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# Craig's Soil Mechanics 7th Edition

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between values of the factors Fs and Fp over the practical ranges of wall geometry and shear strength parameters, particularly in the case of clays. Burland et al. proposed that the factor of safety should be based on net passive resistance on the basis of an analogy with the ultimate bearing capacity of a foundation. Guidance on the selection of suitable factors of safety for use in the above methods is given by Padfield and Mair [15]. Values of �m andM are given in EC7 and BS 8002, respectively. Either gross or net water pressures can be used in design (because, unlike earth pressures, no coefficient is involved), the latter being more convenient. To allow for over-excavation or dredging, the soil level in front of the wall should be reduced by 10% of the depth below the lowest tie or prop, subject to a maximum of 0.5m. Again, a minimum surcharge pressure of 10 kN/m2 should be assumed to act on the soil surface behind the wall. It should be realized that full passive resistance is only developed under conditions of limiting equilibrium, i.e. when the safety or mobilization factor is unity. Under working conditions, with a factor greater than unity, analytical and experimental work has indicated that the distribution of lateral pressure is likely to be of the form shown in Figure 6.24, with passive resistance being fully mobilized close to the lower surface. The extra depth of embedment required to provide adequate safety (whether measured by lumped or partial factors) results in a partial fixing moment at the lower end of the wall and, consequently, a lower maximum bending moment than the value under limiting equilibrium or collapse conditions. In view of the uncertainty regarding the pressure distributions under working conditions it is recommended that bending moments and tie or prop force under limiting equilibrium conditions (i.e. F ¼ 1) Figure 6.24 Anchored sheet pile wall: pressure distribution under working conditions. 198 Lateral earth pressure should be used in the structural design of the wall. The tie or prop force thus calculated should be increased by 25% to allow for possible redistribution of pressure due to arching (see below). Bending moments should be calculated on the same basis in the case of cantilever walls. In limit state design, Case B applies to the determination of maximum bending moment. Effect of flexibility and K0 The behaviour of an anchored wall is also influenced by its degree of flexibility or stiffness. In the case of flexible sheet pile walls, experimental and analytical results indicate that redistributions of lateral pressure take place. The pressures on the most yielding parts of the wall (between the tie and excavation level) are reduced and those on the relatively unyielding parts (in the vicinity of the tie and below excavation level) are increased with respect to the theoretical values, as illustrated in Figure 6.25. These redistributions of lateral pressure are the result of the phenomenon known as arching. No such redistributions take place in the case of stiff walls, such as concrete diaphragm walls. Arching was defined by Terzaghi [25] in the following way. ‘If one part of the support of a soil mass yields while the remainder stays in place, the soil adjoining the yielding part moves out of its original position between adjacent stationary soil masses. The relative movement within the soil is opposed by shearing resistance within the zone of contact between the yielding and stationary masses. Since the shearing resistance tends to keep the yielding mass in its original position, the pressure on the yielding part of the support is reduced and the pressure on the stationary parts is increased. This transfer of pressure from a yielding part to adjacent non-yielding parts of a soil mass is called the arching effect. Arching also occurs when one part of a support yields more than the adjacent parts.’ The conditions for arching are present in anchored sheet pile walls when they deflect. If yield of the anchor takes place, arching effects are reduced to an extent depending on the amount of yielding. On the passive side of the wall, the pressure is increased just below excavation level as a result of larger deflections into the soil. In the case of backfilled walls, arching is only partly effective until the fill is above tie level. Figure 6.25 Arching effects. Embedded walls 199 Arching effects are much greater in sands than in silts or clays and are greater in dense sands than in loose sands. Redistributions of earth pressure result in lower bending moments than those obtained from the free earth support method of analysis; the greater the flexibility of the wall, the greater the moment reduction. Rowe [21, 22] proposed the use of moment reduction coefficients, to be applied to the results of free earth support analyses, based on the flexibility of the wall. Wall flexibility is represented by the parameter � ¼ H4/EI (units m2/kN per m), where H is the overall height of the wall and EI the flexural rigidity. The tie force is also influenced by earth pressure redistribution and factors are also given for the adjustment of the free earth support value of this force. Details of Rowe’s procedure are given by Barden [2]. Rowe’s moment reduction factors should only be used if a factored passive resist- ance (F > 1) has been used for the calculation of bending moments. If bending moments have been calculated for the limiting equilibrium condition (F ¼ 1), Rowe’s factors should not be used. Potts and Fourie [18, 19] analysed a propped cantilever wall in clay by means of the finite element method, incorporating an elastic–perfectly plastic stress–strain relation- ship. The results indicated that the required depth of embedment was in agreement with the value obtained by the free earth support method. However, the results also showed that in general the behaviour of the wall depended on the wall stiffness (confirming Rowe’s earlier findings), the initial value of K0 (the coefficient of earth pressure at-rest) for the soil and the method of construction (i.e. backfilling or excavation). In particular, maximum bending moment and prop force increased as wall stiffness increased. For backfilled walls and for excavated walls in soils having a low K0 value (of the order of 0.5), both maximum bending moment and prop force were lower than those obtained using the free earth support method. However, for stiff walls, such as diaphragmwalls, formed by excavation in soils having a high K0 value (in the range 1–2), such as overconsolidated clays, both maximum bending moment and prop force were significantly higher than those obtained using the free earth support method. For the particular (excavated) wall and material properties considered by Potts and Fourie, the patterns of variation shown in Figure 6.26 were obtained for a factor of Figure 6.26 Analysis of propped cantilever wall in clay by the finite element method. (Repro- duced from D.M. Potts and A.B. Fourie (1985) Geotechnique, 35, No. 3, by permission of Thomas Telford Ltd.) 200 Lateral earth pressure safety (Fr) of 2.0. In this figure,Mfe and Tfe denote the maximum bending moment and prop force, respectively, obtained from the finite element analysis, and Mle and Tle denote the corresponding values obtained from a limiting equilibrium (free earth support) analysis. Pore water pressure distribution Sheet pile and diaphragm walls are normally analysed in terms of effective stress. Care is therefore required in deciding on the appropriate distribution of pore water pres- sure. Several different situations are illustrated in Figure 6.27. Figure 6.27 Various pore water pressure distributions. Embedded walls 201 If the water table levels are the same on both sides of the wall, the pore water pressure distributions will be hydrostatic and will balance (Figure