基于非关联流动法则的圆形隧洞滑移线解答

Slip Line Solution for Circular Tunnels Based on the Non-Associated Flow Rule

圆形隧洞的滑移线方程早在20世纪中期苏联学者已给出解答,并在国内广泛应用.推导过程中假设滑移线与速度矢量方向夹角为45°-φ/2是错误的,理论上滑移线与速度矢量方向的夹角与采用的流动法则有关.该文分别从关联流动法则和非关联流动法则出发,推导了圆形隧洞的滑移线方程和水平方向破裂体深度的表达式.通过与模型试验结果进行对比,对岩土材料应采用基于非关联流动法则的滑移线解答.

The slip line equation for circular tunnels had been solved by Soviet scholars in the middle of 20th century, and widely used in China. But the assumption that the angle between the slip line and the velocity vector was 45°-φ/2 in the derivation had been wrong. Theoretically, that angle was related to the flow rule adopted. The plastic slip line equation of circular tun- nels and the formula of horizontal fracture depth were derived based on both the associated flow rule and non-associated flow rule. Proved by previous model test, the slip line solution based on the non-associated flow rule is recommended for application.