基于非线性统一强度理论下的边坡稳定性极限平衡分析

Limit equilibrium analysis of slope stability based on nonlinear unified strength theory

在边坡稳定性分析中,常采用的强度准则一般较少考虑中主应力对边坡破坏效应的影响,然而岩体的实际应力状况表明中主应力存在,且中主应力对边坡岩体的强度潜能发挥起着重要作用。基于考虑中主应力的统一强度理论下的Hoek-Brown(简称H-B)准则,通过对滑动面上的应力进行假设,并采用泰勒级数简化统一强度理论下的H-B准则表达式,然后根据滑动体满足所有静力平衡条件求解滑动面上的应力,进而得到边坡的安全系数。当中主应力影响系数b=0时(即为基本H-B强度准则),与等效的线性Mohr-Coulomb(简称M-C)强度准则下的瑞典法1、简化Bishop法、Spencer法和Morgenstern-Price(简称M-P)法以及基于统一强度理论下的瑞典法2进行算例对比分析,验证了方法的可行性。同时,以边坡的坡高H、坡角β和b为变量进行参数分析,研究表明:b增大(即中主应力对边坡的破坏效应影响越大)时,计算所得的安全系数增大,由此表明基本H-B强度准则下分析所得的边坡稳定性偏于安全。另外,由于提出的方法能够满足滑动体的所有静力平衡条件,且对未考虑条间作用力影响所得滑动面上的初始正应力进行了修正,故此方法较瑞典法2所得结果要大且更为严格。

The effect of intermediate principal stress on the analysis of slope stability is seldom considered by commonly used strength criteria. However, it is found that the intermediate principal stress exists in the practical rock engineering, and moreover it plays a significant role in potential strength of rock. The intermediate principal stress is considered in Hoek-Brown （H-B） criterion, which is established under the unified strength theory, the simplified expressions for H-B criterion are derived by using Taylor series and the assumption of stresses on slip surface. Therefore, these stresses on slip surface are calculated according to the static equilibrium conditions of the sliding body and the safety factor of slope can also be obtained. When the impact factor of intermediate principal stress b is equal to zero, the expressions in this study convert into the basic H-B strength criterion. The Swedish method 1 is a linear M-C strength criterion, including simplified Bishop method, Spencer method and Morgenstern-Price （M-P） method, which is equivalent to the basic H-B strength criterion. The Swedish method 2 is also established under the unified strength theory, and thus the feasibility of this study is verified by comparing the example results with the Swedish methods 1 and 2. Meanwhile, the effects of slope height H, slope angles β and b are selected to analyze slope stability. The results show that the calculated safety factor increases with increasing slope angle b, which means the impact of intermediate principal stress on slope safety is more obvious. The above results indicate that the obtained slope stability is safer by using basic H-B strength criterion. The proposed expressions satisfy the static equilibrium conditions of the sliding body and amend the initial normal stress on the sliding surface without considering the effect of inter-slice force, and therefore the calculated results are larger and more rigorous than those by Swedish method 2.