Global analysis approach of stability of deep foundation pit slopes reinforced by underground diaphragm walls and prestressed anchor cables

The stability evaluation of deep foundation pit slopes is crucial, including the solution of the factor of safety and the location of the critical slip surface. Prestressed anchor cables and underground diaphragm walls are commonly used to reinforce pit slopes. By means of the dimensional increase technique and the global analysis approach of slope stability, a nonlinear optimization problem is defined for the stability analysis of pit slopes. In the optimization problem, the ordinates of discrete points on the slip surface and the factor of safety are both the decision variables, the objective function is the factor of security, and the constraints are the equilibrium equations and the convexity of the slip surface. Because the objective function is linear and the constraint functions are polynomials of degree three at most, the optimization problem is a classical optimization one that conventional optimization techniques can solve without recourse to modern optimization techniques such as the AI technique. Examples suggest that the proposed procedure is far more efficient and stable than the optimization models based on the methods of slides. At last, applications are demonstrated to ongoing deep foundation pit slopes situated at Tong Zhou - Beijing sub-center.