trimmed to make room for the lagging. Mostof the earth pressure is transferred through thesoil to the pile and very little through thelagging to the pile. However, any remaining voidsbetween the soil and the lagging could permitfurther soil movement.

(b) If large voids exist between the soil and thelagging in (a), they can be filled with grout ormortar to provide full contact (Figure 3(b)).

(c) Lagging set between spacers, the soldier piles andthe soil permits the piles to be included aspermanent reinforcement to the structural wall(Figure• 3(c)). Earth pressure is transferred tothe piles as the excavation is carried to the faceof the piles, but the heavily loaded soil behind

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the piles is then cut away to provide room for thespacers and the lagging. As a resul t , the "earthwall1 moves into the-excavation which can resultin substantial surface settlement (Peck, 1969b).Therefore, this method should not be used unlesslarge settlement adjacent to the excavation isacceptable.

(d) Contact sheeting is placed against the flanges ofthe soldier piles on the wall of the cut t ing,permitting a t ight f i t because the exposed soilcan be trimmed cleanly to the edge of the flange(Figure 3(d)J. I t is the most satisfactory methodfor reducing lateral movements, and also serves toprovide a form for concrete for the permanentwall.

I f there is risk of groundwater building up behind a lagged wal l , orof washing in of soil part icles, drainage holes may be provided or smallgaps may be lef t between the boards to allow drainage, and in such cases af i l t e r material such as a synthetic fabric may be used to prevent loss ofso i l .

Suitable conditions for soldier pi le walls are provided by over-consolidated clays, in al l soils above the water table i f they have atleast some cohesion, and in homogeneous, free-draining soils that can beeffectively dewatered. Unsuitable conditions include squeezing soils suchas soft clays and running soils such as loose sands.

In Hong Kong, so ld ier p i le walls are used mainly for smallexcavations. They are less popular than sheet pi le walls, although soldierpiles instal led in p re -d r i l l ed holes are often used to overcome theproblem of inadequate penetration of sheet piles in areas where rock isencountered at shallow depths below the excavation. They are generallyunsuitable for excavations below the groundwater level , part icularly wherethe retained materials are granular in nature. This is because dewateringmay cause signi f icant loss of material and unacceptable settlement toadjacent structures and land, and provision of a grout curtain behind andbeneath the wall to strengthen the ground and to act as a groundwater cut-off is expensive. For driven soldier pi les, driving of the H-sections maycause heave and settlement of nearby structures (D'Appolonia, 1971). Inhard driving conditions caused by boulders or other obstructions, soldierpiles can be redril led i f necessary, or relocated to avoid the obstruction,which gives them an advantage over sheet pi le walls. Predri l l ing is oftenused in urban areas to avoid the noise and vibration of pile dr iv ing.

3.3 DIAPHRAGM WALLS

The diaphragm walling technique was f i r s t introduced to Hong Kong forthe construction of the New World Centre (Tamaro, 1981). As a result ofi t s successful u t i l i za t ion , the technique was used extensively in theconstruction of the Mass Transit Railway (MTR) underground stations(Openshaw & Marchini, 1980; Mclntosh et a l , 1980; Budge-Reid et a l , 1984)and of deep basements for high-rise buildings (Openshaw, 1981; Chipp, 1983;Craft, 1983; Fitzpatrick & Will ford, 1985; Humpheson et a l , 1986).

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The design and construction of diaphragm walls have been discussed indetail by Xanthakos (1979) and the practical problems associated withdiaphragm walling under Hong Kong conditions have been discussed byOpenshaw & Marchini (1980), Davies (1982), and Craft (1983).

An important local problem is the temporary stability of the slurry-filled trench. The stability of slurry trenches under Hong Kong conditionshas been reviewed by Buttling (1983) and Wong (1984). Wong (1984)considered that both Huder's (1972) method and Schneebeli's. (1964) methodare conservative for cases in Hong Kong where the soil is fill, marinedeposit or colluvium. The reason for this is possibly due to the localpractice of not using the apparent cohesion component of soil strength indesign. A design procedure was proposed (Wong, 1984) for predicting thestability of slurry trenches subjected to heavy surcharge load fromadjoining and adjacent foundations, by taking into consideration theredistribution of surcharge load to soil adjacent to the excavation, andthe redistribution of stresses in the building structure.

In reclaimed land in Hong Kong, the presence of randomly dumped loosebouldery fill is not uncommon. A method for dealing with this problem hasbeen described by Craft (1983). The technique is to first excavate atrench (prior to guide-wall construction) along the line of the diaphragmwall by backhoe to below groundwater level, and to backfill it with a leanmix concrete mixed with bentonite. The lean mix design has to be wetenough to be tremied, strong enough to stabilise the boulders, yet weakenough to be excavated subsequently by clamshell, and of low permeability.The guide-walls are then constructed. Excavation by clamshell is carriedout through the lean mix concrete and as far as possible into theunderlying boulders. Excavation is usually terminated on the basis ofdeclining net progress. At this point, lean mix concrete is tremied intothe excavation. This operation is repeated until the bouldery fill stratumhas been stabilised by the lean mix concrete.

Trench stability in soft clays can be improved by reducing the panellength or increasing the slurry pressure. The slurry pressurecanbeincreasedby either increasing the density of the slurry, or raising thelevel of the slurry above ground level by raised guide-walls; this lattermethod is not favoured by contractors. To increase the density, specialadditives can be used, but the properties of the slurry must not conflictwith the requirements for placing the concrete. Buttling (1983) consideredthat viscosity is a more significant parameter than density with regard todisplacement of bentonite by concrete, and with proper specification thetwo parameters can be independently controlled. In sands and otherpermeable soils, groundwater lowering can be used to improve trenchstability, as stability depends on the net slurry pressure, i.e. thedifference in head resulting from the difference in level between theslurry within the trench and the external groundwater (Fitzpatrick &Will ford, 1985; Humpheson et al, 1986).

During construction of diaphragm walling in weathered granite in HongKong, significant ground movements have been observed causing large surfacesettlement extending a considerable distance from the wall (Davies &Henkel, 1980; Cowland & Thorley, 1984). It is considered that thehorizontal movement adjacent to individual panels was a result of swellingof the weathered granite, which created a compressible zone around thediaphragm wall panel. On construction of adjacent panels the archingaround the compressible zone broke down, and recompression occurred as the

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earth pressure built up. This caused horizontal ground movements to extendback from the wall (Davies & Henkel, 1980; Davies, 1982). The groundmovements can be controlled by increasing the net slurry pressuresupporting the trench, in a similar manner to that described for improvingtrench stability in marine clays and sands.

Corestones or 'bedrock1 (generally taken to be a rock mass containingrock materials wholly or predominantly of grades I to I I I ) encounteredduring the construction of diaphragm walls in weathered granite can bebroken up by grab and chisel (Openshaw & Marchini, 1980). However,diaphragm walling in such cases is extremely expensive due to the cost ofrock excavation. Therefore, i t is common practice to stop the wall on topof bedrock. I f the toe of the diaphragm wall is exposed as the mainexcavation continues into bedrock, the wall w i l l need to be underpinned,and chemical grouting may need to be carried out to provide an effectivecut-off against groundwater.

Diaphragm walling, although expensive when compared with other wallsystems, frequently provides the best solution to many undergroundconstruction problems, and the technique can usually be adjusted to copewith most conditions of d i f f i c u l t ground and adjacent surcharge byadjustment of the panel length, properties of the slurry, level of slurryin the trench and groundwater lowering.

3.4 CAISSON WALLS

Hand-dug caisson retaining walls, often referred to as caisson walls,are widely used in Hong Kong, The caissons are usually dug in stages ofabout one metre depth, by husband miners with their wives serving as winchoperators at the ground surface. Each stage of excavation is lined with aminimum of 75 mm thickness of insitu concrete using a tapered steel shuttersuitably supported and designed for ease of str iking. The shutter remainsin place to provide support for the fresh concrete and surrounding groundwhile the next stage of excavation proceeds. Submersible electric pumpsare commonly used for dewatering at the base of the caissons. Excavationthrough corestones and other obstructions is carried out by pneumaticdri l l ing. Pope (1983) considered that the main advantages of a caissonwall over a conventional retaining wall are :

(a) I t can be constructed without temporary soil cutsor shoring.

(b) I t requires a small plan area and can be usedclose to site boundaries and existing structures.

(c) I t can act as both temporary and permanentretaining structures.

(d) Obstructions, e.g. corestones and boulders, can beovercome without too much d i f f icu l ty .

I t should be noted that some of the above advantages also apply to otherwall types described in this Chapter.

Caisson walls were used in the construction of the MTR undergroundstations (Benjamin et a l , 1978; Mclntosh et a l , 1980) and of deep basements

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for multi-storey buildings (Beattie & Mak, 1982; Addington, 1983). Thecaissons can be contiguous, or closely spaced at about two-diameter centreswith in-filled concrete panels.

Base heave failures have been experienced with hand-dug caissons inHong Kong (Chan, 1987). The mechanism of heave is poorly understood, butit is believed to be the result of slaking and swelling, and hence loss ofstrength, of residual soils and saprolites due to heavy seepage and stressrelief. The presence of weak layers such as clayey marine and alluvialdeposits may also bring about such failures. The possibility of base heaverenders the construction of a deep hand-dug caisson extremely hazardous,particularly when it is carried out below the groundwater table.Moreover, groundwater drawdown for caisson excavation can result in groundsettlement and damage to adjacent structures (Morton et al, 1980a & b;1981). Precautionary measures such as the provision of grout curtainsbehind the caissons to reduce the effect of drawdown can be expensive.Nevertheless, these are commonly applied whenever unfavourable groundconditions are anticipated. The choice of grouts for hand-dug caissonconstruction has been discussed by Shirlaw (1987).

Another problem with caisson wall construction is the installation ofback drainage. Various forms of drainage system have been discussed byMalone (1982) and these are shown in Figure 4. Type I suffers from thedefect that at each stage of excavation the work is undermined. In typeII, the no-fines concrete is generally not an adequate filter for residualsoil/weathered rock. Types III and IV involve placing filter media in adeep, narrow borehole. Type IV also involves the installation ofperforated pipes from the caisson shaft as excavation proceeds. Type Vrequires the installation of conventional horizontal drains. The long-termperformance of these drainage systems will depend greatly on the care takenin design, specification, construction, monitoring and maintenance.

3.5 GROUTED PILE WALLS

The grouted pile walling technique was introduced to Hong Kong in theconstruction of the Tsim Sha Tsui MTR Station (Mclntosh et al, 1980). Themost common form that has been used is the "Pakt-in-Place11 or PIP wallsystem. A PIP pile is formed by boring with a continuous flight hollowshaft auger to the design depth. As the auger is withdrawn, cement-sandmortar is injected through the auger shaft, leaving a formed mortar pile.A reinforcement cage is then lowered into the mortar to form a completereinforced PIP pile. To form a continuous pile wall, PIP piles (A piles)are formed in alternate pile positions in the above manner. The infillpiles (B piles) are then constructed in the same way as the A piles, exceptthat during the auger withdrawal and mortar placement, a high pressureplunger pump is used for injecting cement paste through the pile, whicheffects a vertical mortar cut-off between the B piles and the adjacent Apiles.

A recent innovative form of construction, known as '.pipe pile walling1

has been used to overcome the problem of inadequate penetration whendriving sheet piles through weathered rock with corestones and through oldfoundations. A pipe pile is formed by installing a perforated steel casingin a drillhole greater in diameter than the casing. As the drill assemblyis withdrawn through the casing, suitable grouts are injected through theperforated casing into the surrounding soil. The forming of a pipe pile

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wal l is s i m i l a r to tha t of a PIP w a l l .

The advantages of the pipe p i l e wa l l i ng technique are as f o l l o w s :

(a) The i n s t a l l a t i o n o f t he p i l es invo lves l i t t l enoise and v i b r a t i o n .

(b) The w a l l can p e n e t r a t e t h r o u g h b o u l d e r s ,corestones and hard obs tac les ,

3.6 STRUTTED OR BRACED WALLS

Di f f e ren t schemes fo r s t r u t t i n g are shown in F igure 5. These inc ludethe c ross- lo t s t r u t t i n g and rak ing s t r u t support schemes i l l u s t r a t e d inFigures 5(a) and 5 (b ) . The diagonal s t r u t t i n g technique shown in Figure5(c) i s more s u i t e d t o smal l and p re fe rab ly square excava t ions , e . g .shafts- The disadvantage o f c r o s s - l o t s t r u t t i n g i s ^ t h a t the working spacecan be severely r e s t r i c t e d . Diagonal s t r u t t i n g is sometimes used near thecorners of wide excavations and serves to leave a la rge p o r t i o n o f theexcavation open. Because only a few s t r u t s are used, these s t r u c t u r a lelements can be very large ( t y p i c a l l y , pipe sect ions are used) , and theycan be s u b j e c t t o l a r g e v a r i a t i o n s i n loads due t o t e m p e r a t u r ef l u c t u a t i o n s . In some cases, the s t r u t s are covered or pa in ted w i t h ar e f l e c t i v e pa in t t o minimise temperature e f f e c t s .

Various methods have been devised to expedi te the cons t ruc t i on o f deepbasements t h rough the use o f t h e permanent s t r u c t u r e t o support theexcava t ion d u r i n g c o n s t r u c t i o n . These methods have the advantage ofa f fo rd ing savings of both t ime and resources, but they do demand a h ighdegree o f c o o r d i n a t i o n between the designer and c o n t r a c t o r , and t i g h tcontrol of the sequence o f opera t ions . Figures l ( e ) , l ( k ) and l(m) showexamples of such methods.

B e a t t i e & Yang (1982) descr ibed a p ro jec t i n which an i n d u s t r i a lbu i l d ing was constructed using the "top down1 method. Dur ing c o n s t r u c t i o n ,the p a r t i a l l y completed b u i l d i n g was used to support an excavat ion up t o15m deep. Gar re t t & Fraser (1984) described how the top down method ( i nwhich the columns of a bu i l d i ng below ground leve l are f i r s t cons t ruc tedand then t he permanent s t r u c t u r e i s b u i l t p r o g r e s s i v e l y downwards,support ing the excavation wal ls as they are exposed), the bottom up method( in which the excavation is f i r s t completed and the permanent s t r u c t u r e isb u i l t from the bottom upwards), and a combination o f top down and bottom uptechniques, have been used success fu l l y in the c o n s t r u c t i o n of t he MTRunderground s t a t i o n s .

Connections and d e t a i l s are o f c r i t i c a l importance in an i n t e r n a l l ys t r u t t e d excavat ion. Shoring plans should show :

(a) appropr ia te means f o r pos i t i on i ng and f i x i n g ofs t r u t s and wa l i ngs , and f o r brac ing o f s t r u t s inbo th v e r t i c a l and hor i zon ta l planes t o prov idel a t e r a l s t a b i l i t y ,

(b) d e t a i l s o f web and connect ion s t i f f e n e r s , andbrackets ,

21

(c) details of welding and other means of structuralconnection,

(d) details of connections between raking struts andthe foundation,

(e) sequence of installation and dismantling of allelements of the structure, and

(f) provisions, if any, for wedging and jacking ofstruts to prevent horizontal movement.

Typical connection details are shown in Figures 6 and 7. Proceduresfor prestressing, wedging or jacking to maintain tight contact for allsupport members and to provide for distribution of load to struts andwalings are also very important. Typical prestressing details are shown inFigures 8 and 9. Flat jacks are also commonly used in Hong Kong forprestressing strutted excavations. Preloading to about 50% of the designload is common practice in areas where displacements are of concern.Strut removal can give rise to additional displacements, and these may becontrolled by a combination of well-planned re-strutting and effectivecompaction of the backfill between the wall and the structure.

For walls supported by raking struts, the Canadian FoundationEngineering Manual (Canadian Geotechnical Society, 1985) recommends adetail which involves the construction of trenches in the passive earthbuttresses to accept the raking struts and their footings. It alsorecommends that the distance of a footing from the wall face should be morethan 1.5 times the length of the wall embedded below the toe level of thepassive earth buttress. These measures are intended to limit the lateralmovement of flexible walls.

3.7 TIED-BACK OR ANCHORED WALLS

Some tie-back or anchored systems are shown in Figure 10. Theseinclude 'deadman1 type anchorages, driven piles and grouted anchor systems.In Hong Kong, prestressed ground anchors are commonly used for retainingexcavations. The connecting elements between anchorages and anchor headsare either tie rods or cable strands. Because these elements are commonlymade of high strength steel, usually only a small area of steel is requiredto give the necessary capacity; as a result, the longitudinal stiffnessesof the cables or tie rods are relatively small compared to those of struts.Double corrosion protection of these important structural elements is nowstandard practice in Hong Kong (GCO, 1989).

Because of their relatively low cost and ease of construction inconfined areas, soil nails are being used increasingly in Hong Kong forsupporting excavations (Massey & Pang, 1989).

23

4. LIMIT STATE METHOD OF DESIGN

4.1 GENERAL

In this document, the approach to geotechnical design is discussedusing limit state terminology, A limit state is a performance criterionrelated to a limiting condition beyond which a structure or an element isassumed to become unfit for its purpose. The limit state approach todesign requires the designer to check the adequacy of the structure againstpossible limit states (e.g. ultimate and serviceability limit states) thatcould be of importance during the design life of the structure. There isnothing new about the limit state approach; international standards onstructural use of concrete based on such an approach were available in theearly 1970's. Limit state design is, however, unnecessarily associatedwith the use of probability theory (in the assessment of risk), statisticsof variation (in the assessment of loads and material properties) andpartial safety factors. The application of limit state principles togeotechnical design does not demand the use of these, either singly or incombination. Nevertheless, the possible inclusion of these additionalconsiderations in future geotechnical codes of practice has caused a greatdeal of controversy (see, for example, Boden, 1981; Bolton, 1981; Ovesen,1981; Semple, 1981; Simpson et al, 1981; Smith, 1981). Limit state designof earth retaining structures is advocated in the Draft Model for EurocodeEC 7 : Common Unified Rules for Geotechnics, Design (European GeotechnicalSocieties, 1987), which gives a full account of the use of the underlyinglimit state principles.

A structure should be so designed and constructed that its functionalrequirements are fulfilled throughout its design life. Normally thisrequirement is satisfied by demonstrating that the structure has thenecessary safety against ultimate failure (ultimate limit state) at alltimes, and that the predicted movements and deformations can be tolerated(serviceability limit state). These two so-called 'functional require-ments1 mean that two separate calculations are often performed for eachindividual structure, viz. an analysis against ultimate states of failure,and a deformation analysis of the states of normal use (working condi-tions). In practice, however, which of these analyses should be used isoften dictated by experience; the other analysis may often either beomitted completely or limited to a rough check.

4.2 ULTIMATE LIMIT STATES

An ultimate limit state of a structure is deemed to have been reachedwhen sufficient parts of the structure, the soil around it, or both haveyielded to result in the formation of a failure mechanism in the ground orsevere damage (e.g. yielding or rupture) in principal structuralcomponents. Design against ultimate limit states includes checking againstmodes of failure such as sliding, overturning, bearing capacity, uplift,and hydraulic failure.

Theoretical methods for analysing structures at collapse limit statehave been developed within the framework of plasticity theory. There aretwo common approaches, the kinematic method proposed by Coulomb and thestatic method advocated by Rankine. When dealing with perfectly plasticmaterials, these two approaches provide upper bound and lower bound

24

est imates o f the collapse load r e s p e c t i v e l y . S t a t i c methods, such asstress ana lys is , are known to be pess im is t i c when compared w i t h k inemat ictechniques, such as wedge or s l i p c i r c l e a n a l y s i s , which are known to beinherent ly o p t i m i s t i c . K inemat ica l ly admiss ib le mechanisms are use fu l indetermining the possible degree o f conservat ism in t h e i r s t a t i c counter -par ts . Where s t a t i c a l l y admissible s t ress f i e l d s cannot be e a s i l y d e r i v e d ,i t is necessary to optimise the geometries o f d i f f e r e n t presumed mechanismsto achieve a reasonably low upper bound s o l u t i o n ,

4.3 SERVICEABILITY LIMIT STATES

A s e r v i c e a b i l i t y l i m i t s t a t e o f a s t r u c t u r e is deemed to have beenreached w i t h t he onset o f excess ive deformat ion or o f d e t e r i o r a t i o n .Design a g a i n s t s e r v i c e a b i l i t y l i m i t s t a t e s inc ludes checking aga ins tunacceptable t o t a l and d i f f e r e n t i a l movements, c r a c k i n g , and v i b r a t i o n .

S e r v i c e a b i l i t y l i m i t s t a t e c a l c u l a t i o n s f o r e a r t h r e t a i n i n gstructures involve so lu t i on o f s o i l - s t r u c t u r e i n t e r a c t i o n problems, whichr e q u i r e t he use o f d e f o r m a t i o n p a r a m e t e r s . F i n i t e element methodsi n c o r p o r a t i n g appropr iate s o i l models are we l l s u i t e d t o t h i s t ype o fa n a l y s i s . However, they are present ly too cumbersome and c o s t l y f o rgenera l a p p l i c a t i o n , and a c c u r a t e de terminat ion o f the requ i red s o i lparameters is d i f f i c u l t .

Conven t iona l 'wo rk i ng s t r e s s 1 design methods o f t en con ta in l a r g esafety fac to rs against col lapse which are also intended t o l i m i t the ex ten to f y i e l d i n g in the s o i l ; e l a s t i c s o i l s t ra ins are gene ra l l y considered tobe less damaging than p l a s t i c s o i l s t r a i n s . However, t h i s approach doesnot y i e l d the order o f the l i k e l y deformation o f t he s t r u c t u r e and thead jacen t g round . Design methods a re c o n s i d e r a b l y c l a r i f i e d i f thepred ic t i on o f deformations is kept separate from c a l c u l a t i o n s f o r checkingagainst co l l apse .

25

AN OVERVia OF ANALYTICAL METHODS

5.1 TYPES OF METHODS

Methods f o r a n a l y s i n g e a r t h r e t a i n i n g s t r uc tu res can be broadlyc l a s s i f i e d i n t o the f o l l o w i n g types :

(a) limit analysis,(b) associated stress and velocity fields,(c) beam on elastic foundation,(d) boundary element method,(e) finite element method.

These methods are discussed in the following sections.

5.2 LIMIT ANALYSIS

5.2.1 General

The methods of Coulomb and Rankine are the forerunners of the limitanalysis approach. As discussed in Section 4.2, they provide upper boundand lower bound estimates of the collapse load respectively. Therefore,they are well suited to the analysis of ultimate limit states. However,they cannot predict deformations associated with the collapse load nor canthey yield information prior to the limit state being reached.

5.2.2 Upper Bound Methods

An upper bound s o l u t i o n is obtained by op t im is ing the co l lapse loadobta ined from presumed mechanisms w i th k i n e m a t i c a l l y admiss ib le v e l o c i t yf i e l d s . The v e l o c i t y f i e l d s have t o s a t i s f y t h e v e l o c i t y boundaryc o n d i t i o n s , and have t o be continuous except at c e r t a i n d i s c o n t i n u i t ys u r f a c e s , where t h e normal v e l o c i t y must be continuous but where thet a n g e n t i a l v e l o c i t y may undergo a jump on cross ing t h e boundary. The t r i a lwedge method is normally used to ca l cu l a te ear th pressures ac t i ng on ane a r t h r e t a i n i n g s t r u c t u r e (GCO, 1 9 8 2 ) . Janbu (1957) deve loped ag e n e r a l i s e d procedure o f s l i c e s method which can be adapted f o r ea r thpressure computat ions.

Methods o f s l i c e s such as t h a t o f Janbu (1957) w i l l g i ve upper bounds o l u t i o n s f o r v e l o c i t y f i e l d s which are k i n e m a t i c a l l y admiss ib le . Theyhave advantages in t h a t layered s o i l deposi ts can be analysed, dra ined andundrained s o i l s t rengths can eas i l y be accommodated, and the mechanics o ft h e methods a re known t o most g e o t e c h n i c a l e n g i n e e r s . A l s o , whenprogrammed i n t o a compu te r , these methods can g r e a t l y f a c i l i t a t e thec a l c u l a t i o n s . The d isadvantages, which are common to a l l l i m i t ana lys i sprocedures , are :

(a) No in fo rmat ion on deformat ions can be ob ta ined .

(b) The e f f e c t s o f i n t e r a c t i o n o f m a t e r i a l s w i t hd i s p a r a t e s t r e s s - s t r a i n c h a r a c t e r i s t i c s are notcons idered.

(c) The inf luence o f cons t ruc t ion sequence or unusuali n i t i a l s t ress cond i t ions are not accounted f o r .

(d) A t r i a l procedure must be employed to loca te themost c r i t i c a l f a i l u r e su r face .

5.2.3 Lower Bound Methods

A lower bound solution of the collapse load is determined from astatically admissible stress field which satisfies the stress boundaryconditions, is in equilibrium, and nowhere violates the yield condition.If the upper bound and lower bound solutions coincide, then the resultthe exact solution for the problem considered. is

Numerical analysis using lower bound limit procedures was proposed bySokolovski (1965) following a finite difference scheme. In the Sokolovskiapproach, the equations of equilibrium in two dimensions are combined withthe Mohr-Coulomb failure criterion to give a pair of differential equationsfor the stresses along stress characteristics (i.e. lines along which theMohr-Coulomb criterion is satisfied). The resulting differential equationscan be solved by using finite difference techniques for stresses in the

% a !°n9 *?? soi l;structure interface. The solution yields aion for the collapse load, the earth pressure distribution on the$ d l S t r i b u t i o n in the s o i l mass at the assumed

In L v L ^as ? 2 «PP«-oachSrners oTthenodes alnnn 5eouations? Llower boundthe methodsuited for USP innoted tha? thethe mesh %?4 proems only

the

S t J e S S

a 1 o w e r b o u n d a n a 1 * s i s somewhat s i m i l a r t o theis more f l e x i b l e than Soko lovsk i ' s t echn ique ,

the s o i l mass adjacent to the s t r u c t u r e is model lede 1 f J e n t S

kc o n r \ e c t e d a t ™dal p o i n t s , which a re the

b o u n d a ^ condi t ions are s p e c i f i e d a t thep y i e l d C r i t e r i a < i n t h e f ° ™ . o f c o n s t r a i n t

' c t * m e a n s ° f . l i n e a r Programming techn iques , optimum4 t r e s s e s

tw i t h i n the elements are ob ta ined .

s n a ° W n *}reSS f i e l d ' n w o u l d a P P e a r to bef f f i 1 $ ? f m ° r e C O m p l e x Problems. However,

L ^ ] n c r f ^ v «ry r a p i d l y w i t h the

pBecausei d e a l l yLysmer

s i z e o f] f v «ry r a p i d l y w i t h the s i z e o fa p p l l c a t l o n h a s c u r r e n t l y been l i m i t e d to

S U f f e r f r o m m ^ o f t h e d isadvantages o fa r e m o r e d i f ^ u l t to app l y , t h e i r r S l e in

5.3 ASSOCIATED STRESS AND VELOCITY FIELDS

( r $associated) s t ress and s t r a i n

d e f l e c t i o n ^ r ^ a d To beain ai n i t i a l s t r ess f i e l d is p red ic tedNext, an i n i t i a l s t r a i n % 1 ^ l d Is(1972) and Serrano (1972^ usinoA f te r determinat ion o f the s t a i nassumed s o i l parameters are not

* • ^ development o f c o n s i s t e n tl a

f H ° r - f l X e d d e m e n t s o f s t r u c t u r a lb d ^ T ^ } i s s P e c i f i ^ , and an

° f S o k o l o v s k i ( 1 9 6 5 ) •a s . 1

d e S C r i b e d b ^ J a m e s e t a l

? 0 1 1 d e f o r m a t i o n Parameters.

27

strains. An iterative procedure is then adopted to generate stress andstrain fields which are consistent with all parametric assumptions. Atconvergence, a complete distribution of stresses and strains in the soil isobtained, as well as earth pressures on the structure.

Fundamental questions remain concerning the appropriateness of theassumed stress-strain laws and the effect on the predictions caused by non-coincidence of principal stress and strain increment directions. Also,questions relating to practical applications, e.g. how wall frictiondistributions can be assigned, and how account can be taken of constructionsequences, seepage loadings, structural flexibility, etc., have yet to beanswered. As the method is not fully developed, it is difficult toevaluate its potential as a design tool. Nevertheless, the method doesprovide the geotechnical engineer with a powerful tool to enhance hisunderstanding of the processes involved in soil-structure interaction.

5.4 BEAM ON ELASTIC FOUNDATION

5.4.1 General

The assumption of a beam or slab on an elastic foundation has foundapplication in numerical analysis of sheet piles and strutted excavations.Power series, finite difference, distribution and discrete element methodshave been employed for the solution of the governing differentialequations. In each case, the elastic foundation is assumed to generate areactive pressure proportional to the deflection (Winklerfs (1867)hypothesis) and, in essence, consists of a bed of springs. The soilresponse is usually characterised by a spring constant, which is related tothe 'coefficient of subgrade reaction1. The coefficients of horizontalsubgrade reaction recommended by Terzaghi (1955) are normally used. Thefollowing Sections give a brief review of work based on the Winkler model.

5.4.2 Power Series Method

Rowe (1955a) used t h e power s e r i e s method to so lve the f l e x u r eequat ion f o r can t i l eve red and anchored sheet p i l e wa l l s and presented ther e s u l t s in the form o f design charts s u i t a b l e f o r design o f f i c e use.

5.4.3 Finite Difference Method

Palmer and Thompson (1948) presented a finite difference method forsolving the flexure equation for a sheet pile wall. The solution is of theiterative type and requires a knowledge of the coefficient of subgradereaction and boundary conditions at the extremities of the sheet pile. Animportant characteristic of this method is that the coefficient of subgradereaction need not be a constant but can be a function of depth orpressure.

5.4.4 Distribution Method

Turabi and Balla (1968a) presented a distribution theory of analysisfor the solution of the flexure equation based on the approximate modellingof the soil below excavation level by five linear springs. The formulae

28

obtained are in a form suitable for general use, and tables and charts areavailable for design purposes.

5.4.5 Discrete Element Method

Haliburton (1968) presented an efficient discrete element solutionfor a flexible wall on nonlinear foundation. The wall was divided intoshort equal lengths of beam elements, each of which could rotate withoutbending. The elements could transmit transverse forces and couples, andtherefore transverse and rotational restraints could be applied. Eachelement could also sustain an axial force that contributes only to thebending moment but does not produce any axial deformation. The earthpressure-deflection relationship of the soil is assumed to be nonlinear anda function of depth. For simplicity, the portions of the curve betweenat-rest and passive states and between at-rest and active states wereapproximated by two straight lines with different slopes (Figure 11).Independent curves for the soil on the active and passive sides of the wallwere developed, and the two curves were then superimposed to obtain acombined curve (Figure 12). With the use of a computer, repeated t r ia l andadjustment procedures were carried out until there was no significantdifference between two subsequent deflected shapes of the wall*

Rauhut (1969), in a discussion of Haliburton's paper, showed that ingeneral Haliburton's method did not give good agreement with experimentalresults due to the omission of wall friction and the linear distribution ofdeflection.

Bowles (1988) also modelled the sheet pile wall as beam elements, bututilised the concept of subgrade reaction for soil below the excavationlevel. The matrix stiffness method of analysis was used to obtain thesolution. Ng (1984) demonstrated how a program for the matrix method canbe implemented on a programmable calculator.

5.4.6 Advantages and Limitations

An advantage of the 'beam on elastic foundation1 approach over limitanalysis is its ability to account for structure flexibility and soilstiffness. Thus the effects of stress redistribution in soil as a resultof differential structural deflections are accommodated. Although themagnitude of the shear forces and bending moments in the wall and the strutor anchor loads are not very sensitive to the values of spring stiffness(constant) used in the analysis, the predicted deformations of thesupporting wall are.

The limitations of the 'beam on elastic foundation1 approach are :

(a) There is inherent difficulty in determining theappropriate spring stiffnesses (constants) of thesoil for analysis as these are not fundamentalsoil properties.

(b) The method cannot directly simulate constructionsequence, unusual initial .soil stresses, anddevelopment of wall friction.

29

(c) The method does not yield surface movements behindthe retaining structure.

Haliburton's method of utilising the relationship between lateralearth pressure and displacement is a slightly better way of modelling soil-structure interaction. However, it should be noted that although theinfluence of the horizontal earth pressure at rest on the deformation ofthe wall is taken into account, the uncoupled nature of the soil model andthe difficulty in establishing the relationship between lateral soilpressure and deformation limits the applicability of this method inpractice.

5.5 BOUNDARY ELEMENT METHOD

Wood (1979) developed a boundary element computer program to analysepile groups subject to lateral loads and subsequently extended the programto include the analysis of multi-propped sheet pile and diaphragm walls.The wall was assumed to be a series of discrete beam elements attached tothe soil at common nodes. Only the compatibility of horizontaldisplacements between the wall and the soil was maintained at these nodes.The soil was modelled as an inhomogeneous elastic continuum utilising anapproximate extension of Mindlin's solution (Mindlin, 1936), based on theassumption that the displacement is a function of the local values of theelastic parameters. The initial disturbing force was determined from aconsideration of the coefficient of earth pressure at rest and the out-of-balance earth pressure on either side of the wall. The earth pressureswere derived and compared with the active and passive pressure envelopesobtained from classical theory. An iterative procedure was adopted toensure that the final soil reaction always lies within the active-passiverange. No account was taken of arching. At each excavation stage theincremental movements were computed and the summation of the incrementalmovement results were given. The application of this program to theprediction of the performance of a diaphragm wall is given by Wood & Perrin(1984).

A similar program was also developed by Pappin et al (1985). The soilon each side of the wall was modelled as an elastic solid, the flexibilityof which was generated either by way of the integrals of the Mindlinequations, or by interpolation and sealing of flexibility matricescalculated for a simplified soil profile using finite element methods. Asemi-empirical formulation was also developed to allow for variations insoil stiffness with depth. The wall was modelled by a series of elasticbeam elements. In addition, the earth pressures were limited to withinactive and passive limits. Arching is permitted by considering the soilforces acting on the wall compared with the forces consistent with possiblefailure surfaces within the soil. Other features that can be accommodatedby the program include struts, anchors and the effects of surcharges. Thisprogram has been applied to the prediction of the performance of thebasement for the new Hong Kong Bank headquarters building (Fitzpatrick &Will ford, 1985; Humpheson et al, 1986).

The boundary element method developed by Pappin et al takes archinginto account, and is more rigorous than Wood's approach in the formulationof the soil-structure interaction problem. It also appears to be able toovercome the shortcomings of Haliburton's method. Boundary elementprograms, although not as general as the finite element methods, have a

30

s ign i f i can t advantage over the l a t t e r in t h a t they are much cheaper toapply and s u f f i c i e n t l y accurate f o r most design problems. They aren a r t i c u l a r l y su i t ab le fo r parametric s t u d i e s . The shortcoming o f theboundary element methods is t h e i r i n a b i l i t y to p rov ide i n fo rma t i on on thesurface movement behind re ta in ing s t r u c t u r e s . Other methods are requ i redto corre la te the def lec t ions of r e t a i n i n g s t ruc tu res w i t h su r face movements(see Section 9 .3 ) .

5.6 FINITE ELEMENT METHOD

A complete method f o r so lv ing s o i l - s t r u c t u r e i n t e r a c t i o n problems isthe f i n i t e element method which incorporates a continuum s o i l model. Thismethod o f fe rs the designer an a n a l y t i c a l t oo l which can s imu la te almost a l lof the complex facets of the s t r u t t e d or t ied-back w a l l except u n q u a n t i f i -able v a r i a b l e s such as workmanship or geo log ica l u n c e r t a i n t i e s . Thetechniques involved in the app l i ca t i on o f the f i n i t e element method t o theana lys i s o f s o i l - s t r u c t u r e i n t e r a c t i o n have been discussed by Clough(1972a), Clough & Tsui (1977) and the I n s t i t u t i o n o f S t r u c t u r a l Engineers(1989).

Tsui & Clough (1974) showed tha t the assumption o f plane s t r a i nusually adopted in f i n i t e element analys is o f s t r u t t e d and anchored wa l l scannot be a r b i t r a r i l y ext rapolated to many p r a c t i c a l problems, p a r t i c u l a r l ythose invo lv ing so ld ie r p i l e wa l ls or l i g h t sheet p i l e wal ls« Diaphragmw a l l s , however, were shown to approximately s a t i s f y the cond i t i ons assumedin a plane s t r a i n ana lys is . For a l l types o f wa l ls t h a t have prest resseds u p p o r t s , a c h a r t (which is reproduced in Figure 13) can be used toprov ide a q u a l i t a t i v e index t o t h e a p p l i c a b i l i t y o f a plane s t r a i nanalys is . The dev ia t ion of three-dimensional pressures from a plane s t r a i nd i s t r i b u t i o n is def ined in terms o f the s o i l s t i f f n e s s , the wa l l s t i f f n e s sand the t i e -back spacing. The char t shows tha t the s t i f f e r the w a l l , thecloser the t ie -back spacing, and the s o f t e r the s o i l , t he more accurate isthe assumption of plane s t r a i n cond i t i ons . To s imu la te d iscont inuous w a l lelements such as so ld ie r p i l e s , s t r u t s or t i e -backs in a plane s t r a i nana lys is , the bending s t i f f ness o f the s o l d i e r p i l e s in the wa l l and theaxia l s t i f f n e s s of the s t r u t s or t i e -backs have t o be represented on a' u n i t length 1 bas is . Analyses using t h i s representa t ion y i e l d r e s u l t s t h a tare cha rac te r i s t i c o f the average values between those at the supports andthose a t the mid-point between the suppor ts .

Clough and Mana (1976) demonstrated t h a t s imu la t i on o f excavat ion in af i n i t e element analysis may be s a t i s f a c t o r i l y accomplished by a number o fd i f f e r e n t procedures, provided t h a t appropr ia te inpu t s o i l parameters areused. Both a nonl inear e l a s t i c and an e l a s t o - p l a s t i c s o i l model can bemade t o a r r i v e at t he same pred ic ted excavation behaviour . However,changes in excavation support des ign , which w i l l b r i ng about unan t i c ipa tedperformance, o f ten take place dur ing cons t ruc t i on . I s o l a t i o n o f the f i n i t eelement analysis from the cons t ruc t ion stages can e a s i l y lead to erroneousperformance p r e d i c t i o n s , because impor tan t l a t e r occurrences are notaccounted f o r . Hence, the f i n i t e element ana lys is should be used inpara l e i w i t h an observa t iona l procedure (Peck, 1969a), and al lowanceshould be made f o r r e - a n a l y s e s t o be per fo rmed t o accommodate s o i lparameter re-est imates and cons t ruc t ion changes. Updated s o i l parametersare best obtained by comparing ear ly observed performance w i t h comparablef i n i t e ^ e l e m e n t p r e d i c t i o n s . The design engineer should p re fe rab l y beinvolved dur ing construct ion to monitor the performance o f the excava t ion ,

31

verify the design assumptions, and to effect any necessary amendments tothe design.

The two single most important variables required in a finite elementanalysis are the stiffness of the ground, which mainly affects thedisplacements, and the magnitude of the initial horizontal stresses, whichaffect both the displacements and the bending moments.

It has been found that the values of the soil stiffness determinedfrom small-scale insitu tests or from laboratory tests are less than thoseback-analysed from field measurement of the performance of an excavation.The reduction in stiffness has been attributed to sample disturbance orground disturbance upon insertion of the testing equipment. However,recent field and laboratory studies have demonstrated that conventionalmethods of strain measurement can lead to very significant underestimatesof soil stiffness. Some soils have been found to exhibit nonlinear stress-strain behaviour, with a stiffness at small strain (about 0,01%) higherthan that normally measured in conventional laboratory tests (at about 0.1%strain). The influence of this small strain nonlinearity in soil-structureinteraction has been studied by Jardine et al (1986) using a finite elementanalysis. The nonlinear soil model that was used predicted a pronouncedsettlement trough close to a strutted excavation, which agrees well withthat observed in the field. However, such behaviour cannot be predicted bythe conventional linear elastic soil model.

Martin (1977) showed that the deformation modulus of soils derivedfrom insitu weathering of igneous and metamorphic rocks can be approximatedby the pressuremeter modulus, and that a linear relationship exists betweenthe logarithm of Standard Penetration Test (SPT) 'N1 value and thelogarithm of pressuremeter modulus. A similar relationship has also beenfound for Hong Kong residual soils and saprolites. The Young's modulus, E,of such soils is usually correlated with the N values using pressuremetertests (Chiang & Ho, 1980), plate loading tests (Sweeney & Ho, 1982) andfull-scale tests. Endicott (1984) showed that the E/N ratio for completelyweathered granite back-analysed from the performance of excavations isgreater than that obtained from pressuremeter tests, which in turn isgreater than that from triaxial tests on undisturbed samples of completelydecomposed granite. Chan and Davies (1984) have given a chart which showsthe correlation of soil modulus with SPT JN1 values (Figure 14). Ranges ofE/N ratio have also been given by Fraser*(1985), Ku et al (1985), Ku et al(1985) and Whiteside (1986).

The insitu horizontal stress in the ground is related to the insituvertical stress by Ko, the coefficient of earth pressure at rest. Fromconventional soil mechanics, it is well known that Ko, being dependent onstress history, is not a fundamental soil property. For a- soil in thenormally consolidated (i.e. low Ko) state, the stress change required- toreach the active state is small compared with that needed to mobilisepassive resistance. The contrary is true for a soil in theoverconsolidated (i.e. high Ko) state (Figure 15). Therefore, thehorizontal displacements of the wall and surface settlements behind thewall are dependent on the magnitude of the insitu stress. The existence ofa high insitu horizontal stress would likely result in large walldisplacements and surface settlements. For excavated walls in soils with ahigh initial Ko value (Ko^2), the prop forces and wall bending moments cangreatly exceed those predicted by limit equilibrium methods (Potts &Burland, 1983b; Potts & Fourie, 1984).

32

Geoauide 1 : Guide to Retain ing Wall Design (GCO, 1982) recommendsthat the value of Ko should be not less than 0.5 f o r t he design o f wal lsre ta in ing Hong Kong s o i l s der ived from i n s i t u rock wea ther ing This isdesDite a mean Kn value of 0.32 f o r ' und is tu rbed ' complete ly decomposedqran i te obtained by Chan (1976) in the l abo ra to ry . I t cou ld be argued thatsuch low values were due to the i r r e v e r s i b l e e f f e c t s o f s t r ess r e l i e f .However there is other evidence which suggests t h a t Ko cou ld be t h i s lowin r e s i d u a l s o i l s and s a p r o l i t e s . From the observed performance ofe x i s t i n g s t r u c t u r e s , Lumb (1979) suggested t h a t a c t i v e and a t - r e s tpressures in Hong Kong residual s o i l s and s a p r o l i t e s should be smal le r thanwould be estimated by conventional c a l c u l a t i o n s . End i co t t (1982) obtainedearth pressure coe f f i c i en t s o f 0.19 and 0.17 f o r wa l l movements o f 6 mm and12 mm respect ive ly in a completely weathered g r a n i t e and deduced an a t - r e s tpressure c o e f f i c i e n t between 0.21 and 0.25. The weakening theory fo rr e s i d u a l s o i l s and s a p r o l i t e s proposed by Vaughan & Kwan (1984) haspredicted tha t Ko should be lower than t ha t obtained from Jaky ' s c l a s s i c a lre la t ionsh ip Ko = 1 - s i n 0 ' . Howat (1985) measured very low minimumvalues of ac t ive earth pressure c o e f f i c i e n t Ka i n g r a n i t i c s o i l s and showedthat Ko pressures may be estimated by the f o l l o w i n g fo rmula (Howat & Cater,1985), which takes in to account the unconfined compressive s t r e n g t h , q u :

(7h - uw = ((7V - uw - q u ) ( l - s in 01) (1)

where (Th = hor izonta l t o t a l s t r e s s ,

a\\ = v e r t i c a l t o t a l s t r e s s ,

uw = pore water pressure.

The above equation supports Vaughan & Kwan's p r e d i c t i o n t h a t Ko should beless than (1 - s in 0 1 ) .

Although the data ava i l ab le from the l i t e r a t u r e suggest t h a t t he a t -rest earth pressure of Hong Kong res idua l s o i l s and s a p r o l i t e s could below, no d i r e c t measurements o f Ko in the f i e l d have been r e p o r t e d . Ko

values may be deduced by back-analysing c a r e f u l l y inst rumented excava t ions ,but such values are l i k e l y t o be on the low s ide because, by na tu re o fexcavations, movements can take p lace even when \/ery s t i f f supports areprovided. The use o f s e l f - b o r i n g pressuremeters f o r measuring t h e i n s i t uhor izonta l s t ress should be considered. However, i t should be noted t h a tthe i nse r t i on o f an instrument i n t o s a p r o l i t e s may dest roy any bonding anda l t e r the i n s i t u s t resses. There fore , the e f f e c t o f d i s tu rbance should beassessed.

The advantage o f the f i n i t e element method i n the ana lys i s o f ear thre ta in ing s t ruc tu res l i e s in i t s a b i l i t y t o p r e d i c t both e a r t h pressuresand deformations w i th a minimum o f s i m p l i f y i n g assumptions. Both s t r u c t u r ea " d s ° V . . a r e considered i n t e r a c t i v e l y , so t h a t the e f f e c t s o f s t r u c t u r a lf l e x i b i l i t y are taken i n t o account. L im i ta t i ons in us ing the methodpr imar i l y der ive from the i n a b i l i t y to prescr ibe app rop r i a te c o n s t i t u t i v elaws f o r t he s o i l , and t o de te rm ine t h e pa ramete rs needed f o r thec o n s t i t u t i v e models. However, when u t i l i s i n g the obse rva t i ona l procedureJSfiw . , « * ? ? ' w • f l . n l t e element method o f ana lys is can be expected toS i 1 c t r , t + „ *lgn 1

+n f ° n n a t T a n d accurate performance p r e d i c t i o n s f o r

s o i l - s t r u c t u r e i n te rac t i on problems.

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6. CANTILEVERED OR UNBRACED WALLS

6 .1 GENERAL

A cantilevered wall derives its support from the passive resistancebelow the excavation level (or 'dredge line1) in order to balance theactive pressure from the soil above that level. This type of wall iseconomical only for moderate wall heights, since the required sectionmodulus increases rapidly with increase in wall height (the bending momentincreases with the cube of the cantilevered height of the wall}* Thelateral deflection of this type of wall can be relatively large. Loweringof the excavation level, e.g. by construction activities, erosion and scourin front of the wall, has to be carefully controlled, since the stabilityof the wall depends primarily on the passive resistance developed in frontof the wall.

Cantilevered walls of the flexible type, such as sheet pile walls, arenormally used as temporary supports, e.g. support for the initial stage ofa strutted excavation. When used as permanent supports, they are normallyof the rigid type; in Hong Kong, these usually take the form of caissonwalls (see Section 3.4). When used to retain an excavation of substantialheight, unpropped caisson walls are usually socketed into rock.

In the design of cantilevered walls, there are four primary areas ofgeotechnical consideration :

(a) ultimate limit states,(b) serviceability limit states,(c) earth pressures for structural design, and(d) design water pressures.

In many cases, the consideration of serviceability limit states governs thegeotechnical design.

6.2 ULTIMATE LIMIT STATES

6.2.1 Types of Limit States

The following ultimate limit states are usually considered ingeotechnical design :

(a) Overall instability : the embedment depth of acantilevered wall should be adequate to preventoverturning of the wall.

(b) Foundation failure : the cantilevered wall shouldpenetrate a sufficient depth to prevent base heavein cohesive soils.

(c) Hydraulic failure : the depth of penetrationshould be adequate to prevent hydraulic failure(i.e. piping or heave) in cohesionless soils.

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6.2.2 Overall Stabi l i ty

The overa l l s t a b i l i t y o f can t i levered wa l l s is usua l l y assessed usingl i m i t equ i l ib r ium methods o f analysis in which the c o n d i t i o n s o f f a i l u r eare p o s t u l a t e d , and a fac to r o f safety app l ied to ensure t h a t such af a i l u r e s ta te does not occur.

A cant i levered wal l cannot be in e q u i l i b r i u m w i t h o u t i t s lower endbeing f i x e d , as shown in Figure 16(a ) . For a c a n t i l e v e r e d w a l l r o t a t i n gabout a point near i t s t oe , the t h e o r e t i c a l pressure d i s t r i b u t i o n is o f thef ixed-ear th form, as shown in Figure 16(b) , when the w a l l is at the po in tof co l lapse. The pressure d i s t r i b u t i o n shown is cons iderab ly i d e a l i s e d ,p a r t i c u l a r l y at the point o f r o t a t i o n , 0 , at which i t is assumed t h a t thereis an instantaneous change from f u l l passive pressure i n f r o n t o f t he wa l lto f u l l passive pressure behind the w a l l . The c a l c u l a t i o n o f t he depth o fembedment corresponding to t h i s pressure d i s t r i b u t i o n invo lves equat ing thehor izonta l forces and tak ing moments about 0 to ob ta in two equat ions w i t htwo unknown depths, d and z (Figure 16(b)) • The equat ions obta ined areg e n e r a l l y r a t h e r c o m p l i c a t e d , one being a quadra t i c and one a cubicexpression in both d and z . The so lu t ions fo r d and z are usua l l y obta inedby a process o f i t e r a t i o n .

In view o f the considerable a lgebra ic complexi ty o f the f u l l method,the s i m p l i f i c a t i o n i l l u s t r a t e d in Figure 16(c) is w ide ly used in p r a c t i c e .This s i m p l i f i c a t i o n assumes t h a t t h e d i f f e r e n c e between the passiveresistance at the back o f the wal l and the ac t i ve pressure in f r o n t acts asa concentrated f o r ce , R, at the t o e . By tak ing moments about the toe(thereby e l im ina t ing the force R from the equa t i on ) , the depth o f embedmentin the s i m p l i f i e d model, d 0 > is found. Because o f t h i s s i m p l i f i c a t i o n , thevalue o f d 0 is s l i g h t l y less than the value o f d obta ined from the f u l lmethod and is more l i k e l y to be nearer to d - z / 2 . To account fo r t h i s , theusual p rac t i ce is to increase d 0 by a small amount (up t o 20%) • A s implecheck is usual ly made to ensure tha t the add i t i ona l embedment is s u f f i c i e n tto provide a force at least as la rge as the assumed f o r c e , R. This can beachieved from a simple considerat ion o f ho r i zon ta l e q u i l i b r i u m . In mostcases, a 20% increase in embedment w i l l be conse rva t i ve . This smal ladd i t iona l increase in the value o f d 0 is s p e c i f i c a l l y to account f o r thes i m p l i f i c a t i o n , ra ther than to provide a f ac to r o f s a f e t y .

There are a number o f ways o f apply ing the f a c t o r o f sa fe t y f o r theovera l l s t a b i l i t y o f cant i levered as we l l as propped can t i l e ve red wa l l sembedded in s o i l s . These are :

(a) Factor on embedment depth. A f a c t o r is app l ied tot h e c a l c u l a t e d embedment depth a t l i m i t i n ge q u i l i b r i u m , as explained in the US Stee l SheetP i l i n g Des ign Manual ( U n i t e d S t a t e s S t e e lC o r p o r a t i o n , 1975) and t he BSC General SteelP i l i n g Handbook ( B r i t i s h Steel Corpora t ion , 1986).

(b) Factor on moments based on gross p ressure . Thismethod i s d e s c r i b e d by t h e I n s t i t u t i o n o fS t r u c t u r a l Engineers (1951) and NAVFAC (1982b),and is g i v e n i n Geoguide 1 (GCO, 1982) f o rchecking the adequacy o f penet ra t ion o f a s t r u t t e dexcava t ion . I t cons is ts o f f a c t o r i n g only thegross passive pressure. The water pressure is not

35

f a c t o r e d ,

(c) Fac to r on moments based on net t o t a l pressure.This method is advocated by the BSC General SteelP i l i n g Handbook. The net h o r i z o n t a l pressured i s t r i b u t i o n ac t ing on the wa l l i s de r i ved , andthe f a c t o r o f sa fe ty is def ined as the r a t i o o ft he moment o f the net passive forces to the momento f the net ac t i ve forces*

(d) Factor on moments based on net a v a i l a b l e passiver e s i s t a n c e . This method was developed by Bur landet a l (1981) , and is analogous to the c a l c u l a t i o no f the bear ing capaci ty f o r a s t r i p load . Thef a c t o r o f sa fe ty is taken as the r a t i o o f themoment o f the net ava i l ab l e passive res i s tance t ot h e moment ac t i va ted by the re ta ined m a t e r i a l ,i nc lud ing water and surcharge.

(e) Fac to r on shear s t r e n g t h on bo th a c t i v e andpassive s i des . The shear s t rengths o f the s o i l sare reduced by d i v i d i n g c1 and tan 01 by a f a c t o ro f s a f e t y . These reduced (or mob i l i sed) shears t reng th parameters are then used to c a l c u l a t e thea c t i v e and passive pressures.

( f ) Fac to r on shear s t reng th on passive s ide o n l y .This method is recommended by CIRIA (1974), andis g iven in Geoguide 1 (GCO, 1982) f o r design o fc a n t i l e v e r e d w a l l s . The shear s t reng th o f thes o i l on t h e p a s s i v e s i d e is f a c t o r e d , but nof a c t o r o f sa fe ty is appl ied on the a c t i v e s i d e .

A comparison o f the f ac to r s o f sa fe ty de f ined by methods ( b ) , ( c ) , (d)and (e) was c a r r i e d out by Potts & Burland (1983b) and Symons (1983) .A l s o , t h e f a c t o r s o f sa fe ty def ined by methods ( a ) , ( b ) , (d) and (e) werecompared by Padf ie ld & Mair (1984). These comparisons reveal t ha t the re isno u n i q u e r e l a t i o n s h i p between t h e r e s u l t s o b t a i n e d by d i f f e r e n td e f i n i t i o n s o f f ac to r o f s a f e t y . The choice o f method is l a r g e l y one o fc o n v e n i e n c e , and the f a c t o r o f sa fe ty i s r e l a t e d t o the method used,prov ided t h a t the methods are appl ied c o n s i s t e n t l y . Factors o f sa fe tyapp rop r i a t e to methods ( a ) , ( b ) , (d) and (e) are recommended by P a d f i e l d &Mair (1984) , and these are shown in Table 4 .

The f o l l o w i n g are s p e c i f i c comments r e l a t e d t o each method o f d e f i n i n gf a c t o r o f s a f e t y . Method (a) is emp i r i ca l and should always be checkeda g a i n s t one o f t h e o t h e r methods. Method (b) may g i v e e x c e s s i v epene t ra t i ons at lower angles o f shearing r e s i s t a n c e (0 '< 2 0 ° ) . There fo re ,d i f f e r e n t f a c t o r s o f sa fe ty are recommended f o r d i f f e r e n t ranges o f 0 1 .Method (c) g ives very high fac to rs o f sa fe ty compared w i t h other methods,and is not recommended f o r design unless an excep t i ona l l y h igh f a c t o r o fsa fe ty is spec i f i ed» Compared w i t h other methods, method (d) appears t og i v e a cons i s t en t lumped f a c t o r o f sa fe ty throughout the p r a c t i c a l range o fs o i l s and w a l l g e o m e t r i e s . U n l i k e method ( d ) , the same conceptualframework f o r s lope s t a b i l i t y ana lys is can be app l i ed i f method (e) isadopted. However, an anomalous s i t u a t i o n may occur i n methods (e) and ( f )where s l o p i n g ground occurs . Owing to the d i f f e r e n t f a c t o r s o f sa fe ty

36

adopted fo r slope s t a b i l i t y and f o r ove ra l l s t a b i l i t y o f the w a l l , theangle o f shearing resistance o f the s o i l , a f t e r f a c t o r i n g , may be less thanthe angle of the sloping ground. This can g ive r i s e t o d i f f i c u l t i e s in theevaluation of act ive and passive pressures. For method ( f ) , Geoguide 1(GCO 1982) recommends tha t a safe ty f a c t o r o f 3 should be app l i ed to theshear strength o f s o i l on the passive s i d e . This l a rge f a c t o r o f sa fe ty onshear s t reng th , which is genera l ly considered t o be c o n s e r v a t i v e , is notrelated to the s t a b i l i t y c r i t e r i o n . Ins tead , i t is a p p l i e d f o r the purposeof l i m i t i n g wal l deformation.

Malone (1982) showed t h a t , f o r the case o f l e ve l ground on both sidesof a cant i levered wal l w i th zero water pressure, the s a f e t y f a c t o r on shearstrength (0'=35°) on the passive s ide can be doubled from 1.5 to 3.0 by amoderate increase in s o i l embedment r a t i o (= 1 + d /H , where d and H are asdefined in Figure 16(a)) from 1.8 t o 2.15. Pope (1983) showed f o r thesame s i t u a t i o n t h a t a safe ty f a c t o r o f 1.5 app l i ed t o shear s t rength(0'=4O°) on both act ive and passive sides (method (e ) ) r e s u l t s i n smal lerembedment depth than by apply ing a sa fe t y f a c t o r o f 3 on the pass ive sideonly (method ( f ) ) . The same conclusion can be drawn when t he design waterlevel is at one t h i r d the reta ined height o f the w a l l .

Bica & Clayton (1989) compared a range o f l i m i t e q u i l i b r i u m designmethods fo r cant i levered wal ls i n granular m a t e r i a l s . I t was found tha tapar t f rom the d e f i n i t i o n and magni tude o f f a c t o r o f s a f e t y , theassumptions made in the l i m i t e q u i l i b r i u m ana lys is ( e . g . w a l l f r i c t i o n andmethod o f ca l cu la t i ng earth pressures and t h e i r d i s t r i b u t i o n s ) and thechoice o f method f o r d e t e r m i n i n g s o i l and s o i l / w a l l shear s t reng thparameters ( e . g . use of plane s t r a i n t e s t or t r i a x i a l compression t e s t )can s i g n i f i c a n t l y a f f ec t the resu l t s o f des ign.

For cant i levered wal ls socketed i n to rock , o v e r a l l s t a b i l i t y dependson the l a t e r a l load capacity o f the rock socket . The methods used toassess the load capacity of the rock socket were reviewed by Greenway e t al(1986). Fa i lu re o f the rock socket by movement a long d i s c o n t i n u i t i e s inrock should be considered, as we l l as bearing f a i l u r e o f t h e i n t a c t rockmass. The persistence of a rock j o i n t is usua l ly yery d i f f i c u l t t o assessduring ground i nves t i ga t i on . There fore , i t is usual p r a c t i c e t o ca r ry outrock j o i n t d i scon t i nu i t y surveys dur ing c o n s t r u c t i o n .

6.2.3 Foundation Failure

Bottom heave is a problem which primarily occurs in soft to mediumclays. The failure is analogous to a bearing capacity fai lure, thedifference being that stresses in the ground are relieved instead ofincreased.

Two types of analysis are available for calculating the factor of^ n s t b a s e heave, as shown in Figure 17. The methdd of Terzaghi\S Af n£1? -fOr ?5a21,ow and w i d e e^avations, whereas that by

• (195*6) •1S A u i t a b l e f o r deeP and n a r r o w excavations. NeitherKJoS. th1S e x a c l . i n • *h*t the effect of any wall segment penetrating

^ S ^ 0 " ? e r e b y . r e s i s t i n 9 s o i l movement) is not accountednot'les? t h K f ^ V pS-aiHty a Q a i u S t base heave i s u s u a 1 ^ specified to be

' l * v a ? e s h f / s t r e f l9th corrected in a d ithn o t l e s ? t h K f ^ V p - i H y Q u h e a v e i s u s u a 1 ^ s p e c i f i e d t o beBierrum u g ™ u' n * l * v a ? e . s h f / s t r e f l 9 t h cor rected in accordance w i t hs tmno th i f U U ?h ^ e d ln . t h e a n a l * s i s - ^ uncorrected vane shearst rength i s used, the actual f a c t o r o f safe ty w i t h respect t o base heave

37

may be very close to unity (Aas, 1985).

Where the safety factor falls below 1.5, substantial wall movement canoccur as a result of yielding in the subsoils (Clough et al, 1979; Mana &Clough, 1981). Where limiting movement is the governing criterion, asafety factor not less than 2 is usually required (Clough et al, 1979; Mana& Clough, 1981). If soft clay extends to a considerable depth below theexcavation, the beneficial effects of even relatively stiff walls inreducing deformation have been found to be small. However, if the lowerportion of the wall is driven into a hard layer, the effectiveness of thewall in reducing deformation is increased appreciably (see Section 9.2.6).

A base heave analysis for wide excavation in anisotropic clay wasgiven by Clough & Hansen (1981) and is illustrated in Figure 18. Itappears that unless the 'passive strength1 (undrained shear strength at 90°stress reorientation) of a clay is less than 80% of its 'active strength1

(undrained shear strength at 0° stress reorientation), the base heavefactor of safety will be within 10% of the value obtained by assumingisotropy with respect to the 'active strength1. The marine soils of HongKong appear to show only a slight amount of anisotropy (Lumb, 1977).Hence, anisotropy is normally not considered. The use of field vane shearstrength, corrected in accordance with Bjerrum (1973), in an isotropicanalysis is probably adequate in most cases.

Although it is rare, heave may also occur in cohesionless soils. Thefactor of safety against base heave in these materials can be estimatedfrom Figure 19.

6.2.4 Hydraulic Failure

Where groundwater exists above the base of the excavation, and if thetoe of the cantilevered wall does not penetrate into an impermeable layer,flow will occur under the wall and upward through the base of theexcavation. Instability or gross deformation of the base, involvingpiping or heave, occurs if the vertical seepage exit gradient at the baseof the excavation is equal to about unity. To prevent hydraulic failure,the wall must penetrate a sufficient depth below the base of theexcavation. Design charts for wall penetration required for various safetyfactors against heave or piping in isotropic sands and in layered subsoilsare given in NAVFAC (1982a). These charts are reproduced in Figures 20 and21. A design chart is also given by the Canadian Foundation EngineeringManual (Canadian Geotechnical Society, 1985) which shows that the seepageexit gradient for a circular excavation, in the middle section of the sidesof a square excavation and in the corners of a square excavation, is 1.3,1.3 and 1.7 times that for a strip excavation respectively. For cleansand, exit gradients between 0.5 and 0.75 will cause instability of thebase. To avoid this, wall penetration for a safety factor of 1.5 to 2against piping or heave is usually provided.

6.3 SERVICEABILITY LIMIT STATES

The design of cantilevered walls is currently based on limitequilibrium calculations incorporating a high factor of safety to accountfor both failure and deformation considerations. This approach does notnecessarily achieve the aim of limiting deformation (see Section 4.3).

38

The "beam on e l a s t i c foundat ion1 approach is u s u a l l y employed indeformation analyses. Bowles (1988) modelled the sheet p i l e wa l l as beamelements and the s o i l as e l a s t i c spr ings ( the spr ings can be n o n l i n e a r ) .Pope (1983) proposed a model f o r deformation analyses in which t he groundpressure /d isp lacement curve is approximated by a s e r i e s o f nonl inearsprings and the wal l as a ser ies o f l i near e l a s t i c beam elements. Heshowed t h a t , by carefu l se lec t ion o f the c o e f f i c i e n t o f e a r t h pressure atr e s t and t he s p r i n g s t i f f n e s s e s ( cons tan ts ) , good agreement w i t h theobserved def lected shape could be ob ta ined. Pope a lso showed t h a t theremay be a subs tan t ia l component o f r o t a t i o n fo r a ca isson wa l l t h a t is notsocketed in to rock. He considered tha t f o r a design based on s t a b i l i t yconsiderations alone, even by apply ing a f a c t o r o f s a f e t y o f 3 on s o i lstrength on the passive s i d e , unacceptably la rge deformat ions may s t i l loccur i f the caissons are not socketed i n to rock .

The boundary element method (see Sect ion 5.5) and the f i n i t e elementmethod (see Section 5.6) can also be used in the de fo rmat ion analyses.These methods are superior to those using the subgrade r e a c t i o n approach,because s o i l - s t r u c t u r e i n t e r a c t i o n e f f e c t s can be b e t t e r taken in toaccount. The l a t e r a l displacements o f the wa l l p red i c ted by l i n e a r e l a s t i cspring models can only be regarded as rough es t ima tes , and need t o bechecked by f i e l d measurements.

6.4 EARTH PRESSURES FOR STRUCTURAL DESIGN

I n t h e s t r u c t u r a l design o f the can t i l eve red w a l l , which invo lvesca lcu la t ion o f bending moments and shear f o r c e s , t he magnitude as w e l l asthe d i s t r i b u t i o n o f earth pressures corresponding t o s t r u c t u r a l f a i l u r e arerequ i red. For t h i s purpose, c l a s s i c a l ac t i ve and pass ive e a r t h pressured i s t r i b u t i o n s , which correspond to the l i m i t s t a t e c o n d i t i o n , are usua l l ymod i f i ed i n some a r b i t r a r y manner ( e . g . by the design sa fe t y f a c t o raga ins t o v e r a l l s t a b i l i t y ) . There are t h r e e a l t e r n a t i v e methods o fca lcu la t ing the design bending moment :

(a) The maximum b e n d i n g moment i n t h e w a l l i sc a l c u l a t e d a t l i m i t i n g e q u i l i b r i u m u s i n gunfactored s o i l parameters (F igure 2 2 ( a ) ) . Thedepth o f embedment in the design c o n f i g u r a t i o n isgreater than t ha t corresponding to the l i m i t i n gequ i l i b r i um cond i t i on w i th unfactored parameters,but t h e a d d i t i o n a l depth i s no t used i n theca l cu la t i ons . The bending moment d i s t r i b u t i o n a tl i m i t i n g equ i l i b r i um is then asssumed to be equalt o t h a t a c t i n g i n t he 'working c o n d i t i o n 1 , atwhich a f a c t o r o f s a f e t y i s p rov ided aga ins ts t r u c t u r a l f a i l u r e (Figure 2 2 ( b ) ) .

(b) An earth pressure d i s t r i b u t i o n , which is usua l l yobtained by apply ing a sa fe ty f a c t o r t o the ear thpressures at l i m i t i n g e q u i l i b r i u m , is assumed toact on the design con f i gu ra t i on o f the w a l l . Thew a l l b e n d i n g moment d i s t r i b u t i o n i s t h e nc a l c u l a t e d by c o n s i d e r i n g moment and f o r c eequi l ibr ium.. Passive pressure at excavat ion leve li s , however, not f u l l y mobi l i sed in t he analysesand hence the rea l pressure d i s t r i b u t i o n is not

39

properly modelled. The different methods ofapplying factor of safety to obtain an earthpressure distribution are discussed in Section6,2.2.

(c) The earth pressure distribution which acts on thedesign configuration of the wall is calculated byusing analytical methods such as those based onthe 'beam on elastic foundation' approach (seeSection 5.4), and the boundary element and finiteelement methods (see Sections 5.5 and 5.6).

Methods (a) and (b) are relatively simple for manual computation.However, these methods do not simulate the real soil-wall system, unlikethe methods in (c) which take into account the soil-structure interaction.Another advantage of the methods in (c) is that the lateral displacementsof the wall required in the displacement analyses are also calculated.

If wall deflection is not the prime consideration, method (a) ispreferable to method (b) because the passive resistance in front of thewall close to excavation level is likely to be fully-mobilised even underworking conditions, and the maximum bending moment is strongly influencedby this (Padfield & Mair, 1984).

When method (a) is applied, the design depth of embedment whichexceeds that required to give limiting equilibrium is neglected in thecalculation of bending moment, as shown in Figure 22 (Padfield & Mair,1984). For a reinforced concrete cantilevered wall, the reinforcementshould not be curtailed at the point where the calculated bending moment iszero. It should be taken to the bottom of the cantilever, and on bothfaces, to allow for the small reverse bending moments which may occur nearthe toe.

Another problem with the application of method (a) concerns theassumption on water pressures. Since the design embedment depth is greaterthan that required to give limiting equilibrium, the seepage path round animpermeable wall with the smaller depth of embedment assumed for thebending moment calculation differs from the seepage path corresponding toworking conditions. Strictly speaking, the entire embedment depth of thewall should be used in the calculation of seepage pressures, even for thebending moment calculation. However, this tends to be somewhat cumbersomeand is usually not allowed for. In general, the error in neglecting theadditional seepage length for the calculation of water pressures is rathersmall. Considerations relating to design water pressures are given inSection 6.5.

Bica & Clayton (1989) found that, if plane strain 01 values are usedfor granular materials, many limit equilibrium methods can give unsafepredictions of maximum bending moments when compared with experimentalobservations. If the more conservative triaxial compression 01 values areused, then a few methods can give reasonable estimates of the moments. Itis of interest to note that the available test results show an increase inmaximum bending moment as the depth of embedment is increased beyond thatrequired purely for equilibrium.

In the structural design of caisson walls, because of difficulty inestablishing the 'true1 rockhead levels at design stage, calculations of

40

bending moments and shear forces are o f t en c a r r i e d ou t f o r a range ofdepths t o rockhead. D i f f e ren t re in forcement d e t a i l s are shown on thedrawings f o r d i f f e r e n t socket l e n g t h s , t h e d i m e n s i o n s o f which arede te rm ined by i n s p e c t i o n o f t h e m a t e r i a l s exposed d u r i n g ca issonexcavation.

6.5 DESIGN WATER PRESSURES

Proper eva lua t ion o f water pressure and i t s e f f e c t s is o f utmostimportance in the design o f excavation support systems.

For a re ta in ing wal l which is impermeable, e i t h e r by na tu re o f thewal l mater ia l or as a r e s u l t o f the p r o v i s i o n o f a groundwater c u t - o f f bymeans o f g rou t i ng , a d i f f e rence in water l eve l may e x i s t behind and inf ron t o f the w a l l . Where a r e l a t i v e l y impermeable s o i l layer ( e . g . amarine clay stratum) or an unweathered rock mass o f low p e r m e a b i l i t y ispresent immediately below the toe o f the r e t a i n i n g w a l l , a hyd ros ta t i cwater pressure may act on the w a l l . Groundwater f l o w underneath the wal lcan give r i s e to d i f f e r e n t loading cond i t i ons .

The groundwater f low pa t te rn around an excava t i on , which can a f f e c tthe water pressures, the earth pressures on the a c t i v e and pass ive s i de o fthe re ta i n i ng w a l l , and the p ip ing and heave p o t e n t i a l o f the excava t i on ,depends on the ground cond i t i ons . Figure 23(a) shows a t y p i c a l f l ow-ne taround a re ta i n i ng wal l i n homogeneous s o i l under s t e a d y - s t a t e seepagecond i t i on . The groundwater t ab le shown in t h i s f i g u r e is c lose to theground sur face, a s i t u a t i o n which is commonly encountered i n excavat ionsc a r r i e d out in the reclaimed areas o f Hong Kong. A s i m p l i f i e d waterpressure d i s t r i b u t i o n , as shown in Figure 23(b ) , was proposed by Pad f i e l d &Mair (1984) f o r t he des ign o f can t i l eve red and propped w a l l s . Thiss imp l i f i ed method assumes the hydrau l i c head var ies l i n e a r l y down the backand up the f r o n t o f the w a l l . This g r e a t l y f a c i l i t a t e s t he computat ion o fboth the act ive and passive pressures ac t ing on the w a l l . Pot ts & Bur land(1983a) found t h a t the resu l t s o f a s o i l - s t r u c t u r e i n t e r a c t i o n ana lys isbased on such a s i m p l i f i e d method were s im i l a r to those from an ana lys i s inwhich the water pressures had been der ived from a f l o w - n e t .

Ka iser & Hewi t t ( 1 9 8 2 ) , i n t h e i r d i s c u s s i o n o f t h e e f f e c t o fgroundwater f low on the s t a b i l i t y and design o f excava t i ons , i l l u s t r a t e dthe in f luence o f s o i l l a y e r i n g , hydrau l i c an isot ropy and cont inuous anddiscontinuous lenses o f low permeab i l i t y mate r ia l on the groundwater f l owp a t t e r n . The resu l t an t water pressures in these cases can exceed t h a t i nthe homogenous s o i l cond i t ion (Figure 24) . A knowledge o f the s o i l f a b r i c« h L f f n + i ? + e r ° ?,f u t m o s t imP<>rtance by Pad f ie ld & Mair (1984) , who« ? £ ^ t V e T ! " s S l 1 t ° r s a n d P a r t i n 3 s w i t h i n a c lay s t ra tum may conveywater a t hydrostat ic pressure to the base o f the w a l l .

i h w 2 T n k d e s a \ 1 b e d a b o v e demonstrates the need f o r proper groundn S u S . ™ order t o gain a good understanding o f the ground andt a t h a t V a bclZ* *" th%6QHgn o f e x c a v a t i o " * - For c o n d i t i o n o thershown in Fiautp T ^ 9 h f °U S *V\* th& s i m P l i f i e d w a t e r pressure d i s t r i b u t i o nnet a n a l v s i / . . . i i ? m l K*. b e , f u f f 1 c 1 e n t l y accu ra te , and a proper f l o w -SrourS I teV f l « r °n r J b l l S h e d i t e c h n 1 q u e s d e s c r i b e d m t r e a t i s e s onand oassivp 2 l U 9 > C e d e r 3 r e

1n » «77) . should be c a r r i e d o u t . The a c t i v e

methoTs o T t l P t ^ i r e S H S h ° U l d b e e v a l u a t e d u s i n 9 1 i m 1 ' * e q u i l i b r i u mmethods ( e . g . the t r i a l wedge method and the genera l i sed procedure o f

41

slices (Janbu, 1957)), with due account taken of the piezometric pressureson the potential failure surface and the soil/wall interface. It should benoted that the presence of water pressures (which reduce effective stressesin soil) will lead to an increase and decrease in active and passive earthpressures respectively. Another adverse effect is the possibility ofhydraulic failure (i.e. piping or heave) due to upward hydraulic gradientsin front of the retaining wall (see Section 6.2.4).

For a retaining wall composed of vertical structural elements spacedhorizontally apart (e.g. caissons, soldier piles and pipe piles), somethroughflow of groundwater can occur. If the vertical elements are closelyspaced, 'damming1 of the groundwater can result in a rise in groundwaterlevel. A method for estimating the effect of piles and caissons ongroundwater flow was given by Pope & Ho (1982). Drainage provisions behindan impermeable wall can also affect the flow pattern in the ground(Padfield & Mair, 1984) and their effects should be properly assessed.

Infiltration into the ground can sometimes cause a rise in groundwaterlevel. This can increase the water load acting on the excavation supportsystem in some situations. An example of this is where the rise in waterlevel occurs within the retained height, which may take place if theoriginal groundwater level is close to the ground surface or where animpermeable layer is present within the retained soil mass. Even for aretaining wall which has a vertical drainage layer at its back, steady-state seepage can still occur when there is sufficient water infiltratinginto the retained soil, causing an increase in pore water pressures and areduction in soil shear strength. The steady-state seepage condition ismost likely to occur in a soil with a relatively low permeability, asrainfall of moderate intensity can supply sufficient water to sustain theseepage flow. The effect of infiltration should be taken into account indesign.

Deformation of the ground adjacent to excavations may cause breakageof water-carrying services. In some cases, the amount of water releasedcan adversely affect the stability of excavations. Therefore, it isimportant that the location, size and condition of such services in thevicinity of a proposed excavation are ascertained. In situations wheresignificant water flow can occur in the event of breakage, it will beprudent to allow for the possible increase in water load in the design.Alternatively, consideration should be given to diverting water-carryingservices prior to excavation.

43

7. STRUTTED OR BRACED HALLS

7.1 SINGLE-LEVEL STRUTTED MALLS

7.1.1 General

The behaviour of single-level strutted walls is similar to that ofsingle-level anchored walls in which the anchors are installedhorizontally. The effect of inclined anchors will be discussed in Section8.1.1. The factors which influence the behaviour of an anchored flexiblewall were reviewed by Bjerrum et al (1972). As a result of walldeflection, the earth pressures acting on a flexible wall such as a sheetpile wall are very much different from those predicted by classical earthpressure theories. On the back of the wall, the pressures at the top andbottom are increased due to the smaller outward deflections at theselocations, while the pressures between the excavation and anchor levelstend to be reduced due to the relatively large outward deflections there.This redistribution of earth pressure around a flexible wall may beconsidered the result of arching. Rowe (1952) found in his model tests onsheet pile walls that the arching effects can be considered to consist ofthree parts : that due to flexure below the excavation level, that due toflexure above the anchor level, and that due to reduction in earth pressurebetween the excavation and anchor levels. The flexure below the excavationlevel is the most stable and reliable source of moment reduction. Theflexure above the anchor level could be reduced or destroyed by additionalanchor yielding after excavation, and thus cannot be relied upon in allcases. The moment reduction due to pressure reduction between the anchorand excavation levels is unstable and could be destroyed by anchor yield(or elastic shortening of the struts) and backfill settlement, except inthe case of piles encastre at the anchorage.

As in the design of cantilevered walls, there are four primary areasof geotechnical consideration :

(a) ultimate limit states,(b) serviceability limit states,(c) earth pressures for structural design, and(d) design water pressures.

The c o n s i d e r a t i o n o f u l t i m a t e l i m i t s ta tes r a t h e r than s e r v i c e a b i l i t yl i m i t s t a t e s usua l l y governs the des ign .

7 .1 .2 Ult imate Limit States

(1) Overa l l S t a b i l i t y . The o v e r a l l s t a b i l i t y o f s t r u t t e d w a l l s , asin can t i l e ve red w a l l s , is a lso assessed using l i m i t e q u i l i b r i u m methods o fa n a l y s i s .

There i s a choice between adopt ing a f r e e - e a r t h or a f i x e d - e a r t hp r o c e d u r e f o r a n a l y z i n g o v e r a l l s t a b i l i t y . For a propped w a l l ,cons ide ra t ion o f o v e r a l l s t a b i l i t y in terms o f r o t a t i o n about the propp o s i t i o n is only app l i cab le to f r e e - e a r t h support c o n d i t i o n s . Where f i x e d -ear th suppor t cond i t ions app l y , provided the wa l l is adequately propped anddesigned t o r e s i s t the shear forces and bending moments ac t i ng upon i t ,t h e r e i s no f a i l u r e mechanism re levant t o an o v e r a l l s t a b i l i t y check

44

(Pad f i e l d & Mair , 1984). Propped wal ls designed on t he assumption off i xed-ear th condit ions are the re fo re not considered he re . Assuming f ree-earth support cond i t ions , the depth o f embedment i s u s u a l l y determined bytaking moments about the pos i t i on o f the prop (F igu re 25 ) . The d i f f e r e n tmethods o f applying fac tor o f sa fe ty are discussed i n d e t a i l i n Section6.2.2 .

(2) Foundat ion Heave and Hydrau l i c F a i l u r e . Cons iderat ions offoundation heave and hydraul ic f a i l u r e are discussed in Sect ions 6.2.3 and6.2.4 respec t i ve ly .

7*1.3 Serviceabil i ty Limit States

As in the case of can t i l evered w a l l s , the design o f propped wa l l s iso f t en based on l i m i t e q u i l i b r i u m c a l c u l a t i o n s , us ing a h igh f a c t o r ofsa fe ty t o ensure adequate s t a b i l i t y and t o r e s t r i c t s o i l and wal lmovements to acceptable l e v e l s . A more d e t a i l e d approach is t o employ the'beam on e l a s t i c foundat ion1 approach (see Sect ion 5.4) t o es t imate thela te ra l displacements of the w a l l . However, n e i t h e r method takes in toaccount the i n s i t u stress s ta te o f the s o i l p r i o r t o excava t i on . Both theboundary element and f i n i t e element methods (see Sect ions 5.5 and 5.6) canbe used t o inves t iga te the i n f l uence of i n i t i a l s t resses i n the s o i l onthe behaviour of s i ng le - l eve l propped r e t a i n i n g w a l l s .

An e l as to -p l as t i c c o n s t i t u t i v e law f o r the s o i l was employed by Potts& Fourie (1984) in a f i n i t e element ana lys is t o model t h e behaviour of apropped w a l l . The resu l ts o f t h e i r numerical ana l ys i s showed t h a t , i f as u i t a b l e f a c t o r o f safe ty against ove ra l l s t a b i l i t y is adopted f o r anexcavated wal l in s o i l w i t h a low Ko value ( K o = 0 . 5 ) , t he l a t e r a l wa l lmovements are o f small magnitude and t h e r e f o r e cons i s t en t w i t h cu r ren tdesign phi losophy. However, f o r an excavated wa l l in s o i l w i t h a high Ko

value (Ko=2), r e l a t i v e l y la rge l a t e r a l wa l l movements were p r e d i c t e d , evenat shallow excavation depths w i t h la rge f ac to r s o f sa fe t y aga ins t o v e r a l ls t a b i l i t y . Therefore, i t is important t h a t the i n s i t u h o r i z o n t a l s t r ess ofthe s o i l be c a r e f u l l y assessed in the design o f excava t ions . Wherenecessary , de fo rma t i on ana lyses shou ld be per formed to eva luate thes e n s i t i v i t y o f the design to the assumed value o f Ko .

7.1*4 Earth Pressures for Structural Design

The s t r u c t u r a l des ign o f a propped c a n t i l e v e r w a l l invo lves theca lcu la t ion o f bending moments and shear forces f o r the wa l l and t he propforce from the d i s t r i b u t i o n o f ear th pressures a c t i n g on the w a l l .

••" "t1) Wall Bending Moment. There are th ree a l t e r n a t i v e methods o fca l cu la t i ng the design bending moment :

(a) Assuming f r e e - e a r t h suppo r t c o n d i t i o n s , t h ebending moment d i s t r i b u t i o n i s c a l c u l a t e d atl i m i t i n g e q u i l i b r i u m w i t h u n f a c t o r e d s o i lparameters, as shown in Figure 2 6 ( a ) . As i n thecase of can t i l evered w a l l s , the design depth o fembedment is greater than t h a t corresponding t othe l i m i t i n g equ i l i b r i um cond i t ion w i t h unfactoreds o i l parameters, but the a d d i t i o n a l depth i s not

45

used in the calculations.

(b) An earth pressure distribution, which is usuallyobtained by applying a safety factor to the earthpressures at limiting equilibrium, is assumed toact on the design configuration of the wall(Figure 26(b)). This is in effect the 'fixed-earth support1 analysis. The different methodsfor applying the factor of safety are discussed inSection 6.2.2. It should be noted that the fixed-earth support analysis, which was developed forflexible anchored sheet pile walls embedded insand (Terzaghi, 1953), may be unsafe when appliedto more rigid walls in clays due to the long-termdeformation characteristics of such soils.

(c) The earth pressure distribution which acts on thedesign configuration of the wall is calculated byusing analytical methods such as those based onthe 'beam on elastic foundation1 approach (seeSection 5.4), and the boundary element and finiteelement methods (see Sections 5.5 and 5.6).

Rowe (1955a) used a power series solution to solve the flexureequation for sheet pile walls (see Section 5.4.2). On the active side ofthe wall, triangular and constant active earth pressure distributions areassumed above and below the excavation level respectively. On the passiveside, a coefficient of subgrade reaction which increases linearly withdepth is assumed. Curves showing the relationship between the degree offlexibility of a sheet pile wall and the reduction of bending moment,expressed as a ratio of the maximum moment calculated assuming free-earthsupport conditions, were established for both medium dense and very densegranular soils. Rowe's moment reduction theory was recommended in CIRIA(1974). Rowe then extended his flexibility method of analysis to thesolution of sheet pile walls encastre at the anchorage (Rowe, 1955b),sheet pile walls at failure (Rowe, 1956), sheet pile walls in clay (Rowe,1957a) and sheet pile walls subject to a line resistance above theanchorage (Rowe, 1957b). Rowe's work (1952-1957) was reviewed by Lee &Moore (1968). A similar method of analysis was also given by Richart(1955). Schroeder & Roumillac (1983) found that for flexible anchoredwalls with a sloping excavation line the calculated moments may be reducedby extrapolating Rowe's moment reduction curve.

A finite difference method of solving the flexure equation for sheetpile walls was given by Palmer and Thompson (1948).

Turabi & Balla (1968a) published a distribution theory of analysis byapproximating the soil below the excavation level by five linear springs.A triangular active earth pressure distribution above the excavation levelwas assumed, similar to that assumed by Rowe (1955a). However, in contrastto Rowe (1955a), the application of a constant active pressure below theexcavation level was considered not justified, as the pressure distributionbelow the excavation level can be obtained from the spring reactions. Theylater extended their theory by removing the assumption of linear pressuredistribution above the excavation level (Turabi & Balla, 1968b). In thisrespect, their method is an improvement on Rowe's method.

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Haliburton (1968) presented a d i s c r e t e element method i n which thenonl inear earth pressure-def lec t ion r e l a t i o n s h i p i s approximated by twos t ra igh t l ines w i th d i f f e r e n t s lopes . The impor tant i n f l u e n c e o f the a t -rest earth pressure on the deformation o f the wa l l i s taken i n t o account.Popescu & Ionescu (1977) modif ied Ha l i bu r t on ' s method by approx imat ing theearth pressure-def lect ion r e l a t i o n s h i p by two hype rbo l i c cu rves . However,Rauhut (1969) commented t h a t , in gene ra l , the bending moments ca lcu la tedby Hal ibur ton 's method were l a rge r than those measured i n Rowe's modeltests due t o the fac t tha t wal l f r i c t i o n and the l i n e a r d i s t r i b u t i o n ofdef lect ions were ignored.

A d isc re te element method based on the 'beam on e l a s t i c foundat ion 1

approach was also proposed by Bowles (1988). Un l ike H a l i b u r t o n ' s method,the concept o f subgrade react ion was used f o r the pass ive res i s t ance onlyand, s im i l a r to Rowe's method, Coulomb's theory was used t o c a l c u l a t e theea r th p ressure above t h e excava t ion l e v e l . However, constant a c t i v epressure below the excavation l e v e l was considered unnecessary, as inTurabi & Ba l l a ' s method. Browzin (1982) commented t h a t Bowles' hybr idapproach is not leg i t imate as i t combines cond i t ions a t f a i l u r e (Coulombtheory) wi th condit ions at working load ('beam on e l a s t i c f o u n d a t i o n ' ) .

Maffei et a l (1977b) proposed a model f o r ea r th r e t a i n i n g s t r u c t u r e swhich simulates the step by step cons t ruc t ion o f an excava t i on . This modeltakes in to account the e l a s t o - p l a s t i c behaviour o f t he s o i l as w e l l as i t shysteres is . Wink ler 's hypothesis (Wink ler , 1867) is adopted in c a l c u l a t i n gthe displacements. Although t h i s model is a b e t t e r r ep resen ta t i on o f thes o i l - s t r u c t u r e system than the o ther 'beam on e l a s t i c f ounda t i on 1 methods,the uncoupled nature o f the s o i l spr ings cannot model any a rch ing e f f e c to r i g ina t i ng from other parts o f t he w a l l .

Both the boundary element and f i n i t e element methods t r e a t the s o i l asa continuum and give the best represen ta t ion o f t he s o i l - s t r u c t u r e i n t e r -ac t ion . The app l i ca t i on o f the boundary element and f i n i t e element methodsto pred ic t the performance o f propped wa l l s was c a r r i e d out by Wood &Perr in (1984) and by Bjerrum et a l (1972), Egger (1972) , Hubbard e t a l(1984), Potts & Burland (1983a) and Smith & Boorman (1974) , r e s p e c t i v e l y .

Potts & Fourie (1984) used a f i n i t e element method t o i n v e s t i g a t e t heinf luence o f type o f cons t ruc t ion and o f i n i t i a l s t ress on t h e behaviour o fpropped wal ls (see also Sect ion 7 . 1 . 3 ) . The resu l t s o f t h e i r i n v e s t i g a t i o nindicated t h a t , f o r wa l ls in a low Ko (Ko=0.5) s o i l , the s imple l i m i te q u i l i b r i u m ca lcu la t ions produce conservat ive values o f prop f o r ce andbending moments. For excavated wa l l s i n high Ko (Ko=2) s o i l s , prop f o r c eand bending moments g r e a t l y exceed those ca l cu la ted us ing the l i m i tequ i l i b r i um approach cu r ren t l y in use. Increasing the embedment o f t heexcavated wal ls in high Ko so i l s does not reduce the prop f o r c e or bendingmoments, even though the f a c t o r o f sa fe ty against o v e r a l l s t a b i l i t y i sincreased. Large zones o f f a i l e d s o i l , espec ia l l y in f r o n t o f the w a l l ,were pred ic ted f o r excavated wa l ls i n high Ko s o i l s , and the l a t e r a l ea r thpressures behind the wal l d i f f e r s u b s t a n t i a l l y from the c l a s s i c a l a c t i v ed i s t r i b u t i o n . Passive cond i t ions in f r o n t o f the w a l l are complete lym o b i l i s e d a t sma l l excavation depths and before a c t i v e cond i t i ons areapproached down the back of t he w a l l . In c o n t r a s t , wa l l s i n low Kn s o i l sshowed l a t e r a l pressures wh ich were i n agreement w i t h the c l a s s i c a ld i s t r i b u t i o n s . Act ive pressures down the back of the wa l l are mob i l i sed a tsmall excavation depths and before passive pressures f u l l y develop i n f r o n to t the w a l l . In a l l the cases cons idered, high mobi l i sed angles o f w a l l

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friction were predicted. There is therefore a need to assess the Ko valuein the case of excavated walls.

Smith & Boorman (1974) showed that Rowe's model test results can bereproduced using the finite element method. Potts & Fourie (1985) carriedout a finite element analysis to investigate the effect of wall flexibilityon the behaviour of propped walls. The results showed that, for flexiblewalls of the sheet pile type embedded in low Ko soils, the bending momentsare much lower than those given by the simple limit equilibriumpredictions. As the wall stiffness increases, the bending moments approachthe limit equilibrium value. These results are in full agreement with themodel tests of Rowe (1952). However, for stiff walls in high Ko soils, thebending moments greatly exceed the limit equilibrium values. A similartrend is observed for the prop force. Curves showing the variation in theratios of the maximum bending moment and prop force to those predicted bylimit equilibrium method with wall stiffness, for various insitu Ko values,are given in Figure 27.

For excavated walls in high Ko soils, it appears that the boundaryelement and finite element methods are the only suitable design methods.For walls in low Ko soils, methods in (c) are also better than methods (a)and (b) because the lateral displacements of the wall as well as the wallbending moments and prop force can be obtained. As deformation is notusually the controlling criterion for propped walls, methods (a) and (b),which are conservative and suitable for hand computation, are normallyadopted. In such cases, method (a) is preferable to method (b) because theearth pressure in front of the wall under working conditions is the fully-mobilised passive pressure, as revealed by the finite element method ofanalysis. When method (a) is used, the considerations regardingcurtailment of the reinforcement and allowance for water pressure forcantilevered walls apply also to propped walls (see Section 6.4).

(2) Prop Force. There are two conflicting requirements concerningthe prop positions, viz. the need to install supports at an early stage ofexcavation to restrict movement and the need to install them at a lowenough level to limit the moment acting in the wall (Padfield & Mair,1984). For greatest economy in the wall section, often props are placed sothat moments are equal in the span below and in the cantilevered sectionabove the prop. Shear forces in the wall near the position of the prop maybe critical for concrete walls,

A factor of safety is usually applied to the design prop force. Ifmethod (a) is used for the design moment calculation (see Section7.1.4(1)), resolution of forces allows a solution to be obtained for thehorizontal prop load, which is generally increased by 25% to allow for thepossibility of arching and stress redistribution behind the wall (Padfield& Mair, 1984), If method (b) is used for the design moment calculation,the value of the prop load obtained is very sensitive to the factor ofsafety used. The prop force should always be conservatively assessedbecause, unlike in the structural design of the wall, the consequences offailure are usually very serious. The system of props and waling should beable to withstand the loss of at least one prop.

Raking struts generally allow considerable movement, so it isacceptable to design for active pressure behind the wall, even with severallevels of raking struts.

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7-1.5 Design Water Pressures

Considerations r e l a t i n g to the eva luat ion o f des ign water pressures

are given i n Section 6.5.

7.2 MULTI-LEVEL STRUTTED HALLS

7,2 .1 General

The f a c t o r s which in f luence the behaviour o f m u l t i - l e v e l f l e x i b l es t r u t t e d excavation were reviewed by Bjerrum et a l (1972)* The loads whichmust be res is ted by the s t r u t s in a s t r u t t e d excavat ion depend on twoe n t i r e l y d i f f e r e n t f a c t o r s .

The f i r s t fac to r is the magnitude of the t o t a l a c t i v e ear th pressureexerted by the s o i l behind and beneath the w a l l , down t o t he depth wheres o i l movements are no longer s i g n i f i c a n t . This depends e x c l u s i v e l y on theshear st rength and the un i t weight o f the s o i l behind the w a l l .

The second factor is the d i s t r i b u t i o n o f the ear th p ressu re , whichdetermines how much of the t o t a l ac t i ve ear th pressure w i l l be c a r r i e d bythe s t r u t s . The d i s t r i b u t i o n depends on the amount o f a rch ing and iscont ro l led by the magnitude o f the deformations i n t he s o i l beneath theexcavation r e l a t i v e to those o f the s t r u t s . These deformat ions depend onthe modulus and the un i t weight o f the s o i l beneath t he excavat ion andbehind the w a l l , the width and depth o f the excavat ion * and the depth to af i r m layer . For s o i l s w i th a high modulus, such as dense sands or so f tr o c k , the de fo rmat ions i n t h e s o i l beneath the excavat ion l e v e l arei n s i g n i f i c a n t and there fo re the arching e f f e c t w i l l be s m a l l . In thesecases, the sum of the s t r u t loads w i l l be near ly equal to t he t h e o r e t i c a lRankine va lue. However, the d i s t r i b u t i o n o f ea r th pressure w i l l approachthe shape as shown in Figure 28(a) : the ear th pressure on the upper par tof the wal l i s only s l i g h t l y i n excess o f the t h e o r e t i c a l Rankine va lue andthe arching e f f e c t . i s mainly due t o loca l r e d i s t r i b u t i o n o f ear th pressurebetween the lowest s t r u t and the excavat ion leve l (Bjerrum et a l , 1972).This i s a l so the case f o r excavations in s o i l s w i t h a somewhat lowermodulus i f the width o f the excavat ion is small compared to i t s d e p t h . Forwide excavation in so i l s w i th low modulus, such as s o f t c l a y s , medium s t i f fc l ays , s i l t s and loose sands, the deformations beneath the excavat ion l eve lare l a rge , the arching e f f e c t w i l l be s i g n i f i c a n t and loads w i l l be thrownonto the s t r u t s such t ha t the sum of the s t r u t loads w i l l cons iderab lyexceed the t heo re t i ca l Rankine va lue . The ear th pressure d i s t r i b u t i o n w i l lbe c lose t o the shape shown i n Figure 28(b ) .

The design considerat ions f o r m u l t i - l e v e l s t r u t t e d wa l l s are t he sameas those fo r the case o f s i n g l e - l e v e l s t r u t t e d w a l l s .

7 .2 .2 Ultimate Limit States

The w a l l p e n e t r a t i o n below f i n a l excavation leve l should a l so bes u f f i c i e n t to l i m i t the bending moment i n the w a l l . A check should beca r r i ed out by considering the equ i l i b r i um of the free-ended span below the

owest s t r u t , assuming f i x i t y at t h a t s t r u t (F igure 29 ) . For t he temporary(cons t ruc t ion ) cond i t i on , a f a c t o r o f safe ty not less than 1.5 on pass iveres is tance is usua l ly app l i ed .

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The depth of penetration of the wall below the excavation levelshould be sufficient to prevent foundation heave in cohesive soils (seeSection 6.2.3) or hydraulic failure in cohesionless soils (see Section6.2.4).

7.2.3 Serviceability Limit States

Ground movements around an excavation are usually estimated using themethods given in Section 9.3. However, the lateral deflection of a multi-level strutted wall is of secondary importance and deformation analysis isusually not carried out. If required, the 'beam on elastic foundation1

approach (see Sections 5.4), the boundary element and finite elementmethods (see Sections 5.5 and 5.6) may by be used to predict the lateraldisplacement of the wall.

A parametric study was carried out by Palmer & Kenney (1972) toinvestigate the behaviour of a strutted excavation with fully penetratingsheet pile walls through weak clay to bedrock. The results of their studyshowed that, of the parameters concerning soil conditions, the soildeformation modulus has the greatest influence. The influence of shearstrength and soil/wall adhesion is of minor importance. This may be thecase for an excavation with a fully-penetrating wall. However, in the caseof a partially-penetrating wall, the other parameters might have greaterinfluence. Potts & Fourie (1984) showed that the initial insitu stress hasa considerable influence on the deformation of single-level strutted walls.It is considered that the same is true for multi-level strutted walls.

All of the parameters concerning support conditions are important, butof these, wall stiffness is the most important. The effective strutstiffness depends not only on the stiffness of the struts and walings butalso on the construction methods used to eliminate 'slack' between the walland the walings and struts (such as wedging or other means of filling anygaps between the wall and the walings, and prestressing the struts).

Where it is important to keep soil deformation, and especially surfacesettlement, to a minimum to prevent damage to neighbouring structures andpublic utilities, stiff sheet piles and a stiff support system (i.e. onewith stiff walings and closely-spaced struts) have to be used. However,although these measures will be useful, some surface settlement isinevitable, primarily because of the amount of deformation which occursbelow the bottom of the excavation.

Prestressing of struts for an excavation in weak clay will only reducedeformation by a certain amount. Significant deformation will still occur,and increased strut loads must be anticipated. It is suggested that asmall amount of prestress could be beneficial in ensuring the effectivenessof the support system at an early stage. However, a large amount ofprestress may not provide additional benefits (see Section 9.2.7).

The vertical spacing of struts affects the magnitude of strut loadsand also of wall deflections, particularly where a flexible wall is used.A close horizontal strut spacing could provide a significant contributionto the effective stiffness at a particular strut level. A stiff waling hasa similar effect.

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7.2,4 Earth Pressures for Structural Design

The s t r u c t u r a l design o f m u l t i - l e v e l s t r u t t e d wa l l s i s u s u a l l y basedon t h e s e m i - e m p i r i c a l apparent e a r t h pressure envelopes developed byTerzagh i & Peck (1967) , wh ich was l a t e r summarised by Peck (1969b)(Figure 30)* The fo l low ing four important features o f the Terzaghi & Peckmethod should be noted (Lambe, 1970) :

(a) I t a p p l i e s t o a 'deep1 excava t ion , deep beingde f i ned as "depths greater than about 6 m (20f e e t ) " .

(b) The water t ab le i s assumed to be below the bottomof the excavat ion. Sand is assumed to be d r a i n e d ,w i th zero pore pressure; clay is assumed to beundrained and only t o t a l stresses are cons idered.

(c) The apparent pressure diagrams are not intendedt o rep resen t t h e ac tua l ear th pressure or i t sd i s t r i b u t i o n w i th dep th , but ra the r envelopes fromwhich safe est imates o f the s t r u t loads can beder ived.

(d) The behaviour o f an excavation i n c lay dependsvery much on a s t a b i l i t y number, N c , where Nc =H) /C u . "Ext raord inary la rge movements appear whenthe depth o f a cu t i n c l a y approaches t h a tc o r r e s p o n d i n g t o Nc = 6 o r 7 and when aconsiderable depth o f s i m i l a r c lay a lso extendsbe low t h e bo t tom o f t i re e x c a v a t i o n " ( P e c k ,1969b).

The Canadian Foundat ion Engineering Manual (Canadian GeotechnicalS o c i e t y , 1985} has recommended t h a t h y d r o s t a t i c a l l y d i s t r i b u t e d waterpressures should be added to the apparent pressure envelopes f o r sands ands t i f f to hard f i ssured c l a y s , and t h a t f o r so f t to f i r m c lays an apparentearth pressure smal ler than the hyd ros ta t i c water pressure should not beused. For excava t ions i n deep deposi ts o f s o f t c l a y , Henkel (1971)proposed a r a t i ona l method f o r c a l c u l a t i n g the r e s u l t a n t t h r u s t on t hes ides o f t h e excava t ion as an a l t e r n a t i v e t o t h e apparent pressureenvelopes (Figure 31) .

There are also other semi-empir ica l methods o f ob ta i n i ng h o r i z o n t a ls o i l s t resses and s t r u t loads, e .g . the methods given in Teng (1962) ,Armento ( 1972 ) , T s c h e b o t a r i o f f (1973) and the Japan Society o f C i v i lEngineers ( 1 9 7 7 ) . The apparen t p ressu re enve lopes g i v e n i n t h e s ereferences are general ly conserva t ive , but they are less w ide ly used thanthose o f Terzaghi & Peck. Swatek et al (1972), however, found reasonableagreement w i t h t he Tschebo ta r i o f f pressure envelopes in des ign ing t h esuppor t system fo r a 21 m deep excavat ion in Chicago c l a y . I t appears t h a tthe Tschebotar io f f method may be more appropr ia te when the excavat ion depthexceeds about 16 m.

I t shou ld be noted t h a t none o f these enve lopes are based onmeasurements taken from s a p r o l i t e s , the mate r ia l p roper t i es o f which ares i g n i f i c a n t l y d i f f e r e n t from sedimented sands and c l a y s , and the mass o fwhich f requent ly contains d i s c o n t i n u i t i e s t h a t act as p r e f e r e n t i a l f l o w

51

paths for groundwater and often as potential sliding surfaces.Preferential flow paths have an important bearing on the design againstpiping and heave at the base of the excavations. On the other hand, thepresence of corestones can reduce the magnitude of earth pressures actingon the walls of the excavation (Massey & Pang, 1989).

The apparent pressure diagram derived by Massad (1985) and Massad etal (1985) for the Brazilian lateritic and weathered sedimentary soils showa maximum value of 0.08VH (Figure 32) where VH is the overburden pressure.This is considerably lower than the corresponding value in the Terzaghi &Peck envelope for stiff sedimentary soils of other origins. Wirth &Zeigler (1982) found that the measured strut loads for the Baltimore Subwaystrutted excavation in soils derived from insitu weathering of gneiss-granite and schists were about 70% of the Terzaghi & Peck envelope forsands. Although there are no reported field measurements of strut loadsfor Hong Kong residual soils and saprolites, observations from theperformance of existing structures suggest that active and at-restpressures are smaller than would be estimated by conventional calculations(Lumb, 1977; Endicott, 1982; Howat, 1985). Thus, field measurements ofstrut loads should be carried out in order to establish the apparent earthpressure envelopes for residual soils, which could be much lower than thoseof Terzaghi & Peck.

In the determination of strut loads from apparent pressure envelopes,a reaction at the base of the excavation is assumed to exist. Thisreaction is provided by the passive resistance of the soil beneath theexcavation. Figure 33 illustrates the method given by Goldberg et al(1976) for determining the depth of penetration in 'competent1 soils (e.g.medium dense to dense granular soils and stiff to hard clays), which arecapable of developing adequate passive resistance. In weak soils, such assoft clays, the passive resistance may never reach the value of the activepressure on the retained side, no matter how deep the penetration is. Thismay also apply to a deep excavation in competent soil where the pressure onthe wall below the lowest strut level is in an active state due to a highlateral pressure resulting from surcharge loading. For such cases,Goldberg et al (1976) have recommended that the wall should be driven to adepth required to prevent bottom heave or piping, and be designed as acantilever about the lowest strut level. This approach is similar to thatgiven in NAVFAC (1982b) for limiting the bending moment in the wall (seeSection 7.2.2).

Surcharge loadings should also be included in the apparent pressureenvelopes to determine the strut loads. Support systems for deepexcavations in urban areas are often subjected to asymmetric surcharges. Anasymmetric condition occurs when the foundations of the buildings on thetwo sides of an excavation are of different types or when the buildingshave a different number of floors or are at different distances from theexcavation. Another condition of asymmetry is when the water table hasbeen lowered more on one side of the excavation than the other. Analysisand field measurements by De Rezende Lopes (1985) showed that the wallopposite to the higher surcharges could be subjected to higher internalforces and could even be forced against the retained ground, developingpassive pressure. Hence, both sides of the support system should beconsidered when the excavation is subjected to asymmetric surcharges.

All construction stages of a strutted excavation should be considered,including strut removal stages. The required penetration depth, and the

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sect ions to be used f o r the s t r u t s , wal ings and the w a l l should be adequatef o r a l l c o n s t r u c t i o n s tages. A step by step procedure f o r designings t r u t t e d excavations is i l l u s t r a t e d by an example g iven by NAVFAC (1982b),

Scott et al (1972) showed t h a t the ear th pressure d i s t r i b u t i o n of as t r u t t e d excavat ion in dense sand can be approximated by the extendedDubrova's so l u t i on (Dubrova, 1963) f o r a given wa l l de fo rma t i on . The fourp o s s i b l e t ypes o f d e f o r m a t i o n o f a s t r u t t e d excava t i on f o r which agraphical so l u t i on have been given a l l r e s u l t i n p a r a b o l i c l a t e r a l earthpressure d i s t r i b u t i o n curves.

An e n p i r i c a l method f o r the design o f m u l t i - t i e d diaphragm wa l l s wasf i r s t int roduced by L i t t l e j o h n et a l (1971) and was presented again byJames & Jack (1975) (see Sect ion 8 . 2 . 4 ) . I t i nvo lves a procedure whichca lcu la tes the pos i t i on and magnitude o f a r e s u l t a n t t i e at any stage ofexcavation by t r e a t i n g the wa l l as a s i n g l e - t i e d s t r u c t u r e . I t has theadvantage o f being a r e p e t i t i v e s i n g l e - t i e d wa l l design and is amenable tovary ing s o i l l aye rs . Wood (1983) developed a computer program us ing t h i smethod f o r the design o f m u l t i - s t r u t t e d diaphragm w a l l s .

Bowles (1988) used a d i s c r e t e element method to s imu la te the s tage bystage cons t ruc t ion of a s t r u t t e d excavat ion. Coulomb/Rankine theory wasused to ca lcu la te the earth pressure above the excavat ion l e v e l , and theconcept o f subgrade react ion was used f o r o b t a i n i n g the passive res i s tancebelow the excavation l e v e l . Maf fe i et a l (1977b) proposed a model fo ranalysing m u l t i - l e v e l s t r u t t e d wa l ls which u t i l i s e s the ear th p ressu re -d i sp lacemen t r e l a t i o n s h i p o f the s o i l , as w e l l as invok ing W i n k l e r ' shypothesis (Wink ler , 1867). A l l o f these 'beam on e l a s t i c f ounda t i on 1

approaches can at best g ive approximate values f o r the s t r u t l o a d s , w a l lbending moments and wal l displacements (see Sect ion 5 . 4 ) .

Both boundary element methods and f i n i t e element methods were usedby F i t z p a t r i c k et a l (1985), Humpheson et a l (1986) and Wood & P e r r i n(1984) , and by C larke & Wroth ( 1 9 8 4 ) , E isens te in & Medeiros (1983) ,Fernandes (1985), Garret t & Barnes (1984) , Hubbard e t a l (1984) , Izumi e tal (1976), Palmer & Kenney (1972) , Roth et a l (1979) and Tominaga. e t - a l(1985) respec t i ve ly to p red i c t the performance o f s t r u t t e d excava t ions .Q u a l i t a t i v e agreement between p r e d i c t e d and measured ear th pressured i s t r i b u t i o n s was obta ined. Good q u a n t i t a t i v e agreement, however, requ i resthe choice o f su i t ab l e values o f deformation parameters. Both E isens te in &Medeiros (1983) and Tominaga e t al (1985) used Lambe's (1967) s t ress pathmethod to determine the deformat ion parameters. E isenste in & Medeirosfound t h a t the ana l ys i s , which used a s o i l s t r e s s - s t r a i n model based onplane s t r a i n t e s t r e s u l t s , descr ibes the f i e l d behaviour more c lose l y thanthose based on convent ional t r i a x i a l and s t r e s s - p a t h t r i a x i a l t e s t d a t a .The ca lcu la ted l a t e r a l pressure d i s t r i b u t i o n was a lso found to d i f f e r fromthe semi -empi r i ca l pressure d i s t r i b u t i o n diagrams.

E i s e n s t e i n & Negro (1985) proposed a t h e o r e t i c a l framework f o rs t r u t t e d excavation analys is (F igure 34) . Pressure is uniquely r e l a ted t odisplacement Ah through two main c o n t r o l l i n g f a c t o r s : the a t - r e s t pressurePo and the slope o f the ground reac t ion curve. The former is r e l a t e d tothe i n s i t u v e r t i c a l s t ress by Ko, the c o e f f i c i e n t o f ear th pressure a t r e s t(see Sect ion 5 . 6 ) , and the l a t t e r is a f unc t i on o f the s o i l ' s s t i f f n e s s ands t r e n g t h . The amount o f d i sp lacemen t a l lowed is a f unc t i on o f t heexcavation method and suppor t ing system used. In f a c t , the suppor t ingsystem could be represented by a 'support r eac t i on curve1 as shown i n

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Figure 34. At po in t 'A1 i n t h i s f i g u r e , support and ground would i n t e r a c tand f i n d an e q u i l i b r i u m p o i n t , E. The cons t ruc t i on technique would a f f e c tt h e amount o f d i s p l a c e m e n t , A h j , t a k i n g p l a c e p r i o r t o s u p p o r ti n s t a l l a t i o n . The wa l l and support s t i f f n e s s would be represented by thes lope , n, o f the normal t o the support reac t i on curve shown. Thus, af u n c t i o n could be pos tu la ted t o represent t h e ground response :

e(~R> pr» §» Ko> p^» s t r e n g t h , cons t ruc t ion technique) = 0 . . (2)

o o

S i m i l a r l y , the support response func t ion could be :

S ( ^ , p~, f , Jp flip, support s t i f f n e s s ) = 0 (3)o

These functions could be obtained by numerical modelling, using anappropriate constitutive relationship for the soil. Eisenstein & Negrothen applied this framework to explain that the reason for the low valuesof the lateral pressures observed in the Brazilian lateritic andsedimentary soils (Massad, 1985; Massad et al, 1985) are due to their lowerKo values.

Since the construction technique has a significant influence on thebehaviour of strutted excavations, any application of the finite elementmethod to practical cases should be used in parallel with Peck's (1969a)observational procedure, and allowance should be made for re-analysis to beperformed so as to accommodate soil parameter re-estimates and constructionchanges.

The semi-empirical methods do not consider soil-structure interactionand are conservative, as they generally overestimate the strut loads. Theanalytical methods which take into account soil-structure interaction havea better prospect of giving strut loads closer to reality. Maffei et al(1977a) compared the 'beam on elastic foundation1 approach (Maffei et al,1977b) with the finite element method and found that the lateral stresseson the wall are not very sensitive to the coefficient of subgrade reaction,but the wall displacements are. In terms of professional time and cost toperform an analysis, the finite element method is the most expensive, andthe 'beam on elastic foundation1 approach is cheaper than the boundaryelement method. If the ground displacement is the crucial factor, thefinite element method is the only method capable of making a reasonableprediction.

7.2.5 Design Mater Pressures

Considerations relating to the evaluation of design water pressuresare given in Section 6.5.

7.3 TEMPERATURE EFFECTS

Tempera ture changes may cause s i g n i f i c a n t changes i n s t r u t loads.Chapman et a l (1972) showed t h a t , by using e l a s t i c t h e o r y , the deformat ionmodulus o f the s o i l behind a s t r u t t e d wa l l can be est imated by comparings t r u t - l o a d changes w i t h wa l l d e f l e c t i o n s f o r a given temperature change.

54

By combining the r e l a t i o n s f o r e l a s t i c displacement o f a s t r u t t e d wa l l witht h e e f f e c t o f t e m p e r a t u r e on load and d i sp lacemen t o f a s t r u t , thef o l l o w i n g approximate r e l a t i o n was obtained :

AP = A sE saAT/( l+3nA sE sH/AwEL) . (4)

where AP = load change due to a temperature change o f AT,

As = c ross-sec t iona l area o f s t r u t ,

Es = Young's modulus o f s t e e l ,

a = thermal c o e f f i c i e n t o f expansion f o r s t e e l ,

nAs = t o t a l area of s t r u t s ac t i ng against the wa l lo f area Aw,

H - height o f excavat ion ,

L = length o f s t r u t ,

E = Young's modulus o f s o i l .

Chapman et a l (1972) showed t h a t t h e above r e l a t i o n p rov ides areasonable means f o r es t imat ing the s t r u t load changes which r e s u l t f romtemperature changes. S t ru t load changes w i l l approach the load changes f o ra res t ra ined s t r u t i f the s o i l modulus is h i g h , t h e t o t a l area o f t he s t e e ls t r u t s d i v ided by the area o f the s t r u t t e d wa l l i s low, and the l eng th o fthe s t r u t is large in comparison w i t h the he ight o f t he excava t ion .

For a p e r f e c t l y r es t ra i ned s t r u t , the increase i n s t r u t load due t o atemperature change is g iven by :

AP = A sE saAT (5)

Load changes r e s u l t i n g from la rge temperature increases should beadded to the s t r u t loads i f the apparent ear th pressures are based on datao b t a i n e d f o r r e l a t i v e l y c o n s t a n t t e m p e r a t u r e s , o r sma l l changes i nt e m p e r a t u r e . The t e m p e r a t u r e e f f e c t on s t r u t loads has a l s o beendiscussed by Goldberg et a l (1976) and Massad (1985) .

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8 . TIED-BACK OR ANCHORED WALLS

8.1 SINGLE-LEVEL TIED-BACK WALLS

8 . 1 . 1 General

The f a c t o r s which i n f l uence the behaviour o f t ied-back or anchoredf l e x i b l e wa l l s were reviewed by Bjerrum et a l (1972) and are discussed inSect ion 7 . 1 . 1 . For anchored wa l ls w i th s lop ing anchors, the e f f e c t o f thev e r t i c a l component o f the anchor fo rce should be considered i n design(Figure 35 ) . This v e r t i c a l fo rce may cause poss ib le downward movement o ft h e w a l l when t h e wa l l has not been d r i ven to re fusa l and the po in tres i s tance is low (see Sect ion 8 . 1 . 2 ) .

In t h e design of anchored w a l l s , there are four primary areas o fgeo techn ica l cons ide ra t ion :

(a) ultimate limit states,(b) serviceability limit states,(c) earth pressures for structural design, and(d) design water pressures.

The consideration of ultimate limit states rather than serviceability limitstates usually governs the design.

8.1.2 Ultimate Limit States

(1) Overall Stability. Possible failure mechanisms of anchored sheetpile walls are shown in Figure 36.

The penetration depth is not sufficient in Figure 36(a) to resist theaxial force (due to the anchor) acting on the wall. The vertical componentof the load in the inclined anchor forces the sheet piles downwards intothe underlying soil. The wall will also move outwards because of theinclination of the anchors.

The sheet pile wall in Figure 36(b) rotates about the anchor levelwhen the toe of the wall moves outwards.

The total stability of the cut is not sufficient in Figure 36(c).Failure occurs along a slip surface which passes below the wall.

The failure mechanism in Figure 36(d) is caused by rupture of theanchors or of the walings. The sheet pile wall will, in this case, rotateor fold around a point located just below the bottom of the excavation.This mechanism may develop even when a single anchor rod or strandruptures. This is because arching is unlikely to assist in re-distributingthe lateral earth pressure, unless the anchors are exceptionally close; awaling, if present, may assist. In any case, the load increase in adjacentanchors must equal the load lost in the failed anchor. Rupture of anchorsis most likely to occur when anchor loads are increasing generally, inwhich case additional capacity may not be available and progressivefailure may then take place. Although not specifically mentioned by Broms& Stille (1976), bond failure (anchor pull-out) is another mechanism whichcan be considered to have the same effects.

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The flexural resistance of the sheet piles has been exceeded in Figure36(e). One or several plastic hinges develop at the levels where thepositive or negative bending moments reach a maximum. At failure, thewall folds around these hinges,

Broms & Stille (1976) reported failures of anchored sheet pile wallsin the soft clays of Sweden. The failure mechanisms shown in Figures36(a), 36(b) and 36(c) predominate. These indicate the importance ofconsidering the vertical support of anchored sheet pile walls and otherpossible factors, such as reduction of shear strength of the clay due toexcess pore water pressures caused by pile driving nearby, which candecrease the axial load carrying capacity of the sheet pile. The failuremechanism shown in Figure 36(d) has also occurred. Failure of the anchorswas caused principally by the lateral expansion of the soil due to frostaction, and was seldom caused by stress corrosion of the anchor bars or byslippage of the anchor bolts or the wedges. The latter generally occurredduring the development stage of new anchor systems. The failure mechanismshown in Figure 36(e), caused by yielding of the walings or of the sheetpiles, has not occurred in Sweden and also appears to be rare in otherparts of the world. This indicates that the methods currently used forthe design of walings and sheet pile walls are safe.

Daniel & Olson (1982) reported an anchored bulkhead failure in stifffissured clays due to a lack of understanding of soil behaviour underconditions involving significant excavation near the bulkhead. The designwas- adequate for undrained conditions, but was inadequate for fully drainedconditions.

In Hong Kong, there is no need to consider frost effects. The designof anchors and the structural design of sheet pile walls are discussed inSection 8.1.4. The deep seated failure in Figure 36(c) can be analysedusing appropriate slope stability analyses, such as those discussed in theGeotechnical Manual for Slopes (GCO, 1984).

The toe failure mechanism, Figure 36(b), can be assessed using limitequilibrium methods of analysis, and the free-earth support method ispreferred to the fixed-earth support method. The different methods forapplying the factor of safety are discussed in detail in Section 6.2.2.

Rowe (1952) derived a flexibility number, p, for sheet pile walls :

n ~ L ; • . . . - . . • • . (6)

where L = length of sheet pile,

E w = modulus of elasticity of sheet pile material,

Iw = moment of inertia of sheet pile cross-section.

It should be noted that p is not dimensionless, and is not applicable tocohesive soil. The values of p. which delineate 'stiff1 piles (whosebending moments can be calculated reasonably accurately using the free-earth support method) from "flexible1 piles (whose bending moments aresmaller than those calculated using the free-earth support method) aregiven by log P = -3.5 and log P = -4.125 for loose sand and dense sand

57

respectively. These values, however, are in the imperial units adopted byRowe (viz. feet for L, lbf/in2 for Ew and in

4/ft for I w).

Browzin (1981) developed a dimensionless flexibility number, p^t forcohesive frictional soils :

'd ~ T ^ - d " K K2 c v

Ka

where V = effective unit weight of soil,

B - width of sheet pile,

c = cohesion of soil in terms of total stress,

Ka = coefficient of active earth pressure.

For the free-earth support conditions, p^ must be less than five forloose soils and less than one for dense soils. The limiting length for thesheet piles can be calculated from these limiting values of p^. When thesheet pile length is greater than the limiting value, the bottom end of thesheet pile can be considered to be fixed.

The stability against penetration failure (Figure 36(a}) is adequateif the side resistance and reaction at the base or toe of the wall issufficient to overcome the vertical component of the anchor forces. Browzin(1977) showed that, for walls with inclined anchors in cohesion less soils,the required driving depth is nearly the same as for walls with horizontalanchors. Also, the skin friction capacity of the piles is much higher thanthe shear stresses generated by the vertical component of the anchor load.Browzin (1982) subsequently showed that the condition of sinking of pilesin cohesive soils is not critical because of the lower anchor forcesresulting from the great depth of penetration that is needed for stabilityagainst overturning.

Anchored walls with sloping anchors in cohesive soils should bedesigned to avoid the following three conditions that involve a singlestability number, 4c/FH :

(a) overturning,(b) sinking of the piles with sloping anchors, and(c) heave at the bottom of the excavation (see

Section 8.1.2(2)}.

A graph presented by Browzin (1981) shows the relationship between thestability number and the parameter M 1 + H/d (where H is the retainedheight of the excavation and d is the depth of penetration) for the abovethree conditions of equilibrium (Figure 37). From the. graph, which wasderived for an essentially cohesive soil (0=O°~1O°), it can be seen thatstability against overturning requires larger values of 4c/TH thanstability against sinking except when # = 0°, where the lines representingoverturning and sinking conditions intersect at (3 = 3.7. This leads to theconclusion that stability against overturning is the governing conditionfor anchored walls with sloping anchors. The equation developed forstability against overturning also shows the high sensitivity of therequired depth, d, to the assumed angle of internal friction, 0, a fact

58

also pointed out by Kovacs et al (1974).

Browzin (1983) later presented universal design charts (Figures 38 to40) for calculating the required depth of penetration for stability againstoverturning, using the free-earth support method. The depth of penetrationis particularly sensitive to the assumed values of 0 and c.

Nataraj & Hoadley (1984) developed a pressure diagram to reduce thecomputational effort in the design of anchored walls in sands using thefree-earth support method.

(2) Foundation Heave and Hydraulic Failure, Considerations forfoundation heave and hydraulic failure are discussed in Sections 6.2.3 and6.2.4 respectively.

8.1.3 S e r v i c e a b i l i t y L im i t States

D e f o r m a t i o n c o n s i d e r a t i o n s f o r anchored w a l l s a re u s u a l l y o fsecondary importance and are s i m i l a r t o those f o r s i n g l e - l e v e l s t r u t t e dw a l l s , which are discussed in Sect ion 7 . 1 . 3 .

8.1 .4 Earth Pressures for Structural Design

The ca l cu la t i on o f bending moments f o r anchored wa l l s is s i m i l a r t ot h a t f o r s i n g l e - l e v e l s t r u t t e d w a l l s , which is d iscussed i n Sect ion7 . 1 . 4 ( 1 ) .

As discussed in Section 8 . 1 . 2 ( 1 ) , bending f a i l u r e o f the wa l ings oro f sheet p i l e s r a r e l y occurs i n p r a c t i c e . This i nd i ca tes t h a t thecu r ren t l y used design methods are adequate.

S imi la r to s t r u t t e d w a l l s , a f a c t o r o f sa fe ty is app l ied t o t he des ignanchor f o r c e . Further allowances ( e . g . s a c r i f i c i a l t h i ckness ) are requ i redi f corrosion problems are expected. Anchors are u s u a l l y i n c l i n e d , and t h i shas three poss ib le e f fec ts :

(a) The value o f Ka i s increased due t o reve rsa l o fwal l f r i c t i o n under working cond i t i ons (however,at f a i l u r e , the wa l l f r i c t i o n reve r t s t o the usuald i r e c t i o n , so no change needs t o be made to theca lcu la t i on o f Ka f o r ove ra l l s t a b i l i t y ) .

(b) Sett lement o f the wa l l and the re ta ined s o i l isincreased.

(c) The anchor tens ion is greater than the equiva lenthor izon ta l prop f o r c e .

A comprehensive t reatment o f the design o f anchors is given by Hanna( 1 9 8 0 ) , B r i t i s h Standards I n s t i t u t i o n (1989) and Geospec 1 • ModelS p e c i f i c a t i o n f o r Prestressed Ground Anchors (GCO, 1989). Factors o fsa fe ty f o r anchor design i n Hong Kong are given in Geospec 1 .

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8.1.5 Design Water Pressures

Considerations relating to the evaluation of design water pressuresare given in Section 6*5.

8.2 MULTI-LEVEL TIED-BACK WALLS

8.2.1 General

The behaviour of multi-level tied-back walls is shown qualitatively inFigure 41 (Hanna, 1968), The use of inclined anchors causes verticalloading of the wall as construction progresses, and inadequate bearingcapacity at wall base level can contribute to wall failure. As the wall isloaded, displacements of the wall relative to the retained soil mobilizefriction on the embedded wall and strains within the soil mass. Verticalwall movements resulting from wall compression and settlement of the wallbase are responsible for lateral movements of the wall system.

Observed behaviour of tied-back wall systems (Clough, 1972b) suggeststhat tied-back walls generally yield smaller deformations than struttedwalls. Finite element analyses by Clough & Tsui (1974) have shown thatmuch of the difference in behaviour is due to the fact that tied-back wallsystems are usually prestressed, while strutted wall systems are usuallynot, and that over-excavation of the temporary excavation platform, aproblem associated with strutted walls, can lead to substantial increase inmovement.

The process of development of earth loadings for strutted and tied-back walls is fundamentally different. For a strutted wall, active earthpressure is partially mobilised behind the wall, and the loads whichdevelop are primarily a function of soil type and strength. Because of thehigh stiffness of the struts and the sequence of excavation, the top of thewall becomes essentially fixed after the first strut is installed, and thewall rotates about the top strut as excavation proceeds. This leads tohigher loads near the top of the wall than would be indicated byRankine/Coulomb theory. A tie-back system, on the other hand, has twopossible modes of behaviour, both of which differ from that of a struttedwall. In the first mode, the wall is prestressed with a resultant greaterthan that of the active or partially active condition. Under thesecircumstances the system responds more akin to a foundation slab on soil,and the earth loading on the wall is primarily dictated by the loadingdistribution assumed in the design prestress diagram and relative wall andsoil stiffnesses. In the second mode, the tied-back wall is prestressed tolower levels, i.e. total resultant equal to or less than that of activeconditions, and the loadings on the wall are developed in a manner similarto a strutted wall. However, the upward redistribution of loads whichoccurs in a strutted wall does not occur in the case of a tied-back wallbecause the tie-back elements are very flexible, and the top of the wallwill continue to rotate outwards as excavation progresses. Thus, the loadsdeveloped resemble those of a conventional triangular earth pressuredistribution, instead of those usually developed in a strutted wall.

The design considerations for multi-level tied-back walls are the sameas in the case of single-level tied-back walls.

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8.2.2 Ultimate Limit States

The failure mechanisms in Figure 36 are also possible for multi-level

anchored walls.

The design of the anchors and the structural design of the wall arediscussed in Section 8.2.4. The stability against the deep-seated failureshown in Figure 36(c) can be assessed using appropriate slope stabilitymethods (GCO, 1984).

The vertical component of the anchor forces for multi-level anchoredwalls could be large. Stability against penetration failure is thereforean important consideration. The side resistance and the reaction at thewall base must be adequate to balance the vertical anchor forces. For thisreason, it is common for multi-level anchored walls to be founded on rock.

Anderson et al (1983) reviewed four methods of checking the overallstability of anchored retaining walls, viz. the German method (GermanSociety for Soil Mechanics and Foundation Engineering, 1980), theOstermayer (1977) method, the French method (Bureau Securitas, 1972) andthe method by Littlejohn et al (1971). Jhey found that all four designmethods resulted in stable systems, both at the end of construction andafter backfill loading. The determination of anchor prestress loads by themethod by James & Jack (1975) was found to be based on erroneous earthpressure assumptions (see Section 8.2.4). More consistent behaviour wasfound in tests designed using the method by Littlejohn et al (1971) foroverall stability, particularly on surcharge loading, indicating that alogarithmic spiral method may be the most appropriate to use. However,Schnabel (1984) commented that the German and French methods are wrong, asthey assume the tie-back pulls on the soil without pushing on the wall. Heconsidered that only the Ostermayer method is correct because it considersthe tie-backs as internal forces in the soil wedge between the wall and theanchors. The method by Broms (1968) also recognizes this. A comprehensivereview of methods of analysing overall stability of anchored retainingwalls is given in British Standards Institution (1989).

The depth of penetration of the wall below excavation level should besufficient to prevent foundation heave (see Section 6.2.3) or hydraulicfailure (see Section 6.2.4).

8.2.3 SerYiceability Limit States

As in the case of multi-level strutted walls, deformation analysis ofmulti-level tied-back walls is of secondary importance and is usually notcarried out. If required, the 'beam on elastic foundation1 approach (seeSection 5.4), the boundary element and finite element methods (see Sections5.5 and 5.6) can be used to predict the lateral displacement of the wall.

Maffei et al (1977a) found that the wall displacement is verysensitive to the assumed coefficient of subgrade reaction. In theirparametric study of the behaviour of tied-back walls, Clough & Tsui (1974)found that for a wall founded on rock, the wall movement and the soilsettlement behind the wall can be substantially reduced by increasing theprestress load, the wall rigidity and the tie-back stiffness. The use ofhigher prestress loads can eliminate the wall movement at the wall top butis not able to prevent wall movement near the bottom of the excavation. As

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a result, soil settlements occur in all stages of the excavation. Thedecrease in wall movement is not in direct proportion to the increase inwall rigidity and tie-back stiffness. Stroh (1975) showed that the wallmovement is more than twice as large where clay is present below the wallcompared with the case where the wall is founded on rock, and that the wallmovement decreases almost linearly as the length of anchors increases.

8.2«4 Earth Pressures for Structural Design

The earth pressures that act on an anchored wall depend on the wallstiffness relative to the soil, the anchor spacing, the anchor yield andthe prestress locked into the anchors at installation.

Two conventional design methods which ignore the effects of wallrigidity, excavation depth and tie-back spacing on the earth pressuredistribution acting on the wall are outlined below.

An empirical method first introduced by Littlejohn et al (1971) waspresented again by James & Jack (1975). This method is also recommended bythe Canadian Foundation Engineering Manual (Canadian Geotechnical Society,1985). Wood (1983) developed a computer program using this method (seeSection 5.5). It can take account of the continuous wall construction,excavation and anchoring stages, and the procedure is applicable to varyingsoil layers. Certain basic assumptions are made in the method, e.g. thesoil pressure distribution is assumed to be triangular and the wall isassumed to yield progressively as excavation proceeds. In addition, apoint of contraflexure in the wall is assumed to occur at a location wherethe factor of safety against overturning is unity. Full-scale monitoringstudies (Littlejohn & Macfarlane, 1975) have indicated that walldeflections and bending moments, which occur as excavation proceeds, followa similar pattern to those predicted by this empirical design method.Moreover, the monitoring results suggest a triangular pressure distributionfor a semi-rigid anchored diaphragm wall, which is different from thetrapezoidal distribution assumed in the design of strutted excavations.

Anderson et al (1983) found from their laboratory scale tests that thedetermination of anchor prestress loads by the method of James & Jack(1975) is based on erroneous earth pressure assumptions. They suggestedthat the method should be modified so that only half of the passivepressure acts in front of the wall, and that the mean of the active and at-rest pressures acts behind the wall.

The Canadian Foundation Engineering Manual (Canadian GeotechnicalSociety, 1985) suggests three possible values of earth pressure actingbehind the wall :

(a) If moderate wall movements can be permitted, orwhere foundations of adjacent buildings extend tobelow the base of the wall, the pressure may becomputed using the coefficient of active earthpressure Ka.

(b) If foundations of buildings or services existbehind the top of the wall at a distance smallerthan the height of the wall and not closer thanhalf the height, the pressure may be computed

62

using a coefficient K = 0.5(Ka + K o ) .

(c) If foundations of buildings or services exist atshallow depth, at a distance smaller than half theheight behind the top of the wall, the pressuremay be computed using the coefficient of earthpressure at rest Ko.

The Manual also suggests that the passive pressure should be reduced toaccount for the wall movement required to develop it.

Another empirical method often adopted is the use of apparentpressure diagrams similar to the Terzaghi & Peck envelopes used in struttedexcavations. A considerable variety of methods for calculating anchorprestress loads exists (Table 5), and Figure 42 shows reported magnitudesof design prestress diagrams used in practice. Terzaghi & Peck envelopesfor strutted excavations are also shown in the figure. It can be seenthat, in most instances, prestressing loads applied to tied-back walls arehigher than the upper limit values for strut loads.

Laboratory-scale tests on rigid multi-anchored walls by Hanna &Matallana (1970), Hanna & Abu Taleb (1971, 1972), Plant (1972) and Hanna &Dina (1973) showed that a trapezoidal earth pressure distribution, with theearth pressure coefficient equal to 0.5(Ka + K o ) , is appropriate. Forflexible multi-level tied-back walls, laboratory-scale tests by Hanna &Kurdi (1974) showed that a rectangular earth pressure distribution appearsreasonable.

dough & Tsui (1974) used a finite element method to investigate thebehaviour of a tied-back sheet pile wall in clay. Their study showed thatthe calculated pressures are more triangular in shape than the designtrapezoidal diagram, and the calculated pressures tend to concentrateslightly at the anchor levels, a phenomenon observed by Hanna & Kurdi(1974). The triangularization of these pressures is apparently caused bythe movements of the flexible tie-back supports. Anderson' et al (1983)found from laboratory-scale tests that a trapezoidal earth pressuredistribution assumption is realistic if excavation is being carried out towall base level. However, a triangular pressure distribution is morerealistic if excavation terminates some distance above wall base level. Inpractice, excavation would usually stop some distance above the wall baseto minimize base movements, and field observations at the Guildhall Re-development in London (Littlejohn & MacFarlane, 1975) would seem to confirmthe latter distribution.

As discussed in Section 8.2.1, there are two possible modes ofbehaviour for tied-back walls, depending upon the prestress level employed.Ideally, prestress just sufficient to minimize settlements behind the wallshould be used, bearing in mind that some settlement will always occurregardless of the prestress load, due to the unloading of the soil at thebottom of the excavation. Observed movements of actual tie-back systemssuggest that the optimum level of prestress to minimize movements liesslightly above the load levels recommended by Terzaghi & Peck (1967) forstrutted walls. Satisfactory performance can easily be obtained, however,using lower prestress levels if movements are not a primary concern(dough, 1975). J

Hanna & Kurdi (1974) found that the maximum bending moment in a multi-

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anchored w a l l decreases w i t h increas ing wa l l f l e x i b i l i t y . I f the w a l lheight is taken to be the f r ee span between two consecutive anchor l e v e l s ,trends o f reduc t ion in bending moment w i th f l e x i b i l i t y s i m i l a r t o Rowe'scurves (Rowe, 1952) can be ob ta ined .

Anderson et a l (1982) found from labora to ry -sca le tes ts tha t in orderto r e s t r i c t movement o f anchored wa l ls suppor t ing b a c k f i l l w i th a un i fo rmsu rcha rge l o a d i n g , a r e c t a n g u l a r pressure d i s t r i b u t i o n , and an ear thpressure c o e f f i c i e n t o f Ko f o r the surcharge component appear reasonable.For a l i n e or s t r i p l o a d i n g , they suggested t h a t in order to r e s t r i c tmovement, t h e s t r i p l o a d i n g component o f t h e r e c t a n g u l a r p r e s s u r ed i s t r i b u t i o n should be 1.3 t imes the maximum hor i zon ta l s t ress p red ic ted bye l a s t i c t h e o r y .

A n a l y t i c a l methods which take s o i l - s t r u c t u r e i n t e r a c t i o n i n t ocons ide ra t ion can be used t o determine the magnitude and d i s t r i b u t i o n o fe a r t h p ressu res ac t i ng on mul t i -anchored w a l l s . The 'beam on e l a s t i cfounda t ion 1 approach was app l ied by Bowles (1988) and Maf fe i et a l (1977b),the boundary element methods by Wood (1979) and Pappin et a l (1985), andthe f i n i t e element methods by Clough et al (1972) , Clough & Tsui (1974) ,B a r l a & Masca rd i ( 1 9 7 5 ) , Murphy et a l (1975), Stroh & Breth (1976),Rosenberg et a l (1977) , Simpson et a l (1979), S t i l l e & Fredricksson (1979)and Hata et a l (1985), to model the wa l l /anchor /excavat ion system, Maf fe iet al (1977a) found t h a t , using the 'beam on e l a s t i c foundat ion 1 method,the h o r i z o n t a l stresses ac t i ng on the wa l l are not very s e n s i t i v e t o thec o e f f i c i e n t o f the subgrade reac t ion when these stresses are compared w i t hthose obta ined by the f i n i t e element method. As i n . t h e case o f m u l t i - l e v e ls t r u t t e d w a l l s , the f i n i t e element analys is (as we l l as other a n a l y t i c a lmethods) should be used in p a r a l l e l w i t h an observat iona l procedure, anda l lowance^ s h o u l d be made f o r r e - a n a l y s e s t o be performed so as toaccommodate s o i l parameter re-est imates and cons t ruc t ion changes. So i lparameters are best r e f i ned by comparing the observed performance a t ea r l ystages o f excavat ion w i th f i n i t e element p r e d i c t i o n s .

Summarising, the a v a i l a b l e methods a r e , i n increas ing order o f cost o fper forming an a n a l y s i s , the method o f apparent pressure diagrams, the semi-emp i r i ca l method by James & Jack (1975), the 'beam on e l a s t i c foundat ion 1

approach, the boundary element and the f i n i t e element methods.

8.2.5 Design Water Pressures

Considerations relating to the evaluation of design water pressuresare given in Section 6.5.

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9 . GROUND MOVEMENTS AROUND EXCAVATIONS

9.1 GENERAL

This chapter considers only ground movements caused by deepexcavations. An excellent review of movements of excavation supportsystems in soft clay is given by Clough & Schmidt (1981). Ground movementscaused by pile driving and dewatering are discussed in the state-of-the-artreport by D'Appolonia (1971)•

9.2 FACTORS INFLUENCING MOVEMENTS

9.2.1 Effect of Stress Changes

Figure 43 illustrates, in a qualitative manner, the stress changes andstrains experienced by two soil elements near an excavation. The stresspaths are typical for a normally consolidated plastic clay. Both thereduction in total vertical and horizontal stress, and the change inequilibrium pore water pressure, are important. The table in the figurelists the stress changes and the strains brought about by the excavationand the change in seepage conditions.

The critical factor that determines the inward movement of the sidesof the cut below excavation level, and hence the magnitude of settlement,involves the proximity of the unloading stress path _for element B to thefailure envelope. If the effective stress points B\ and B s s, are wellwithin the effective stress failure envelope, Kf, i.e. if local yield isavoided, then the heave will be small and the lateral movement of the soilbelow excavation level will be small. On the other hand, if the effectivestress points for element B approach the failure envelope and passive localyield occurs, then the movements will be large.

9.2.2 Dimensions of Excavation

The deeper the excavation, the greater is the decrease in totalstress, and thus the larger are the movements of the surrounding soil.

9.2.3 Soil Properties

In clays, it has been shown (Clough et al, 1979; Mana & Clough, 1981)that the maximum lateral wall movement could be correlated with the factorof safety against basal heave, which in turn depends on the shear strengthof the soil. The rate and magnitude of movement increase rapidly as thefactor of safety approaches one.

. If a clay is presumed to be isotropic when it is in fact anisotropic,the basal heave factor of safety may be much lower and lateral wallmovements as well as ground surface settlements may be larger than expected(Clough & Hansen, 1981).

Wall movements and ground settlements are smaller in stiff soils, suchas granular soils and stiff clays, than in soft soils, such as soft andmedium clays and compressible silts (Peck, 1969b).

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9.2.4 Initial Horizontal Stress

For excavated wa l ls in s o i l s w i t h a high i n i t i a l Ko v a l u e , large so i land wal l movements are experienced even at shal low depths o f excavat ion.The w a l l behav iou r i s dominated by v e r t i c a l un load ing caused by theexcavation process, and la rge movements s t i l l occur even i f the wa l l isf u l l y res t ra ined from ho r i zon ta l movement. For w a l l s in s o i l s w i t h a lowKo v a l u e , t h e d isp lacements are much smal ler i n magnitude (Pot ts andFour ie, 1984).

9.2.5 Groundwater Conditions

In p r a c t i c e , a p e r f e c t l y w a t e r t i g h t wa l l p e n e t r a t i n g an impermeables o i l layer at the bottom of the excavat ion does not e x i s t . Where waterflows i n to the excavat ion, a decrease in groundwater pressure w i l l occur.This w i l l cause an increase in e f f e c t i v e s t ress and se t t l emen t o f the s o i lsurrounding the excavat ion. Where groundwater has not been brought undercomplete c o n t r o l , l a rge , e r r a t i c and damaging se t t l ement due t o the f l ow orthe migrat ion of f i nes in to the excavat ion are not uncommon*

9.2.6 Stiffness of Support System

The support system stiffness depends on the stiffness of the wall andits supports, the spacing between supports, and the length of wall embeddedbelow the excavation bottom. A valuable study into the effect of wallstiffness and support spacing was carried out by Goldberg et al (1976), andthe results are presented in Figure 44, in which the stability number FH/CU

is plotted versus the stiffness parameter EwIw/h4, where E WI W is the

stiffness of the wall, h is the distance between supports, FH is theoverburden pressure, and Cu is the undrained shear strength of the soil.

Various boundary lines are drawn to establish zones of expectedlateral wall movements. These data suggest that an increase in EwIw/h

4 hasa • significant effect in reducing movements. The movement is also afunction of the factor of safety against basal heave, being moresignificant at lower factors of safety than at higher ones.

Increasing the stiffness of the strut or the tie-back decreasesmovements, but this effect shows diminishing returns at very high values ofstrut or tie-back stiffness.

Movements are also reduced as the depth to an underlying firm layerdecreases and when the wall toe is embedded into the underlying firm layer.

9.2.7 Effect of Preloading

Preloading removes slack from the support system, and thus eliminatesthis potential source of movement. Each application of preload reduces theshear stresses set up in the soil due to previous excavation activities.This means that the soil is partially unloaded, and its stress-strainresponse is stiffened until the next excavation step generates shearstresses that reload the soil beyond its maximum previous level of shearstress. This temporary stiffening of the soil also leads to reducedmovements.

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Use of preloads in the struts or tie-backs reduces movement, althoughthere are diminishing returns at higher preloads. Very high preloads may,in fact, be counter-productive, since local outward movements at supportlevels can damage adjacent utilities.

Clough & Tsui (1974) showed that the prestress loads in tie-backscalculated in accordance with a triangular at-rest pressure diagram areless effective in reducing movements than those obtained from thetrapezoidal pressure diagram of the shape recommended by Terzaghi & Peck(1967) for calculating strut loads for strutted excavations. Clough (1975)also found that the optimum effect of prestress loads in reducing systemmovements can be achieved by using levels slightly greater than thoserecommended by Terzaghi & Peck (1967). Model tests by Hanna & Kurdi (1974)have confirmed this conclusion. Clough & Tsui (1974) also showed thatmovements of the tied-back wall, and the soil settlements behind the wall,can be substantially reduced by a judicious choice of prestress load andsupport system stiffness.

O'Rourke (1981) considered that, in most cases, cross-lot strutsprestressed to 50% of their design load will be sufficiently rigid torestrict further movement at the level of the supports, and sufficientlylow in load to avoid being overstressed as additional excavation occurs.

9.2.8 Effect of Passive Soil Buttresses

The effectiveness of these in controlling movements in excavation insoft to medium clay was studied by Clough & Denby (1977) using the finiteelement method. They used the term "berm11 for a passive soil buttress.Figure 45 shows the theoretical relationships between settlements behindbermed sheet pile walls and the stability number, ^H/CU5, where CU5 is theundrained shear strength at the base of the excavation, for the conditionof excavation after the berm has been removed and the rakers installed.

At low stability numbers, increases in berm size produce minimalmovement reduction. For intermediate stability numbers, increases in bermsize show a diminishing effect. At high stability numbers, increasing froman intermediate to a large berm leads to a large reduction in settlements.However, this reduction is an exarrple of false economy, since at largestability numbers, large movements occur even with large berms becausedeep-seated movements take place beneath the berms. As a result, theeffectiveness of the berms is diminished.

9.2.9 Associated Site Preparation Works

Site preparation may include the following activities :

(a) relocation and underpinning of utilities,

(b) dewatering of aquifers above and below the baseof the excavation,

(c) construction of the excavation support system, and

(d) the installation of deep foundations.

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In some cases, the movements associated with the site preparationworks will exceed those which occur as a result of the excavation andsupport process. The relocation of u t i l i t i es , for example, may have alocally severe impact on an adjacent property, especially when trenching iscarried out close to pipelines and communication conduits,

Dewatering may consolidate the soil over an area which substantiallyexceeds the area affected by excavation-induced movements. Also, i t oftencauses settlements well in excess of excavation settlements. However, inareas which have been subjected to earlier dewatering act iv i t ies,settlements due to further dewatering are smaller than those in virginground due to the stiffer response of the preconsolidated soi l .

Wall construction may require predrilling for soldier piles, the useof vibratory hammers to install sheet piles, or the excavation of slurrypanels for concrete diaphragm walls. Each of these can cause permanentmovements, the magnitude and distribution of which wi l l vary according tothe soil conditions, site history and details of the constructionprocedures,

9.2.10 Influence of Construction Factors

A review of the influence of construction factors on excavationmovements was made by Clough & Davidson (1977), and useful specific casehistory accounts were provided by Broms & Sti l le (1976), Hansbo et al(1973), Lambe et al (1970), O'Rourke et al (1976), White (1976) and Zeevart(1972).

Additional movements of excavations, and even local failure, have beenproduced by late installation of supports, over-excavation, pile driving,caisson construction, loss of water through holes for tie-backs and jointsor interlocks of slurry or sheet pile walls, remoulding and undercutting ofclay berms, and surcharge loads from spoil heaps and constructionequipment.

Lambe (1970, 1972) demonstrated that variations in wedging techniquesbetween the waiings and struts, and differences in excavation procedure,can result in doubling of the wall and soil movements* Clough & Tsui(1974) used a finite element analysis to show that over-excavation couldlead to a 100% increase in movement.

Because these factors cannot always be quantified, i t is d i f f icu l t tomake accurate prediction of movements. However, many of the undesirableeffects of these factors have been identified, and they can therefore beanticipated and controlled through good specifications, well-plannedconstructTon procedures and close supervision and monitoring. The designermust consider how the excavation and subsequent construction should be£n™ *«°7kf i d . e n t i f * critical construction factors and, where possible,allow for them in performance estimates and specifications.

9,3 PREDICTIVE METHODS

9.3.1 Types of Methods

Prediction of soil movements behind a supported excavation can be made

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by the following methods :

(a) emp i r i ca l methods,(b) semi-empi r ica l methods,(c) the method o f v e l o c i t y f i e l d s , and(d) t he f i n i t e element method.

9 .3 .2 Empirical Methods**•

Set t lement behind excavat ions can be est imated based on data obtainedf rom p r e v i o u s e x c a v a t i o n s i n s i m i l a r s o i l c o n d i t i o n s ; Peck (1969b)summarised data on set t lements behind excavations to produce the usefu lchar t shown in Figure 46. Sett lements presented as a percentage o f theexcavat ion depth were p l o t t e d against d is tance from the excavat ion d i v idedby excavat ion dep th . Three d i f f e r e n t zones, as def ined in the f i g u r e , werei d e n t i f i e d . Genera l l y , where workmanship is average or above average ands o i l cond i t i ons are not espec ia l l y d i f f i c u l t , set t lements should not exceedone percent o f the excavat ion depth . In cases where seepage can occur ands o i l c o n s o l i d a t i o n r e s u l t s , the one percent f i g u r e can be exceeded (Lambeet a l , 1970). I t should a lso be noted tha t cons t ruc t i on technique can havea s t rong in f l uence on movements o f s t r u t t e d systems (see Sect ion 9 . 2 . 1 0 ) .

O'Rourke et a l (1976) compiled set t lement data associated w i t h s o l d i e rp i l e and lagging excavat ion in the dense sand and interbedded s t i f f c layo f W a s h i n g t o n , U.S.A. (F igure 47 ) . Expressed as a percentage o f theexcavat ion dep th , the sur face set t lements were equal to or less than 0.3%near the edge o f the cut and 0.05% at a d is tance equal t o 1.5 t imes theexcavat ion depth . A comparat ive study o f s t r u t t e d excavations in the s o f tc lay o f Chicago using temporary berms and rak ing s t r u t s was a lso c a r r i e dout by 0'Rourke e t a l (1976). The data are p l o t t e d in dimensionless formin F igure 48. Three zones o f ground displacement can be d i s t i ngu i shed andr e l a t e d t o t he s a l i e n t c h a r a c t e r i s t i c s o f c o n s t r u c t i o n . These zonesapproximate to the th ree zones o f set t lement de l inea ted by Peck (1969b),w i t h the except ion t h a t the widths o f the set t lement zones are notablys h o r t e r . This ind ica tes t h a t the set t lements associated w i th the Chicagoexcavat ions are conf ined to areas t ha t are comparat ively nearer the edgeso f the excavat ions .

Based on these s t u d i e s , 0 'Rourke (1981) noted t h a t the s t r u t t e dexcavat ions were genera l l y ca r r i ed out in th ree prominent stages (Figure49) :

(a) I n i t i a l e x c a v a t i o n b e f o r e s t r u t t i n g . Thee x c a v a t i o n was deepened b e f o r e suppo r t s werei n s t a l l e d . Thus, deformat ion o f the wa l l occurredp r i m a r i l y as a c a n t i l e v e r - t y p e movement. Theh o r i z o n t a l s t r a i n s produced i n t h i s mode o fdeformat ion form a t r i a n g u l a r p a t t e r n o f contourst h a t decrease in magnitude w i t h depth and d is tanceaway from the w a l l .

(b) Excavat ion to subgrade a f t e r i n s t a l l a t i o n o f uppers t r u t s . As the supports were i n s t a l l e d , the upperp o r t i o n o f the wa l l was r e s t r a i n e d from f u r t h e rl a t e r a l movement. In the deeper p o r t i o n o f thee x c a v a t i o n , inward b u l g i n g o f the wa l l caused

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t e n s i l e s t r a i n s , t h e c o n t o u r s f o r which wereinc l ined at approximately 45° to the v e r t i c a l .

(c) Removal o f suppor ts . As the bottom s t r u t s wereremoved to b u i l d t h e underground s t r u c t u r e ,fu r the r inward bu lg ing o f the wa l l o c c u r r e d . Whenthe upper s t r u t s were removed, t h e w a l l wassuppor ted i n i t s lower p o r t i o n by t he subways t r u c t u r e , r e s u l t i n g i n a c a n t i l e v e r - t y p ede fo rma t i on a t t h e upper p o r t i o n o f the w a l l .Consequen t l y , t h e c u m u l a t i v e s t r a i n s were acomposite o f the ho r i zon ta l d i s t o r t i o n assoc ia tedwi th inward bu lg ing a t depth and the d i s t o r t i o nassociated w i th c a n t i l e v e r movement a t the upperlevels of excavat ion.

Thus , t h e s o i l s t r a i n s are c lose l y r e l a t e d t o the modes o f wa l ldeformat ion. A q u a n t i t a t i v e r e l a t i o n s h i p between the d isp lacement pa t te rnof the wal l and movement o f the ground sur face ad jacent to the excavat ionwas developed by O'Rourke (1981) and is shown in F igure 50. A c o e f f i c i e n tof deformat ion, CQ, was def ined as the r a t i o o f the c a n t i l e v e r movement ofthe w a l l , S w , to the sum of t h i s c a n t i l e v e r component and the inwardbulg ing component, S w ' , o f the displacement. I t should be noted t h a t thedata summarised in Figure 50 p e r t a i n t o excavat ions where the w a l l s havebeen d r i v e n to a s t i f f s o i l l a y e r , and thus do not have s i g n i f i c a n tmovement a t the bottom.

The f i e l d data in Figure 50 show t h a t the l i m i t s f o r the r a t i o ofhor izonta l to v e r t i c a l movement (se t t lement ) are approx imate ly equal t o 0.6and 1.6 f o r wa l l deformation caused so le l y by inward bu lg ing ( i . e . w i t h thew a l l f i r m l y supported at an ear ly stage o f excavat ion) and s o l e l y bycan t i lever movement, r e s p e c t i v e l y . These bounds compare favourab ly w i t hthe l i m i t s determined from model t e s t s in sands performed by M i l l i g a n(1983) (see Section 9 .3 .4 ) .

Clough et a l (1979) and Mana & Clough (1981) reviewed case h i s t o r i e so f sheet p i l e and so l d i e r p i l e wa l l s in c lays supported p r i m a r i l y byc ross - l o t s t r u t s . The r e s u l t s ' are summarised i n F igure 5 1 , which showstha t the maximum l a t e r a l movement can be co r re l a ted w i t h t he f a c t o r o fsa fe t y aga ins t basal heave def ined by Terzaghi (1943) . The movementsincrease rap id l y below a f ac to r o f sa fe ty o f 1.4 t o 1.5, w h i l e a t h igherfactors o f safety the nondimensional movements l i e w i t h i n a narrow rangeof 0.2% to 0.8%. Moreover, the re do not appear t o be any s i g n i f i c a n td i f fe rences in l a t e r a l movements between sheet p i l e w a l l s whose t i p s areembedded in an under ly ing s t i f f layer and those whose t i p s remain i n themoving clay mass.

Mana & .Clough (1981) p l o t t e d maximum set t lement data versus l a t e r a lwairmovements as shown in Figure 52. This f i g u r e shows t h a t se t t lementsrange from 0.5 to 1.0 times the l a t e r a l wa l l movements. I f se t t lements are^ " S S ^ J f f S i ^ J 1 * 1 1 ^ V b 6 1 t 0 l a t ^ a l wa l l movements, then Figure

t ^ / h ^ J } i 7 f n 197l] s u m m d r J s e d t h e data from a v a i l a b l e l i t e r a t u r e ont i e d - b a c k w a l l movements, as shown in Figure 53. General ly the w a l lmovements and sett lements are we l l below one percent T thef E x c a v a t i o n

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depth, although in a few instances values above one percent appear. Thedata were re-plotted in Figures 54 and 55, where the percentage movement isplotted against the maximum ordinate of the design prestress diagram forsands and stiff clays respectively. The maximum prestress pressure is madenondimensional by the product of unit weight and excavation height. It canbe seen that, for both sands and stiff clays, the movements decrease withincreasing prestress. The design pressure levels suggested by Terzaghi &Peck (1967) are also shown in the figures. The data suggest that theoptimum effect of prestressing in reducing movements is achieved by usingpressure levels slightly greater than those of Terzaghi & Peck (1967)•Further data on movements of the crest and settlement of the ground behindtied-back walls are given in British Standards Institution (1989).

A large amount of data have been obtained during the construction ofthe Mass Transit Railway (MTR) in Hong Kong. Stroud & Sweeney (1977)reported ground movements caused by the installation of a diaphragm walltest panel. Morton et al (1980a & b) found that the settlements induced bythe MTR construction can generally be separated into those resulting fromwall installation, dewatering and station box excavation. Settlementscaused by the diaphragm wall construction were found to be significant.The reason for this was thought to be due to the breakdown of arching asthe length of wall was constructed, and the high lateral swelling potentialof the completely decomposed granite (Davies & Henkel, 1980). Cowland &Thorley (1984) also reported significant settlements due to slurry trenchexcavation up to a distance equal to the depth of the trench away.Significant settlements were measured at some buildings even when the wholeof the base of their foundations was outside the theoretical active wedge.A relationship was found between maximum building settlement and the ratioof the foundation depth to trench depth (Figure 56). Dewatering was theprominent cause of building settlement at some of the MTR stations.Relatively large wall deflections occurred during excavation. However, thebuilding settlements were usually low, the ratio of maximum lateral wallmovement to building settlement being of the order *of 4:1. While theground conditions and the causes of settlement of adjacent buildingsdiffered from site to site, the total settlements recorded were,surprisingly, found to be related to their foundation depths as shown infigure 57.

Settlement data associated with the construction of the MTR IslandLine were compiled by Budge-Reid et al (1984). The settlements caused bydiaphragm wall installation, station box dewatering and diaphragm boxexcavation are shown in Figures 58, 59 and 60 respectively.

It should be noted that while Figures 56 and 58 give general empiricalrelationships for estimating settlement due to slurry trench installation,the fundamental factor affecting settlement is the effective stress changein the completely decomposed granite. Unfortunately, the only datarelating settlement and the effective slurry pressure are those given byDavies & Henkel (1980).

Very few settlement monitoring data associated with deep excavationsfor basement construction in Hong Kong have been published. Morton & Tsui(1982) presented very limited ground movement data for the construction ofthe deep basement of the China Resources Building. Well documentedsettlement monitoring data for the construction of the new Hong Kong Bankheadquarters building were given by Fitzpatrick & Will ford (1985) andHumpheson et al (1986).

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9.3.3 Semi-empirical Methods

The following semi-empirical methods have been proposed to relate thesettlement of the ground behind an excavation with the lateral movement ofthe supporting wall.

Caspe (1966) presented a method of analysis which relates thesettlement profile behind an excavation with the wall deflection. Threekey assumptions were made in the analysis :

(a) There is a surface behind the wall which definesthe limit of significant soil deformation,

(b) The variation in horizontal strain in the soil atany level between the above surface and the wallis assumed.

(c) At all points, the vertical strain is assumed tobe related to the horizontal strain by thePoisson's ratio, p.

Kane (1966) commented that the third assumption is incorrect, as thevertical strain should be related to horizontal strain by v/{l»v) underplane strain conditions. Consequently, the predicted settlement profile nolonger matches the measured profile. Bowles (1988) modified Caspe1s methodand obtained reasonable matching with the measured settlement profi le.

Another method was proposed by Bauer (1984) to obtain a reasonableestimate of ground loss around excavations in sands, and this isillustrated in Figure 61.

9.3.4 Method of Velocity Fields

The method of velocity fields has been discussed in Section 5.3.

Bransby & Milligan (1975) showed that the deformations in the soilbehind a flexible cantilever retaining wall could be predicted from thecorrection of the wall using a simple velocity f ield. The method depends°J1 ? ^ l P?rameter> the angle of dilation, which can be related to the£ 9 l f f - i f r l c i l2I ! u s 1 n? t h e s t r e s s dilatancy relationship of Rowe (1962).fir S i !• i d n g l e o f d i 1 a t i o n t 0 w i * h i n 50 is sufficiently accuratefor ail practical purposes.

l 1 *Wi!h dn dncho r o r suPP°rt near the top, Milligan (1983,numJL nf .a i !+ - t h i e P d t - t e? o f d1*Placements could be divided into a

? ! L 1 J J1 V e l / i simple zones, which could be related to thein S c h arrMnn ",V* ^ t h t S e 20nes a r e l i n k e d ^ * ™re complex zonewithout rha™ C0UJd Oc?ur- For t h e case i n w h i c h t h * ^oi 1 is deforming

^ d S i m p 1 e v e l 0 ^ i t y f ie ld could apply,ive of the mode of deformation of the wall.

9.3.5 Finite Element Method

f t ^ s " ^ ^ ^ only the f in i te elementtakes account of the interaction between all the components within

73

the retaining system (Institution of Structural Engineers, 1989}• Theinherent assumptions that have to be made in applying the finite elementmethod to the prediction of ground movements were discussed by Borland(1978). The soil parameters required for a finite element analysis arediscussed in Section 5.6.

Bur land et al (1979) back-analysed measurements of movement usingfinite element techniques to provide insitu deformation parameters forLondon Clay, and used the derived parameters successfully in predicting andcontrolling ground movements around major excavations in critical locationsin London.

Recent field and laboratory tests reveal that some soils exhibit ahigher stiffness at small strain (see Section 5.6). Jardine et al (1986)used the finite element method incorporating a soil model that featuressmall strain nonlinearity to predict the settlement behind a struttedexcavation. Good agreement with the observed field behaviour wasobtained.

Potts & Fourie (1984) used a finite element analysis which incorpor-ated an elasto-plastic soil model, to investigate the behaviour of a singlepropped retaining wall. The results of their study showed that, forexcavated walls in soils with a high initial Ko value, large soil movementsoccur even at shallow depths of excavation. This behaviour is related tothe vertical unloading due to the excavation process. Large movementsstill occur even if the wall is fully restrained from horizontal movement.For walls in soils with a low Ko value, the soil movements are much smallerin magnitude.

Mana & Clough (1981) used a finite element model to verify the trendof field data, which indicate that there is a well-defined relationshipbetween the maximum lateral movement and the basal heave factor of safety(Figure 62). The range of field data in Figure 51 are superimposed ontoFigure 62, and these nicely bound the finite element trend curve. Theresults of the finite element analysis also showed that the maximum groundsettlements range from 0.4 to 0.8 times the maximum lateral wall movements(Figure 63). However, the field data showed that the maximum groundsettlements were from 0.5 to 1.0 times the maximum lateral wall movements(Figure 52). The slightly larger ratio of settlement to lateral movementobserved for some of the field cases is probably due to the effects ofsmall amounts of consolidation, or traffic or surcharge loading behind thewall.

Based on their finite element studies, Mana & Clough (1981) proposedthe following procedures for estimating wall movements and ground surfacesettlements for a strutted excavation in soft to medium clays :

(a) Compute the factor of safety against basal heaveusing Terzaghi's approach at each constructionstage where movements are desired. The factor ofsafety at each stage is to be used in theprediction procedures, except in the case wherethe factor of safety increases at laterexcavation stages due to the presence of anunderlying strong layer. In this instance, thekey factor of safety is the minimum which developsduring excavation.

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fb) Estimate the maximum l a t e r a l wa l l movements A h m a x

between the fac to r o f safety and w a l l movements,using the r e l a t i o n s h i p i n Figure 62. The maximumground s e t t l e m e n t Avma<x can a lso be es t imatedd i r e c t l y , assuming tha t i t is in the range o f 0.6to 1.0 times the maximum wa l l movements,

(c) Based on the wal l s t i f f n e s s f a c t o r , E w I w / P h 4 , thes t r u t s t i f f n e s s f a c t o r , S k /FH, the depth to f i r mlayer E^, and the excavat ion w id th B, determinethe inf luence c o e f f i c i e n t s a\\, or$» ap» and ae»using Figures 64, 65, 66 and 67 r e s p e c t i v e l y .

(d) Determine the i n f l u e n c e c o e f f i c i e n t f o r t h edesign s t r u t preloads using Figure 68.

(e) Se lec t a va lue f o r t h e modulus m u l t i p l i e r M(=E /C U ) , based on a v a i l a b l e t e s t d a t a or oni n f o r m a t i o n found i n t he l i t e r a t u r e - Thend e t e r m i n e t h e modu lus m u l t i p l i e r i n f l u e n c ec o e f f i c i e n t , aw> from Figure 69.

( f ) Using the value of Ah^dx obtained in s tep (b) andthe i n f l u e n c e c o e f f i c i e n t s determined i n steps( c ) , ( d ) , and ( e ) , a rev ised value fo r the maximuml a t e r a l movement i s est imated as :

Ahjfiax = Ahmax <*W a $ c*D a B a ? a M . . • . (8)

(g) A revised estimate for the maximum groundsettlement is. obtained by assuming that i t isequal to 0.6 to 1.0 times Ahjfjax.

(h) The ground settlement profile is established usingthe value of the maximum settlement from step (g)and Figure 70.

•-dough & Tsui (1974) carried out finite element analyses to study thedifference in behaviour between tied-back and strutted walls in clay. Theresults of their study showed that, in the case of walls with "equivalent1conditions, the tied-back wall moved more than the strutted wall, andsettlements behind the tied-back wall were also larger. This wasattributed to the movement of the anchorages in the retained soil mass.However, in practice, the tied-back wall is usually prestressed and thestrutted wall is not, and over-excavation often occurs during constructionof the strutted wall. In these cases, the finite element analyses showedthat the tied-back wall moved less and ground settlements were smaller thanthose for the strutted walls.

Although the method of Mana & Clough (1981) for predicting movementsis. primarily designed for cross-lot strutted walls, i t can be used in itspresent form for tied-back walls, provided that the anchors are embedded inan unmoving soil or rock mass. Should the anchorages be subjected tomovement, the method is no longer applicable, since this will introduceadditional displacements that are not considered in the method.

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10. REVIB* OF LOCAL DESIGN PRACTICE

Local guidance on the design o f excavat ion support systems and onp r e d i c t i o n o f ground movements around excavations is given in Chapters 7and 10 o f Geoguide 1 : Guide to R e t a i n i n g Wa l l Design (GCQ, 1982)r e s p e c t i v e l y . These chapters o f the Geoguide are based heavi ly on overseasp u b l i c a t i o n s from the 1970 's . Some o f the major fac to rs which in f luencedes ign , c o n s t r u c t i o n and con t ro l o f excavations f o r basement cons t ruc t i onin urban areas o f Hong Kong are reviewed by Sivaloganathan (1986).

S t r u t t e d e x c a v a t i o n s are u s u a l l y designed, or at leas t they arechecked, using the apparent pressure diagrams g iven by Peck (1969b) and theJapan Soc ie ty o f C i v i l Engineers (1977). These pressure diagrams are knownto be c o n s e r v a t i v e . Apparent pressure diagrams, w i th maximum pressuresless than those g iven by Peck, were der ived fo r American and B r a z i l i a nres idua l s o i l s (see Sect ion 7 . 2 . 4 ) . However, t he re are no repor ted f i e l dmeasurements o f s t r u t loads to es tab l i sh the apparent pressure diagrams f o rHong Kong r e s i d u a l s o i l s and s a p r o l i t e s .

D e s p i t e i t s l i m i t a t i o n s (see Sect ion 5 . 4 ) , the 'beam on e l a s t i cf o u n d a t i o n 1 approach is commonly used in Hong Kong for the design o fe x c a v a t i o n s u p p o r t sys tems . The va lues o f c o e f f i c i e n t o f subgrader e a c t i o n recommended by Terzaghi (1955), al though known to be conservat ive(Habibagahi & Langer, 1984), is normally employed in the c a l c u l a t i o n s . Thed i s c r e t e element method u t i l i s i n g the r e l a t i o n s h i p between l a t e r a l ear thpressure and displacement has a lso been used. The boundary element methodwas employed to p r e d i c t the performance o f the basement for the new HongKong Bank headquarters b u i l d i n g ( F i t z p a t r i c k & W i l l f o r d , 1985; Humpheson eta l , 1986) . However, the re are no repor ted case s tud ies in which the f i n i t eelement method is used fo r the design o f excavat ion support systems.

I n p r e d i c t i n g ground movements around excavat ions, the s e t t l m & o tcurves aJLJBscJc.^JLaSStL} and O ' R o u r k e e t a] (1976) (which are given inGeoguide 1) are o f t en used. I t T s T o u b t f u l whether these curves, whichwere compiled from data in North America, are d i r e c t l y app l icab le t o HongKong r e s i d u a l s o i l s and s a p r o l i t e s . / A large amount o f data have beeno b t a i n e d d u r i n g t h e c o n s t r u c t i o n o f t h e Mass T r a n s i t Railway (MTR)underground s t a t i o n s and other deep basement excavat ions.^ Some o f the MTRset t lement data have been publ ished ( js.g. Morton et a f , J . 9 8 0 _ a & b andBudge-Re4d et a ] , 1984). I t would t h e r e f o r e be use fu l to t r y to es tab l i shset t lements curves from these d a t a , s i m i l a r to those der ived by Peck, f o rHong Kong res idua l s o i l s and s a p r o l i t e s .

An important parameter t h a t a f f ec t s the magnitude o f the s t r u t l oads ,and the deformat ion o f the s o i l , is the c o e f f i c i e n t o f ear th pressure atr e s t , Ko (see Sect ion 5 . 6 ) . Although there is evidence to suggest t ha t thei n s i t u h o r i z o n t a l s t ress in Hong Kong res idua l s o i l s and s a p r o l i t e s is low,i n s i t u measurement o f Ko is l a c k i n g .

Fa i l u res o f sheet p i l i n g in Hong Kong were reviewed by Malone (1982).Case h i s t o r i e s o f excavat ion support f a i l u r e s in other count r ies are g ivenby Sowers & Sowers (1967), Broms & S t i 11 e (1976), and Daniel & Olson(1982). These s tud ies show t h a t f a i l u r e s o f the excavat ion support systemare seldom due to inadequacies in des ign . Instead they are o f ten caused bypoor c o n s t r u c t i o n p rac t i ce and inadequate s i t e supe rv i s i on . This ind ica test h a t c u r r e n t design methods are adequate.

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11. GEOTECHNICAL CONTROL OF EXCAVATIONS IN H0N6 KONG

All private development in Hong Kong is controlled by the BuildingAuthority under the Buildings Ordinance and its subsidiary Regulations(Government of Hong Kong, 1985). The geotechnical aspects of submissionsare checked by the Geotechnical Control Office. Practice Notes listing therequirements on submissions are issued by the Building Authority toAuthorized Persons and Registered Structural Engineers. The followingPractice Notes are relevant to excavation submissions :

(a) PNAP : 74 - Dewatering in Foundation and BasementExcavation Works.

(b) PNAP : 78 - Requirements for a GeotechnicalAssessment at General Building Plan Stage -Building (Administration) Regulation 8(1)(ba),

(c) PNAP : 83 - Requirements for QualifiedSupervision of Site Formation Works - BuildingOrdinance section 17.

Practice Note PNAP : 78 lists the circumstances under which ageotechnical assessment of a site for the proposed works is required to besubmitted to the Building Authority at the "general building plans11 stage,i.e. the stage at which planning and fundamental approval for building isgiven. One of these circumstances is when the depth of the excavationexceeds 7.5 m. This requirement permits specialist geotechnicalinvolvement at a stage when the developer's planning is still flexible,thus avoiding possible delays due to objections or constraints whendetailed engineering plans are submitted. It should be noted that,irrespective of the depth of excavation, the Building Authority can, underthe Buildings Ordinance, require the details of excavation and lateralsupport to be submitted for agreement or approval.

Where dewatering is to be undertaken to facilitate excavation works,the Practice Note PNAP : 74 lists the general requirements that should beconsidered when preparing foundation and basement excavation submissions tothe Building Authority. These include the submission of the following :

(a) the details of the dewatering proposals,

(b) an assessment of the effects of excavation anddewatering,

(c) the method and sequence of construction,

(d) the location and details of instrumentation formonitoring the effects of the works on adjoiningbuildings, streets, land and underground services,the time interval between reading of instrumentsand the limiting criteria for movements andgroundwater level drawdown,

(e) the ground investigation report, includinglaboratory testing results,

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( f ) shor ing/underpinning d e t a i l s , and

(g) piezometric and set t lement mon i to r ing r e c o r d s .

Pract ice Note PNAP : 83 l i s t s the requirements f o r t h ree classes ofq u a l i f i e d supervis ion of s i t e format ion and r e l a t e d works . Superv is ion bya f u l l t ime resident engineer ( v i z . c lass ( i i i ) s u p e r v i s i o n ) i s normallys p e c i f i e d by the B u i l d i n g A u t h o r i t y f o r works w h i c h i n v o l v e deepexcavations in reclaimed ground, and excavat ion and l a t e r a l support worksi n v o l v i n g compl ica ted wo rk ing procedures and s t ag i ng o f works* TheAuthor i zed Person /Reg is te red S t r u c t u r a l Eng inee r i s r espons ib l e forensuring tha t the required superv is ion is p rov ided .

I t should be noted t ha t at the t ime o f p u b l i c a t i o n o f t h i s document,l e g i s l a t i o n is being f i n a l i s e d t o incorpora te p r o v i s i o n s i n the Bu i ld ing(Administrat ion) Regulations which r e f e r s p e c i f i c a l l y t o the submission ofan excavation and l a t e r a l support p l a n . When enac ted , these regu la t ionsw i l l empower the B u i l d i n g A u t h o r i t y t o r e q u i r e t h e s u b m i s s i o n ofcomprehensive in format ion r e l a t i n g to the design o f excavat ions and thela te ra l support system. A P rac t i ce Note is a lso being prepared t o g ives imple g u i d e l i n e s on t h e r e q u i r e m e n t s f o r t h e s u b m i s s i o n o f suchin format ion.

For excava t ions c o n s t r u c t e d f o r p u b l i c a u t h o r i t i e s , checking ofsubmissions is also car r ied out by the Geotechnical Cont ro l O f f i c e whereth i s is warranted in the i n t e r e s t o f pub l i c s a f e t y .

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12. CONCLUSIONS AND RECOMMENDATIONS

A review of the state of the art of designing excavation supportsystems and of predicting ground movements around excavations leads to thefollowing conclusions :

(a) Failures of excavation support systems are seldomdue to inadequacies in design methods, but ratherare caused by poor construction practice (e.g.inadequately planned working procedure and poorstructural detailing) and inadequate sitesupervision. This indicates that current designmethods are adequate.

(b) For the design of excavation support systems andthe prediction of movements around excavations inHong Kong, the recommendations given in Geoguide 1(GCO, 1982), the Terzaghi & Peck (1967) diagramsfor strut loads, and Peck's (1969b) settlementcurves respectively, are often employed. The'beam on elastic foundation1 approach and theboundary element method are also used.

(c) Proper evaluation of water pressure and itseffects is of utmost importance in the design ofexcavation support systems. The groundwater flowregime can have a significant effect on the waterpressures, the earth pressures and the piping andheave potential of the ground. Proper groundinvestigation is necessary to obtain informationon the ground and groundwater conditions fordesign. The location, size and condition ofwater-carrying services in the vicinity of theproposed excavation should also be established.

(d) Ground movements around excavations can be causedby many factors, some of which cannot bequantified with confidence. Therefore, it isessential that a monitoring system is implementedduring construction to check design assumptionsand to provide warning to allow precautionarymeasures to be undertaken where required.

(e) There are no reported field measurements of strutloads to establish the apparent pressure diagramsfor Hong Kong residual soils and saprolites, whichmay be lower than those of Terzaghi & Peck (1967).

(f) Conservative values of coefficient of horizontalsubgrade reaction recommended by Terzaghi (1955)are usually employed in the 'beam on elasticfoundation1 approach. Back analysis of monitoringdata from excavations should be carried out toobtain more realistic values of ground stiffnessfor Hong Kong residual soils and saprolites.

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(g) Although there is some evidence t o suggest t h a tthe i n s i t u hor i zon ta l s t ress in r es idua l s o i l s andsapro l i t es is low, measurements o f Ko are l a c k i n g .S u i t a b l e methods f o r measuring Ko in the f i e l dshould be i n v e s t i g a t e d .

(h) A l a r g e amount o f s e t t l e m e n t d a t a has beenob ta i ned d u r i n g t h e c o n s t r u c t i o n o f t h e MassT r a n s i t Rai lway underground s t a t i o n s and o the rdeep basement excavat ions. I t would be use fu l tot r y t o e s t a b l i s h s e t t l e m e n t curves f rom theseda ta , s i m i l a r t o those der ived by Peck, f o r HongKong res idual s o i l s and s a p r o l i t e s *

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99

TABLES

101

LIST OF TABLES

Table PageNo. No.

1 Advantages and Disadvantages of Various Temporary 103and Permanent Support Systems (after Institutionof Structural Engineeers, 1975) (two sheets)

2 Factors Involved in the Choice of a Support System 105for a Deep Excavation (NAVFAC, 1982b)

3 Design Considerations for Strutted and Tied-back 106Walls (after NAVFAC, 1982b)

4 Recommended Factors of Safety for Overall Stability 107of Cantilevered and Propped Halls (Padfield &Mair, 1984)

5 Methods for Calculating Anchor Prestress Loads 108

105

Table 2 - Factors Involved in the Choice of a Support Systemfor a Deep Excavation (NAVFAC, 1982b)

y

Requirements

1. Open excavationarea

2J Low initial cost

3/ Use as part of «' ! permanent /

\ structure

h. Deep, soft clay/ subsurface

conditions

5. Dense, gravellysand or claysubsoils

6. 'Deep. oyercon - isolidated clays \

' 7. Avoid dewatering

8. Minimizemovements

9. Wide excavation/ (greater than

20m wide)

10. Narrow excava-tion (less than20m wide)

Lends Itself to Use of

Tie-backs, raking struts orcantilevered walls

Soldier pile or sheet pilewal ls; combined soil batterwith wall

•biaphragm or cylinder \pile walls

\Strutted or raker-supported diaphragm orcylinder pile walls

Soldier pile, diaphragm orcylinder pile walls

Struts, long tie-backs orcombination tie-backs andstruts

t Diaphragm walls, possiblyI sheet pile walls in soft

subsoils

High preloads on stiffstrutted or t ied-back walls

Tie-backs or raking struts

Cross-lot struts

Comments

-

-

Diaphragm walls mostcommon as permanent walls

Tie-back capacity notadequate in soft clays

Sheet piles may loseinterlock on hard driving

High insitu lateralstresses are relieved inoverconsolidated soils.Lateral movements maybe large and extenddeep into soil

Soldier pile walls arepervious

Analyze for stability ofbottom of excavation

Tie-backs preferred exceptin very soft clay sub-soils

Struts more economical buttie-backs sti l l may bepreferred to keepexcavation open

107

Table 4 - Recommended Factors of Safety for Overall Stability ofCantilevered and Propped Walls (Padfield & Mair, 1984)

Method

(a)Factor onEmbedmentDepth, Fd

(b)Factor onMomentsBased onGrossPressure,FP

M lI u i

Factor onMomentsBased on NetAvailablePassiveResistance,

(e)Factor onShearStrength onBoth Activeand PassiveSides. Fs

Legend :

Effectivestress

*Tota lstress

Effectivestress

0'>3O°0 = 20 to 30°

0 ' < 20°

•To ta lstress

Effectivestress

•To ta lstress

Effectivestress

•Tota lstress

Totai stress

Design Approach A

Recommended rangefor moderately

conservative

( c \ 0 *

Temporary

works

1.1 to 1.2(usually

1.2)

*"i A2.0

1.2 to 1.5

1.51.2 to 1.5

1.2

2.0

1.3 to 1.5(usually

1.5)

2.0

1.1 to 1.2(usually 1.2except for

0' > 30°when lowervalue maybe used)

1.5

factors are

parameters

Permanentworks

1.2 to 1.6(usually

1.5)

1.5 to 2.0

2.01.5 to 2.0

1.5

1.5 to 2.0(usually

2.0)

1.2 to 1.5(usually 1.5except for

0 '>3O°when lowervalue maybe used)

speculative

Design Approach B

Recommended minimumvalues for worst

credible parameters

(c' = 0 , 0')

Temporary

works

Not

mended

1.0

1.01.0

1.0

1.0

1.0

Permanentworks

1.2

1.2 to 1.5

1.51.2 to 1.5

1.2

1.5

1.2

Comments

This method isempirical. Itshould always bechecked againstone of the othermethods.

These recom-mended Fp valuesvary with 0* tobe generallyconsistent withusual values ofFs and Fr .

Not yet testedfor cantilevers.A relatively newmethod withwhich little designexperience hasbeen obtained.

The mobilisedangle of wallfriction, 6m, andwall adhesion,Cwm, should alsobe reduced.

,and they should be treated with caution.

108

Table 5 - Methods for Calculating Anchor Prestress Loads

Reference

Clough,Weber & Lamont (1972)

Grant (1985)

Hanna & Matailana (1970)

Larson, Willette, Hail &Gnaedinger (1972)

Liu & Dugan (1972)

Mansur & Alizadeh (1970)

McRostie. Burn & Mitchell (1972)

NAVFAC (1982 b)

Oosterbaan & Gifford (1972)

Weber (1982)

Method

Terzaghi & Peck rules (0.4 FH)

Terzaghi & Peck rules (0.25-0.3 FH)

Pressures halfway between active andat - rest

Pressures between active and a t - res t

15 x wall height (in psf)

At - rest pressures

Terzaghi & Peck rules (0.4 VH)

Sands: 0.4-0.5K0VH(rectangular distribution)

Stiff to very stiff clays : 0.15-0.3FH(rectangular distribution)

Soft to medium clays: 0.5-0.6FH(triangular distribution)

Active pressures

Terzaghi & Peck rules (30 x wall height(in psf) )

109

FIGURES

110

Ill

LIST OF FIGURES

Figure P a g e

No. N o -

1 Types of Temporary and Permanent Support Systems 117(after Institution of Structural Engineers, 1975)(seven sheets)

2 Factors Causing Collapse of Sheet Pile Walls 124(after Malone, 1982)

3 Methods for Transferring Earth Pressure from 125Lagging to Soldier Piles (Peck, 1969b)

4 Types of Caisson Mall Drainage System (Malone, 1982) 126

5 Strutted Mall Support Systems (Clough, 1975) 127

6 Typical Connection Details for Horizontal Struts 128(Goldberg et al, 1976)

7 Typical Connection Details for Inclined Strut and 129Horizontal Waling (Goldberg et al, 1976)

8 Prestressing Details for Struts (Goldberg et al, 1976) 130

9 Prestressing of Pipe Strut at a Corner Using 131Brackets as Reaction (Goldberg et al, 1976)

10 Tie-back Support Systems (Clough, 1975) 132

11 Nonlinear Relationship for Soil behind Flexible 133Retaining Structure (Haliburton, 1968)

12 Nonlinear Relationship for Soil below Excavation 134Level of Flexible Retaining Structure(Haliburton, 1968)

13 Maximum Percent Deviation of Actual Stress 135Distribution from Uniform Pressure Distributionof Plane Strain Assumption (Tsui & Clough, 1974)

14 Correlation between Young's Modulus and 136SPT fN' Value (Chan & Davies, 1984)

15 Approximate Stress Paths Followed by Normally 137Consolidated and Overconsolidated Soil ElementsBehind, and in Front of, a Retaining Wall(Padfield & Mair, 1984)

16 Fixed-earth Support Conditions for a Cantilevered 138Wall (Padfield & Mair, 1984)

17 Methods of Basal Heave Analysis in Cohesive Soils 139(Clough et al, 1979)

112

Figure Pa9eNo. No-

18 Ratio of Factor of Safety against Basal Heave for 140Anisotropic Soil to that for Isotropic Soil forWide Excavation (B > 15 m) (Clough & Hansen, 1981)

19 Basal Heave Analysis in Conesionless Soils 141{NAVFAC, 1982b)

20 Penetration of Cut-off Wall to Prevent Hydraulic 142Failure in Homogeneous Sand (NAVFAC, 1982a)

21 Penetration of Cut-off Wall to Prevent Hydraulic 143Failure in Stratified Soil (NAVFAC, 1982a)

22 Calculation of Maximum Bending Moment in a 144Cantilevered Wall (Padfield & Mair, 1984)

23 Pore Water Pressure Distribution across a 145Retaining Wall under Steady-state SeepageCondition (Padfield & Mair, 1984)

24 Groundwater Flow Patterns and Resultant Water 146Pressures behind Excavations (Kaiser & Hewitt, 1982)

25 Free-earth Support Conditions for a Propped 147Wall (Padfield & Mair, 1984)

26 Calculation of Maximum Bending Moment in a 148Propped Wall (Padfield & Mair, 1984)

27 Effect of Wall Stiffness on Bending Moment and 149Prop Force of a Propped Retaining Wall(Potts & Fourie, 1985)

28 Deflection of a Sheet Pile Wall and Re- 150distribution of Active Earth Pressure(Bjerrum et al, 1972)

29 Calculation of Embedment Depth of Sheet Pile 151Wall below Excavation Level (NAVFAC, 1982b)

30 Apparent Pressure Diagrams for Computing 152Strut Loads in Strutted Excavations(Peck, 1969b)

31 Calculation of Strut Loads in Excavation in 153Soft Clay (Henkel, 1971)

3 2 Apparent Earth Pressure Diagrams for Measured 154Strut Loads in Excavations in L a t e r i t i c andWeathered Sedimentary Soils (Massad et a l , 1985)

33 Calculation of Embedment Depth of Sheet P i l e Wall 155in Relatively Uniform Competent Soi l Conditions(Goldberg et a l , 1976)

113

Figure PageNo. No.

34 Ground and Support Reaction Concept for a Strutted 156Excavation (Eisenstein & Negro, 1985)

35 Comparison between Tied-back and Strutted Walls 157(Broms & Stille, 1976)

36 Failure Mechanisms of Anchored Sheet Pile Walls 158(Broms & Stille, 1976)

37 Stability Number versus Depth Parameter for 159Three Conditions of Equilibrium : Overturning,Sinking and Soil Heaving (Browzin, 1981)

38 Design Chart for Calculating Embedment Depth of 160a Propped Wall in Cohesive Frictional Soils(Browzin, 1983)

39 Values of k for Correcting Depth Parameter 1p for Anchor Location /M (Browzin, 1983)

40 Design Chart for Calculating Embedment Depthof a Propped Wall in Cohesionless Soils(Browzin, 1983)

41 Idealised Force System on an Anchored Wall(Hanna, 1968)

42 Prestress Design Pressures Reported forTied-back Wall (Clough, 1975)

43 Stress Paths for Soil Elements near Excavation I 6 5

(Lambe, 1970)

44 Effects of Wall Stiffness and Support Spacing on I66

Lateral Wall Movements (after Goldberg et al, 1976)

45 Relationship between Maximum Settlement and l 6 7

Stability Number for Different Batters(after Clough & Denby, 1977)

•ICO46 Observed Settlements behind Excavations lo°

(after Peck, 1969b)

47 Summary of Settlements Adjacent to Strutted 1 6 9

Excavations in Washington, D.C. (O'Rourke et al,1976)

48 Summary of Settlements Adjacent to Strutted 1 7 0

Excavations in Chicago (O'Rourke et al, 1976)

49 Horizontal Strains Associated with Various 1 7 1

Stages of Strutted Excavation Construction{O'Rourke, 1981)

114

Figure fNo. No*

50 Ratio of Horizontal to Vertical Ground Movement as 172Function of Coefficient of Deformation ofFixed-end Walls (O'Rourke, 1981)

51 Relationship between Factor of Safety against Basal 173Heave and Nondimensional Maximum Lateral WallMovement for Case History Data (Clough et al, 1979)

52 Relationship between Maximum Ground Settlements and 173Maximum Lateral Wall Movements for Case HistoryData (Mana & Clough, 1981)

53 Observed Movements of Tied-back Wall Systems 174(Clough, 1975)

54 Relationship between Prestress Pressure and 175Tied-back Wall Movement for Sands (Clough, 1975)

55 Relationship between Prestress Pressure and 176Tied-back Wall Movement for Stiff Clay(Clough, 1975)

56 Maximum Building Settlements due to Slurry Trench 177Excavation as a Function of Foundation Depth(Cowland & Thorley, 1984)

57 Relationship between Total Building Settlements 178and Depth Factor at Hong Kong Mass Transit RailwayStations (after Morton et al, 1980a)

58 Maximum Building Settlement due to Diaphragm Wall 179Installation (Budge-Reid et al, 1984)

59 Average Rate of Building Settlement for Each 180Metre Drop in Piezometric Level for VariousFoundation Systems and Subsoil Conditions(after Budge-Reid et al, 1984)

60 Settlement of Buildings during Excavation of 181Station Box Resulting from Lateral WallMovement (Budge-Reid et al, 1984)

61 Semi-empirical Method to Estimate Settlement 182(Bauer, 1984)

62 Analytically Defined Relationship between 183Nondimensionalized Maximum Lateral Wall Movementand Factor of Safety against Basal Heave(Mana & Clough, 1981)

63 Analytically Defined Relationship between Maximum 184Lateral Wall Movement/Ground Settlement and Factorof Safety against Basal Heave (Mana & Clough, 1981)

115

Figure PageNo. No.

64 Effect of Wall Stiffness on Maximum Lateral Wall 184Movement/Ground Settlement (Nana & Clough, 1981)

65 Effect of Strut Stiffness on Maximum Lateral Wall 185Movement/Ground Settlement (Mana & Clough, 1981)

66 Effect of Depth to Firm Layer on Maximum Lateral 185Wall Movement/Ground Settlement (Mana & Clough, 1981)

67 Effect of Excavation Width on Maximum Lateral Wall 186Movement/Ground Settlement (Mana & Clough, 1981)

68 Effect of Strut Preload on Maximum Lateral Wall 186Movement/Ground Settlement (Mana & Clough, 1981)

69 Effect of Modulus Multiplier on Maximum Lateral 187Wall Movement (Mana & Clough, 1981)

70 Envelopes to Normalized Ground Settlement Profiles 187(Mana & Clough, 1981)

116

117

118

119

Permanent structural frame

^sssvWusssWum^umssuggg

Permanentretaining wallwhich provideslateral supportduring excavation,e.g. diaphragmwall »-

Temporary struts enable passivesoil buttress to be removedbefore structural frame is completed

(e) Permanent Wall Constructed Prior to Excavation (Diaphragm Wallor Contiguous Bored Pile Wall) and Braced from CentralPermanent Construction

-Diaphragm wall, boredpiling or sheet piling

-Ground anchor installedduring excavation

(f) Ground Anchors

Note : Advantages and disadvantages of these systems ore given in Table 1.

Figure 1 - Types of Temporary and Permanent Support Systems (afterInstitution of Structural Engineers, 1975) (Sheet 3 of 7]

128

129

130

131

132

133

134

135

136

300

E2

He

o

c

oo

oLU

DO

cI

50

10

Cont. Plaza buildingresidual soil

.(Martin, 1977)

Derived frompumping tests

Normally loadedsands

7/

Derived from plate andpile tests, Hong Kong'PhilcoxJ-962)

Bank of China building- Virgin compressionTomlinson, 1953)

= ION•Residual soil[Martin, 1977)

Bank of China , plate test(Tomlinson, 1953)

50 100 150 200 250

SPT Blowcount (N blows/300 mm)

Figure 14 - Correlation between Young's Modulus andSPT 'W Value (Chan & Davies, 1984)

13?

138

139

140

Anisotropic Strength Ratio. Ks = "ao

Figure 18 - Ratio of Factors of Safety against Basal Heave forAnisotropic Soil to that for Isotropic Soil for WideExcavation (B > 15 m) (after Clough & Hansen, 1981)

141

142

143

Cut-off w

Finesand .

. X

X*

7

Y.w. •Fine sand

•IT 1

1 X

• "O

• Coarse sand *.£

Impervious

Coarsesand• y

. Coarse• sand • *Fine sand"

X

. -a

'. X*

Impervious

Homogeneous* sand . * . *, •

Very fine layerTclay soil)

/ X ss sImpervious1

Homogeneous sandVery fine layer (day soil)

(a) Coarse Sand Underlying Fine SandPresence of coarse layer makes flow in the fine materialmore nearly vertical and generally increases seepage gradientsin the fine material compared to the homogeneous cross-sections of Figure 20.If top of coarse layer is below toe of cut-off wall at adepth greater than width of excavation, safety factors ofFigure 20(a) for infinite depth apply.If top of coarse layer is below toe of cut-off wall at adepth less than width of excavation, then uplift pressures aregreater than for the homogeneous cross-sections. If permeabilityof coarse layer is more than ten times that of fine layer,failure head (Hw) = thickness of fine layer (H2).

(b) Fine Sand Underlying Coarse SandPresence of fine Iqyer constricts flow beneath cut off walland generally decreases seepage gradients in the coarse layerIf top of fine layer lies below toe of cut-off wall, safety factorsare intermediate between those derived from Figure 20 forthe case of an impermeable boundary at (i) the top of finelayer, and (ii) the bottom of the fine layer assuming coarsesand above the impermeable boundary throughout.If top of fine layer lies above toe of cut-off wall, safety factorsof Figure 20 are somewhat conservative for penetration required.

(c) Very Fine Layer in Homogeneous SandIf top of very fine layer is below toe of cut-off wall at adepth greater tljidn width of excavation, safety factors ofFigure 20 assuming impermeable boundary at top of finelayer apply.If top of very fine layer is below toe of cut-off wall at a depthless than width of excavation, pressure relief is requiredso that unbalanced head below fine layer does not exceedheight of soil above base of layer.

To avoid bottom heave when toe of cut-off wall is in orthrough the very fine layer, (FSH3 + FCH5) should be greaterthan FWH4.V$ = saturated unit weight of the sandVc = saturated unit weight of the clayVw = unit weight of waterIf fine layer lies above subgrade of excavation, final conditionis safer than homogeneous case, but dangerous conditionmay arise during excavation above fine layer and pressure

as in the precedinc

Fiqure 21 - Penetration of Cut-off Wall to Prevent HydraulicFailure in Stratified Soil, (after NAVFAC, 1982a)

144

146

147

148

149

2£0

200

160

120

80

40 -

M = Maximum observed bendingmoment

MLE= Maximum bending momentfrom a limit equilibriumcalculation

P - Wall flexibility number

. . see also; « i w Section 8.1.2 equation [6))

0-1-5 1-5-0-5 0-5

log p

(a) Variation in Bending Moment with Wall Stiffness ( F r * 2 )

350

300

250

- 200

^ 150

100

50

P = Maximum observed prop forcePLE= Maximum prop force from

a limit equilibriumcalculation

-1-5 1-5-0-5 0-5

log p

(b) Variation in Prop Force with Wall Stiffness ( F r = 2 )

Notes : (1) For definition of Fr. refer to Table L.

(2) P is in units of - j ^ .

Figure 27 - Effect of Wall Stiffness on Bending Moment and Prop Forceof a Propped Retaining Wall (Potts & Fourie, 1985)

150

151

152

Struts

v/////////.

0.65KQ?H 1.0KVH

Ka = tan 2 145" ! ) K = 1-mVH

m= 1-0 except where theexcavation is under-lain by deep softnormally consolidatedclay, then m = CH

(a) Sands (b) Soft to MediumClays

(c) Stiff-fissuredClays

Figure 30 - Apparent Pressure Diagrams for Computing StrutLoads in Strutted Excavations (Peck, 1969b)

154

"a 0-5Ha

1-0H

0-05 0-10VH-i—r

I J !

ES6{059HH j

rj

! i! f ES2j (0.50H)-! i

jUES 1: (0-57H)

0-08 VH

(a) Apparent Earth Pressures (b) Suggested Envelope

Legend:ESH{ )

Experimental sectionDepth of excavationDistance of the centre of pressure from the bottom of excavation

Figure 32 - Apparent Earth Pressure Diagrams for Measured Strut Loadsin Excavations in Lateritic and Weathered SedimentarySoils (Massad et al, 1985)

155

Position oflowest strut

Bottom ofexcavation

Active

Legend

Ka

Pt

Active earth pressure coefficientPassive earth pressure coefficientFrom apparent earth pressure diagram (Figure 30)

Notes: (1) Compute Re = 0-5PtL.(2) Compute depth X such that Pp = Re «• Pa.

w i th minimum factorof safety of 1.5 for passive coefficient, i.e. K'p< -r r .

(3) Check Mmax < yield moment of sheeting.(4) Drive to depth d = 1-2 X .

Figure 33 - Calculation of Embedment Depth of Sheet Pile WallRelatively Uniform Competent Soil Conditions(Goldberg et al, 1976)

in

157

CO

CD

43

c

o

oCO

o!

no

CD

O)

158

I

(a) Penetration Failure (b) Toe Failure

(c) Slope Failure

Soil Failure

(d) Rupture of Anchors

/v

(e) Yielding of Sheet Piles

Structural Failure

Figure 36 - Failure Mechanisms of Anchored SheetPile Walls (Broms & Stille, 1976)

159

1.3

1.2

X

cJ

X=L

Ax = Horizontalcomponent ofanchor load

Ap = Anchor load

Nomenclature

2 3 iM

Depth Parameter . P = 1 + -r

Anchored WaltLegend :

Anchor pullOverturning

SinkingHeave

Fiaiire 37 - Stability Number versus Depth Parameter fory Three Conditions of Equilibrium : Overturning,

Sinking and Soil Heaving (Browzin, 1981)

160

161

As.VHH

0.90.80.70.60.5

0.90.80.70.60.5

0-90.80.70-60-5

0.90-80-70-60.5

0-90.80-70-60.5

0.90.80-70-60.5As.VH

Note

0.1

0

0

00111

01122

01223

11234

12346

0.1

0.2

0

0111

01123

11234

11235A.12357

0.2

0.3

1A.

1112

A. =01223

A. =11234

A. =123

6= 2.

12358

0-3

0.4

A =

11

= 1.i

1122

1-61123

1.8112

52.0

123

6U

12

58

0.4

0.5

1.2

111

i

1123

11234

12346

12346

12357

0.5

0.6

1112

1223

11234

11235

11234

01122

0.6

0.7

1122

1223

01122

00000

0

0.8

01112

00

0.1

12357

12469

134710

135711

135913

23610150-1

See Figure 38 for nomenclature

0.2

12468

124610

X135711

X135812

X136914X -24610150-2

0.3

X -12469X -134710= 3135711= 4135812= 5.1358136.01369130.3

0.4

2.812469

3.212489

61246100124810

012469

12357

0.4

0.5

12346

12346

01234

01123

000

0.6

00000

1

0.1

2461016

2471118

2471219A. =2481321X -2581423X =

25914240-1

0.2

X2461016A.2471117

I =2471118

: 12247121918247121920

0.3

= 7136914

= 8135913

10135812

0.4

11246

01234

Figure 39 - Values of k for Correcting Depth Parameter P forAnchor Location^ (Browzin, 1983)

162

163

ExcavationStage

A J

C A

Ground surface

Anchors

The Wall System

ExcavationStage

1

Ni

[^—Side

I

friction ( t )

i f

V, = PE1 * 2TI

rrN,N2

H

V2 = PE, • ETl V1+V2 ETl

Notes : (1) N1 + N2+ N3 = Area under design pressure diagram.(2) Values of P^ , P2 and P3 may change as excavation continues.(3) Test loading of anchor will temporarily modify load distribution,

Figure 41 - Idealised Force System on an Anchored Wall (Hanna, 1968)

165

Note: Initially there is no flow andultimately there is steady-stateseepage.

Stresses and Strains for SoilElements near an Excavation Soil Element A Soil Element B

Initial (Static) Pore Pressure, us BOBO

Pore Pressure at Steady - state Flow, uSs At Ass BiB,

Pore Pressure upon Unloading Decreases Decreases

Pore Pressure during Consolidation Decreases increases

Strain upon Unloading Vertical compression Vertical extension

Strain during Consolidation Vertical compression Vertical extension

Undrained Shear Strength duringConsolidation Increases Decreases

Figure 43 ~ Stress Paths for Soil Elements near Excavation (Lambe, 1970}

I I =>

10

10

102 103 10* 105

Me>veme»nts> 1\

\>m

i

+0**

gem

>^

nerall)

^ —^ "

MtDverne<

nts ger25 mm

»erall y

Flexible Stiff

(kN/m3 )

Legend :

h Vertical distance between support levels or between support level and excavation baseModulus of elasticity of wall material Moment of inertia of wall per unit length

F igure 44 - E f f e c t s o f Wall S t i f f n e s s and Support Spacing on L a t e r a l Wall Movements ( a f t e r Goldberg et a l» 1976)

168

Distance from ExcavationMaximum Depth of Excavation

CO

coaauX

UJ

E

3

Xo2:

5-1

in

Notes: (1 ) Zone I -Sand and soft to hard clay, average workmanship.(2) Zone n-(a) Very soft to soft clay.

(i) Limited depth of clay below bottom of excavation(ii) Significant depth of clay below bottom of

excavation but Nb<5.U.(b) Settlements affected by construction difficulties.

(3) Zone II-Very soft to soft clay to a significant depth belowbottom of excavation and with Nb>5-1A ,yuwhere Nb = -7~ and Cub is as defined in Figure 31.

(4) The data used to derive the three zones shown in this figure aretaken from excavations supported by soldier piles or sheet pileswith cross-lot struts or tie-backs.

Figure 46 - Observed Settlements behind Excavations (after Peck, 1969b)

169

171

Lateral walldisplacement (mm)

30 20 10 0

Lateral walldisplacement ( mm )

30 20 10 0

Stage 1

Lateraldisplacementprofile

-toStage'

-Horizontal soilstrain contour(interval =0.5x103)

(a) Stage 1: InitialExcavation

Stage 2-

(b) Stage 2: Excavationto Subgrade

Medium sandand gravel

Stiff clay

Interbeddeddense sandand stiff clay

Dense sandand gravel

Hard clay

10 £

20

25

Lateral walldisplacement (mm J

30 20 10 0

Stage 2-

Stage 3-

-1.0

(c) Stage 3: Removal ofStruts

Maximum displacement fromwall rotation and translation

1 0

-Maximum displacementfrom inward bulging

(d) Principal Componentsof Wall Movement

s

10 I

15 8"Q

20

25

Legend :

y Soil movement vector

L.ILJ0 Vector scale ( mm )0 \ H o r i z o n t a l s c a l e t m )

Figure 49* Horizontal Strains Associated with Various Stages ofStrutted Excavation Construction (O'Rourke, 1981)

172

2%

X Q)

• s i

CC Q

Upper level struts

Sw20

1.5

1.0

0 .5

C D =S w

S w + S w

L a t e r a l d i s p l a c e m e n t

p r o f i l e a t e d g e o f e x c a v a t i o n

Legend:a Model test after Milligan (19831

0.2 0.4 0.6 0.8

Coefficient of Deformation, Cp

1.0

Case SymbolMaximumDepth (ml Support Soil Location

18Soldier piles & lagging, 5 strutlevels

Sand andstiff clay

Washington,D.C.

13Soldier piles & lagging, 3 levelsof struts and rakers

Soft tomedium clay Chicago, III.

Sheet pile, 3 raker levels Soft tomedium clay

Chicago, III.

13 Slurry wall, 2 levels oftiebacks and rakers

Soft tomedium clay Chicago. III.

Soldier piles & lagging, 2 rakerlevels

Soft tomedium clay Chicago, III.

Sheet pile, 2 raker levelsSoft tomedium clay Chicago, III.

USheet pile, 3 levels of strutsand rakers

Soft tomedium clay

San FranciscoCalifornia

Figure 50 - Ratio of Horizontal to Vertical Ground Movement as Function ofCoefficient of Deformation of Fixed-end Walls (0'Rourke, 1981)

177

178

186

187

3.0

oo00II

og

JZ

2.01.5

1.00.8

0.6

0.4

0.2

FOS

*

N

• >1.5

-F0

I

S ^ 1.0

100 200 300 400 600 800 1200 2000

Modulus Multiplier, M(=-J-)

Figure 69 - Effect of Modulus Multiplier on Maximum LateralWall Movement (Mana & Clough, 1981)

Distance from Excavation. xMax. Depth of Excavation, H

0.5 1.0 1.5 2.0 2.5 3.0

FOS > 1.5

//Jk- X

Av

Figure 70 - Envelopes to Normalized Ground SettlementProfiles (Mana & Clough, 1981)

188

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Sol id000 map)

and, in

Hong Kong and Kowloon : Solid andSuperficial Geology (1:20 000 map)(1986), 1 map.

Clear Water BaySuperficial Geology(1989), 1 map.

: So l i d and(1:20 000 map)

HK$20

HK$20

(US$3.50)

(US$3.50)

192

Map HGM 20,Sheet 13

Map HGM 20,Sheet 14

Map HGM 20,Sheet 15

Map HGM 20 ,Sheet 16

Map HGP 5 ,Sheet 6-NW-B

Map HGP 5A,Sheet 2-SW-C

Map HGP 5B,Sheet 2-SW-C

Map HGP 5A,Sheet 2-SW-D

Map HGP 5B,Sheet 2-SW-D

Shek Pik : Solid and SuperficialGeology ( 1 : 2 0 000 map), i npreparation.

Cheung Chau : Solid and SuperficialGeology ( 1 : 2 0 000 map), inpreparation.

Hong Kong South and Lamma Island :Solid and Superficial Geology (1:20000 map) (1987), 1 map.

Waglan Island : Solid and SuperficialGeology (1:20 000 map) (1989), 1 map.

Yuen Long : Marble in the DesignatedArea Northwest New Territories (1:5 000map) (1988), 1 map.

Deep Bay : Superficial Geology (1:5 000map) (1989), 1 map.

Deep Bay : Solid Geology (1:5 000 map)(1989), 1 map.

Shan Pui : Superficial Geology (1:5 000map) (1989), 1 map.

Shan Pui : Solid Geology (1:5 000 map)(1989), 1 map.

HK$20 (US$3.50)

HK$20

Free

HK$10

HK$10

HK$10

HK$10

(US$3.50)

US$ prices shown above are for overseas orders and are inclusive of surfacepostage to anywhere in the world.

ORDERING INFORMATION IS GIVEN ON THE REVERSE SIDE OF THE TITLE PAGE.