chapter 73 design of soil reinforced slopes and structures

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ICE Manual of Geotechnical Engineering © 2012 Institution of Civil Engineers www.icemanuals.com 1093

doi: 10.1680/moge.57098.1093

CONTENTS

73.1 Introduction and scope 1093

73.2 Reinforcement types and properties 1093

73.3 General principles of reinforcement action 1094

73.4 General principles of design 1096

73.5 Reinforced soil walls and abutments 1097

73.6 Reinforced soil slopes 1102

73.7 Basal reinforcement 1104

73.8 References 1106

73.1 Introduction and scopeThe concept of reinforced soil structure consists of placing (typically horizontal) layered reinforcing elements with suf! -cient axial tensile stiffness within a soil mass to improve its tensile and shear capacities. This allows the construction of reinforced soil slopes and reinforced soil walls at signi! cantly steeper angles – which would be unstable without the reinforce-ment. When used as basal reinforcement, this also allows the construction of embankments over poor ground or areas prone to subsidence that would otherwise fail without the reinforce-ment in their foundations.

The idea of introducing reinforcing elements to improve the strength of ! ll can be traced back to the earliest human times, when primitive people used sticks and branches for the rein-forcement of mud dwellings. The earliest remaining example of reinforced ! ll is the Aqar Quf ziggurat built in modern Iraq by the Babylonians around 3000 BC, using clay bricks, reinforced with woven mats of reed laid horizontally on layers of sand and gravel, with plaited ropes of reed passing through the structure. Parts of the Great Wall of China built more than 2000 years ago also adopted a form of reinforced ! ll where tamarisk branches were used to reinforce a mixture of clay and gravel.

In the early 1960s, Henri Vidal introduced and developed the modern form of reinforced ! ll using " at metallic reinforced strips laid horizontally on a frictional ! ll. In the late 1960s and 1970s, extensive studies of reinforced soil structures sponsored by national bodies, notably the Laboratoire central des ponts et chaussées (LCPC) in France, led to a fuller understanding of the concepts involved and a better acceptance of the method. More or less simultaneously, advances in synthetic fabrics led to the development of geotextiles and geogrids. These new materials were soon put to good use in the construction of geosynthetic-reinforced soil structures and as basal reinforcements. It should be noted that reinforced soil is the general term for reinforcing

elements placed within a soil mass and covers both metallic and polymeric reinforcement. The term ‘reinforced earth’ is the trademark for the Reinforced Earth Company – using its founder’s (Henri Vidal) ‘Terre Armée’ concept.

This chapter introduces the various types of reinforcements and their properties, discusses the general principles of the reinforcement action and provides guidance for the design of reinforced soil structures. Reinforced soil walls and abut-ments, reinforced soil slopes and basal reinforcement are then covered in more detail. Particular forms of reinforcement such as anchored earth (Chapter 89 Ground anchors construction), soil nails (Chapter 74 Design of soil nails), and particular application of basal reinforcement such as load transfer plat-forms (Chapter 70 Design of new earthworks) are discussed elsewhere in this manual.

73.2 Reinforcement types and properties73.2.1 Types of reinforcementThere are essentially two main types of reinforcement, de! ned by their extensibility.

Extensible reinforcement: de! ned in BS 8006 (BSI, 1995) as rein- !

forcement that sustains the design loads at strains greater than 1% and which are usually polymeric.

Inextensible reinforcement: de! ned in BS 8006 as reinforcement !

that sustains the design loads at strains less than or equal to 1% and which are usually metallic.

The design life of the reinforcement can vary from a few months (e.g. basal reinforcement for embankment on soft ground) to up to 120 years (e.g. walls, abutments and slopes). The princi-pal function of the reinforcement is to withstand tensile loads; the ability of the reinforcement to perform its primary func-tion, both initially and throughout its design life, will largely depend on the material from which it is produced.

Chapter 73Design of soil reinforced slopes and structuresSebastien Manceau Atkins, Glasgow, UKColin Macdiarmid SSE Renewables, Glasgow, UKGraham Horgan Huesker, Warrington, UK

Reinforced soil structures are composite constructions involving some form of reinforcement (usually geosynthetic or metallic), generally installed in horizontal layers within a soil mass. The reinforcement layers extend beyond the potential failure surface, absorb the tensile strains that would otherwise cause failure of the non-reinforced soil and redistribute them in the soil beyond the failure plane. This chapter aims to introduce the general concepts of soil reinforcement, the various materials and general principles involved in the design of reinforced soil structures. Reinforced soil walls and abutments, reinforced soil slopes and basal reinforcement are discussed.

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independent of time. Hence, the tensile yield strength of metal-lic reinforcement will reduce over time, almost uniquely due to corrosion.

Corrosion in metallic reinforcement is essentially a process of oxidation; this forms a protective oxide layer which tends to retard further corrosion. The effects of corrosion are con-sidered in design by allowing for a loss of the cross-sectional area of the reinforcement. BS 8006 provides guidance on the prescribed sacri! cial thickness to allow for at the design stage, which varies depending on:

particular metal or alloy and corrosion protection used; !

design service life of the reinforcement; !

corrosivity of the ! ll, soil or environment in which the reinforcement !

is placed (e.g. high acidity soil, which would be highly corrosive).

73.3 General principles of reinforcement action

73.3.1 Effects of introducing reinforcements in soilWhen an inclined or vertical load (due to soil self-weight or surcharge) is applied to a soil, this will generate axial compres-sive strain in the soil and a corresponding lateral tensile strain. The maximum load that can be applied to a soil is limited by its internal shear strength. The introduction of reinforcement into the soil (of adequate stiffness) improves the shearing resistance of the soil (shear strength of reinforced soil = mobilised shear-ing in the soil + mobilised tensile force in the reinforcement) and has the effect of reducing both the axial compression and lateral deformations.

Deformation of the soil along a potential failure plane causes shear forces to develop in the soil and tensile forces to develop in the reinforcement intercepting the failure plane. The reinforcement

73.2.2 Properties of polymeric reinforcementPolymeric reinforcement can take a variety of forms, such as grids, meshes, strips (commonly used to reinforce slopes and walls) and geotextile sheets (commonly used for basal reinforcement).

All polymers are essentially nonlinear viscoelastic mate-rials, and as such are load rate dependent. In addition, polymers are subject to creep and their behaviour is therefore time dependent.

When subjected to a constant load, all materials will increase in strain over time. This phenomenon is known as creep and is signi! cant in polymers at ambient temperatures. The ten-sile rupture strength of polymeric reinforcement will reduce over time, predominantly due to creep from an initial short-term ultimate tensile rupture strength (UTS) to a tensile creep rupture strength at the end of the selected design life. The propensity of polymeric reinforcement to creep will be primar-ily dependent on the particular polymer used to produce the geosynthetic reinforcement (e.g. polypropylenes tend to have a greater creep propensity than polyesters).

Isochronous curves plot the tensile load against the strain for a given time (during which the reinforcement has been subjected to the tensile force). The curves are derived from extensive testing and interpolations following guidelines in PD ISO/TR 20432 (BSI, 2007) and are unique to each proprietary geosynthetic reinforcement. The stress axis is generally nor-malised by expressing the tensile load as a percentage of the initial short-term UTS of the reinforcement.

These curves enable the designer to establish both the initial strains and post-construction strains for polymeric reinforce-ment at a given load/stress level; strains must remain below prescribed design limits. BS 8006 imposes varying service-ability limits on post-construction strain depending on the type of structure considered. Post-construction strains are limited to 0.5% for bridge abutments and retaining walls with perma-nent structural loads, and to 1.0% for retaining walls with no applied structural loading. For slopes where deformations are not critical, post-construction strains in the order of 5% may be acceptable. There usually is no limit on post-construction strain for basal reinforcement (used for embankment on soft ground) but there can be limits imposed when the basal rein-forcement is used over areas prone to subsidence.

Additionally, the curves allow the designer to determine the variations of the reinforcement stiffness with time.

A typical set of isochronous curves are shown in Figure 73.1.

73.2.3 Properties of metallic reinforcementMetallic reinforcement can take a variety of forms, such as grids, meshes, strips, bars or rods (commonly used to reinforce walls and abutments).

Creep in metallic reinforcement is generally negligible in ambient temperatures. Metallic reinforcement can there-fore be assumed to exhibit linear elastic behaviour to yield,

100

90

80

70

60

Tens

ile fo

rce

(% U

TS

)

50

40

30

20

10

0 0 1 2 3 4 5 6

Strain (%)

1 day

1 year

7 8 9 10

Creep strain ! 0.5%

1 month

10 years 114 years

2 min

Wide width constant loading rate

tensile test

Figure 73.1 Typical isochronous curves for polyester-based reinforcementCourtesy of Huesker (Isochrones for Stabilenka product)


Design of soil reinforced slopes and structures


At this point, further deformations will only occur as a result of additional loading, or through stress relaxation, or creep, of the reinforcement over time.

The stress–strain response of soil will vary depending on a number of factors including mineralogy and stress history; similarly, the stress–strain response of reinforcement will vary depending on a variety of factors including its form, manufac-turing process and raw material. It is generally not practical to develop a set of compatibility curves for every soil type and proprietary reinforcement product available. BS 8006 provides practical recommendations for addressing strain compatibility by adopting certain values depending on the type of reinforced soil application. For example, ! p would be adopted for walls and steep slopes where mobilised strains and deformations are considered more critical to the overall performance, and ! cv for shallow slopes and basal reinforcement over soft soils where deformations are considered less critical.

73.3.3 Interaction between soil and reinforcementReinforcement develops a bond with the soil through either friction (for granular soils) or adhesion (for cohesive soils). There are two interaction modes:

direct sliding, in which a block of soil slides over a layer of !

reinforcement;

pull-out (bond), in which a layer of reinforcement pulls out of the !

soil after mobilising the maximum available bond stress.

73.3.3.1 Direct sliding

The sliding resistance of geotextile reinforcement is gener-ated over the full plan area of contact. The sliding resistance of geogrids and strips is generated from both direct contact between the reinforcement and the soil, and from soil-to-soil contact through the apertures or adjacent to the reinforcement.

Modi! ed direct shear tests are suitable for measuring the coef! cient of direct sliding between soil and any type of reinforcement.

is most effective when placed in the direction in which the ten-sile/lateral strains develop. However, in most practical reinforced soil applications, the reinforcement is installed horizontally (with the exception of soil nails which are commonly inclined at an angle between 10 and 20° from the horizontal).

73.3.2 Strain compatibilityThe relative magnitude of the shear force mobilised in the soil and the tensile force mobilised in the reinforcement will be a function of deformations and the relative stiffness properties of both soil and reinforcement (stiffer reinforcement will carry a higher percentage of the mobilised force). The magnitude of mobilised soil shearing resistance and the mobilised reinforce-ment strain need to be considered to provide equilibrium.

Inextensible (metallic) reinforcement will absorb, through frictional contact, the disturbing forces in the active zone at low soil deformations and transfer these forces beyond the fail-ure plane. For more extensible polymeric reinforcements, the issue of strain compatibility becomes increasingly important – to ensure design reinforcement strain limits remain compatible with mobilised soil strains.

Figure 73.2 shows the mobilised shear resistance of a typi-cal granular soil and the typical mobilised reinforcement force (time constant).

From the graph in Figure 73.2(a) it can be seen that as strains develop, the mobilised shear resistance in the soil increases (and the required reinforcement force to satisfy equilibrium decreases) up to a point where the mobilised shear strength reaches a maximum or peak strength ! p. Beyond this point (! m), increasing deformations result in reducing shear strength towards a minimum value ! cv (shear strength at constant volume) independent of strain, with a corresponding increase in the force required to satisfy equilibrium. At the same time, as strains develop, the force mobilised in the reinforcement corresponding to a speci! c loading period (td) and temperature (Td) increases (Figure 73.2(b)).

Strains develop until a strain level is reached (in both the soil and the reinforcement) whereby the force mobilised in the rein-forcement is that required to satisfy equilibrium (Figure 73.3).

!!p

!!cv

"3

Pr

td

Td°

!!Q

!!m

"r(a) (b)

Figure 73.2 Relations for strain compatibility: (a) mobilised soil shearing resistance, (b) mobilised reinforcement force. Pr = mobilised reinforcement force; td = loading period; Td = temperature; " 3 = maximum tensile strainReproduced, with permission, from CIRIA SP123, Jewell (1996), www.ciria.org

Available force -extensible reinforcement

Required force

Expected equilibrium

Rei

nfor

cem

ent f

orce

Tensile strain

Available force -inextensible reinforcement

Figure 73.3 Typical compatibility curve for determining equilibrium in reinforced soilAdapted, with permission, from CIRIA SP123, Jewell (1996), www.ciria.org




internal failure. The value of fn depends on the class of risk for the structure and introduces additional safety for structures where the consequences of failure are most onerous. This fac-tor is applied both as an additional material factor and as an additional resistance factor on the reinforcement strength and ! ll reinforcement interactions, respectively.

73.4.2.1 Partial material factors

A partial material factor of safety on reinforcement (fm) is applied on the reinforcement capacity to account for uncertainty on the reinforcement properties (manufacture and extrapolation of test data), susceptibility to damage during construction (e.g. due to shape and size of ! ll used) and environmental effects (e.g. temperature, exposure to ultraviolet radiation).

The partial factor for rami! cation of internal failure (fn), as discussed above, is also applied to further reduce the reinforce-ment design strength and therefore acts as an additional mate-rial factor.

A partial material factor of safety is applied on soil strength parameters (fms) to account for uncertainty on the characteristic value of the soil parameters considered.

73.4.2.2 Partial load factors

Partial load factors are applied to increase the soil self-weight (ffs), the external dead loads (ff) and the external live loads (fq). For walls and abutments, the worst load combination for the various design criteria must be identi! ed and considered in the design.

BS 8006 uses high values for partial load factors on ! ll or soil self-weight, which is one of the parameters that is likely to be well known and not subject to large variations. However, it should be borne in mind that the values of partial factors of safety provided in BS 8006 have been speci! cally calibrated for reinforced soil structures. Even if the logic behind a partic-ular partial factor looked at in isolation is not always apparent, the overall application of the full set of partial factors of safety leads to safe designs.

73.4.2.3 Partial resistance factors

For the internal failure mechanisms (i.e. within the soil/reinforcement block) involving ! ll/reinforcement interaction, a partial factor of safety on pull-out resistance (fp) is applied to the resistance generated by ! ll/reinforcement interaction behind the potential failure surface, when this intersects a layer of rein-forcement. A partial factor of safety on sliding resistance along reinforcement (fs) is also applied to the resistance generated by ! ll/reinforcement interaction when the base of a potential failure surface coincides with a layer of reinforcement.

The partial factor for rami! cation of internal failure (fn) is also applied to further reduce the ! ll/reinforcement resistances (pull-out and direct sliding) and therefore acts as an additional resistance factor.

For the external mechanisms (e.g. sliding or bearing capac-ity), a partial factor on sliding resistance along soil (fs) is applied

For cohesive foundation soils, subject to undrained loading, the bond stress developed between the soil and the reinforce-ment is directly related to the undrained shear strength of the soil by an adhesion factor, which will normally have a value less than unity.

73.3.3.2 Pull-out

The pull-out resistance of geotextile reinforcement is generated from surface shear over the full plan area. Geogrids develop pull-out resistance partly from surface shear and partly through bear-ing resistance from the transverse members of the geogrids. It is usually suf! cient for the design to calculate the bond coef! cient from theoretically derived values for these two components.

For narrow, rough, strip reinforcement embedded in dense cohesionless ! ll, the shear stresses developed during pull-out lead to dilatancy in the ! ll, which causes the vertical effective stress to locally rise above the overburden pressure. This gives rise to an enhanced pull-out resistance. It is generally recom-mended that ! eld pull-out tests be carried out to verify the bond strength of these types of reinforcement.

Pull-out tests are relatively dif! cult to perform and can be signi! cantly in" uenced by the boundary conditions of the test. They can, therefore, be unreliable.

73.4 General principles of designThe design of reinforced soil structures and slopes is not cov-ered by the Eurocodes. In the UK, design of reinforced soil structures follows BS 8006 Code of Practice for Strengthened/Reinforced Soils and Other Fills (or HA68/94 Design Methods for the Reinforcement of Highway Slopes by Reinforced Soil and Soil Nailing Techniques; Highways Agency, 1994). BS 8006 follows a limit state approach and provides partial factors of safety calibrated for reinforced soil structure design through the assessment of historical data. It should be noted that the stan-dard was ! rst published in 1995 and that a new version has been published in 2010. The following text applies to both standards as there have been minimal changes between the two.

73.4.1 Limit state approachReinforced soil structures are designed against the occurrence of ultimate limit states (ULS) and serviceability limit states (SLS). ULSs are associated with collapse, rupture or major damage, and SLSs with excessive settlement or deformations.

73.4.2 Partial factors of safety approachBS 8006 provides various partial factors of safety which are used to generate the overall safety of reinforced soil structures. Although BS 8006 does not speci! cally group them in this fashion, it is convenient to think of the partial factors of safety as being introduced to reduce material properties and resis-tances, and increase loads (a similar approach to that used in the Eurocodes).

A partial factor for rami! cation of internal failure (fn) is also introduced to account for the rami! cations (consequences) of




Polymeric reinforcements are not in" uenced by electro-chem-ical properties, but the in" uence of chemicals on the propri-etary polymeric reinforcements need to be assessed.

In certain circumstances, provided durability and compat-ibility with the reinforcement have been considered, cohesive ! lls, pulverised fuel ash, colliery spoil, argillaceous materials and chalk can be used (for details, refer to BS 8006, section 3). The selection and speci! cation of ! ll for reinforced soil struc-ture should be considered as early as possible in the project, and aspects such as sustainability, availability, impacts on design and costs should be borne in mind. The use of material other than class 6I/6J ! ll (provided durability and compatibility with the reinforcement have been considered) may lead to a design requiring longer, more closely spaced and stronger reinforce-ments, and to increased earthworks ! ll testing requirements during construction. However, the use of alternative material could also lead to a signi! cant reduction in the quantities of selected ! ll to be imported – if site-won material can be re-used (thus reducing the quantity of material to be disposed of off-site). It could also reduce haulage costs if sources of acceptable ! lls are identi! ed in the vicinity.

73.5.2.2 Reinforcement

The reinforcement in reinforced soil walls and abutments consists of either metallic strips or polymeric geogrids. The reinforcement properties and the principles of their interaction with the ! ll are discussed in sections 73.2 and 73.3 above.

73.5.2.3 Facing

The facing provides local support to the ! ll between reinforce-ment layers, prevention against weathering of the exposed soil and an aesthetically acceptable ! nish. Common facing types include full height panels, discrete panels, segmental blocks and wrap-arounds. They are constructed of concrete (reinforced or mass), steel, wood or polymers. Discrete panels (in hexago-nal, square or cross patterns) are the most commonly used with metallic reinforcement, and segmental blocks are commonly used with polymeric reinforcements for permanent structures where a hard facing is acceptable. Wrap-arounds for polymeric reinforcement can provide a green ! nish but are more suscep-tible to ultraviolet degradation, accidental damage and vandal-ism. They are commonly used in temporary structures.

73.5.3 Common geometries and typical dimensionsFigure 73.5, in which L is the reinforcement length, illustrates common reinforced soil retaining wall and abutment geome-tries that can be used for assessing options at conceptual design stage and for preliminary sizing. These dimensions are given relative to the mechanical height H. For a wall, the mechani-cal height is derived as the vertical distance between the base of the reinforced soil block and the intersection of the ! nished pro! le and a line at 1V:0.3H from the front bottom corner of the reinforced soil block. For an abutment, H is the vertical height between the base of the reinforced soil block and the ! nished

to the resistance generated by soil/soil interaction on any hori-zontal plan, either within or at the base of the reinforced soil structure where there is soil to soil contact. A partial factor on bearing capacity resistance (fms) is also applied to the resistance generated by the ultimate bearing capacity. Please note that BS 8006 considers this partial factor of safety as a material fac-tor (hence the notation fms) however, bearing capacity is not an intrinsic soil property and, therefore, in the following the partial factor on bearing capacity is considered as a resistance factor.

73.5 Reinforced soil walls and abutments73.5.1 GeneralReinforced soil walls and abutments are composite structures consisting of ! ll, reinforcement and a facing, as illustrated in Figure 73.4. Provided the reinforcement layout and properties are adequate to prevent an internal failure of the reinforced soil block, the block of reinforced soil retains the soil at its back as a mass gravity structure, and transmits and spreads the effects of surcharges and earth pressures over its wide base. Reinforced soil walls are cost-effective soil retaining structures that can tolerate large settlements. Reinforced soil structures with a face within 20° from the vertical can be analysed as reinforced soil walls.

73.5.2 Materials73.5.2.1 Fill

Both the mechanical and chemical properties of the ! ll need to be assessed. Generally, frictional class 6I/6J ! ll of the Speci! cation for Highways Works (Highways Agency, 1993) is used in the construction of reinforced soil walls and abut-ments. When steel metallic reinforcements are used, the elec-tro-chemical properties of the ! ll also need to be considered.

Figure 73.4 3D section through reinforced soil structureCourtesy of Terre Armée Internationale




applied bearing pressure (refer to Chapter 53 Shallow founda-tions for further details on bearing capacity).

At the base of the reinforced soil block, sliding should be checked either on a soil/soil interface or, if a layer of reinforce-ment is provided at the base of the reinforced soil structure, on a soil/reinforcement interface.

Any potential slip failure passing at the back of the rein-forced soil structure should also be checked using traditional slope stability analysis software.

For the settlement check, both the settlement of the founda-tion soil and the internal settlement of the reinforced ! ll should be considered (refer to Chapter 70 Design of new earthworks for further details on ! ll self-settlement). However, when prop-erly compacted, the selected ! ll used in reinforced soil walls and abutments will produce small internal settlements, and this component is often neglected.

In current UK practice, the internal stability of the reinforced structure is often designed by suppliers who do not generally assess the external stability. Instead, they provide target values for allowable bearing capacity of the foundation soil to prevent bearing capacity failure; target values for the shear strength of the foundation soil to prevent sliding; and SLS applied bear-ing pressures at the base of the reinforced soil block to allow an assessment of the settlements to be undertaken. It is critical to understand the limitations of such suppliers’ designs and to ensure that:

The external stability is adequately assessed, based on the actual !

ground investigation information and that, where required, ground improvement is applied to the foundation soil (or the geometry of the reinforced soil block is amended, or a combination of both) to ensure external stability is satis! ed.

The responsibilities of the various parties and the objectives/ !

speci! cation of the design are clearly de! ned (for most com-mon applications, BS 8006 will provide a safe basis for design). Furthermore, notwithstanding the expertise of the suppliers, sup-pliers’ designs should not be taken at face value.

All other aspects such as drainage, services, fencing, aesthetics !

that could have an impact on the design are considered and com-municated between the parties involved, to ensure an integrated overall design is achieved.

The court case that followed subsidence on a load transfer platform in Enniskillen, Northern Ireland (High Court of Justice in Northern Ireland, Queen’s Bench Division, 2005), whilst not covering a reinforced soil wall or abutment, illus-trates what can go wrong when the principles above are not followed.

73.5.4.2 Internal stability

Within the reinforced mass, there are two zones delimited by a potential failure surface. In the active zone (between the face of the wall and a potential failure surface) the ! ll sheds shear stress into the reinforcement and induces a tensile force in it. The reinforcement transfers this tensile force in the resistant

pro! le at the back of the abutment. Dimensions chosen for pre-liminary sizing may need amending following detailed design.

Other geometries including trapezoidal walls can be designed to suit particular site requirements.

73.5.4 Elements of designThe design of reinforced soil walls considers two distinct aspects.

The external stability covers the design of the reinforced soil !

structure as a unit and follows the principles used for a general mass gravity retaining structure.

The internal stability covers the internal mechanisms within the !

reinforced soil block and deals with considerations of stress distri-bution and reinforcement layout.

73.5.4.1 External stability

For external stability the following ULSs and SLSs should be considered:

bearing and tilt failure – ULS; !

sliding – ULS; !

slip failure – ULS; !

settlement – SLS. !

The factored applied bearing pressure at the base of the rein-forced soil block (qr) is derived using a Meyerhof distribution (equivalent rectangular distribution on a reduced area) as:

qR

L erv=2

(73.1)

where

Rv resultant of all factored vertical load components;L reinforcement length at the base of the wall;e eccentricity of resultant load Rv about the centre line

of the base of width L.

The bearing capacity of the foundation soil derived using traditional bearing capacity equations must be greater than the

H H

H1

H1

Arc tan 0.3

(a) Part height wall (b) Abutment

and " 7mL " 0.7 H L " (0.7 H + 2)

Figure 73.5 Common geometries and typical dimensions for (a) a reinforced soil wall; and (b) an abutmentReproduced with permission from BS 8006–1 © British Standards Institution 2010




Tensile force in reinforcement

Both the tie-back wedge and the coherent gravity methods cal-culate the maximum factored tensile force in the jth layer of reinforcement Tj which is given as:

Tj = Tpj + Tsj + Tfj (73.2)

where:

Tpj tensile force at jth layer of reinforcement generated by self-weight of ! ll, surcharge and retained back! ll;

Tsj tensile force at jth layer of reinforcement generated by vertical load applied to a strip;

Tfj tensile force at jth layer of reinforcement generated by horizon-tal load applied to a strip.

The component due to the ! ll self-weight, surcharge and retained back! ll is given as:

Tpj = K #vj Svj (73.3)

where:

K earth pressure coef! cient. For extensible reinforcement (tie-back wedge method) active earth pressure coef! cient Ka shall be used throughout the structure. For inextensible reinforcement (coher-ent gravity method) values varying between at rest earth K0 at the top of the structure and active Ka lower down the structure shall be used.

#vj vertical stress acting on the jth layer of reinforcement assuming the Meyerhof distribution. The derivation of #vj varies slightly between the tie-back wedge and the coherent gravity method (re-fer to BS 8006 for details).

Svj Vertical spacing of the reinforcement at the jth level in the wall.

The component due to any vertical load applied to a strip is given as:

Tsj = K ## vj Svj (73.4)

where ## vj is the increase in vertical stress generated by strip vertical loading at the level of the jth layer of reinforcement. The tie-back wedge method assumes a simple 2V:1H dispersion of the strip load through the reinforced ! ll. The coherent gravity considers the dispersal based on the Boussinesq equation for strips with an edge on the front face of the wall, and applies the principle of superposition to represent strip at a distance from the front face of the wall. The mathematics involved in the original coherent gravity method can be cumbersome and the 2010 revi-sion of BS 8006 allows the use of the simple 2V:1H load disper-sal assumption in conjunction with the coherent gravity method.

The component due to any horizontal load (FL) applied to a strip is given as:

Tfj = $ j FL Svj (73.5)

where $ j FL is the horizontal stress generated by strip horizon-tal loading at the level of the jth layer of reinforcement. The

zone (between the potential failure surface and the back of the wall) where the reinforcement sheds shear stress into the ! ll (Figure 73.6).

Laj = length of reinforcement within the active zone.

Lej = length of reinforcement within the resistant zone

%s = slope angle

For the internal stability, the following ULSs and SLSs are considered:

Local stability of a layer of reinforcement – ULS: !

rupture of the reinforcement (or/and connection); !

breakdown of the interaction between the ! ll and the reinforce- !

ment (pull-out or/and direct sliding);

instability of a wedge of any size or shape assumed to behave as !

a rigid body – ULS;

deformations – SLS. !

Extensible reinforcements in which the design load is sustained at an axial tensile strain greater than 1% (polymeric reinforce-ment) are designed using the tie-back wedge method which is based on a theoretical approach.

Inextensible reinforcements in which the design load is sus-tained at an axial tensile strain less than 1% (metallic rein-forcement) are designed using the coherent gravity method. This method is mainly empirical and is based on observations on instrumented reinforced soil structures.

Both methods follow broadly similar steps which are sum-marised below.

Activezone

!s

Resistantzone

Reinforcement

LejLaj

Figure 73.6 Internal stability of reinforced soil wall. Laj = length of reinforcement within the active zone, Lej = length of reinforcement within the resistant zone, %s = slope angleReproduced with permission from BS 8006–1 © British Standards Institution 2010




tie-back wedge method assumes a dispersion of the strip load at 45° + & /2 from the back of the strip through the reinforced ! ll. The coherent gravity assumes a dispersion of the strip load at 45° from the back of the strip through the reinforced ! ll.

The various components of the tensile force in the jth layer of reinforcement (for the tie-back wedge method) are illus-trated in Figure 73.7.

Local stability checks

For each layer of reinforcement, check that the design tensile strength of the reinforcement is greater than the factored ten-sile force to prevent rupture of the reinforcement. Also, for each layer of reinforcement, check that the design adherence capacity of the reinforcement behind the failure wedge being considered is greater than the factored tensile force to prevent pull-out of the reinforcement.

For extensible polymeric reinforcement subject to creep the serviceability criterion is generally more critical than the ULS local stability check (see ‘Serviceability’ on page 1102 below).

Surface failure/lines of maximum tension

In the tie-back wedge method, the failure plane with the most tensile force needs to be determined by considering the stability of wedges, of any size or shape, assumed to behave as rigid bod-ies. The friction along the potential failure plane and the tensile resistance of reinforcement beyond the failure plane (rupture capacity or pull-out capacity, whichever is the smallest) must be greater than the disturbing applied loads.

In the coherent gravity method, results of monitoring installed along reinforcements have shown that the tensile force varies along the reinforcement. Lines of maximum tension are de! ned (the shape of the line considered depends on whether strip loadings are applied or not) and the tensile force in the reinforcement is calculated on these de! ned failure surfaces. Provided the local stability checks (rupture and pull-out) are satis! ed on these de! ned failure surfaces, there is no require-ment to carry any further wedge stability analysis (unless the geometry or loadings are unusual).

The failure plane in the tie-back wedge method and the lines of maximum tension in the coherent gravity method are illus-trated in Figure 73.8.

Connections

The tensile force in the connection between the facing and the reinforcement depends on their properties. Unless the facing is stiff (e.g. full height panel with no movement capacity at connections), the tensile force in the connection will be less than the maximum tensile force calculated. However, the ten-sile force at connection is signi! cant and the connection has to be designed to prevent rupture under this load throughout the design life. When metallic reinforcements are used, the connec-tion generally involves a bolting arrangement that leads to the tensile capacity at the connection being less than that of the full bar – and this detail is particularly vulnerable to corrosion.

L - 2 ej 2 ej

ej = eccentricity of the resultant vertical load at the j th layer of reinforcement

Surcharge Q1Surcharge Q2

Backfill +Q2 earthpressure

Tpj = K #vj Svj

#vj

Svj

hj

Fill selfweight

Tpj - Self-weight of fill, surcharge and retained backfill

Tsj = K '# vj Svj

'#vj

21

Svj

hj

2

1

Ts j - Vertical load from strip (tie back wedge method)

45-#'/2

Svj

hj

FL

$j FLTfj = $j FL Svj

Tfj - Horizontal load from strip (tie-back wedge method)

Figure 73.7 Tensile force in the jth layer of reinforcement




SL Vertical load from stripFL Horizontal load from strip

Wh% Self weight of fill in the wedge and any surchargeRh% Resultant reaction acting on potential failure planeTh% Tensile force to be resisted by the reinforcement

SL

%

FL

%'

Th%

Rh%

Wh%

SL

FLTh%

Wh%

SL

FL

Rh%

Vary h and % to obtain the maximum tensile force to be resisted by the reinforcement

The triangular shaded area highlights the specific wedge forwhich the forces diagram is presented on the right hand side

0.3H

Tj

Lej

A1

2

1N1

M1 B1

H1

za

za = min: 2(d + b/2) or H1

d

bCL

j

0.4H

0.2H

H

Tie back wedge

Coherent gravity

The lines of maximum tension can be assumed as illustrated above

h

Figure 73.8 Surface failure/lines of maximum tension. Coherent gravityReproduced with permission from BS 8006–1 © British Standards Institution 2010




reinforced soil walls and abutments. As discussed in section 73.5.2.1 for reinforced soil walls and abutments, the selection and speci! cation of ! ll for reinforced soil structure should be considered as early as possible in the project. Aspects such as sustainability, availability, impacts on design and costs should be borne in mind. Site-won material is often used as an eco-nomic and sustainable ! ll for reinforced soil slopes. Properties of particular signi! cance are the drained shear strength param-eters (& and occasionally c , although effective cohesion should be used with great care) which will govern the soil reinforcement pull-out capacity, and the maximum particle size which will govern the risk of mechanical damage during construction – and hence the reinforcement rupture capacity.

73.6.2.2 Reinforcement

For reinforced soil slopes, geogrids are predominantly used. The reinforcement properties and the principles of their interac-tion with the ! ll are discussed in sections 73.2 and 73.3 above.

73.6.2.3 Facing

For shallow slopes (no steeper than 45° from the horizontal) it is generally possible to place the ! ll without permanent or temporary supports. Intermediate short secondary geogrids are often placed between layers of main reinforcements to prevent small shallow seated failures in the front face. Some form of erosion mat is often provided to ensure that the topsoil placed does not erode in the short term, and to facilitate the establish-ment of vegetation. Health and safety issues associated with cutting grass on relatively steep slopes should be considered.

For steep slopes (steeper than 45° from the horizontal) the facing is generally built using either wrap-around or steel mesh. In a wrap-around detail, the reinforcing geogrid or geotextile is folded through 180° to form the face and is anchored back into the ! ll or connected to the next layer (up) of reinforcement. Temporary formwork is often required to allow placement and compaction of the ! ll. In a steel mesh facing arrangement, the reinforcing geogrid or geotextile can be connected directly to the steel mesh, or continued behind the face of the steel mesh and returned into the ! ll to allow for the future deterioration of the sacri! cial steel facing. In both cases, topsoil is placed just behind the facing to facilitate the establishment of vegeta-tion. In addition to health and safety issues associated with cut-ting grass on such steep slopes, the dif! culties of establishing, irrigating and maintaining vegetation on them requires careful consideration.

Typical reinforced soil slope con! gurations are presented in Figure 73.9.

73.6.3 Elements of designSimilar to the design of reinforced soil walls and abutments, the design of reinforced soil slopes considers both external and internal stability. In current UK practice, the stability of reinforced soil slopes is often designed by suppliers who, unless they are provided with adequate information, tend to

Facings

Finally, the facings are designed structurally to resist the con-nection tensile loads, any externally applied loads (e.g. impact loadings from traf! c) and the effect of any construction toler-ance. In the case of segmental block facings, sliding and move-ments between blocks and overtopping of the blocks above the uppermost layer of reinforcement must be checked.

Serviceability

Deformations post-construction can happen as the result of creep of polymeric reinforcement, where the tensile stiffness decreases with time from an initial short-term value. In order to limit movements due to creep, the capacity of the reinforcement should be considered in conjunction with a limiting post-con-struction value of strain (typically 0.5% for abutments and 1% for walls) at the end of the design life, using isochronous load strain curves. For metallic reinforcement, creep is negligible.

73.5.5 ConstructionFactors affecting the construction of reinforced soil walls and abutments include:

nature and properties of the soil at the base of the reinforced soil !

block;

site controls and placement and compaction requirements for the !

speci! ed ! ll;

safe storage and handling of the reinforcement; !

facings; !

simplicity and robustness of the connection detail; !

requirements for drainage; !

site constraints; !

end use; !

erection rate. !

Buildability is discussed in more detail in BS 8006 and in Chapter 86 Soil reinforcement construction. Recommended construction tolerances are also presented in BS 8006.

73.6 Reinforced soil slopes73.6.1 GeneralReinforced soil slopes are composite structures consisting of ! ll, reinforcement and facing. The front face is usually grassed up to provide a green slope ! nish. A distinction is made between ‘shallow slopes’ de! ned as no steeper than 45° from the horizontal, and ‘steep slopes’ de! ned as being between 45° and 70° from the horizontal.

73.6.2 Materials73.6.2.1 Fill

Generally, frictional ! ll will be used as ! ll for reinforced soil slopes, but the range of ! ll that can be used is wider than for




Two-part wedge mechanism

The two-part wedge mechanism is an extension of the Coulomb wedge approach as illustrated in Figure 73.10. The mecha-nism may take any form (i.e. (1, (2 and X can vary) provided the mechanism outcrops at the toe of the slope and the inter-wedge boundary is vertical. By resolving the forces acting on the wedges (which requires assumptions on the inter-wedge bound-ary conditions), the out-of-balance force that needs to be taken by the reinforcement can be assessed for each mechanism. For each slope there is a unique critical two-part wedge mechanism for which the out-of-balance force that needs to be taken by the rein-forcement is maximum. For more details on the two-part wedge mechanism, refer to HA68/94 (Highways Agency, 1994).

Considering the simple case of a slope with " at ground at the top and no surcharge, the maximum factored total force to be taken by the reinforcement Tmax can be expressed as:

Tmax = 0.5 K ) H 2 (73.6)

where:

K non-dimensional parameter equivalent (but not equal) to an earth pressure coef! cient;

) ! ll unit weight (kN m-3);

H ! ll height (m).

The factored tensile force in the jth layer of reinforcement Tj is given as:

Tj = K ) zj Svj (73.7)

where:

zj depth below crest level to jth layer of reinforcement;

Svj vertical spacing at jth layer of reinforcement.

concentrate on internal stability and the principles enounced in section 73.5.4.1 apply. In addition, compound stability, where the potential failure surface is partly within the reinforced soil zone and partly behind it, should also be considered.

73.6.3.1 External stability

For external stability the following ULSs and SLSs are considered:

bearing and tilt failure – ULS; !

sliding – ULS; !

slip failure – ULS; !

settlement – SLS. !

73.6.3.2 Internal stability

Similar to reinforced soil walls and abutments, a potential fail-ure surface delimits an active zone and a restraint zone. For the internal stability, the following ULSs and SLSs are considered:

local stability of a layer of reinforcement – ULS; !

rupture of the reinforcement (or/and connection); !

breakdown of the interaction between the ! ll and the reinforce- !

ment (pull-out or/and direct sliding);

deformations – SLS. !

Internal stability assessment is generally undertaken using one of many limit equilibrium methods available. The most commonly used are the two-part wedge mechanism and the method of slices, which are discussed below. Other methods, such as a non-circular analysis, a log spiral or a coherent grav-ity method, could be used.

Erosionprotectionmat

Primary (main)reinforcement

Secondaryreinforcement

Shallow slope

Steep slope with steel mesh facing

Steelmeshfacing

Steep slope with wrap-around facing

ReinforcementReinforcement

Geotextile separatorGeotextile separator

Figure 73.9 Typical reinforced soil slope confi gurations




pull-out resistance or the rupture strength of the reinforcement) is greater than the tensile load generated in the layer.

The overall reinforcement provided shall be suf! cient to pre-vent slope failure and it shall be veri! ed that:

F TdT s Fjj

n

RSFF DFFTdeTT see j+=1

(force equilibrium) (73.10)

M Mj

n

RS D+ ( )TdT s Yj jYTdeTT see j=1

(moment equilibrium)

(73.11)

where

Yj vertical distance from centre of rotation of slip to the reinforcement layer under consideration;

FRS (MRS) restoring force (moment) due to shear strength of soil;

FD (MD) disturbing force (moment) due to the weight of soil and surcharge.

73.6.3.3 Compound stability

Compound stability considers failure mechanisms where the potential failure surface is partly within the reinforced soil zone and partly behind it. The principles for analysing compound stability are similar to those for analysing internal stability.

73.7 Basal reinforcement73.7.1 GeneralReinforcement can be introduced at the base of embankments over poor ground to avoid ULS failure through shear in the foundation of the embankment and/or SLS failure through excessive deformations. It should be noted that BS 8006 still limits the applications of basal reinforcement to foundations for earthworks. The common applications are:

Basal reinforcement over soft to very soft foundation soil to con- !

trol initial ULS stability of the embankment without controlling the settlement.

For each layer of reinforcement, a local stability check should be undertaken. The design tensile strength of the reinforcement should be greater than the factored tensile force to prevent rup-ture of the reinforcement. The design adherence capacity of the length of reinforcement (Lej) behind the wedge considered should be greater than the factored tensile force to prevent pull-out of the reinforcement.

For each layer of reinforcement, the smallest of the design tensile strength and the design adherence capacity can be referred to as the design capacity of the jth layer of reinforce-ment: Tdesj. For the local stability check, it should be con-! rmed that for each layer of reinforcement:

Tdesdd Tj jT (73.8)

The overall reinforcement provided should be suf! cient to pre-vent rupture of the two-part wedge mechanism, and it should be checked that:

Tdesdd Tjj

n

=maTT x

1

(73.9)

Slice method for circular slip mechanism

The method of slices is traditionally used for unreinforced soil slopes and is adapted to take into account the effects of intro-ducing the reinforcement layers. The additional restoring forces and moments provided by the reinforcing elements beyond the slip failure are considered in the calculations of the slope sta-bility factor of safety. BS 8006 only considers moment equi-librium and suggests that inter-slice forces are ignored in the calculations. However, most current slope stability software allows for analyses using both force and moment equilibrium, and will consider some form of inter-slice interaction.

For each layer of reinforcement, a local stability check (Figure 73.11) should be undertaken and it should be veri-! ed that the design capacity of the reinforcing layer (either the

(2

Lej

Critical failure surface

TdesjTj

X

Wedge 1

Wedge 2

Svj

(1

Figure 73.10 Two-part wedge mechanism

Lej

Yj

TdesjTj

Critical failuresurface

Figure 73.11 Circular slip failure mechanism




reinforcement. Strain compatibility between the reinforcement and the soft foundation soil should be satis! ed in order to achieve a maximum bond coef! cient. This is particularly the case when dealing with sensitive foundation soils that exhibit rapid strength loss post-peak, hence the strain in the reinforcement (SLS case) should not exceed the strain at which the peak shear strength is mobilised in the foundation soil (see section 73.3.2).

The ULS limit equilibrium mechanisms to consider are:

deep-seated failure; !

lateral sliding; !

extrusion. !

73.7.2.1 Deep-seated failure

The analysis of deep-seated failure is generally performed using the method of slices for a circular failure mechanism described in section 73.6.3 above. The reinforcement pro-vided should have a suf! cient design capacity Tdes (against rupture and pull-out beyond the failure mechanism) to provide moments and forces equilibrium. In the case of basal rein-forcement, it is also necessary to ensure that the length of rein-forcement within the failure surface mechanism is suf! cient to prevent pull-out (Figure 73.12).

73.7.2.2 Lateral sliding

The reinforcement provided shall have a suf! cient design capacity Tdes (against rupture and pull-out beyond the failure mechanism) to resist the outward thrust (active earth pressures)

Basal reinforcement combined with another form of ground !

improvement technique over soft to very soft foundation soils (typically piled embankment with basal reinforcement acting as a load transfer platform) to control both the initial ULS stability and long-term SLS settlements of the embankment.

Basal reinforcement over foundation soils prone to subsidence !

(e.g. mining) where the reinforcement is designed to span the void (ULS stability) and limit the deformations at the top of the embankment.

This chapter will focus solely on the ! rst application of a sim-ple basal reinforcement over soft to very soft foundation soil. For details of the other applications, refer to BS 8006.

The products used in basal reinforcement applications gen-erally consist of geotextiles or geogrids, but products such as steel meshes are sometimes considered.

73.7.2 Basal reinforcement for an embankment on soft to very soft groundWhen constructing an embankment on soft soil, shear failures are likely to develop through the foundation soil. The problem is always more acute in the short term (during construction) since soft soils will consolidate and strengthen over time due to the dissipation of the excess pore water pressures generated in the soil by the construction of the embankment. Once consolidation is complete, the basal reinforcement is often redundant. Basal reinforcement is often used in conjunction with other construc-tion techniques (e.g. staged construction discussed in Chapter 70 Design of new earthworks) to limit the capacity required from the

Q

Forces equilibrium:

Moments equilibrium:

Tdes

LeLa

Check:Pull out resistance over La > Tdes

FDTdesFRS "+

MDYTdesMRS "&+

Hf

Y

Figure 73.12 Basal reinforcement – deep-seated failure. Q = surcharge loading, Hf = height of embankment, La = length of reinforcement within active zone, Le = length of reinforcement within resistant zone




Hs within the reinforced soil, the rectangular block of soil is in equilibrium. The restoring forces are the adhesion along the base of the soil block, the adhesion between the reinforcement and the soil at the top of the block and the passive earth pres-sures on the outward side of the block (Figure 73.14).

73.8 ReferencesBritish Standards Institution (1995). Code of Practice for Strengthened/

Reinforced Soils and Other Fills. London: BSI, BS 8006.British Standards Institution (2004). Eurocode 7: Geotechnical

Design, Part 1: General Rules. London: BSI, BS EN 1997–1.British Standards Institution (2007). Guidelines for the Determination

of the Long-Term Strength of Geosynthetics for Soil Reinforcement. London: BSI, PD ISO/TR 20432.

from the embankment ! ll and any surcharge which is at a maximum at the top edge of the embankment slope. Again, it is also necessary to ensure that the length of reinforcement within the failure surface mechanism is suf! cient to prevent pull-out (Figure 73.13).

73.7.2.3 Extrusion

Extrusion assumes the outward lateral displacement of a rect-angular block of soft soil under the embankment ! ll. The rein-forcement provided shall have a suf! cient design capacity Tdes (against rupture and pull-out beyond the failure mechanism) to resist the tensile load generated by the outward foundation shear. In addition, it is also necessary to ensure that at any depth

QForces equilibrium:

Tdes

LeLa

Check:Pull out resistance over La > Tdes

Tdes " Factored active earth pressures

Factored activeearth pressures

fqfffs HQfKaHfKaTdes &&&+&&&&" 2

21 '

H f

Figure 73.13 Basal reinforcement – lateral sliding. Ka = active earth pressure coeffi cient, ) f = fi ll unit weight

QForces equilibrium:

alpha' = adhesion factorCutop = undrained shear strength base of embankmentCubase = undrained shear strength at depth HsHs = Depth to base of soil layer under consideratio

TdesLeLa

Hf

HsFactored activeearth pressures

Factored passiveearth pressures Check La sufficient to ensure

stability of light blue box at alldepth Hs

Laf

CuTdes

ms

top &&" 9$

Laf

Cu

ms

top &&9$

Laf

Cu

ms

base &

Figure 73.14 Basal reinforcement – extrusion. $ ! = adhesion factor, Cu top = undrained shear strength base of embankment, Cu base = undrained shear strength at depth Hs, Hs = depth to base of soil layer under consideration




CIRIA (1996). Soil Reinforcement with Geotextiles. Special Publication 123 (SP123) [out of print].

Geotechnical Engineering Of! ce, Civil Engineering Department, the Government of the Hong Kong Special Administrative Region (2002). Guide to Reinforced Fill Structure and Slope Design. Geoguide 6.

British Standards Institution (2010). Code of Practice for Strengthened/Reinforced Soils and Other Fills. London: BSI, BS 8006–1.

High Court of Justice in Northern Ireland, Queen’s Bench Division (Commercial List) (2005). Enniskillen Case on Load Transfer Platform as a Good Warning Story – Neutral Citation No [2005]. Belfast: NIQB 68, delivered 24 October.

Highways Agency (1993). Speci! cation for Highway Works. Manual of Contract Documents for Highway Works. London: Highways Agency.

Highways Agency (1994). Design Methods for the Reinforcement of Highway Slopes by Reinforced Soil and Soil Nailing Techniques. Design Manual for Roads and Bridges. HA 68/94. London: Highways Agency.

73.8.1 Further readingAssociation Française de Normalisation (AFNOR) (2009). Calcul

Géotechnique, Ouvrages de Soutènement, Remblais Renforcés et Massifs en Sol Cloué. Norme Française NF P 94–270.

British Standards Institution (2006). Execution of Special Geotechnical Works – Reinforced Fill. London: BSI, BS EN 14475.

It is recommended this chapter is read in conjunction with

! Chapter 23 Slope stability

! Chapter 69 Earthworks design principles

! Chapter 72 Slope stabilisation methods

! Chapter 86 Soil reinforcement construction

All chapters in this book rely on the guidance in Sections 1 Context and 2 Fundamental principles. A sound knowledge of ground investigation is required for all geotechnical works, as set out in Section 4 Site investigation.


chapter 73 design of soil reinforced slopes and structures

Documents

queens bench division

british standards institution

strengthened reinforced soils

composite structures consisting

coherent gravity method

potential failure surface

load transfer platform

soil nailing techniques