建筑物抗滑稳定分析中“潘家铮最大最小原理”的证明

On Pan’s principles of soil and rock stability analysis

对滑坡和边坡稳定分析中的潘家铮原理的理论意义和证明作出理论阐述。潘氏原理指出：１）滑坡如能沿许多滑面滑动，则失稳时，它将沿抵抗力最小的一个滑面破坏（最小值原理）。２）滑坡体的滑面肯定时，则滑面上的反力（以及滑坡体内的内力）能自行调整，以发挥最大的抗滑能力（最大值原理）。对潘氏原理的证明是建立在Ｄｒｕｃｋｅｒ准则和Ｓａｒ－ｍａ的斜分条边坡稳定分析方法基础上的。证明中使用了虚功原理和塑性力学的上、下限定理。列举了算例说明使用潘氏原理可以获得和闭合解一致的计算成果。

This paper gives a formal demonstration on Pan Jiazheng’s principles of soil and rock stability analysis, which states that: (1) among all possible slip surfaces of a soil or rock structure, the real one renders the minimum resistance against the external load; (2) the real internal force or stress distribution along the slip surface is the one that provides the maximum resistance against the external load. The demonstration was based on Drucker's Postulates and Sarma's stability analysis method of nonvertical slices. The virtual work principle and the upper and lower bound theorems in plasticity played an important role in the theoretical work. The paper also presents an example which shows that by proper implementations of Pan's principle, it is possible to find the accurate results given by the closedform solutions.