Application of the Upper and Lower-bound Theorems to Three-dimensional Stability of Slopes

Rigorous Solution of Slopes’ Stability considering Hydrostatic Pressure

“…The position of the stress discontinuity line can be determined according to (15) and (21) in the slip line field.…”

“…(2) To get the stress discontinuity line In the active region, the specific approach is to firstly select the point F in the grid. The stress discontinuity line is drawn by (15) and (21). A group of the maixmum principal stress direction angles of the stress discontinuity line in the active region is assumed as θ + .…”

“…A group of the maixmum principal stress direction angles of the stress discontinuity line in the active region is assumed as θ + . Then, the direction angle θ − , the tangential direction angle of the discontinuity line w, and the coordinate of each point in the line AF in the passive region can be obtained by the (13) and (15). And the slip line field of the region II can be obtained by solving the Cauchy problem.…”

“…For the slope stability, it is sometimes not necessary to get the variation of stress field and strain field, only to get the ultimate load. Based on the extremum principal [11], the lower bound (LB) [12,13] solution can be got by static analysis for limit equilibrium problems and the upper bound (UB) [14][15][16][17] solution can be got by dynamic analysis. If the lower bound solution satisfies all the kinematic conditions or the upper bound solution satisfies all the static conditions, the solution will be the rigorous one.…”