广义H-B强度准则下破碎岩质边坡稳定分析极限平衡变分法  

Limit equilibrium variational method for stability analysis of fractured rock slopes under generalized H-B strength criterion

作　　者：邓东平[1] 徐润冬 彭一航 DENG Dongping;XU Ruidong;PENG Yihang(College of Civil Engineering,Central South University,Changsha,Hunan 410075,China)

机构地区：[1]中南大学土木工程学院,湖南长沙400075

出　　处：《岩石力学与工程学报》2025年第4期959-976,共18页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(52278380);湖南省自然科学基金资助项目(2023JJ30670)。

摘　　要：由于岩体剪切失效行为往往呈现为复杂的非线性特征,使得现有理论方法在开展破碎岩质边坡稳定性分析方面存在一定的挑战。在此,提出岩质边坡稳定性极限平衡变分法,其利用变分法构建滑面与滑面应力微分控制方程,并应用极限平衡原理建立边坡安全系数和滑面应力未知变量计算公式。进一步,针对广义Hoek-Brown强度准则下滑面形状–滑面正应力–滑面瞬时剪切强度参数的相互嵌套关系,实施离散计算方式与耦合关联求解策略,破解非线性强度准则直接引入的难题。基于此,将边坡全局变分极值问题视为众多确定边界变分极值问题。随后,以滑面参数为优化变量,并以最小边坡安全系数和变分极值条件为优化目标,引入多目标优化遗传算法,实现可动边界横截条件解除与变分控制条件严格满足下边坡临界滑面精准快速搜索。通过算例对比分析,本文方法的可行性与实用性得以验证。现有研究将有助于边坡稳定性极限平衡理论发展和完善,并为复杂条件下破碎岩质边坡稳定性分析提供一种行之有效的计算思路。Due to the complex nonlinear characteristics often exhibited in the shear failure behavior of rock mass,existing theoretical methods face challenges in analyzing the stability of fractured rock slopes.In this study,a limit equilibrium(LE)variational method for assessing the stability of rock slopes is proposed.This method utilizes the variational method to derive the differential control functions for the slip surface and its associated stress.Additionally,the LE principle is employed to establish the calculation formulas for the factor of safety(FOS)of the slope and the unknown variable related to the slip surface stress.Furthermore,to address the interdependent relationship among the shape of the slip surface,the normal stress on the slip surface,and the instantaneous shear strength parameters under the generalized Hoek-Brown(H-B)strength criterion,a discrete calculation approach coupled with a correlational solving strategy is applied to overcome the challenges posed by the direct incorporation of the nonlinear strength criterion.Building on this foundation,the global vraiational extremum problems of the slope are considered as multiple deterministic boundary variational extremum problems.Subsequently,the slip surface parameters are treated as optimization variables,with the objective of minimizing the slope FOS while satisfying the variational extreme conditions.A multi-objective optimization genetic algorithm is introduced to achieve a precise and rapid search for the critical slip surface of the slope,ensuring the removal of movable boundary cross-sectional conditions and strict adherence to the variational control conditions.The feasibility and practicability of the proposed method are verified through comparisons with several examples.This research contributes to the advancement and refinement of the LE theory for slope stability and provides an effective computational framework for the stability analysis of fractured rock slopes under complex conditions.

关 键 词：边坡工程 破碎岩质边坡 广义H-B强度准则 稳定性分析 极限平衡变分法 多目标遗传算法 

分 类 号：P642[天文地球—工程地质学]