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General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

Author(s): Shiguo XIAO, Yuan QI, Pan XIA
Affiliation(s): Key Laboratory of High-Speed Railway Engineering, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China; more
Corresponding email(s): xiaoshiguo@swjtu.cn
Key Words: Active earth pressure; Tensile strength cut-off; Variational calculus method; Pseudo-static method; Strip surcharge

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Abstract: According to the limit equilibrium state of soils behind rigid walls and the pseudo-static approach, a general closed-form solution to seismic and static active earth pressure on the walls, which considers shear and tension failure of the retained soil, is put forward using a variational calculus method. The application point of the active resultant force specified in the proposed method is explained with a clear physical meaning related to possible movement modes of the walls. In respect of the derived nine dependent equations reflecting the functional characteristics of the earth pressure, the proposed method can be performed easily via an implicit strategy. There are 13 basic factors related to the retained soils, walls, and external loads to be involved in the proposed method. The tension crack segment of the slip surface is obviously influenced by these parameters, apart from vertical seismic coefficient and geometric bounds of the surcharge, but the shear slip segment maintains an approximately planar shape almost uninfluenced by these parameters. Noticeably, the proposed method quantitatively reflects that the resultant of the active earth pressure is always within a limited range under different possible movements of the same wall.

考虑土体抗拉强度的刚性挡土墙地震和静态主动土压力的一般变分解

作者：肖世国^1,2，齐远²，夏攀³
机构：¹西南交通大学，高速铁路线路工程教育部重点实验室，中国成都，610031；²西南交通大学，土木工程学院，中国成都，610031；³西南交通大学，地质工程系，中国成都，610031
目的：传统的主动土压力计算方法在考虑土体抗拉强度时的假设不合理，具有明显的局限性。本文考虑土体剪切屈服和拉伸破坏准则，不假设滑裂面形态，并基于墙后填土主动极限平衡条件与变分极值原理，提出刚性挡土墙的地震和静态主动土压力的一般解析解，确定相应于墙体可能运动模式的主动土压力合力值及其作用点的变化范围。
创新点：1.采用变分法，建立同时考虑土体剪切和拉伸破坏的刚性挡土墙地震和静态主动土压力的紧凑解析解；2.确立相应于墙体平动和转动复合运动模式的刚性挡土墙主动土压力的可能变化范围，以及其合力作用点的合理范围；3.揭示13个基本参数对主动土压力的影响规律，并定量确定剪切-拉裂复合模式的滑裂面形态以及作用于滑裂面上的法向应力。
方法：1.基于刚性挡土墙后侧土体的主动极限平衡状态，通过拟静力法引入等效地震力，并根据拉格朗日乘子法和变分极值原理，建立考虑土体剪切与拉裂破坏的地震（含静态）主动土压力的隐式求解方程；2.运用MATLAB中的fsolve函数，通过叠代计算与精度控制，得到主动土压力的计算结果。
结论：1.所提方法算得的地震和静态主动土压力，与试验及理论结果具有较好的一致性，且本方法的适用性更为广泛；2.同一刚性挡土墙在不同的运动模式下，墙后主动土压力有所不同，但其总是在有限范围内变化；3.随着土压力合力作用点在其合理变化范围内逐渐升高，滑裂面剪切段的形态逐渐由平面向曲面发展；4.墙后土体表层的张拉裂隙深度受竖向地震系数、条形荷载分布宽度及其距墙顶水平距离的影响均很小，但受其余10个参数的影响较大。

关键词组：主动土压力；抗拉强度；变分法；拟静力法；条形超载

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考虑土体抗拉强度的刚性挡土墙地震和静态主动土压力的一般变分解

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