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# Craig's Soil Mechanics 7th Edition

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shear strength parameters. In Case C, the active thrust and passive resistance due to the self-weight of the soil are permanent unfavourable and favourable actions, respectively, for both of which the partial factor is 1.00. The active thrust due to surface surcharge loading is normally a variable unfavourable action and should be multiplied by a partial factor of 1.30. In the current UK code of practice for earth-retaining structures, BS 8002: 1994 [5] (which will be superseded by EC7), it is simply stated that design loads (including unit weight), derived by factoring or otherwise, are intended to be the most pessimistic or unfavourable values. The factors applied to shear strength are referred to in BS 8002 as mobilization factors, minimum values of 1.20 and 1.50 (with respect to maximum strength) being specified for drained and undrained conditions, respectively, the same factor being applied to both components of shear strength in the drained case. These values are intended to ensure that both ultimate and serviceability limit states are 186 Lateral earth pressure satisfied; in particular, except for loose soils, their use should ensure that wall dis- placement is unlikely to exceed 0.5% of wall height. In determining characteristic values of shear strength parameters consideration should be given to the possibility of variations in soil conditions and to the quality of construction likely to be achieved. According to BS 8002, the shear strength used in design should be the lesser of: 1 the value mobilized at a strain which satisfies serviceability limit states, represented by the maximum (peak) strength divided by an appropriate mobilization factor; 2 the value which would be mobilized at collapse after large strain has taken place, represented by the critical-state strength. The use of the value specified above is intended to ensure that conservative values of active pressure and passive resistance are used in design. Thus, under working condi- tions (at a deformation governed by the serviceability limit state), the active pressure is greater than, and the passive resistance less than, the respective values at maximum shear strength. If collapse were to occur (an ultimate limit state), the shear strength would approach the critical-state value: consequently, the active pressure would again be greater than, and the passive resistance less than, the corresponding values at maximum shear strength. However, Puller and Lee [20] have questioned the applica- tion of a constant mobilization factor because lateral wall movement is not constant with depth, especially in the case of flexible walls. Also, in the case of layered soils, peak strength is attained at different strains in different soil types. The design value of the angle of wall friction (�) depends on the type of soil and the wall material. In BS 8002 it is recommended that the design value of � should be the lesser of the characteristic value determined by test and tan�1 (0:75 tan�0), where �0 is the design value of angle of shearing resistance. Similarly, in total stress analysis, the design value of wall adhesion (cw) should be the lesser of the characteristic test value and 0.75cu, where cu is the design value of undrained shear strength. However, for steel sheet piling in clay, the value of cw may be close to zero immediately after driving but should increase with time. 6.6 GRAVITY WALLS The stability of gravity (or freestanding) walls is due to the self-weight of the wall, perhaps aided by passive resistance developed in front of the toe. The traditional gravity wall (Figure 6.18(a)), constructed of masonry or mass concrete, is uneco- nomic because the material is used only for its dead weight. Reinforced concrete cantilever walls (Figure 6.18(b)) are more economic because the backfill itself, acting on the base, is employed to provide most of the required dead weight. Other types of gravity structure include gabion and crib walls (Figures 6.18(c) and (d)). Gabions are cages of steel mesh, rectangular in plan and elevation, filled with particles generally of cobble size, the units being used as the building blocks of a gravity structure. Cribs are open structures assembled from precast concrete or timber members and enclosing coarse-grained fill, the structure and fill acting as a composite unit to form a gravity wall. Gravity walls 187 Limit states which must be considered in wall design are as follows: 1 Overturning of the wall due to instability of the retained soil mass. 2 Base pressure must not exceed the ultimate bearing capacity of the supporting soil (Section 8.2), the maximum base pressure occurring at the toe of the wall because of the eccentricity and inclination of the resultant load. 3 Sliding between the base of the wall and the underlying soil. 4 The development of a deep slip surface which envelops the structure as a whole (analysed using the methods described in Chapter 9). 5 Soil and wall deformations which cause adverse effects on the wall itself or on adjacent structures and services. 6 Adverse seepage effects, internal erosion or leakage through the wall: con- sideration should be given to the consequences of the failure of drainage systems to operate as intended. 7 Structural failure of any element of the wall or combined soil/structure failure. The first step in design is to determine all the forces on the wall, from which the horizontal and vertical components, H and V, respectively, of the resultant force (R) acting on the base of the wall are obtained. Soil and water levels should represent the most unfavourable conditions conceivable in practice. Allowance must be made for the Figure 6.18 Retaining structures. 188 Lateral earth pressure possibility of future (planned or unplanned) excavation in front of the wall, a minimum depth of 0.5m being recommended: accordingly, passive resistance in front of the wall is normally neglected. For design purposes it is recommended that a minimum surcharge pressure of 10kN/m2 should be assumed to act on the soil surface behind the wall. In the case of cantilever walls (Figure 6.18(b)), the vertical plane through the heel is taken to be the virtual wall surface. No shear stresses act on this surface, i.e. � ¼ 0; therefore the Rankine value of Ka is appropriate. Surcharge pressure in front of the virtual back of a cantilever wall is a variable favourable action and should be neglected. The position of the base resultant (Figure 6.18(e)) is determined by dividing the algebraic sum of the moments of all forces about any point on the base by the vertical component V. To ensure that base pressure remains compressive over the entire base width, the resultant must act within the middle third of the base, i.e. the eccentricity (e) must not exceed 1⁄6B, where B is the width of the base. If pressure is compressive over the entire width of the base, there will be no possibility of the wall overturning. However, the stability of the wall can be verified by ensuring that the total resisting moment about the toe exceeds the total overturning moment. If a linear distribution of pressure (p) is assumed under the base, themaximum andminimumbase pressures can be calculated from the following expression (analogous to that for combined bending and direct stress): p ¼ V B 1� 6e B � � ð6:27Þ The sliding resistance between the base and the soil is given by S ¼ V tan � ð6:28Þ where � is the angle of friction between the base and the underlying soil. Ignoring passive resistance in front of the wall, the sliding limit state will be satisfied if S � H If necessary, the resistance against sliding can be increased by incorporating a shear key in the base. In the traditional method of design, the ratio S/H represents the lumped factor of safety against sliding, the serviceability limit state being satisfied by an adequate