ECE 2311_Stability of Slopes.pdf - ECE 2311 Soil Mechanics...

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ECE 2311: Soil Mechanics II Stability of Slopes i 7 STABILITY OF SLOPES .............................................................................................. 1 7.1 Vertical cut in a purely cohesive material ............................................................... 1 7.1.1 Lower-bound solution ..................................................................................... 2 7.1.2 Upper-bound solution ..................................................................................... 3 7.2 Stability of an infinite slope against translational slip ............................................. 4 7.2.1 Slope of dry soil ............................................................................................. 4 7.2.2 Slope of undrained clay - total stress analysis ................................................. 6 7.2.3 Slope under water - effective stress analysis .................................................... 7 7.2.4 Uniform flow parallel to slope - effective stress analysis ................................. 8 7.2.5 Uniform horizontal flow effective stress analysis ....................................... 10 7.3 Stability of slopes against circular slip .................................................................. 12 7.3.1 Undrained stability - total stress analysis ....................................................... 12 7.3.2 Drained stability - effective stress analysis .................................................... 15
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ECE 2311: Soil Mechanics II Stability of Slopes 1 7 STABILITY OF SLOPES Soils with sloping surfaces may be the result of natural processes or they may be man made. Gravitational and seepage forces tend to cause instability in those slopes. The most important types of slope failure are sketched in Fig. 7.1. Rotational slip occurs in homogeneous soils. The movement takes place along a curved surface (circular or non circular) in such a way that the moving mass slips down at the top of the slope and bulges up near the toe of the slope. Translational and Compound slips occur when an adjacent stratum of significantly different strength is present, which influences the shape of the failure surface. Translational slip tends to occur where the hard stratum is at relatively shallow depth, more or less parallel to the surface of the slope. Compound slip usually occurs if the hard stratum is at greater depth. It generally is a combination of rotational and translational slip. Equilibrium systems and mechanisms are used in the analysis of slope stability. For the vertical cut in a purely cohesive material a lower- and upper-bound solution is obtained. The stability of infinite slopes, above and under water is analysed using an equilibrium system. Finally, the stability of embankments and earth dams is investigated by using a mechanism. 7.1 Vertical cut in a purely cohesive material A well known problem in geotechnics is the calculation of the stability of a vertical slope in a purely cohesive material ( = 0, c 0 or u = 0, s u 0). Fig. 7.2 depicts a vertical cut in such a material. A lower- and an upper-bound solution have to be found for the maximum possible cutting depth h c , on basis of a constant cohesion c and a constant unit weight . circular rotational slip non-circular rotational slip translational slip compound slip Fig. 7.1: Types of slope failure.
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ECE 2311: Soil Mechanics II Stability of Slopes 2 7.1.1 Lower-bound solution In this case the unit weight of the soil should be incorporated in the balance equations, because the weight of the soil is the driving force causing the instability. The balance equations then become: 0 xx zx x z (7.1) 0 xz zz x z (7.2) A simple equilibrium system is drawn in Fig. 7.3. It consists out of three zones connected by discontinuity lines.
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