基于推广SMP准则的边坡稳定性分析

Slope stability analysis based on the extended SMP criterion

相比土工问题中通常采用的Mohr-Coulomb(MC)准则,推广的SMP(spatially mobilized plane)准则考虑了中主应力对土体强度的影响,该文比较了基于上述两准则计算得到的边坡稳定性差异。首先,通过求解三次方程将推广的SMP准则转化为应力点到等倾轴的距离ρ和应力张量第一不变量I1的线性函数,从理论上推导了平面应变条件下推广的SMP准则与MC准则之间的等效关系。然后,推导了非关联流动法则条件下基于推广的SMP准则的理想弹塑性模型的向后Euler本构积分算法,并将其编入FLAC有限差分软件,通过边坡稳定性分析的数值计算验证了理论推导结果:在平面应变条件下采用非关联流动法则时,推广的SMP准则等效于土体强度参数提高15%后的MC准则,即基于推广的SMP准则的边坡安全系数比MC准则高15%。

Unlike the commonly used Mohr-Coulomb（MC） criterion,the extended spatially mobilized plane（SMP） criterion takes into account the effect of the intermediate principal stress on the soil strength.This paper compares slope stabilities based on these two criteria.A new expression of the extended SMP criterion is first presented as a linear function of ρ and I1 to develop a theoretical relationship between the extended SMP criterion and the MC criterion for the plane strain condition.A backward Euler method is used to integrate the constitutive model based on the extended SMP criterion implemented in FLAC.The numerical results coincide well with the theoretical derivation and indicate that for the plane strain condition the extended SMP criterion is equal to the MC criterion with 15% higher strength parameters,which means that the safety factor of slopes based on the extend SMP criterion is 15% higher than with the MC criterion.