多滑面块体的分块极限平衡分析法

BLOCK-DIVIDING LIMIT EQUILIBRIUM ANALYSIS METHOD WITH MULTIPLE SLIDING-PLANES

单面滑动块体存在2个及以上非临空面,双面滑动块体存在3个及以上非临空面,且这些非临空面的面上构成块体时,传统的块体理论在计算稳定系数时可能存在问题。基于此,提出分块极限平衡分析法,该方法沿非临空面交棱将块体进行分块,在忽略分块间的垂向剪力(即可考虑分块间的水平法向力和剪切力)前提下,通过满足各分块的垂向力平衡和滑动方向上的总体力平衡,求解特定滑动方向的稳定系数。然而,由于块体往往不对称,人为很难给定真实的滑动方向,与滑动方向垂直的水平方向上存在不平衡力。通过改变滑动方向(0°～360°),当不平衡力为0时,计算达到3个正交方向上的力平衡,并由此确定出块体实际的潜在滑动方向。此时的稳定系数为最小值或接近最小值,其含义类似潘家铮最大最小原理。该法可以很好地解决多滑面块体的稳定分析问题。通过考题验证,与传统块体理论进行对比,解释非对称双面滑动向单面滑动渐变过渡时稳定系数与滑动方向的连续变化。最后,通过实例对该法进行应用。

When single-plane sliding block has more than one joint face, double-plane sliding block has more than two joint faces, and the block is above these joint faces, some defections of stability calculation in traditional block theory may occur. So, block-dividing limit equilibrium analysis method is presented. The method divides block along the intersection edge of joint faces and neglects the vertical shear force between dividing-blocks i.e. takes horizontal normal force and shear force into account; as to an assumed sliding direction, by satisfying vertical force equilibrium of every dividing-block and whole force equilibrium in the sliding direction, the factor of stability can be solved. However, the non-equilibrium force in the horizontal direction perpendicular to the assumed sliding direction is always existent, because the block is usually non-symmetrical and the assumed sliding direction is not the practical one. By changing the sliding direction from 0°to 360° , when the non-equilibrium force gets to zero, the solutions satisfy force equilibrium in three othogonal directions; and the actual potential sliding direction can be determined rather than assumed. In this case, the factor of stability is minimum or close to minimum, whose meaning is similar with Pan＇s principle of the maximum and the minimum. The method can solve well the stability analysis of multiple sliding-planes block. By contrasted with traditional block theory, themethod is validated; and the continuous change of factor of stability and sliding direction with gradual transition from non-symmetrical double-face sliding to single-face sliding can be interpreted properly. At last, a practical engineering case is studied.