基于非线性破坏准则的边坡稳定性分析

Slope stability analysis based on non-linear failure criterion

Baker提出的非线性破坏准则是一种广义的岩土体强度准则,常规的M-C强度准则、格里菲斯强度准则以及Hoek-Brown强度准则均为其特例。该准则通过大量的三轴试验引入无量纲强度参数A,n和T,其中A为尺度参数用于控制剪切强度的大小;n为准则曲线的次数用于控制曲率;T为转换参数用于控制准则曲线与σ轴的位置,并反映其无量纲拉伸强度。以Baker非线性强度准则为基础,以极限分析上限法为工具,采用"切线法"思想研究了静、动荷载下边坡的稳定性,将边坡的稳定性问题转化为含多变量的数学优化问题,并给出其最优解。通过算例分析,研究了非线性强度参数对边坡稳定系数与屈服加速度系数的影响。结果表明:边坡稳定系数随无量纲参数A,T的增大而增大;边坡屈服加速度系数随坡高、坡角的增加而降低。

The non-linear failure criterion proposed by Baker is a generalized geotechnical strength criterion, and the conventional criterion such as M-C, Griffith and Hoek-Brown strength criteria are all special cases of it. The criterion introduced three non-dimensional parameters A, n, T which can be obtained through triaxial tests, and have clear physical significance. Specifically, A is a scale parameter controlling the magnitude of shear strength, T is a shift parameter controlling the location of the criterion curve and o＇-axis and representing a non-dimensional ten- sile strength, and n controls the curvature of the envelope. Here, based on the Baker criterion, we studied the slope dynamic and static stability using upper bound theorem, transferred the problem to a mathematical optimiza- tion problem in a multi-variables expression, and gave the optimal solutions. Then, the influence of the nonlinear strength parameters on slope stability factor and yield acceleration factor are studied through an example. The re- sults show that the slope stability factor increases with the increase of non-dimensional parameters A and T, and the yield acceleration factor decreases with the increase of slope height and slope angle.