Limit analysis of stability of circular foundation pit

Circular foundation pits often appear in civil engineering. In order to obtain the critical depth of the non-supported circular foundation pit, the upper-bound method in plasticity mechanics was employed. The assumed slip surface in analysis was the rotational logspiral surface. The kinematically admissible velocity field was obtained according to the associated flow rule for Coulomb material, and the optimization model of the critical depth was established and solved with SQP optimization algorithm. The variations of the critical depth with the slope angle, the ratio of depth to radius of pit and the internal friction angle of soil were studied. The arch effect of the circular foundation pit makes the critical depth larger than the critical height of the plane slope; however, when the ratio of depth to radius of pit approaches zero, the upper-bound solution of the former approaches that of the latter. If the ratio of depth to diameter of pit is less than 10, the arch effect may be ignored and the foundation pit can be analyzed as the plane slope with the method of slices. Comparison between upper-bound solution and the solution from limit equilibrium method showed that the former is closer to the true solution than the latter.