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73 Figure 7-9. Active failure plane angle based on M-O equation. 1. Calculate the active pressure PAE1 and active failure plane M-O method may be used, such as the well-known, graphical angle (AE1) for the backfill material. Graphs such as Fig- Culmann method illustrated in Figure 3-1. The principles of ures 7-8 and 7-9 may be used for simple cases. the Culmann wedge method have been incorporated in the 2. If AE1< 1/2, the solution stands and PAE1 gives the correct Caltrans' computer program CT-FLEX (Shamsabadi, 2006). seismic active pressure on the wall. This program will search for the critical failure surface corre- 3. If AE1 > 1/2, calculate the active pressure (PAE2) and active sponding to the maximum value of PAE for nonuniform slopes failure plane angle (AE2) for the native soil material. For and backfills, including surcharge pressures. cohesive (c-) soils, solutions described in Section 7.3 may For uniform cohesive backfill soils with c and strength be used. Also, calculate the active pressure (PAEi) for the parameters, solutions using M-O analysis assumptions have given interface between two soils from limit equilibrium been developed, as discussed in Section 7.3. However, the equations. The larger of PAEi and PAE2 gives the seismic ac- most versatile approach for complex backfill and cut slope tive pressure on the wall. geometries is to utilize conventional slope stability programs, as described in Section 7.4. In most cases, the native soil cut will be stable, in which case it will be clear that the active pressure corresponding 7.2.2 Seismic Passive Earth Pressures to the cut angle 1/2 will govern. For more complex cases in- volving nonuniform backslope profiles and backfill/cut slope The M-O equation for passive earth pressures also is shown soils, numerical procedures using the same principles of the in Figure 7-6. The seismic passive pressure becomes impor- tant for some wall types that develop resistance from loading of the embedded portion of the wall. If the depth of embed- ment is limited, as in the case of many gravity, semi-gravity, and MSE walls, the importance of the passive earth pressure to overall equilibrium is small, and therefore, using the static passive earth pressure is often acceptable. In the case of nongravity cantilever walls and anchored walls the structural members below the excavation depth depend on the passive earth pressure for stability and therefore the effects of seismic loading on passive earth pressures can be an important contribution. Work by Davies et al. (1986) shows that the seismic passive earth pressure can decrease by 25 per- cent relative to the static passive earth pressure for a seismic Figure 7-10. Application of M-O method for coefficient of 0.4. This decrease is for a = 35 degree material nonhomogeneous soil. and no backslope or wall friction.