基于尖点突变理论的非均质土坡失稳判据分析

An Instability Criterion for Inhomogeneous Slope Based on Cusp Catastrophe Theory

为避免失稳判据的主观人为性,将非线性突变理论运用于非均质边坡稳定性评价中。结合工程算例建立非均质土坡数值计算的力学模型,采用强度折减有限元法对土坡进行稳定性分析,通过建立坡体内部水平方向最大位移与强度折减系数的尖点突变模型,将失稳判据量化为一个确定的突变特征值,比较各级强度下的水平最大位移突变特征值与0的关系确定土坡稳定安全系数,并将所得结果与塑性区贯通判据、计算不收敛判据及Spencer法计算结果进行对比分析。结果表明:以尖点突变模型为失稳判据能确定出土坡稳定形态与强度折减系数的定量关系,展现土坡失稳过程的突变性,其物理意义明确,计算结果客观,求解出的安全系数精度较高。该失稳判据为非均质土坡稳定性分析的较优判据。

In order to avoid the subjective factitiousness of instability criterions,the nonlinear catastrophe theory is applied to evaluate the stability of inhomogeneous slope.A numerical mechanical model in association with strength reduction FEMwas adopted to analyze soil slope stability.Through establishing the cusp catastrophic model of the maximum horizontal displacement and strength reduction coefficient,the instability criterion was quantified as a de-termined catastrophe eigenvalue.Furthermore,safety factor was obtained according to the relationship between ca-tastrophe eigenvalue of maximum horizontal displacement and zero in the presence of different strength reduction co-efficients.The obtained safety factor was compared with that from other two criteria （plastic zone penetration and misconvergence）and Spencer’s procedure of limit equilibrium.Results indicate that the relation between slope sta-bility and strength reduction coefficient can be quantified by this cusp catastrophic model and the catastrophe of slope instability process can be reflected.This instability criterion has high calculation precision and definite physi-cal meaning.