土体极限分析的基本方程与广义极限平衡法

对屈服条件与屈服函数的极值条件进行了讨论，在不需要流动法则的情况下建立了速度方程。平衡方程、屈服条件与屈服函数的极值条件、速度方程就是土体极限分析的基本方程。这样，对荷载、速度边界条件（包括荷载与速度边界同时存在），均构成了完备的极限平衡问题。对边坡稳定问题的上、下限定理给出了严密的证明，并建立了求解极限平衡问题的广义极限平衡法，均质土的计算结果表明，圆弧滑动面的广义极限平衡法与对数螺旋面的上限解法基本一致。

Fundamental equations for limit analysis of soil mass and generalized method of limit equilibrium

The extreme conditions of yield condition and yield function are discussed;and a velocity equation is established under the condition that no flow rule has been required.The equilibrium equation,extreme conditions of yield condition and yield function,and velocity equation are the fundamental equations for limit analysis of soil mass,which constitute a complete limit equilibrium problem of the boundary conditions for loading and velocity,including the coexistence of boundary conditions for loading and velocity.The upper and lower bound theorem of slope stabilization is rigorously proved;and a generalized method of limit equilibrium has been established to solve the problem of limit equilibrium.The calculated result of homogeneous soil indicates that the generalized method of limit equilibrium for a circular slip surface is basically identical with the upper bound solution for a logarithmic spiral surface.