An improved limit equilibrium method for rock slope stability analysis under stress-based calculation mode for slip surface  

滑面应力模式下岩质边坡稳定性极限平衡法

作　　者：DENG Dong-ping ZHANG Dian PENG Yi-hang CHEN Hao-yu 邓东平;张典;彭一航;陈浩宇(School of Civil Engineering,Central South University,Changsha 410075,China)

机构地区：[1]School of Civil Engineering,Central South University,Changsha 410075,China

出　　处：《Journal of Central South University》2025年第1期262-287,共26页中南大学学报(英文版)

基　　金：Project(52278380)supported by the National Natural Science Foundation of China;Project(2023JJ30670)supported by the National Science Foundation of and Technology Major Project of Hunan Province,China。

摘　　要：This study proposes an alternative calculation mode for stresses on the slip surface(SS).The calculation of the normal stress(NS)on the SS involves examining its composition and expanding its unknown using the Taylor series.This expansion enables the reasonable construction of a function describing the NS on the SS.Additionally,by directly incorporating the nonlinear Generalized Hoke-Brown(GHB)strength criterion and utilizing the slope factor of safety(FOS)definition,a function of the shear stress on the SS is derived.This function considers the mutual feedback mechanism between the NS and strength parameters of the SS.The stress constraints conditions are then introduced at both ends of the SS based on the spatial stress relation of one point.Determining the slope FOS and stress solution for the SS involves considering the mechanical equilibrium conditions and the stress constraint conditions satisfied by the sliding body.The proposed approach successfully simulates the tension-shear stress zone near the slope top and provides an intuitive description of the concentration effect of compression-shear stress of the SS near the slope toe.Furthermore,compared to other methods,the present method demonstrates superior processing capabilities for the embedded nonlinear GHB strength criterion.传统极限平衡理论不易与非线性强度准则相结合,也难以有效地揭示岩质边坡拉-压剪切破坏特征,原因在于其自身所采用的条块划分与条间力假设模式。为此,本文将条块划分与条间力假设模式改进为滑面应力计算模式。在此模式中,滑面正应力被分解为已知基本正应力和未知附加正应力两项,并应用Talyor级数展开式表达未知附加正应力项,从而构建出合理的滑面正应力函数。然后,融入广义非线性H-B强度准则,并利用边坡安全系数定义,建立滑面正应力与滑面强度参数互馈机制下滑面剪应力函数。为了实现近坡顶处滑面拉剪应力区有效模拟与近坡脚处滑面压剪应力集中效应直观描述,基于空间一点应力关系,提出滑面端部应力约束条件。随后,根据滑动体所满足的整体力学平衡条件和滑面端部应力约束条件,推导得岩质边坡安全系数和滑面应力解答。通过对比分析,本文方法的合理性与可行性得以验证,且与其他方法相比,本文方法在计算模式和非线性强度准则处理手段上更具优势,其对发展和完善岩质边坡稳定性极限平衡理论有着重要的积极作用,为类似复杂条件下岩质边坡稳定性分析提供了一种切实可行的计算思路。

关 键 词：stability of rock slope nonlinear GHB strength criterion limit equilibrium method stress function on slip surface stress constraint conditions at both ends of slip surface 

分 类 号：O17[理学—数学]