Abstract: According to upper bound theorem of the limit analysis method, we analyzed the velocity field at the bottom of active slip zone ABC and transition zone BCD and passive slip zone BDE in a foundation pit. Virtual work-rate equation of plastic area at the bottom of the foundation pit was established. On this basis, the upper-bound solution to the depth of support excavations which meets the requirement of stability against upheaval was induced, and the stability safety factor k was solved when the support depth t was given. Engineering examples verified that the upper-bound solution and the formula of stability safety factor k are rational. The results could provide reference for the calculation of support depth in similar foundation pits, and improve the correctness of bottom soil stability in foundation pit.

Key words: excavation support, support depth, limit analysis method, upper-bound solution, safety factor