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Les murs de soutènements encastrés: théorie, pratique et interprétation
B. SIMPSON, Arup Geotechnics, UK W. POWRIE, University of Southampton, UK
ABSTRACT: Embedded retaining walls commonly comprise steel sheet piling or concrete walls, built as diaphragm walls in slurry trenches or using piling methods. Since the early 20th century, sheet piling has been in common use, particularly for waterfront structures and temporary works. More recently, concrete walls have been used extensively for construction of basements and underground infrastructure in urban areas. The performance and design of embedded walls has been debated extensively by Terzaghi, Brinch Hansen, Rowe, Tschebotarioff and many more recent authors, whilst codes of practice aim to specify design procedures. Although understanding has increased in some respects, controversy remains, notably in relation to distribution of earth pressures on walls subject to flexure, adoption of working or collapse states in design, and application of safety factors. This paper aims to summarise and extend this debate, and to suggest future developments which might help to clarify understanding and design procedures RÉSUMÉ: Les murs de soutènements encastrés, murs en palplanches ou béton, comprennent la réalisation de panneaux de parois moulées ou de pieux. Au vingtième siècle, les murs en palplanches furent régulièrement employés en front de mer et pour les travaux temporaires. Récemment, les murs en béton furent largement utilisés lors de la construction de sous-sols et d’infrastructures enterrées en zone urbaine. La performance et le dimensionnement des murs de soutènement furent longuement discutés par différents auteurs. Les normes ont pour but de spécifier les procédures de dimensionnement. Malgré l’accroissement de la compréhension, le sujet reste fortement controversé particulièrement sur la répartition de la poussée des terres sur des murs soumis à la flexion, sur la définition de l’état ultime et l’état de service et sur l’application des facteurs de sécurité. Cette publication vise à résumer et élargir le débat, ainsi qu’à suggérer une démarche qui pourrait clarifier les procédures de dimensionnement. 1 HISTORICAL BACKGROUND Embedded retaining walls are walls that penetrate into the ground and rely to a significant extent or even completely on the passive resistance of the ground for their support. In the first half of the twentieth century, embedded walls were generally formed of either soldier piles or steel sheet piles, the latter being the subject of most of the debate and development of design methods. In the second half of the century, concrete walls formed either in slurry trenches or by contiguous or intersecting (secant) piles became increasingly common, often retaining natural clay rather than coarse grained soils. Classical methods of retaining wall analysis can be traced back to the work of Coulomb (1776) and Rankine (1857). Coulomb carried out upper bound calculations assuming a planar wedge failure mechanism from which he derived the limiting (active) force on a retaining wall, as a function of depth below the retained soil surface. This form of calculation does not indicate a unique stress distribution. Rankine carried out lower bound calculations based on the assumption that the stress field behind the wall was in a uniform state of plastic equilibrium; from this he derived limiting earth pressures which, due to his assumptions, increased linearly with depth in uniform materials. For the simple case of a frictionless wall in uniform soil, the two solutions coincide provided it is assumed that the active force calculated using Coulomb’s approach results from a lateral earth pressure that increases linearly with depth. Rankine’s calculation gives lateral earth pressure coefficients, that is ratios of horizontal to (notional) vertical effective stress, at any depth. These form the basis of most limit equilibrium analyses of embedded retaining walls. Although Coulomb’s original approach was based on a consideration of the overall equilibrium of an entire wall, it can be used to calculate earth pressure coefficients if it is assumed that the total lateral thrust results from a lateral earth pressure distribution that increases linearly with depth. Later workers have used more complex calculations to determine earth pressure coefficients, based on either upper bound (following Coulomb) or lower bound (following Rankine) approaches, to refine the results and to extend them to include wall friction, sloping ground surfaces, and non-vertical walls. For example, Sokolovski (1960) used a lower bound method, while Caquot & Kerisel (1948), and most other workers, used upper bounds. The degree of refinement is now such that the practical difference between the bounds is small, at least in cases where it can be assumed that earth pressures increase linearly with depth. It is considered that all the authors noted throughout this paper would agree that the active and passive forces calculated in this way are limits that cannot be infringed. However, there has been a considerable debate about how the earth pressures giving rise to these forces may be distributed, linearly or otherwise, both at collapse and under working conditions. Earth pressure redistribution, and the distinction between design approaches based on lateral stress distributions at collapse (or an ultimate limit state) and under working conditions (or a serviceability limit state), are two of the key issues addressed in this Paper. 1.1 Idealised stress distributions at collapse Unpropped embedded walls rely entirely for their stability on an adequate depth of embedment. They are not supported in any other way, and will tend to fail by rotation about a pivot point near the toe. An idealised stress distribution at failure, based on limiting active or passive stresses in zones of soil where the wall is moving away from or into the soil, is shown in Figure 1a. An embedded wall propped at the crest will tend to fail by rigidbody rotation about the prop, with the idealised effective stress distribution at failure shown in Figure 1b. With the stress distributions shown in Figure 1 and limiting active and passive lateral earth pressures, the equations of moment and horizontal force equilibrium can be used to determine
which should ideally be chosen with regard to the rate of increase in stress in front of the wall with wall movement. in which an increase in the height of the centre of passive pressure was attributed to the effects of wall bending. were established by authors such as Blum (1930).b (from Burland et al 1981) compares the ratios (H/h) of the overall wall height H to the retained height h calculated using various factors of safety (Fp=2.
the two unknowns in each case. Fp=2 is unduly conservative at values of φ' less than about 27°. Krey’s assumed distribution of passive pressure. rather larger movements than are acceptable under working conditions are required for the stresses to rise to the passive limit. A real wall must be sufficiently remote from collapse not to deform excessively under working conditions and must also have margins of safety to guard against unexpected conditions. the wall would be expected under working conditions to be in equilibrium under the action of the active pressures in the retained soil. when the wall is on the verge of rotational failure. This is traditionally achieved by applying a factor of safety F to one or more of the parameters in the collapse calculation.e. Certain of the traditional methods of applying a factor
Figure 2. as shown in Figure 2a. Some alternative forms of the factor F are shown in Figure 2. the stresses in the soil behind the wall fall to their active values after only a small movement of the wall (Terzaghi 1943). Figure 4 illustrates that. In other words. except that the passive resisting force was assumed to be distributed as shown in Figure 3. In many soils. or inappropriate in some circumstances. Figure 4a. and may well result in a local increase in lateral stress in the soil at that level. In these cases.5) with (H/h) at collapse (Fs=1). some of whose findings are summarised below. In general.Figure 1. these stress distributions are statically determinate. The stresses behind the wall are at their minimum possible values (the active limit). In front of the wall. particularly sands. for an effective stress analysis. and lower-thanpassive pressures in the soil in front of the wall.
. and the acceptable limit of deformation. In Blum’s method.
Figure 3. with a factor of safety applied as a reduction to the linear passive pressure (Fp. In these conditions. Nonetheless. the earth pressures were assumed to increase linearly with depth. The stress distributions shown in Figure 1 are highly idealised. Potts & Fourie 1984) and analyses of real walls (Powrie 1996) that limit equilibrium calculations using the full (unfactored) soil strength and the stress distributions shown in Figure 1 can give a reasonable indication of the embedment depth at the onset of large wall movements.
of safety are now known to be potentially unsafe. Procedures for the design of anchored walls. Definitions of factors of safety. and the pore water pressures below the water table are hydrostatic). It is therefore necessary to increase the depth of embedment beyond that required merely to prevent collapse.2 Factors of safety for idealised stress distributions at collapse The stress field distributions shown in Figure 1 correspond to limiting conditions. 1955) on sheet pile walls. while the stresses in front of the wall are at their maximum possible values (the passive limit). The full passive pressures are therefore reduced by a factor Fp. for various values of φ' with a smooth wall (δ=0) and a water table on both sides of the wall at the level of the excavated soil surface (i. summarised by Terzaghi (1943). it has been shown with reference to both finite element studies (e. 1. to estimate the depth of embedment required for serviceability and safety. Potts & Walsh (1981). Krey’s (1936) approach was similar to that of Blum (1930). Fs=1. after CIRIA 104. Although current practice in the UK is generally to apply the factor of safety (Fs) to the soil strength. based on the idealised stress distribution at collapse (Figure 1b). This presages Rowe’s work (1952. This is the traditional procedure given in the former UK code of practice for retaining walls. This was identified and discussed by Burland. Wall bending is just one possible factor causing a redistribution of the lateral stresses away from the linear-with-depth assumptions that stem from the simple application of classical earth pressure theory. a prop or anchor plate will be of finite depth. Idealised linear effective stress distributions. this has not always been the case.g. as defined below). there is no seepage around the wall. CP2 (IStructE 1951) and elsewhere. This places the point of action of the passive force slightly higher and so gives a reduced tie force and bending moment. the in situ lateral earth pressure coefficient Ko=σ'h/σ'v is close to the active limit. At that time these were generally sheet pile walls.
On the other hand. Rowe 1952. This may be the case.3 Investigations of stress states under working and collapse conditions During the 1940’s and 50’s. Through the assumption of simple idealised deformation mechanisms. In an attempt to take advantage of this.9. Figure 4c shows the ratio of the overall wall length H to the retained height h (H/h) as a function of the non-dimensionalised undrained shear strength 2cu/γh. By considering the variation in Fp with H/h at constant cu (2cu/γh=0. The application of a factor of safety in some other way (e. Burland et al (1981) proposed a further “revised” factor of safety. For the following reasons. provided that the strength parameters are selected conservatively. Williams & Waite (1993) suggest that it might be acceptable in an effective stress analysis. This can be illustrated further by the extreme example of the use of a factor of safety on passive pressure coefficient in the case of a wall of zero embedment depth. Fs=1 (i. If this is done. at which the bending moment is zero. Williams & Waite 1993) describe the use of a "fixed earth support" calculation for a propped embedded wall. for example).b). as illustrated in Figure 2d. The calculations could alternatively be carried out by seeking an embedment depth that will limit the maximum bending moment to a required value.g. 1955. an increase in the depth of embedment d).at least for stiff walls that are either unpropped or propped at the top (Bolton et al 1990a. Padfield & Mair (CIRIA Report 104 1984 on the design of retaining walls embedded in stiff clays) recommend against its use. Design calculations involve many uncertainties. so that their effects from derived quantities will result from the calculation.e.Figure 4. Given that in increase in H/h corresponds to an increase in the wall length H at constant retained height h (i. as shown by Burland et al (1981) and summarised above. 3. to reduce the risk of mistakes. this result is clearly unrealistic. so it appears to give no real advantage in design. the number of factors should be kept to a minimum. and potentially dangerous. so it is not necessary to apply a factor of safety to determine the design embedment depth. Thus the application of the factor of safety to soil strength can in principle be quite clearly correlated with an acceptable level of deformation under working conditions. Increasing the depth of embedment of a flexible wall may result in a reversal of bending moment near the base and a consequent reduction of the major bending moment at higher level. A net pressure diagram based on fully-active and fully-passive pressures is plotted. Simpson (2000) points out that factors should be applied to the uncertainties themselves. the mobilised soil strength can be related to wall movement .1 over the range 10°≤φ'≤35°.5. Fr. it is considered that the application of the factor of safety to the soil strength represents the most appropriate approach in the design of an embedded retaining wall. 2. using the factor Fnp as shown in Figure 2c. and materials properties. the idealised stress distribution shown in Figure 5 is statically indeterminate.0) times the moment of the net pressure behind the wall. but Figure 4 shows that this success must have relied very heavily on the selection of conservative strength parameters: Fnp=2 corresponds to a factor of safety Fs (on soil strength) of rather less than 1. including loads. Williams & Waite (1993) adopt a conventional proposal that the prop force and the depth of embedment may be calculated by assuming that the point of contraflexure. Their reluctance to recommend against using the method is probably linked to their observation that it has been used successfully in sheet pile cofferdam design for more than 50 years. occurs at the level where the net pressure acting on the wall is zero. Without a further assumption. calculated using Fs=1. Factor of safety calculated using various methods against factor of safety on soil strength (after Burland et al 1981). For walls propped at the crest. and the depth of embedment is chosen such that the moment about the prop of the net pressure in front of the wall is equal to a factor Fnp (normally 2. at limiting equilibrium). effects of loads. 1. 1956). This method is fundamentally unsound.e. the "net pressure method" is described in the British Steel Sheet Piling Handbook (1988). As soil strength is often the principal uncertainty in geotechnical design. with the idealised effective stress distribution and bending moments shown in Figure 5.g. Fp=1. This work
. it follows that this is where the factor of safety should be applied. on passive pressure coefficient.
For a total stress analysis. the calculated embedment depth will be somewhat greater than that in a free earth support analysis. Figure 4 shows that an apparently satisfactory numerical value of Fnp=2 may correspond to a factor on soil strength (Fs)
which is little greater than unity (Burland et al 1981). some authors (e. Tschebotarioff 1951. considerable research effort was focussed on the effect of wall flexibility on reducing bending moments and prop loads to below those calculated on the basis of fully active lateral stresses in the retained soil (Terzaghi 1943 1954. 1.5 and Fp=2. Their justification for this factor was that it gave results consistent with Fs. net pressure or depth of embedment) can give unexpected results. it may be seen that Fp is reduced as H/h is increased.
It might be noted that vibration can equally cause an increase in active pressures in the absence of arching. the structure is then de
Figure 6. Rowe (1955) presented an analysis of anchored sheet pile walls in which it was assumed that the lateral effective stress behind the wall had fallen to the active limit. Similar design methods are also used for structures (such as slabs and shells) which might have been designed by the application of the theory of elasticity. If the wall was more flexible. 1. factored by the value needed for wall equilibrium. and in such a case the usual concept of allowable stresses is not suitable. but that in “a mass of clean sand” a reduction in bending moment of 50% could be expected as a result of this phenomenon. In other fields of engineering such problems are investigated by considering the state of failure. Brinch Hansen was arguing for design based on analysis of states of ultimate failure. In the discussion to Terzaghi’s paper. Rowe (1952) found that the lateral stress distribution in front of the wall depended on the relative importance of the bending component of wall deformation. in contrast to a design based on the stress state at ultimate failure. bending effects are most significant when the wall is propped at the crest. and described as the “actual distribution”. where H is the overall height of the wall and EI is its bending stiffness. Measured bending moments were in agreement with those from a limit equilibrium calculation based on a fully-active triangular stress distribution behind the wall and a smaller-than-passive triangular stress distribution in front (i. and hence on the bending stiffness of the wall. earth pressures can be caused to redistribute in various different ways by relatively small movements of props or anchors. but in the light of Rowe’s finding that very small yield of the anchor could lead to a return to linearly distributed earth pressures. noted below. Terzaghi’s “assumed (unbroken line) and real (dashed line)” active pressure distributions. 1. This led to smaller anchor loads and bending moments than those given by the (factored) limit equilibrium calculation. or by variations in the stiffness of the ground. taking account of early work by Rowe..
represented a change in emphasis. so that the deflexion at dredge level was significantly greater than that at the toe. which depends on the existence of shearing stresses . Brinch Hansen raised another important idea. after Terzaghi (1943).
signed so as to possess a certain safety against failure. Fixed earth support conditions for a flexible embedded wall propped at the crest: (a) idealised stresses. Terzaghi recognised this as a form of arching and argued that “since arching is maintained solely by shearing stresses in the soil. and we will return to it later in the paper. about the position of the prop). as it was directed at identifying lateral stresses under working conditions for use directly in design. the stress distribution in front of the wall was approximately triangular. and concluded that “there is no longer any justification for assuming fixed earth support without considering flexibility of the sheet piles”. Terzaghi concluded that “it does not seem justified to rely on the benefits to be derived from a difference between the real pressure distribution and the distribution computed on the basis of the Coulomb theory”. the centroid of the stress distribution in front of the wall was raised (Figure 8b). This was investigated by Rowe (1952) in a series of model tests on anchored sheet pile walls of various stiffness. This debate continues today. (b) deformed shape. In working conditions. and the change of lateral
. Vibrations are the most important influence of this sort”. Rowe quantified the stiffness of a wall by means of a flexibility ρ=H4/EI. In general terms. so that the deflexion at the level of the excavated soil surface was of the same order as the deflexion at the toe. This continued the debate about the distribution of active earth pressures.. rather than in-service states. This has the effect of increasing the load on the ties and reducing the bending moment in the wall.4 Comments of Terzaghi and Brinch Hansen Terzaghi (1943) noted that the flexure of a retaining wall could lead to redistribution of the active earth pressure. wall deformation occurs partly due to rigid body rotation (in the case of a propped wall. retaining dry sand. If the wall was stiff. He concluded that an adequate theory for the evaluation of this effect was not available. and partly due to bending (Figure 7).” In effect. The concepts of redistribution of active earth pressure were again noted.Figure 5. On the other hand. as shown in Figure 6. “The problem of the design of flexible anchored bulkheads is evidently one in which proportionality between total load and maximum stress does not exist. it is no less permanent than any other state of stress in the soil. more in keeping with the ideas of Krey (1936).5 The work of Rowe For a wall of given overall length H and flexural rigidity EI. every external influence which causes a supplementary settlement of a footing or an additional outward movement of a retaining wall under unchanged static forces must be expected to reduce the intensity of existing arching effects.e. Terzaghi (1954) was a seminal paper on Anchored Bulkheads. Figure 8a).
Frimann Clausen & Duncan (1972) The Fifth European Conference on Soil Mechanics and Foundation Engineering. For sheet pile walls in sand. Δpb = mxy/d (1) where d is the embedment of the wall. Rowe (1956) presents experimental data indicating prop loads in excess of the
ing walls with retained height ratios h/H in the range 0.) Rowe's design chart (Figure 9) represents his analytical solution to within ±10% for anchored walls with retained height ratios h/H (where H = h + d) in the range 0. Stress distributions behind and in front of (a) stiff and (b) flexible embedded walls (after Rowe 1952). the results of the analyses could be presented as a single moment reduction curve for design use. depending on the level of prestress. it must be remembered that only the component of the bending moment due to effective stresses should be reduced.6 – 0.002H sup-
Figure 7.2γH in magnitude. however. If the chart is used in such circumstances. anchor depths βH in the range 0≤β≤0. because Rowe has m in lbf/ft3 and ρ in ft5/lbf. the validity of the analysis based on fully active pressures in the retained soil as a "benchmark" probably depends on the initial lateral stresses being low. (The passive pressures were reduced by the amount needed to give equilibrium with linear pressure diagrams. A state-of-the-art report on “Earth pressures on flexible structures” was prepared by Bjerrum. Rowe's design chart may not be suitable for walls where the groundwater level in the retained soil is high. Pre-stressing of props or anchors could lead to higher wall bending moments. Moment reduction as a function of wall flexibility (after Rowe 1955). Figure 9.1≤β≤0. with a rather softer response that an effectively unyielding modern prestressed anchor which gives a more or less fixed force. mρ is in consistent units.free earth support values for anchors yielding up to 0. (The free earth support bending moment was calculated with fully active pressures behind the wall and a passive pressure coefficient dictated by the requirements of equilibrium. and with different degrees of anchor yield.
effective stress from the initial state Δpb in front of the wall at a depth x below formation level was given by the expression. this definition of soil stiffness is unusual. He concluded that. because retained height ratios h/H of less than 0. and therefore provide evidence of earth pressure redistribution (arching onto a prop that is effectively rigid in comparison with the wall) as failure is approached. leading to a reduction in earth pressures between the anchor and the dredge level. Rowe carried out analyses of walls of various retained height ratio α = h/H and depth βH to the anchor point. within the ranges of these variables likely to be encountered in practice. the moments in the wall will be smaller
. It notes. with and without surcharges at the retained soil surface.
Figure 8. y is the deflexion and m is a soil stiffness parameter. held in Madrid. Frimann Clausen & Duncan (1972). in which the preexcavation lateral earth pressure coefficient is low. the type of anchor available at that time would have been a dead man.in2.65-0.3. Rowe normalised his results with respect to the bending moments calculated in a limit equilibrium calculation with active pressures behind the wall and lower-than-passive pressures in front.2. Although Rowe describes how m may be measured or deduced. For anchored walls. and a movement at the anchor point of up to 0. as already stated).008H. according to Rowe (1956) on prop forces). Components of wall displacement and definition of a “stiff” wall. the report notes Rowe’s view that arching effects. In consistent units. could (being dependent on an unyielding anchor) be unstable and so should not be used to advantage in design. However. surcharges acting at the retained soil surface of up to 0.8 and 0. this gives a reasonable upper bound on bending moments (but not necessarily. that “when additional anchor yield and backfill settlement do not destroy the arching between dredge and anchor level. Rowe’s approach is equivalent to assuming a coefficient of subgrade reaction mx/d that increases linearly with depth from zero at the surface. Also.6 Bjerrum. These data show a consistent increase in tie load (relative to the free earth support value) with increasing retained height ratio. In a later paper. 1.65 would probably be required. This curve (Figure 9) shows the bending moment as percentage of the free earth support value as a function of the logarithm of mρ. and may not apply in the case of an embedded wall in an overconsolidated clay. addressed the theme “Structures subjected to lateral forces”. The report considered both anchored and braced excavations.75. and the question of arching in active earth pressures was a major theme of both the report and the discussion contributions to the conference session. mρ is dimensionless: however Rowe's values have to be multiplied by 144 to achieve this.
Thus the Danish approach. giving reduced earth pressures either towards the bottom of the excavation. conditions at collapse) of increasing sophistication. Figure 12 shows a simple design example involving a propped retaining wall supporting an 8m deep excavation. If the anchor is placed below the crest. the report clearly anticipates that arching effects will take place. Harbours and Waterways (1996) recommends the use of Blum’s method for sheet pile walls anchored near the top. earth pressures can be caused to redistribute in various different ways by relatively small movements of props or anchors. It should be noted that. In his verbal presentation. that the beneficial use of arching in design will not lead to ultimate failure of an embedded wall. Results obtained on the basis of these documents are shown in Figure 13. Redistribution of earth pressure. the forthcoming revision is noted towards the end of the paper). the expected sense of wall rotation would lead to increased lateral pressures (as a result of the tendency towards passive conditions) in the soil above the prop. and also depends heavily on knowledge of practical successes and failures.e. provided there is sufficient ductility in the structure to allow moderate displacements to take place and that the overall active/passive force envelope is respected. on both active and passive sides of the wall. and.8 Stress states under working and collapse conditions In working states. and the discussion will be illus-
trated by reference to three documents drafted in the last 2 to
Figure 10. even where full analysis of these is not possible. involving either rigid body rotation of the wall or bending failure. or by variations in the stiffness of the ground. Brinch Hansen 1953. 2 RECENT CODES AND ADVISORY DOCUMENTS Codes of practice. Reduction of earth pressure. in this state. the wall at failure would simply move a little more and arching would be re-established. safety factors are applied as factors on the strengths of the soil.
Figure 11. Mortensen 1995). For braced excavations. and will be discussed below. are published in many countries. Bjerrum seemed to have favoured allowing the full effects of arching. after Mortensen (1995). The choice between design for a working state (or a serviceability limit state) or an ultimate collapse limit state will be discussed further later in the paper. as a minimum. the stiffness of the prop or anchor is effectively much greater than that of the failing structure. after EAU (1996). in the ground beneath the excavation. and (b) they attempt to inform the user on the degree of conservatism to be adopted in deriving parameter values used as a starting point for design calculations. It may be concluded. is internally consistent and makes the ambiguous argument about arching in the working state unimportant to design. Put another way. BS8002 (British Standards Code of Practice for Earth Retaining Structures (1994)).7 Danish and German practice In parallel with the developments described above. These are: CIRIA 104 (Report 104 of the Construction Industry Research and Information Association by Padfield & Mair (1984)). The purpose of this section of the paper is to discuss some of the
principle features of these codes. which allowed significant redistribution of active earth pressure used to advantage in reducing calculated bending moments (Bretting 1948. However. Danish practice was based on plasticity theories (i. although pressures above the prop will tend to increase. considerations of yield at the support points are not relevant and it is reasonable to assume that full arching takes place. Their development is related to understanding of the behaviour of structures. rather than in reducing bending moments. but it appears that this debate has never been properly concluded. This will result in a very significantly reduced passive earth pressure coefficient. 1. 3 decades which take differing approaches. if the support point were to move slightly. Hence. if states of failure are considered.
. In these designs. The German Committee for Waterfront Structures. Two features of these documents require definition and discussion before the individual documents are considered: (a) they use the language of limit state design. more recently. though appearing to take a more optimistic view of arching phenomena. the report’s main emphasis for braced excavations is the effect of arching in increasing strut loads. and EC7 (Eurocode 7: this paper considers mainly the ENV version published in 1995.than those calculated by Rowe’s method”. with stress redistribution as shown in Figure 11 to account for increased lateral stresses in the vicinity of the prop or anchor. and other advisory documents which substitute for codes. or. soil/wall friction will be in the opposite direction to that in the passive zone in front of the wall. This is reflected in the dependence of stress redistribution on anchor depth indicated in Figure 11. An example from Mortensen (1995) is shown in Figure 10. in deep deposits of soft clay. 1. However.
and drained strengths of materials. strengths. the term is sometimes used to be equivalent to “partial factor design”.1 Limit state design Draft Euronorm 1990 defines ultimate limit states (ULS) to be those that concern the safety of people and the safety of the structure. It requires that the following be considered where relevant: • loss of equilibrium of the structure or any part of it. In design. whether a single value or a range. In total. It is important to note that this definition does not mention what type of analysis will be used in studying the limit state. but it is difficult for codes to set requirements for them which have generality. rupture. loads and geometric features. Older codes generally gave little guidance or even discussion of this matter. EC7 and BS8002. it could be inferred that all approaches to design are essentially limit state design. assuming that the designer will come to the process of calculation with a defined set of parameter values.
design” defines limit states as “states beyond which the structure no longer satisfies the relevant design criteria”. This. and checking that even for these.2 Ultimate and serviceability limit states 2. Thus. cu. transformation of the structure or any part of it into a mechanism. or whether the materials will be responding elastically or in a plastic mechanism. Stresses which will be mobilised in this
. or at least to indicate what degree of caution has been assumed when factors of safety have been written into the codes.
Figure 13. in limit state design attention is directed to unexpected. a broad appreciation of serviceability requirements often dictates the type of construction adopted . the attention of the designer is on what it is expected will actually happen. Whilst it is true that partial factor design and limit state design have developed together. previous experience. with the construction performing in a successful manner. Draft Euronorm 1990 defines serviceability limit states (SLS) as those that concern the functioning of the structure or structural members under normal use. It is proposed that the most useful understanding of limit state design can be obtained by contrasting it with “working state design”. however. methods using explicitly probabilistic techniques have no specific relationship to limit state design. Rather. Some of the more recent documents have attempted to give definition to the process of selecting values from the available information. In the latter. of the particular limit state. failure caused by fatigue or other time-dependent effects. If it is taken that the basis of limit state design is to avoid the occurrence of limit states. would render the term useless and fail to identify the main feature of approaches taken in some of the more recent codes. and margins between them and the limiting strengths of materials are required. damage and. Comparison of results for CIRIA 104. 2. for example. undesirable and hopefully unlikely states in which the construction is failing to perform satisfactorily. the present authors would agree with Krebs Ovesen (1995) that the two approaches are actually quite separate. but this has rarely been developed in an explicit manner. the comfort of people and the appearance of the construction works. or to “probabilistic design”. Hence there is an implicit probabilistic element in the approach. The degree of pessimism to be associated with the parameters depends on the severity. considered as a rigid body. cost of repair. either by designers or code drafters.but reliable calculation of ground movements is usually very difficult. or consequences. Alternatively. an ultimate limit state has occurred despite the fact that the wall has merely deflected “elastically” without forming a mechanism in the ground. They are sometimes given more precise definition in contracts. It notes that serviceability requirements should often be agreed for each individual project. and various tests including both index tests and direct measurements of relevant quantities. if a structure supported by a retaining wall collapses because of wall displacement. Similarly. loss of stability of the structure or any part of it. etc . This is done by taking pessimistic values for the leading parameters involved in the design. including supports and foundations. Design example. sequence of construction. 2. Serviceability limit states are generally more difficult to define since they refer to a subjective appreciation of relatively minor problems. publications. this information is often quite limited in extent and may contain both uncertainties and inconsistencies.3 Conservatism in parameter values Practical design involves the selection of parameter values. from information derived from diverse sources including site observations. All the documents discussed here refer to both undrained strength. to be used as
The term limit state design may be used so broadly as to be meaningless or with various alternative.steel or concrete embedded wall. narrower definitions. and incompatible. the definition is based entirely on the practical issues of degrees of danger. The latest draft of Euronorm 1990 “Basis of
Figure 12. the structure would not fail. • failure by excessive deformation. by implication.working state are calculated. By contrast. number of strutting levels.
the factors given for the Burland-Potts-Walsh method often led to slightly more economic designs than obtained from the other methods. have been used for a wider range of materials.5 1. For concrete walls. It proposed that cantilever and singly propped walls could be designed using simple. For steel sheet piles. including effects of site history. CIRIA 104 gave two alternative approaches for which the designer was to consider “moderately conservative” or “worst credible” values of parameters. to include a degree of caution in their chosen values. however. φ′ cu φ'≥ 30o φ'= 20-30o φ'≤ 20o cu
The factors included in Table 1 were selected partly on the basis of current use and partly in order to ensure that comparable designs would be obtained from all the alternative methods.0 1. Thus it seems that designs by this method. they also know that if they enter most code procedures with worst credible values they will obtain uneconomic designs. For propped walls. c′. φ′ cu
1. many of its recommendations. construction processes. two features may make the walls stronger than required by CIRIA 104.5 1. All three of the documents noted above have attempted to help designers to understand how pessimistic they should be in making assessments of parameter values. In the absence of other available guidance.relevant.5 1. soil structure. these results are also shown in Figure 13. Worst credible values are “the worst which the designer could realistically believe might occur”. the approach “used most often in practice by experienced engineers”. probably have unnecessary length The very short walls shown in Figure 15 were derived using assumptions about water pressure different from the other designs. For drained conditions. Although this exercise was part of the development of EC7. CIRIA 104 did not attempt to dictate one particular approach to safety factors. 2. This is often greater than that found from calculation (b). using the factor on strength method (Fs) as an illustration. Figure 2c should not be used since the factor of safety used has very little real effect on the design. but rather a value which is very unlikely to be exceeded”. which yield earth pressure distributions redistributed from those shown in Figure 1. It can be seen that the British design. at least without considerable infringement of the margins of safety normally required on the material properties of the wall structure.0 1. CIRIA 104 also gave different factors for temporary and permanent works. in calculations. serviceability requirements for crack widths often increase the reinforcement beyond that required for the ULS design. it is required that the worst credible c′=0. CIRIA Report 104 was limited by intention to the design of cantilever and singly propped embedded retaining walls in stiff clays. Thus if ever the wall should need to use the length calculated in (a). with φ′ set. Hence it is difficult to be certain from the experience of designs carried out in this way and successfully implemented whether the calculated bending moments are in fact too small. linear diagrams of active and passive pressure. Factors of safety proposed by CIRIA 104 (simplified)
Method Moderately conservative Worst credible parameters parameters Temp Perm Temp Perm 1. “not the worst physically possible. EC7 requires “characteristic” values of soil parameters. using the strength method of CIRIA 104. the walls are either longer than they need to be. Figure 15 shows the result of a study carried out in 1990.0
2. quite sensibly.5** 1. and for multi-propped and even non-embedded walls. in effect.0 -
1. The factors shown in Table 1 were to be used for determination of the length of the embedded wall. involving both geotechnical and
. though the document does not use that term.5 Eurocode 7 Eurocode 7 (EC7) is the geotechnical member of a unified set of codes for complete design. Nothing new is intended here. but provided differing values to be used with any of the methods illustrated in Figure 2.2 to 1. as illustrated in Figure 1.2 to 1.5 -
c′. This process is illustrated in Figure 14.4 CIRIA Report 104 Published in 1984.0 1. in which a cantilever retaining wall in stiff clay was designed for permanent conditions by representatives from seven different European countries. and a factor of safety was then applied to the derived bending moment to derive an ULS design value on which the structural section would be based. In practical design. gave a wall longer than would have been adopted.2 -
** lower values for φ′≥30
c′. even after the latter has been factored to obtain the ULS design value (the bending moment indicated for CIRIA in Figure 13).2 ** 1. Its factors have also been used in conjunction with finite element and subgrade reaction methods. In normal practice. the moderately conservative values were used unfactored.0 -
1. which shows the results of the two separate calculations.5 1. Table 1. BS8002 requires “representative” values of both peak and critical state soil strengths. this is not possible for cantilevers. in most of the other countries. simply that best practice. CIRIA 104 gave two alternative approaches for which the designer was to consider “moderately conservative” or “worst credible” values of parameters. the representatives were asked to design the wall “as they would in their normal national practice”. It can be seen that this has a greater effect than all other considerations. Definitions of these terms will be noted below.5 to 2. as noted above. and so on.0 2. In order to derive its structural strength. On the other hand. ie what they really consider to be most likely. a different calculation was required.0 1. some redistribution of earth pressure is likely. φ′. but prefer.0 1. 2. including factors of safety. Drained strength is defined in terms of angle of shearing resistance. however. so this approach became popular for competitive tendering. and effective cohesion. the aim is to remind the designer to consider all the available information. reducing the bending moment below that shown in Figure 14a. the strength provided by (b) will be insufficient to allow this. at a critical state value. This is not surprising since the strength factors given by CIRIA 104 for clays are greater than generally used outside the UK. It is doubtful whether there is any practical difference between moderately conservative (CIRIA 104). apparently successfully.2 2. resulting in the table of factors shown in Table 1. a point which must be considered in all designs. For this. Calculation (a) is used to derive the length and implies a bending moment which is then disregarded (the broken line in Figure 13). In practice. This approach gives an inconsistency of length and strength.5 1. however. and for propped walls. Moderately conservative values are said to be “a conservative best estimate”. is employed as the norm. especially for propped walls. or not strong enough. It specifically recommended that the net total pressure method. characteristic (EC7) and representative values (BS8002).5 2. though it acknowledged that more complex pressure distributions exist in reality. it is often found that in order to drive the steel sections to the depths required by CIRIA 104 they have to be stronger than required for the ULS bending moments. with incompatible length and strength. In all cases. so removing this possible extra margin.0 1. for comparison with other methods. the factors of CIRIA 104 have sometimes been used with methods which take advantage of redistribution. recognised by experienced engineers.2 1. engineers rarely use genuine “best estimates”.5 1. or the lengths too great.
and resort is only made to displacement calculations if this suggests that serviceability could be marginal. the section on retaining walls requires that the designer first makes an assessment of likely displacements on the basis of experience. but with an important change in the definition of characteristic values for geotechnical design. In EC7. EC7 defined characteristic geotechnical parameter values as a cautious estimate of the value affecting the occurrence of the limit state. This is partly because ultimate limit states are more readily defined. EC7 retaining wall comparison. No specific requirements about the use of peak or critical state values are given.4
1. and the structure are to comply with all three cases. EC7 notes that “the design methods and factors of safety required by this code for ultimate limit state design are often sufficient to prevent the occurrence of [serviceability limit states] provided the soils involved are at least medium dense or firm. In structural codes.50 1. The partial factor methods were initially developed by engineers with an interest in probabilistic methods. ie whichever limit state is under consideration. as discussed above. However. The ENV version of EC7 requires that designs be checked for three “cases” or sets of partial factors. the length of wall determined from geotechnical calculation. difficult and possibly spurious calculations. external loads and soil properties may combine in varying degrees.35 1. as shown in Table 2. Two calculations required by CIRIA 104: (a) for length and (b) for bending moment. The two sets of factors specified for Cases B and C ensure that both safety and reasonable economy can be obtained for a wide range of design situations. characteristic values are generally defined as a fractile of the results of particular. though Case A is generally non-critical for embedded retaining walls. In particular. using “characteristic “ and “design” values.00 1. consistently with other Eurocodes. and that it is to represent what actually governs behaviour in the ground. In common with other Eurocodes. particularly in geotechnics. The designer’s expertise and understanding of the ground are all encapsulated in the characteristic value. rather than a value derived from statistical manipulation of test results.a failing of many lumped factor methods.00 Variable Unfavou -rable 1. Partial factors from ENV1997-1. EC7 requires that embedded retaining walls be designed as though the level of the soil surface of the supporting (passive) soil were up to 0.
drafters wanted to avoid demands for unnecessary. Table 2. in which uncertainties in ground loads. The selection of characteristic values is discussed at greater length by Simpson & Driscoll(1998).2 1.00 Favour -able 0. The Eurocodes generally adopt both a limit state format and partial factor methods. This makes it possible to ensure that the length and strength of the wall are compatible.30 1.
but in practice the values adopted in the codes have been selected on a more pragmatic basis. for example.3 1. required by some highly overconsolidated clay deposits in which large at rest horizontal stresses may induce substantial movements in a wide area around excavations. The limit state approach generally requires that both ultimate and serviceability limit states be considered. it is
intended that the design will proceed from geotechnical to structural aspects without difficulty or confusion. and the code
1) Compressive strength of soil or rock. however.00 1.1 1.
Both the geometry. A Figure 15. soil fabric and structure.0 1. However. the more reliable of the available calculations deal with strength limits and failure mechanisms rather than serviceability requirements. he is to consider both project-specific information and a wider body of geotechnical knowledge and experience.25 tan φ
Ground Properties c' cu
1.structural requirements in a consistent manner.4
change designs very much from previous practice but will provide adequate margins of safety in a wide variety of situations .50 1. Thus. this means that ground and structure displacements must be considered. specified laboratory tests on specimens of material. Surrounding text makes it clear that this ‘cautious estimate’ is an assessment made by the designer.0 1. Thus the designer is to take account of time effects. in relation to its variability. brittleness. Special concern is. the effects of construction processes and the extent of the body of ground involved in a limit state. it is recognised that calculation of displacement is particularly difficult. with the aim that they will not
Case Figure 14. as must structural serviceability requirements such as crack widths. B C
Actions Permanent Unfavo -urable 1.2 1.5m below any level reasonably foreseen by the
.0 1. the calculations in EC7 are primarily directed to the ultimate limit state. In addition. Eurocode 7 follows the approach adopted in the other Eurocodes and most modern structural codes. and partly because.0 1. and adequate construction methods and sequences are adopted.95 1.” It can be seen from this that the choice of partial factor values adopted in the code is partly influenced by the need to prevent serviceability failures whilst relying on mechanism calculations.
The final design of the structure depends on the structural code in use as well as the geotechnical code. the broken line in Figure 13 which is disregarded in the CIRIA method. as is usually the case.6 BS8002 BS8002 is the British Standard Code of practice for Earth retaining structures. In the absence of international agreement.designer. producing the results marked STW in Figure 13. simple earth pressure diagrams like that shown in Figure 1 can be used. fall into Class 4 for which local buckling prevents the attainment of the full elastic moment of resistance (MR). Clearly. into the significance of clutch slippage and the possible advantages or limitations of crimping the clutches. which allows plastic design. It includes fac-
tors. In this example. but it is also permissible to take advantage of redistribution calculated by numerical analysis or other rules such as those illustrated in Figures 10 and 11. the full elastic MR can be used and the full plastic MR can just be attained for Class 2. Eurocode 3 Part 5 also requires that the effect of slippage between unwelded U-section sheet piles be allowed for. the ULS and SLS requirements of the two codes being compatible. as noted above. Economies of up to 30% in materials are anticipated as a result of this procedure. For design of reinforced concrete walls. discussed below.
Bolton et al (1990a. But for greater economy. which are in effect partial factors or strength factors. designers need to be aware how sensitive the structures are to this geometric parameter.
Figure 17. published in 1994. especially for walls with small penetration into highly frictional soils (Simpson & Driscoll 1998). this was also acknowledged in EC7. being based on the belief that serviceability rather than ultimate limit
states should govern design of retaining walls.2 on peak values of tanφ′ and c′. and a finite element program SAFE. Its approach to safety and serviceability is different from most other recent documents. with large displacement. In contrast to CIRIA 104 and BS8002. Hence using a mobilisation factor M to limit the proportion of strength mobilised should also limit wall displacements. with values fairly similar to EC7 Case C. so the on-going debate about the limits appropriate to concrete in the ground requires urgent resolution. For example.5 on cu. However. The length and bending moment calculated using EC7 for the example shown in Figure 13 were derived from Case C and the strut force from Case B. Design of struts to Case C only would give a reduction in strut force of 20 to 30%.5m unplanned excavation was to increase the bending moment by 39% and the strut force by 48%. The representative soil strength is said to be a “conservative estimate
. The length from EC7 is somewhat less than the previous British practice. how codes should best deal with this remains a matter of debate. It is often found that the structural design of embedded walls is dominated by SLS crackwidth limits. the program STAWAL uses pressure diagrams like those of Figure 1. such as trench sheeting. The EC7 bending moment is less than the CIRIA moment calculated using factored strength. though EC7 saw factors primarily as covering uncertainty in relation to ultimate limit state design. the EC7 calculations were repeated using the FREW program. Very thin sections. For a simple conservative design. Moment-curvature curve considered in EC3 Part 5. Larger sheet pile sections fall into Class 1 for which a prescribed degree of rotation at a plastic hinge is allowed. with the express purpose of limiting displacements of walls at the serviceability limit state. In essence. Its requirements are simply that equilibrium must be demonstrated. these are regarded as “mobilisation factors”.
be related to the proportion of the soil’s strength which has been mobilised. EC7 does not specify how the earth pressure distribution to be used for the design of embedded walls. and M = 1. For steel sheet pile walls. the significance of this is left to national decision.b) showed that the displacements of retaining walls could be related approximately to the shear strains occurring in the ground and that these shear strains could in turn
Figure 16. For more robust sections in Class 3. 2. represented by CIRIA 104. and earth pressures have been redistributed towards the prop. with compatible strains and using loads and strengths with the specified partial factors applied. but the governing value is given by Case B. EC7 Case C ULS design. Figure 16 shows an acceptable ULS design calculation in which the propped wall is just stable. which might be considered undesirable. since these proved to be the critical cases. Thus. EC7 interfaces with Eurocode 2. and is underway. Further research is required. Figure 17 shows the moment-curvature relationships allowed for four classes of sheet piling (Schmitt 2000). but more than that adopted for ULS design by CIRIA 104. EC7 interfaces with Eurocode 3 Part 5. the effect of the 0. This was intended to give a margin for unexpected events which cannot reasonably be covered by factors of safety. M. Simpson & Driscoll (1998) show that for cantilevers the effect may be even greater. Design values used in limit equilibrium calculations are derived from representative values by dividing strength terms by M = 1.
BS8002 also has a requirement for “unplanned excavation”. they recommend that the results of BS8002 design should be used for ULS design of the wall. and it stipulates a minimum surcharge of 10 kPa to be imposed behind all retaining walls. and that for SLS the same mobilisation factors should be used but that unplanned excavation should be omitted from the calculations. they are being modified in a forthcoming revision. The strength of an embedded wall must be sufficient to use its length. why factors of safety are needed and why their values should be judged so that further economies can gradually be achieved. the traditional application of a factor of safety to the passive earth pressure coefficient appeared to give unrealistically large depths of embedment. Large errors are likely to be spotted. not really relevant to embedded walls. are clear.2. slightly more severe than that of EC7. their full effect is difficult to quantify. to some extent associated with this. • Some structures do not have SLS requirements. It soon became clear that the design methods developed for sheet pile walls in sands were not necessarily applicable to much stiffer concrete walls in overconsolidated clays. A wall that was successful in limiting movements would then have to with-
ues which are more adverse than the most likely values”. “conservative values” are “val-
2. These two requirements. BS8002 results for the design example of Figure 12 are shown in Figure 13. taken together. a second check on the strength parameters is obtained by requiring “representative” values of two strengths of the soil: peak strength (c′p. The latter process requires very little additional effort on the part of the designer whilst providing the benefits of a double check. • The ULS design value of the shear strength should never be greater than a cautious (ie “characteristic”) estimate of the critical state strength of the material. there was a concern that the traditional application of a factor of safety to the passive earth pressure coefficient might in any case not be appropriate.1 General Perhaps the most significant developments in embedded retaining walls have been 1. as illustrated for two shear strength tests in Figure 18. avoiding step changes which might have unpredictable results. It is therefore unwise to derive length and strength from separate. Peak and critical state shear strengths. expressed here in the terminology of EC7: • The designer should check that the ULS design (factored) value of any parameter is never more optimistic than his assessment of the worst value which could credibly govern the field situation. An attempt to overcome some of the problems for reinforced concrete walls has been made by Beeby & Simpson (2001). have been found to be rather severe. an element of human error can often be identified. The calculated length is similar to EC7. sometimes (particularly for temporary works) in conjunction with the Observational Method of construction (Peck 1969a. but BS8002 leads to a high value for bending moment. unrelated calculations. and. and to some sheet pile walls. BS8002 recommends that structural forces and bending moments calculated using its mobilisation factors should be used both as SLS and ULS design values for structural design. either moderately conservative and worst credible. beyond strength mobilisation and physical uncertainties. the lateral stresses in the retained soil might not fall to the active limit with wall movements small enough to be acceptable under working conditions. including numerical methods. but errors of up to 50% may not be. tending “towards the limit of the credible range of values”. This leads to some practical difficulties: • It clearly means that SLS will generally govern structural design. For drained behaviour. The interface between geotechnical and structural design has been seen by designers as BS8002’s greatest weakness. and also may lead to an underestimate of prop forces. φ′crit). which enabled the construction of very stiff embedded walls in overconsolidated clay deposits. but the critical state requirement may govern when c′p is significantly large. Secondly. This effectively precludes methods which take advantage of stress redistribution. The critical state strength of a soil is the strength available at large shear
Figure 18.of he mass strength of the soil”. if displacement is not a critical criterion. especially in temporary works. tanφ′crit is very unlikely to be less than tanφ′p/1. This applies to structural failure of masonry structures. CIRIA 104 offers two alternative calculations whilst BS8002 requires that both peak and critical state values be considered in the process of deriving a single value for one calculation. BS8002 requires that the earth pressure distribution used for design will be of the simple form shown in Figure 1. 2. Although some of the effects of factors of safety. Reinforced concrete design to modern codes generally starts from ULS calculations with SLS as an additional check. First. or mobilisation factors. the introduction from the early 1960’s of diaphragm and bored pile installation techniques. In practice the ULS structural strength will inevitably exceed the demands of BS8002 by a further margin. owing to the high in situ lateral earth pressures associated with overconsolidated clays. Some uncertainties are appreciated at the time of design and others are not known. It was thought that.
strains when any dilation has ceased. The design values must not exceed the representative critical state strength of the soil. mainly because it has no provision for redistribution of earth pressures. 3 RECENT DEVELOPMENTS IN UNDERSTANDING 3. so it is inconvenient to have a design governed by SLS requirements. or peak and critical state. This is a valuable process because it reminds the designer to consider explicitly the range of variability of the material and how its available strength could change in response to deformation. especially for small retaining walls. the development of novel and more economical temporary and permanent support systems. Nicholson et al 1999). but investigations often also reveal that many successful structures had errors in their designs or construction which did not cause failure because there were sufficient margins of safety. In practice. When failures occur. For embedded walls.7 Some recommendations Both CIRIA 104 and BS8002 suggest that the designer consider two different values. φ′p) and critical state strength (c′=0. The present authors recommend that two checks should always be made. This gives an additional reason. with different factors applied to the different values in design calculations. The possibility of unplanned excavation must be considered very carefully by designers and possibly as a code specification.
Common methods of representing an earth berm in a limitequilibrium analysis are • as an equivalent surcharge (Padfield & Mair 1984.e. and • by carrying out a single (NAVFAC Design Manual 7. unloading from high horizontal stresses. there may still be upward movement. • The raised effective formation level approach is conservative but less so. who showed that the application of a factor of safety to the passive earth pressure coefficient Fp=2 is unduly conservative (in comparison with a uniform factor of safety on soil strength) at values of φ' less than about 27° . The maximum slope S will be governed by soil and groundwater conditions. Fleming et al 1992). the factor of safety is increased significantly if a larger berm is used. In given ground conditions. giving factors of safety between 15% and 25% less than the multiple Coulomb wedge analysis for the berm/wall geometries
investigated. Similar results were reported from a non-linear model with high stiffness at small strain and more normal water pressures by Simpson (1992).2 Berms Berms have been used to help stabilise embedded retaining walls for decades (Peck 1969b). the bench width B and the slope S (Figure 19). The difficulty of analysis may explain why berms have often been used in conjunction with the Observational Method (Tse & Nicholson 1993. The degree of
conservatism increases with decreasing embedment depth. The degree of conservatism increases with in-
creasing berm size and decreasing embedment depth. • For a berm of a given geometry. while if the berm is removed in sections along its length to allow permanent supports to be installed.stand bending moments much greater than those based on fully active conditions in the retained soil. • The equivalent surcharge method is highly conservative.i. Powrie & Daly and Daly & Powrie (submitted) describe the results of a series of plane strain centrifuge model tests of embedded cantilever retaining walls of various embedment depths supported by berms of different sizes. Gourvenec et al 1997). • by means of a raised effective formation level (Fleming et al 1992: Figure 20). However. values typical of clays (Figure 4). They also analyse the model tests using each of the three limit equilibrium methods outlined above. the drainage conditions assumed in design and the length of time for which the berm is required to remain effective will be important. who also showed that a substantial drop in bending moments could occur if the stiffness of the wall is modelled for a cracked concrete section. increasing the size of the berm is more effective in enhancing wall stability than increasing the depth of embedment of a wall supported by a smaller berm. In soils of low permeability. 3. Finite element analyses carried out by Potts & Fourie (1984) appeared to show that an embedded wall in an overconsolidated clay deposit could indeed suffer bending moments much larger than those associated with fully active conditions in the retained soil. Definition of berm geometry.
Figure 20. will move more rapidly towards the active condition than some of the analyses suggest (Powrie et al 1998). while H and B may be limited by considerations of space and access. giving factors of safety between 5% and 11% less than the multiple Coulomb wedge analysis. These analyses neglected both the stress relief and recent stress history resulting from wall installation. • For a wall of given embedment. with the following results. The first of these was addressed by Burland et al (1981). Their analyses were carried out with using a linear / MohrCoulomb model and with zero pore water pressures. so that soil/wall friction in this zone may not act upward on the wall as usually assumed in passive conditions – at least in the working state. a three dimensional analysis may be required to assess stability. • The berm prevents swelling of the soil immediately in front of the wall below formation level.
. the mobilisation factor shows no significant increase as the depth of embedment of the wall is increased.02 1986) or multiple (Figure 21) Coulomb wedge analysis. Consideration of more recent analyses and field data suggests that the lateral earth pressure coefficient might be expected to fall by about 10% to 20% as a result of wall installation. Representation of a berm by raising the effective formation level. Powrie et al 1993. the degree of support offered by a berm will depend on the height H. and beneficial wall fric-
Figure 19. Indeed. It is possible that the soil behind the wall. but is less sensitive to berm size. Most methods of representing the effect of a berm in a limit equilibrium analysis are semiempirical even if conditions on site approximate to plane strain.
Perhaps the main shortcoming of the analyses described above is that they refer to conditions of plane strain. Check on berm effect using multiple Coulomb wedges. followed by excavation (30 days) and propping (1 day) of each of the other two 5m bays in turn.e. Easton et al (1999) deduced a relationship between berm height and the equivalent uniform increase in formation level in front of the wall to give the same maximum wall movement (Figure 24). Along the wall.e. the berm was divided into three central bays 5m in length and two outer bays each 30 m in length. when several sections along the berm are removed simultaneously. (The data points and solid lines represent confirmed findings. β =25 to 50%). for a given wall/berm geometry. In practical terms. β = B/(B+B'). It can be seen in Figure 22 that • if the degree of discontinuity β of a berm supported wall is less than its critical value βcrit. the sections removed should be separated by a section of intact berm between one and three times as long as the section removed (i.e. they assume that the berm remains intact over the entire length of the wall throughout the excavation and construction period. Normalised wall crest displacement at the center of the unsupported section against degree of discontinuity β for different excavated bay lengths B. the results showed that • removal of a section of an earth berm will result in localised displacements in the vicinity of the unsupported section of the wall. The analysis involved excavation of the berm from the central bay over a period of 30 days and placement of a formation level prop slab (1 day).g. the length of the unsupported bays should be as small as possible. a formation level prop) can be installed. In reality. This is because the maximum wall movement (at the centre of the unsupported section) begins to increase with β above β=25%. displacements increase linearly with the length of the unsupported sections. ground conditions and time period there is a critical degree of berm discontinuity β (=B/(B+B')) that is independent of the length of the unsupported section B.
Figure 22. in the case of a road cutting. • wall movements during removal of a berm in sections can be minimised by reducing the width of the sections removed. if the passive wedge starts to move. In general terms. and • a number of sections can be removed simultaneously without increasing wall movements. Gourvenec & Powrie (2000) carried out a series of three dimensional finite element analyses to investigate the effect on wall movements of the removal of sections of an earth berm supporting an embedded retaining wall in overconsolidated clay. and
Figure 21. and the minimum wall movement (at the centre of the supported section) increases with β when β>50%. the magnitude and extent of which increase with the length of the berm section removed and with time following excavation.
tion. it will usually be necessary to remove the berm in sections so that the permanent support (e. The analyses were carried out for soil strength parameters φ’ = 22° (c’ = 0 and 20 kPa) and φ’ = 28° (c’ = 0 and 10 kPa). as long as successive unsupported sections are separated by a sufficient length of intact berm. as may well occur with construction of a long retaining wall in bays. • if β exceeds its critical value then displacements become a function not only of the length of the unsupported section but
• as β is increased above its critical value displacements increase more rapidly with continued increases in β. In other words. and finally the two outer (30m) bays together (30 days in total). with berms of different height within the profile envelope indicated. at the onset of collapse. Easton et al (1999) carried out three dimensional finite element analyses of a berm supported retaining wall having the cross sectional geometry shown in Figure 23. and the broken lines conjecture. the degree of discontinuity β may be defined by the ratio of the excavated length to the total length i.also of the degree of discontinuity. For a wall along which bays of length B are excavated simultaneously at regular intervals separated by sections of intact berm of length B'. • If minimisation of wall movements is critical. i. Then.)
. as the additional wall movement (compared with the case of an intact berm) increases in proportion to the length of berm section removed. By carrying out comparative analyses in which excavation and propping took place with a uniform dredge level in each bay.
Temperature-induced axial loads may account for a significant proportion of the total load carried by a prop installed at a low temperature. Anchors can be prestressed. it is quite possible that this approach may have overestimated the pore water pressures (if long term equilibrium conditions had not yet been achieved) and underestimated the lateral effective stresses. Low-level props might be restrained with an effectiveness of perhaps 65%.) A flexibility number quantifying the relative importance of wall deflexions due to bending and rigid body rotation (Figure 7) may then be identified as (γ/G*) ÷ (γH4/EI) = G*H4/EI. Clough et al (1989) defined a sys-
In all cases. In this respect they are unlike the passive deadman anchors investigated by Rowe. Prop temperatures were also measured. the coefficient of thermal expansion of the prop. 2.Figure 24. giving the advantage of an open site unimpeded by props. temporary prop loads similar to those measured in the field (neglecting temperature effects) were calculated using limit equilibrium and finite element analysis. but this is partly a result of the overall berm envelope adopted in this case. 3. reinforced concrete walls at Canada Water and Canary Wharf. the overprediction of prop loads seemed to be the result of a consistently conservative set of design assumptions rather than any flaw in the underlying soil mechanics principles. φ’=22°. In the absence of non-uniformities due to a lack of fit at the ends of a prop. in which the opportunity for rigid body rotation may be limited.
For the stiff. However. and the degree of end restraint provided by the wall and the soil behind it. Powrie & Batten (2000) and Batten & Powrie (2000) investigated this with reference to field data and analyses of the temporary prop loads developed during the construction of the London Underground Jubilee Line Extension stations at Canada Water and Canary Wharf. the key factors were the effect of wall installation and the timescale of excess pore water pressure dissipation in low permeability strata. increasing the berm height above about 5 m has little effect.5 Wall flexibility In general terms. realistic prop loads were calculated on the basis of fully-active conditions in the retained soil and pore water pressures in equilibrium with the prevailing groundwater regime. For props near the crest of a stiff wall. bending moments due to wall rotation and/or temperature gradients across the prop of the same order as those due to self-weight effects must be expected. This might be viewed as analogous to Rowe’s dimensionless group mρ. while bending deformation depends on γH4/EI.
Figure 23. For multi-propped walls. The provision of temporary props is costly in terms of money. a lack of fit between the walings and the ends of a prop could increase secondary bending effects substantially . in order to reduce wall and ground movements. Hence the prestress can be used to dictate the distribution of earth pressures on the wall.a point which may need to be considered in design. Wall/berm cross sectional geometry investigated by Easton et al (1999). Although in design a margin of safety is essential to allow for events such as the accidental removal of a prop. In finite element analyses. to assess their influence on prop loads. However. both under working conditions and at collapse. the results presented by Powrie & Batten (2000) and Batten & Powrie (2000) suggest the following 1. 3. (G* is the rate of increase of shear modulus G with depth. In limit equilibrium analyses.4 Grouted anchors Grouted and proprietary ground anchors can also be used as temporary supports. time and risk to the site operatives involved in installing and removing them.
. Relationships between berm height and equivalent uniform increase in formation level. In general terms.3 Temporary props Embedded walls retaining the sides of large excavations are often supported at some stage in the construction process by temporary props at one or more levels. provided that appropriate soil parameters and input assumptions were used. 3. unaffected by wall displacement. the degree of end restraint could be of the order of 50%. and because they are usually fairly extensible they give a relatively constant force. The advantages of reducing the number of temporary props and/or eliminating some levels of propping in a large excavation are therefore considerable Until the mid-1990’s. it may be shown that on excavation in front of an embedded wall in a soil of unit weight γ. Temperature-induced loads can be estimated from the anticipated temperature rise. rigid body rotation is governed by γ/G*. 3. but the range of temperature experienced by a prop may reduce with depth within the excavation. there was a widely-held view within the construction industry that the procedures used in design tended to overestimate actual prop loads.
for a given factor of safety against basal heave. rather than increasing to values > 1 after the end of construction. Although performing hand calculations may be good for developing understanding. Figure 16 shows an extreme example in which the wall is on the point of
Figure 25. FREW works within the upper bound approach. computed by finite element runs each with 100 load cases. with no interaction between them. the redistribution of earth pressure to the prop is apparent. Addenbrooke et al (2000) defined a further measure of wall flexibility. Additional evidence against the long-term re-establishment of in situ lateral stresses comes from Page (1995).
failure. for example due to creep. particularly in evaluation of the needed coefficient of subgrade reaction which is not a material parameter and so cannot be related simply to soil test results or theories of deformation behaviour. use and speed of calculation of FREW are very similar to a subgrade reaction program. a best fit linear increase is first found. which is then adjusted in accordance with an energy-based formulation published by Pappin et al (1986). However. Details of the centrifuge model were broadly as given by Powrie & Kantartzi (1996). but without the assumption of linear increase of limiting earth pressure with depth. have been inverted to give stiffness matrices and pre-stored. with the earth pressures at the interface with the wall limited by active and passive considerations. This is a particular problem in stiff clays. 4. for a given initial stress regime and prop stiffness. based on finite element analyses. they showed that. This seems unlikely: provided that the soil can sustain shear stresses. described further belowfull finite element analyses. Proportionate addition of the two matrices has been shown by comparison with finite element analysis to give a good approximation to the stiffness matrix of ground with any linear increase of stiffness with depth. but is just satisfying EC7 Case C. Page carried out plane strain centrifuge model tests using overconsolidated speswhite kaolin clay. FREW represents a linear elastic continuum. They then produced a design chart. it is very tedious and prone to error in all but the simplest examples. h is the distance between supports. it is quite possible for the lateral stress some distance away from the wall to differ from the lateral stress acting on the wall itself – provided of course that the condition of horizontal equilibrium is satisfied. they rely heavily on precedent and experience.e. which relate to changes of stress over short distances potentially causing local failures within the soil mass. so a return to in situ values would involve very high final earth pressures. The overall width of the model was 55 m at field scale. discussed earlier. the input. it is likely that the coefficient of earth pressure will tend towards unity. as described by Pappin et al. To model the elastic continuum. Many walls are designed quite
adequately using software as in (b).rather than straincontrolled). Subgrade reaction methods may also assist in the understanding of earth pressure distribution and are generally found to give bending moment results similar to more advanced finite element models. which may extend into 3D analysis. more detailed constraints on the earth pressure distribution. in which the stress changes associated with the excavation of a diaphragm wall trench under bentonite slurry and subsequent concreting were simulated.
. whereas subgrade reaction represents the ground as a set of individual springs. The elastic continuum redistributes earth pressures in a fairly realistic manner and the limits on earth pressure ensure that the degree of redistribution is comfortably within the strength capacity of the ground. except that at the opposite end of the centrifuge strongbox from the trench the initial in situ lateral stresses were maintained (i. some of the available theo-
ries about redistribution of earth pressures (eg as shown in Figures 10 and 11) improve the economy of design by these methods.tem stiffness EI/γwhav4. Reading and Malden generally indicate a slight reduction in the measured lateral stresses near the wall over an eight year period following construction (Carder & Darley 1998). 3. To the user. while Figure 26 shows the earth pressure distribution computed by FREW for EC7 Case C in Figure 13. One of these represents ground with constant stiffness with depth. and hence ground movements. Total lateral stress transducers installed in the soil near the trench measured no tendency for the reinstatement of the in situ lateral stresses following hardening of the model diaphragm wall and the establishment of long term equilibrium pore water pressures. 4 ANALYTICAL METHODS Analytical methods which are used in the design of embedded retaining walls may be divided into five types: a) hand calculations. this boundary was stress. which they termed the displacement flexibility number Δ = EI/h5. such as SPOOKS c) subgrade reaction analyses such as MSHEET or WALLAP d) pseudo finite elements such as FREW. However. For irregularly varying stiffness. There are however other. where the in situ Ko is greater than unity. to relate the system stiffness to maximum lateral wall displacements. two flexibility matrices. support systems with the same flexibility number will result in practically the same maximum wall deflection and ground displacement profile. which has units of kN/m4 in plane strain (i. In both cases. and the other with linearly increasing stiffness from zero at the surface. Hackney. finding equilibrium between active and passive pressures b) software which replicates (a) and may have rules or theories about how the active pressures are redistributed for propped walls. By means of an extensive series of finite element analyses of undrained excavations in stiff clay.e. Long-term measurements behind embedded walls retaining London Clay at Walthamstow. Comparison of subgrade reaction model and FREW. As with Clough et al (1989). with overall limits on active and passive forces.6 Long-term lateral stresses Designers are sometimes concerned about the possibility of the in situ lateral stresses becoming re-established against the wall. if the soil tends to creep so that in the long term shear stresses reduce. with EI in kNm2/m). where γw is the unit weight of water and hav is the average distance between the supports. However.1 FREW The set-up of a subgrade reaction program is compared with that of FREW in Figure 25. FREW is used for both SLS and ULS checks.
the friction on the wall having a significant moment about its neutral axis. On this and other projects it has been found that although the Brick model gives a good match to the best available small strain laboratory tests it tends to over-estimate displacements measured in full scale constructions in stiff clay. used to allow access for the diaphragm walling. They can also be used powerfully to provide insights into details of the problem. as shown in Figure 29. especially for 3D work. The finite element analysis allows for this. Finite element methods offer the opportunity to model the stress-strain properties of the ground as accu
Figure 28. showing computed bending moment diagrams for a double skin sheet pile cofferdam and the permanent diaphragm walls.
The contours on Figure 29 show the computed piezometric levels and the arrows indicate computed displacement. with arches spanning between them in plan. A finite element study was carried out when the project was built to determine likely wall movements. of a strutted excavation. which generally acts in a beneficial manner. This example used the Brick model developed for analysis of excavations in stiff clay and published by Simpson (1992). Figure 27 is a cross section through both temporary and permanent works for a deep station box. with a piled wall between.2 Finite element and finite difference programs Finite element and finite difference programs make it possible to study the “complete” problem. with the behaviour of the wall itself as a secondary consideration. Nevertheless. Figure 28 shows an embedded wall consisting of concrete barrettes placed normal to the line of the wall. that “plane sections do not remain plane” as assumed in ordinary beam analysis. It is evident from the earlier sections of this paper that the behaviour of embedded walls in service is complex and depends critically on the non-linear stress-strain properties of the ground. one of the advantages of such analysis is the possibility of involving both the wall and other connected structure in a complete interaction analysis. The reasons for this require further inves
Figure 26. Some of the embedded walls in this project were T-section diaphragm walls. 4. Barrette wall with shotcrete arches. The lack of adequate models. and more recently time-dependent analy-
Figure 27. particularly of the small strain stiffness of undisturbed natural clays.Simpson (1994) noted that omitting to check vertical equilib-
ses have been performed to check likely long term movement. water pressures on the back of the wall are permanently relieved by drainage. may partly explain why relatively few analyses have been published. and that vertical shear forces between soil and wall help to restrict displacement. such as the construction of a diaphragm wall panel. formed of sprayed concrete.
. The emphasis in numerical analyses has often been on computation of ground movements. EC7 Case C calculation in FREW. Interaction analysis between four embedded walls. for example.
rium is often a cause of wall failure. however. These effects are not considered by either subgrade reaction programs or FREW. as discussed above.
tigation. in 2 or 3 dimensions. overall. They are automatically included in finite element analyses. In this project. and also of the structure. which are sufficiently thick.
which is to have a particular emphasis on improving economy in design. Taipei. then factoring these. The first of these approaches is based on carrying out calculations using characteristic values of loads and material properties. shown in plan in Figure 30. have been in 2D. etc. This was the essential problem with the net pressure method described above. it was shown that a soft clay of similar marine origin could be modelled using essentially the same parameters. but in the absence of these. on long sides of the excavation. 5 THE FUTURE Developments in the foreseeable future may be considered in two groups: (a) developments of codes and standards. numerical analyses have been used to study details of behaviour. This often requires considerable approximation. The problems might be overcome by introducing additional rules. Thus. externally to the Eurocode. The ground conditions involved were principally firm clays.
velopment of Brick was that it should be able to cover as wide a range of soil behaviour as possible. as opposed to details. while action effects would be computed bending moments. after Ou et al (1996). In this context resistances are quantities such as bearing capacity or passive force or earth pressure. displacements and piezometric levels. the major changes from the ENV (ie EC7 1995) to EN version of Eurocode 7 will be (a) a less prescriptive approach to overdig (BS8002 plans a similar change). which is scheduled for publication in 2002 and will be discussed further here. both their 3D analysis and their method of correcting 2D results worked well. the practice of calculating characteristic action effects. EN1997-1.1 Codes and standards In general. Section through barrette wall. Safety factors are then applied at a later stage in the process to action effects. EAB-100. to provide alternative approaches to that of the ENV. mainly because the walls near the corners of the excavation were computed to be less heavily loaded. is considered to be problematic. as opposed to actions. They concluded that steel quantities could be reduced by about 25% overall for the project they studied. In relation to embedded walls. given the pre-consolidation pressure (Simpson 1992). it was found that a 2D analysis gave very close agreement with field measurements. Lee et al (1998) also compared results at midsides and near corners of a basement. introducing the use of infinite elements in order to reduce computing demands. formed in diaphragm walls. I2 and I3.
rately as knowledge allows. or to predict the behaviour of complete structures. Plan of the Hai-Hua building. particularly since the stiffness of ground is usually very non-linear. 5. though this method has not been proposed for use with Eurocode. and it is difficult to use field measurements to improve predictions when the effect of the geometric approximation may be large. Most finite element analyses carried out to date of complete constructions. To date. Simic & French (1998) used a 3D analysis of an underground station box.
for 3D work. and resistances. It is hoped that they may be used further in future to help resolve some of the outstanding issues in the codes which where discussed above. prop forces. in which a sheet pile retaining wall is required. and parameters were developed for a Duncan and Chang model. Forthcoming documents include an English translation and revision of the German Recommendations of the Committee for Excavations. For many situations factors can be tuned to give similar results wherever they are applied in the calculation procedure. and a full 3D analysis of the complete excavation was not undertaken. showing that the relative difference depended on features such as the stiffness of propping systems and the depth below the excavation to relatively rigid strata. Here. which are still significant
Figure 30. the situation shown in Figure 31. much of which has been available for some time. so one of the principles adopted in de-
sults. Owing to the limitations of computing power. The paper concentrates on displacements. and the formal “EN” version of Eurocode 7 Part 1.Figure 29. and (b) derivation of new technical information. Ou & Shiau (1998) extend this work. they investigated carefully the effects of mesh gradation and also developed correlations between 2D and 3D re-
. At inclinometer positions I1. Ou et al (1996) report a study related to the excavation for the Hai-Hua building. A wide range of stress states often results from an analysis. to seek savings in reinforcement when comparing results with plane strain analysis. Some interesting 3D examples from recent publications are noted here. This results in a useful development of understanding of the likely significance of 3D effects. and (b) the introduction of two further sets of partial factors. as opposed to material strengths. but the 3D effects were important at inclinometers I4 and I5. showing drains. although it was initially developed for stiff London Clay. the development of codes and standards is based on reconsideration of existing information. can lead to unsafe situations in some cases. However. a replacement for Report 104 of the UK Construction Industry Research and Information Association.
factors applied to the action effects.9m will be sufficient provided the tie has a design resistance of 75 kN/m. as shown in Figure 34.35 0
The second alternative approach to be included in EN1997-1 essentially has the ENV factors of Cases B and C used in combination. then applies a factor to it. such as the tie force in this case. the ENV approach would give a length of 14m for a cantilever.29 5.93
B-2CC
11. come too late in the calculation. Relevant calculations are summarised in Table 3. For economy.29 5.0 35
2 ⁄3 -1 0. Now suppose that. for reasons external to the design calculations. a cantilever wall could proFigure 31.6m. It is important to place the factors near the source of the uncertainty they represent.6m was sufficient to give equilibrium as a cantilever using unfactored characteristic soil properties.0.3
2 ⁄3 -1 0. vide equilibrium with a length of 11. Situation for which a retaining wall is required.4 75
Characteristic state 17 35 1. The design requirements now are to check that the wall is sufficiently stable with a tie at 1m depth. the designer wants to adopt the minimum allowable design tie force.56
bedded retaining walls are still poorly understood.86
B-2CP
11. characteristic state.Using unfactored soil strengths. and to find the required design resistance for the tie. it is decided that the length of the wall will be 12m and further safety is to be provided by an anchor acting at 1m from the top of the sheet pile as shown in Figure 31. as shown in Figure 32. Since a wall length of 11. any system of factoring would indicate that it requires a longer length to work safely as a cantilever.2 New technical information This paper has noted that many features of the behaviour of em-
Case C without anchor 17 35 1.
Figure 33. Tied retaining wall: ENV approach. so Case C determines the design. Table 3.25 29.22 8. for both
Figure 32. For example.
γ kN/m3 φ′k ° γφ φ′d ° δ/φ′ active δ/φ′ passive Kad Kpd Design anchor force kN/m Length m
2 ⁄3 -1 0. However. Summary of calculations for tied retaining wall. This will inevitably lead to more conservative design.
5. as shown in Figure 33. Hence an approach which calculates this characteristic action effect.25 29. Tied retaining wall. This could occur because sheet piles of 12m length are readily available. or possibly because the sheet pile wall is already in place when the required depth of excavation in front of it becomes known.4 -
Case C with anchor 17 35 1. The calculation for Case B is less severe. Calculations to Case C confirm that a length of 11. will require a minimum design tie force of 0. the minimum tie force calculated for a 12m length using characteristic properties is 0. Cantilever: ENV approach.
Many design guides and codes have been drafted. The application of factors of safety is also still in dispute. Hence in a collapse analysis it is appropriate to allow for arching. (b) results of field monitoring. It is important that codes convey to designers what degree of conservatism they are to adopt in assessing parameter values. Some recent work on these topics has been summarised. Modern techniques. Both of these sources inform designers about likely modes of behaviour and may help to rule out some of the more unlikely suggestions. or sets of partial factors. Potts. Also. e. 3D analyses are also viable in the design of more major structures.
. seems to be encouraging more monitoring because clients see a direct benefit from the measurements taken. This paper has argued that safety factors can most generally and most usefully be applied to soil strength. The use of data loggers to obtain continuous records of prop loads. 2000. physical models and especially field monitoring will clarify the issues that remain and so enable design procedures to be unified on a more widely accepted basis of understanding. As collapse approaches. The use of a “double check” on a parameter value provides extra assurance with negligible extra effort on the part of the designer. especially using the centrifuge. in a matter of minutes. narrowing down the options to be considered both in design and code drafting. & Dabee. a renewed interest in the Observational Method. rather than to passive resistance. three dimensional numerical analysis can be used to investigate in general terms three dimensional effects. 6 CONCLUDING REMARKS Embedded retaining walls have had increasing use through the twentieth century. To date.working states and collapse states.b). Nevertheless. give an opportunity to re-visit some of this work and perhaps to resolve more of the outstanding questions. Much was learnt from the laboratory modelling of Terzaghi. and earth/pore water pressures is improving our knowledge of construction sequence and transient effects on the overall performance of retaining walls. Tschebotarioff. They must also provide a margin for minor errors. and it was also possible to obtain some information on earth pressures and structural effects. or structural load effects such as bending moments and prop forces. rotational moments. Several of the newer codes of practice or design guides allow some reduction of bending moment related to redistribution. It is hoped that further investigation.
REFERENCES Addenbrooke. It is vital to renew momentum in this monitoring process if knowledge is to develop. New technical information can be expected from three main sources: (a) better numerical analysis. whether due to rotation or bending failure. Bolton et al (1990a. which tend to displace under load. Increasing computing power now makes it possible to carry out 2D analyses. the approach of Eurocode 7 ENV1997-1. Modern techniques could be
performance and design requirements. any form of support which does not itself fail is effectively rigid compared to the collapsing wall. and details such as temperature effects on struts and behaviour of berms. The question of redistribution is also related to the choice between design based on analysis of working or collapse states. 718-726. and (c) new modelling data. however. in which two “cases”. Whatever procedures are used for basic design calculations. Stiff props displace much less. which are inevitable both in design and construction. possibly from centrifuge testing. and research and debate have improved understanding of both
tinues. New techniques such as use of optical fibres and possibly satellite positioning should add to the possibilities of accurate measurement achieved economically. but take a little longer and require a greater degree of expertise. Rowe and others including. Once quantified. J ASCE Geotechnical and Geoenvironmental Engineering. In general terms. It is noted in this paper that some of the early dispute about this related to deadman anchors. due to excavation or prop removal in bays or sections along a retaining wall or corners in near-square excavations. and particularly in the period 1960 to 1990. the ground movements associated with them. field monitoring added greatly to knowledge of ground movements associated with retaining structures. it remains essential for the designer of embedded walls to understand their behaviour. In the UK. D. more recently. whilst prestressed anchors give guaranteed forces which can largely dictate the equilibrium earth pressure distribution. The redistribution of earth pressures caused by wall flexure has been particularly contentious and still merits further research. the significance of construction sequence and procedures. Direct measurement of earth pressures remains problematic. including the publication of a CIRIA report by Nicholson et al (1999). with large concrete walls becoming very important to the development of deep basements and underground infrastructure.M. three dimensional effects can be used with more confidence to achieve an economic construction sequence and overall structure. B. including some degree of arching whereby active pressures are reduced between stiff support points. are analysed. using relatively sophisticated soil models. T. Displacement flexibility number for multipropped retaining wall design. The factors allow for uncertainties in soil properties and a necessary limitation on the degree to which soil strength is mobilised in the working state.g.I. Hence allowance for a degree of arching seems appropriate to these more modern forms of wall support. debate con-
used with advantage to revisit some of these problems. August. is preferred. using advanced numerical analysis.
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Simpson_powrie_2001 Embded Retaining Wall Arup by Magdy Bakry29 viewsEmbedDownloadDescriptiondetailed analysis of embedded bored piles and sheet piles retaining wallsdetailed analysis of embedded bored piles and sheet piles retaining walls Read on Scribd mobile: iPhone, iPad and Android.Copyright: © All Rights ReservedList price: $0.00Download as PDF, TXT or read online from ScribdFlag for inappropriate contentShow moreShow less
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