严格三维极限平衡法

A RIGOROUS THREE-DIMENSIONAL LIMIT EQUILIBRIUM METHOD

通过取整个滑体为受力体并基于滑面应力修正,实现满足所有6个平衡条件的严格三维极限平衡法。由此所导致的平衡方程组具有良好的数值特性,其Newton法不依赖于初值的选择。从理论上证明了解的存在性,对于?=0°的工况,还证明解了的唯一性,给出安全系数的显式表达式。数值求解时,通过化域积分为边界积分而无需再对滑体进行条分。新方法能够适应任意形状的滑面。

Up to now, there is no three-dimensional limit equilibrium method that is able to satisfy all six equilibrium conditions. While formulating the equilibrium conditions, the whole sliding body is taken as the loaded object. By means of remedy of the total normal pressures acting on the slip surface, a rigorous limit equilibrium method for the three-dimensional stability analysis of slope is realized, which satisfies all the six equilibrium conditions and accommodates to slip surfaces of any shape. The system of equations herein formulated enjoys excellent numerical properties. Its Newton method is independent of the choice of the initial iteration values. The existence of solution is proved theoretically. In case of internal friction angle φ= 0°, moreover, that the solution is unique is also proved; and an explicit expression for safety factor is given. Meanwhile, in order to simplify the preprocessing and to improve the precision of the analysis, the volume integrals over the sliding body are transformed into the boundary integrals. The division of the sliding body is accordingly unnecessary.