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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%。
Compared with the commonly used Mohr-Coulomb (MC) criterion in geotechnical problems, the generalized SMP (spatially mobilized plane) criterion considers the influence of mid-principal stress on soil strength. This paper compares the slope calculated based on the above two criteria Stability differences. First of all, by solving the cubic equation, the generalized SMP criterion is transformed into the linear function of the distance between the stress point and the equatorial axis and the first invariant I1 of the stress tensor. The generalized SMP criterion and MC Equivalence between guidelines. Then, the backward Euler constitutive integral algorithm of the ideal elastoplastic model based on the generalized SMP criterion under the non-associated flow rule is deduced. The Euler’s constitutive integral algorithm is programmed into FLAC finite difference software and verified by numerical calculation of slope stability analysis The results of the theory deduction: When applying the non-associated flow rule under the plane strain condition, the generalized SMP criterion is equivalent to the MC criterion after the soil strength parameter is increased by 15%, that is, the slope safety factor based on the extended SMP criterion is higher than the MC criterion 15%.