摘要
Mohr-Coulomb准则在Mohr应力空间中具有最简形式,同时也因其非常可靠而在经典的极限分析或极限平衡法中得到了最广泛的应用。然而,应力空间中的Mohr-Coulomb屈服面是非光滑的,这给基于变形分析的弹塑性有限元法中的本构积分带来了巨大的麻烦。此外,在求解强度问题时,基于载荷控制法(LCM)的求解器很难将有限元模型带入极限平衡状态。针对这些问题,本研究给出了以下解决方案。首先,设计了适用于带非光滑屈服面的塑性本构积分算法GSPC。GSPC对任意大小的应变增量都收敛,数值特性远优于现有的返回-映射算法。还为弹塑性有限元分析定制了一个位移控制法(DCM)求解器,该DCM能将有限元模型带入极限平衡状态而不存在收敛性方面的问题,计算效率和鲁棒性都远优于现有的基于LCM的求解器。最后,结合强度折减法,建议了求解边坡安全系数的割线法,并给出了极限平衡状态下坡顶拉裂缝位置和深度的确定技术。
The Mohr-Coulomb yield criterion takes on the simplest form in the Mohr stress space,which has thus been most extensively applied in limit analysis and limit equilibrium methods because of its accuracy.However,the Mohr-Coulomb yield surface in the stress space is non-smooth,causing huge troubles to the constitutive integration in the deformation based finite element plasticity analysis.In addressing strength problems,meanwhile,solvers based on the load controlled method(LCM)are hard to bring the finite element model to the limit equilibrium state.Aiming at these issues,the solution schemes are proposed as follows.First,an algorithm named GSPC is designed for the constitutive integration for plasticity with non-smooth yield surfaces.GSPC is always convergent for arbitrary large strain increments,with far more excellent numerical properties than the return-mapping methods available.A solver based on the displacement controlled method(DCM)is developed for the finite element plasticity analysis.The DCM solver is able to bring easily the finite element model into the limit equilibrium state,with no convergence issue,and far more efficient and robust than any LCM solvers.At last,combined with the strength reduction method,the secant method for the factor of safety of slopes is developed,and the location and depth of tension cracks at the slope top are proposed.
作者
郑宏
张谭
王秋生
ZHENG Hong;ZHANG Tan;WANG Qiu-sheng(Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education,Beijing University of Technology,Beijing 100124,China)
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2021年第2期301-314,共14页
Rock and Soil Mechanics
基金
国家自然科学基金(No.52079002)
关键词
塑性本构积分
Mohr-Coulomb屈服面
位移控制法
边坡稳定性
拉裂缝
constitutive integration for plasticity
Mohr-Coulomb yield surface
displacement controlled method
slope stability
tension cracks
