spatial stress-deformation analysis for diaphragm walls

8/12/2019 Spatial Stress-Deformation Analysis for Diaphragm Walls

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AIN SHAMS UNIVERSITY

FACULTY OF ENGINEERING

Vol. 37, No. 3, September 30, 2002

SCIENTIFIC BULLETIN

Received on : 1/6/2002

Accepted on : 21/8/2002

PP. : 75-90

SPATIAL STRESS-DEFORMATION ANALYSIS FOR

INSTALLATION OF A DIAPHRAGM WALL

SAYED M. EL-SAYED1 AHMED H. ABDEL-RAHMAN

2

ABSTRACT

There is an escalating need for acceptable techniques to estimate building

settlements associated with the trenching process of diaphragm walls. Prediction

of the deformation patterns resulting from insitu wall installation can be

achieved through monitoring more case histories and upgrading the available

analysis techniques by rigorous evaluation of the measured data. The objective

of the present research is to present a three-dimensional back analysis of

measured building settlements compiled during installation of a diaphragm wall

in Greater Cairo. The numerical analysis showed that building settlements in the

vicinity of the diaphragm wall trench depends predominantly, among other

factors, on the foundation type of the proximate buildings and the paneled

construction of the wall.

Keywords: Diaphragm wall; paneled construction; secondary and primary

panels; trenching; excavation; field measurements; nonlinear analysis; finite

element; three-dimensional analysis.

. .

.

1Assistant Professor, Structural Engineering Dept., Ain Shams University, Cairo, Egypt.

2Assistant Professor, Civil Eng. Dept., Engineering Research Division, National Research Center of Egypt.


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1. INTRODUCTION

Requirements with respect to control of ground movements during insitu

wall construction vary greatly. Walls constructed in soils with no nearby

structures pose little concern with respect to movements; nevertheless, ground

movements are the key design issue for excavations located in urban areas.Recently, many diaphragm walls have been constructed in Greater Cairo, which

considered one of the most congested cities in the world, for several purposes

such as basements, underground garages, cut-and-cover tunnels and subway

stations. Diaphragm wall construction in Greater Cairo imposes many

engineering challenges regarding the stability of the excavated panels and the

hazard effect of the resulting deformation field on adjacent structures. The

geotechnical conditions encountered during the construction of diaphragm walls

in Greater Cairo are typically alluvial soils with a shallow groundwater table.

These conditions are classified as problematic from the geotechnical point ofview especially if the constructed wall is located near to structurally sensitive

buildings (El-Sohby and Mazen, 1985). It is typically assumed that deformations

will be small if there is an adequate factor of safety against overall instability of

the trench (Goldenberg et al., 1976); however, building settlements of more than

2 inches were recorded during trenching whereas no stability problem was

reported (Cowland and Thorley, 1985).

Different researches reported settlement distribution associated with the

installation of diaphragm walls (Clough and ORouke, 1990; Thompson,1991 &

Abdel-Rahman and El-Sayed, 2002). Maximum settlement at wall locations was

found to range between 0.04% to 0.15% of the trench depth depending on the

configuration of the wall, the soil and groundwater conditions of the site and the

workmanship quality. The limit of the settlement trough is estimated to range

between twice to three times the trench depth.Recently, three-dimensional models were utilized to study the behavior of

grounds in trenching. Gourvenec and Powrie (1998) concluded that the lateral

stress reduction and the deformation fields estimated using plane-strain analysis

of a diaphragm wall installation in stiff overconsolidated clay are generallyoverestimated compared with the three-dimensional analysis. Ng and Yan

(1998) employed a non-linear elastoplastic finite difference scheme to perform aback-analysis of a diaphragm wall installation. They concluded that settlementtrough extended to one-and-half times the trench depth with the peak of the

trough located close to the trench side.

In the current research, a three-dimensional finite element back analysis

of a case history is presented. The analysis is performed using a nonlinearconstitutive relationship to analyze the measured settlement monitored for

buildings founded on shallow and deep foundations during the execution of

diaphragm wall panels.


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2. THE CASE HISTORY

The presented case history is a diaphragm wall constructed to be used for

the basement of a multistory building in Greater Cairo. The wall is located at

1.80m, 3.15m, 3.25m and 7.12m far from existing buildings founded on piles

and shallow foundations. The wall depth is 21.00 m and the wall thickness is0.60 m. Five buildings (designated A, B, C, D and E) are located near to the wall

as shown in Fig. (1). Buildings (A), (B) and (C) are twelve to fourteen stories

founded on deep foundations (piles) with lengths ranging between 14.00 m, and

16.00 m; i.e., shorter than the executed diaphragm walls. Buildings (E) and (D)

are three and five stories respectively founded on shallow foundations.

The subsurface soil condition at the site consists mainly of a top fill layer

appeared from ground surface to a depth of about 2.0 m. The fill is mainly a

mixture of sand, silt, and broken bricks. A sandy silt layer appeared after the top

fill layer and extended to a depth of about 5.0 m. A layer of sand with some siltfollowed the sandy silt layer and extended to a depth of 11.0 m. A layer of

graded sand with some gravel followed the previous layer and extended to the

end of boreholes at 25.0 m. The ground water table appeared at a depth of about

2.0 m from ground surface. Fig. (2) presents the subsurface soil profile with the

estimated mechanical parameters for the different layers.

Thirty-one settlement points were used to monitor the building

settlements associated with the diaphragm wall installation and excavation of the

basement as shown in Fig. (1). The construction arrangement of the diaphragm

wall panels is sequentially marked in Fig. (1) as well. Fig. (3) shows the time

variation of the settlement for the different settlement points located around the

wall. The settlement gradually increased for all points due to the construction of

more panels with time. No point had a settlement recovery due to concrete

pouring. Some points had an abrupt upsurge of settlement after June 24, 2001due to a mild earthquake, which took place between observations. Another

increase of settlement occurred on July 9, 2001 due to the rupture of a main

water pipeline near building (A). These sudden escalations of settlement may be

due to some kind of soil meta-stable structures that collapsed during the soildisturbance.

3. THREE DIMENSIONAL MODELING OF THE PROBLEM

3.1. Soil Constitutive Modeling

The soil nonlinear behavior was identified by variable modulii dependent

on the confining pressure and the stress path. The soil constitutive relationship is

expressed in an incremental form to account for the path-dependency. Using the

incremental form of the constitutive matrix [Det], the tangential element stiffness

matrix [Ket] can be written as:


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[ ] [ ] [ ][ ]=element

eet

t

eet )Volume(dBDBK (1)where the [Be] is the element strain-nodal displacement matrix. The loadingmodulus (Et) and the unloading-reloading modulus (Eur) are presented by the

following forms:[ ]

n

a

32

ftp

SLR1KE

= (2)

n

a

3aurur

ppKE

= (3)

Where( ) ( )

+

=

sin2cosc2

sin1SL

3

31

(4)

Rf = the ratio between the ultimate and the failure deviator stresses.pa = the atmospheric pressure.

n = the stiffness exponent.

K = Duncan's loading modulus coefficient.SL = the ratio between the deviator stress and the ultimate deviatoric pressure

(estimated by Mohr-Coulomb failure criterion).

Kur = unloading-reloading modulus coefficient.1&3= the major and the minor principal stresses (assuming 2 =3, and c &

are the soil shear parameters).

The variation of the modulus coefficient (K) with depth is shown inFig.(2). Details of the used constitutive model are illustrated by Duncan and

Chang (1970), and Duncan et al. (1984).

3.2. Procedure of Iterations

It is not possible to predetermine the regions subjected to loading or

unloading to assign either the loading modulus or the unloading modulus. The

correct modulus is defined in the iterations according to a parameter called the

loading level depending on the deviator stress, the shear strength parameters and

the confining pressure as follows:

a

3

p)sin1(

2SLLL

= (5)

The loading level (LL) is calculated for each gauss point and compared to

the maximum value reached during the loading history at the same gauss point

(LLmax). The modulus (E) depends on the parameter LL as following:

If ( maxLLLL ), loading is taking place and the used modulus equals to Et

If ( maxLL75.0LL ), unloading is taking place and used modulus equals to Eur

If ( maxmax LL75.0LLLL >> ), the modulus E is calculated by interpolation between

Etand Euras shown in Fig. (4).


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3.3. Bentonite Slurry and Concrete Modeling

Bentonite slurry is presented by a weak material with a unit weight of

1.06 gm/c.c and an infinitesimal modulus of elasticity. The concrete is presented

by an incrementally hardening elastic material.

3.4. Meshing and Geometrical Modeling

The soil, the bentonite slurry and the diaphragm wall are modeled using

three-dimensional hexahedral elements. Formulation and programming of the

finite element are explained by El-Sayed (2001). The employed three-

dimensional finite element mesh and the position of the wall panels are shown in

Fig. (5). The problem was discretized into 924 elements. The boundary

conditions are shown in Fig. (5-a). Three vertical boundary planes have the

conditions of symmetry; the fourth vertical plane represents the truncation

boundary for the far deformation field in which it is presented by horizontalroller to facilitate the introduction of the initial insitu stress condition. The

bottom horizontal plane is prevented from all deformations.

3.5. Construction Sequence Modeling

Three consequent panels are considered in the analysis identified by the

Roman numbers I, II & III, as shown in Fig. (5-b). The number sequence

presents the construction order of the panels. The mesh dimension is minimum

in the direction of the wall since Gourvenec and Powrie (1998), and Ng and Yan

(1998) concluded that the mutual effect of far panels is not significant in this

direction.Trenching is modeled by removing a cluster of ground elements from the

finite element meshing; conversely, concreting is simulated by adding new

elements to the mesh. The required changes in the mesh are applied to

reconstruct the residual force vector {R} resulting from the difference between

the applied force and the straining forces. The residual vector and the stiffness

matrix [Kt] are calculated at the beginning of each iteration (Newton-Raphson),

i.e. the (i+1)thiteration is described as follows:

{ } [ ]

{ }

=++ =

elementsofNo.

1e elemente

tt

i

T

e

tt)Volume(dBF

[ ] { } { }RUK tt

1i

tt

1it

tt

i

+

+

+

+

+ =& (6)

where {F} is the nodal forces and { }U& is the incremental displacement. The leftsubscript denotes the iteration process and the left superscript donates a

sequential pseudo time index. If the iteration superscript is zero, the matrix or

vector is calculated at the end of the previous time step. The stress increment

can be calculated from the strain {} using the following modified Euler

integration scheme:

{ } { } [ ] [ ] { }UBD tt 1ieettt

2/1i

tt

i

tt

1i&

+

++

+++

+ + (7)The effect of buildings having shallow foundations on the trench ispresented by an additional surcharge of 4 t/m2at level (-2.00) while a surcharge


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of 15 t/m2was presented at level (-16.00) to study the case of structures having

deep foundations. The values of the surcharges were assumed according to the

number of stories of the buildings.

4. RESULTS

The two cases of buildings having deep foundations and buildings having

shallow foundations were studied at three longitudinal sections (1, 2 & 3) for the

panels (I, II & III); the locations of the sections are shown in Fig. (5-b).

Deformations of both cases are governed by the occurrence of yielded zones

surrounding the trench. The maximum stress level (SLmax) which can be

considered as a measure of the soil yield stress, is shown in Fig. (6-a) for the

case of the deep foundations while Fig.(6-b) shows the results for the case of

shallow foundations. The stress level approaches unit at the trench boundary

which indicates a partial yield zone that is more significant towards the

buildings located close to the trench locale. The major intensification in the

maximum stress level is located near the foundation levels of the deep and the

shallow foundations. The pile foundations have more extended yield zone.

Fig. (7) presents the results of the settlement away from the diaphragm

wall for the case of deep foundations. The maximum settlement is adjacent to

the trench due to excavation of the close panel while the interaction of

settlement troughs associated with different panels is more likely to govern the

settlement field beyond its maximum value. The maximum settlement was

identified at section (1) and section (2) for the primary panels (I) & (II) with avalue of 10 mm (0.048% of the maximum trench depth). A good correspondence

between the measured building settlement and the predicted settlement envelope

is shown in Fig. (7-d).

Fig. (8) shows the settlement profile for the case of shallow foundations.The settlement troughs in this case resemble a bow with a maximum value

located at a distance of one meter away from the trench. The interaction between

different troughs is more pronounced far away from the wall. The maximumsettlement is 6.1 mm for panel (I) which presents 0.03% of the maximum trench

depth. Fig. (8-d) shows a fair matching between the measured settlements andthe predicated envelope.

The lateral deformations of the trench side for both cases are shown inFig. (9). The maximum lateral displacement was estimated as 16.3 mm (i.e.

0.077% of the trench depth) at depth of 16 m for the pile foundations and 9.9

mm (i.e. 0.047%) at depth of 2 m for shallow foundations. The pronounced

increase at the level of foundation in both cases is generally believed to beattributed to the spread of the yield zone beneath at that level.

The relation between the maximum settlement and the maximum

horizontal displacement was depicted in Fig. (10). In both of foundation types,


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the maximum settlement was about 61% of the maximum horizontal

displacement although different deformation profiles were assessed.

5. CONCLUSION

The case history presented in this paper included the construction of

diaphragm wall paneling in the vicinity of buildings founded on shallow and

deep (piles) foundations. The depth of the diaphragm wall panels was deeper

than the pile tip. Three-dimensional back analysis was performed, and compared

with the field settlement compiled during the wall installation. The analysis

demonstrates that the maximum settlement is more likely to be governed by the

close panels while the settlement trough beyond its maximum value is

significantly affected by the interference of the settlement troughs resulting from

other proximal panels. The maximum settlement is more probable to occur due

to primary panels than secondary ones.

The maximum settlement observed in buildings having pile foundations

was about 0.048% of the maximum height of the trench while the settlement of

buildings having shallow foundations is only about 0.03% of the maximum

trench height. The maximum lateral deformation near the trench is about

0.077% of the trench depth for piles and 0.047 % of the trench depth for the case

of shallow foundations. The variation in deformation may be figured out by the

considering the constitutive behavior of ground and the spread of a limited yield

zone created by trenching near the shallow and deep foundation levels. A

significant yield zone was created beneath the piles resulting in formation of asubstantial lateral deformation at the piles' tip. The maximum settlement in both

cases was estimated to be 61% of the lateral displacement.

6. REFERENCES

1. Abdel-Rahman, A. H. and El-Sayed, S. M., 2002, "Settlement TroughAssociated with Diaphragm Wall Construction in Greater Cairo", the

Journal of the Egyptian Geotechnical Society, accepted for

publications.2. Clough, G. and O'Rourke, T., 1990, "Construction Induced Movements

of Insitu Walls", Design and Performance of Earth Retaining

Structures, ASCE Geotechnical Special Publications 25, pp. 439-470.

3. Cowland, J. W. and Thorley, C. B. B., 1985, Ground and BuildingSettlement Associated with Adjacent Slurry Trench Excavation.

Ground Movements and Structures Proc., Third Int. Conf., University

of Wales Institute of Science and Technology, J. D. Geddes, ed.,

Pentech Press, London, England, 723-738.


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4. Duncan, J. M. and Chang, C. Y., 1970, Nonlinear Analysis of Stressesand Strains in Soils, Journal of Soil Mech. And Found. Div., ASCE,

Vol. 96, No. SM5.

5. Duncan, J. M., Seed, R. B., Wong, K. S. and Ozawa, Y., 1984,FEADAM84: A Computer Program for Finite Element Analysis ofDams, Virginia Polytechnic Inst. And State Univ., Dept. of Civil

Engineering, USA.

6. El-Sayed, S. M., 2001," Elastoplastic Three-dimensional Analysis ofShielded Tunnels, with Special Application on Greater Cairo Metro",

Ph.D. Thesis, Ain Shams University, Cairo, Egypt.

7. El-Sohby, M.A. and Mazen, O., 1985, Geology aspects in CairoSubsurface Development , Proc. of the 11st. ICSMFE, San Francisco,

Vol. 3, pp. 2401-2405.

8. Goldberg, D. T., Jaworski, W. E. and Gordon, M. D., 1976, "LateralSupport and Underpinning Vol. III. Construction Methods", Report

No. FHWA-RD-75-130, prepared for Federal Highway Administration,

Office of Research & Development, Washington D.C.9. Gourvenec, S. M. and Powrie, W., 1998, "Three-dimensional Finite-

element Analsysis of Diaphragm Wall Installation", Geotechnique, Vol.

49, No. 6, pp. 801-823.

10.Ng, C. W. W. and Yan, R. W. M., 1998, "Three-dimensional Modellingof a Diaphragm Wall Construction Sequence", Geotechnique, Vol. 49,

No. 6, pp. 825-834.

11. Thompson, P., 1991, A Review of Retaining Wall Behavior inOverconsolidated Clay during Early Stages of Construction, MphilThesis, Univ. of London, London, England.


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Fig. (1): Layout of the wall and the settlement points

Fig. (2): Soil profile and geotechnical parameters

Fill

SAND-SILT

Fine SAND and some silt

Graded SAND, some gravel

Depth (m)

Duncan's modulus coefficient K

200 400 600

180

300

480

600

(0.00)

(-2.00)

(-5.00)

(-11.00)

c=0, =28o, =17 kN/m3

c=0, =30o, =18 kN/m3

c=0, =33.5o, =19 kN/m3

c=0, =36o, =20 kN/m3

0.6 m

(-21.00)

Diaphragm wall

GWT


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-10

-9

-8

-7

-6

-5

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-3

-2

-1

0

Initial 7/

610/6

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21/6

24/6

26/6

28/6 2/

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7/7

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DATE

Settlement(mm)

Point (1)

Point (7)

Point (12)

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0

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Settlement(mm)

Point (2)

Point (8)

Point (13)

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Point (3)

Point (9)

Point (14)

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Point (10)

Point (15)

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Point (5)

Point (16)

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Point (6)

Point (11)

Point (17)

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Point (18)

Point (27)

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Point (19)

Point (28)

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Point (20)

Point (29)

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Point (21)

Point (30)

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Point (22)

Point (24)

Point (23)

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Settlement(mm)

Point (25)

Point (31)

Point (26)

Fig. (3): Settlement (mm) vs. time for the monitoring points


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Fig. (4): Effect of stress path on soil stiffness.

Fig. (5): Mesh details (a) Isometric view showing the mesh;

(b) Isometric view of the panels I, II & III and the sections 1,2 & 3

LLmax0.75 LLmax

Et

Eur

LL

E

1

1

3

Et

Eur

12.00 m12.00 m

21.00 m

29.00 m

58.00 m

(a)

S

S

F

S

B

F: Far field

S: Symmetrical conditions

B: Bottom of the mesh

SEC 1

SEC 3

SEC 2II

III

I

(b)

3.00 m

6.00 m

3.00 m


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(a)

(b)

Fig. (6): The maximum stress level (SLmax)

(a) The case of pile foundations;

(b) The case of shallow foundations


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0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45 50 55 60

Distance from trench (m)

Settlement

(mm

Excavation of Panel I

Excavation of Panel II

Excavation of Panel III

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45 50 55 60


Settlement

(mm




0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45 50 55 60


Settlement

(mm)




0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40 45 50 55 60

Distnace from Trench (m)

Settlement(mm)

Maximum predicated settlement

Measured

Fig. (8): Settlement troughs for shallow foundations (a) Section 1; (b) Section 2;

(c) Section 3; (d) Calculated settlement envelope vs. measured values

(a)

(b)

(c)

(d)

Settlement(

mm)

Settlemen

t(mm)

Settlement(mm)

Settlement(mm

)


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0

3

6

9

12

15

18

21

0 2 4 6 8 10 12 14 16 18

Lateral Deformation (mm)

Depth(m)

Section 1

Section 2

Section 3

(a)

0

3

6

9

12

15

18

21

0 2 4 6 8 10 12 14 16 18

Lateral Deformation (mm)

Depth(m)

Section 1

Section 2

Section 3

(b)

Fig. (9): Lateral deformation of the trench side

(a) The case of pile foundations;(b) The case of shallow foundations

(-2.00)

(-16.00)


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0

2

4

6

8

10

12

14

16

18

0 2 4 6 8 10 12 14 16 18

Maximum horizontal displacement (mm)

Maximumv

erticaldiplacement(mm)

Fig. (10): Relation between maximum horizontal and vertical displacements

Piles

Shallow found.Vertical = Horizontal

Vertical = 0.5 Horizontal

Vertical = 0.61 Horizontal

Maximum vertical displacement (mm)

Maximumhorizontaldisplacem

ent(mm)

spatial stress-deformation analysis for diaphragm walls

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