基于极限应力状态条件的主动土压力解析

doi:10.13722/j.cnki.jrme.2024.0329

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摘要为探究非光滑的挡土墙主动土压力分布特征及墙后土体处于主动极限平衡状态时的应力状态，以墙后无黏性土为研究对象，建立极限应力状态条件下挡土墙的主动土压力计算方法。首先，假定当滑动土楔处于极限平衡状态时，滑裂面、墙土界面处的土体单元及楔体内部单元都达到极限应力状态，及土楔中小主应力传递为圆弧形主应力迹线。基于上述假定，将滑动土楔沿最小主应力迹线分层为若干个圆弧形薄层单元，继而利用静力平衡对该薄层单元进行受力分析，推导出极限应力状态下挡土墙的主动土压力。分析墙土摩擦角对主动土压力的分布形式、大小、合力作用点及对墙底的倾覆力矩的影响规律，并与Coulomb等土压力理论进行比较。理论分析结果表明：(1) 主动土压力随深度呈凸形非线性分布，挡土墙背的粗糙度，即墙土摩擦角的取值，对非线性分布形式有显著影响。当挡土墙背光滑( = 0°)时，土压力分布退化为Coulomb直线分布；随着墙土摩擦角的增加，土压力分布曲线逐渐左移，曲线的拐点位置升高，非线性效应愈加明显。(2) 随着墙土摩擦角的增大，主动土压力的合力逐渐减小，合力作用点的位置受非线性分布的影响而逐渐提升，对墙底的倾覆力矩先减小后增加。(3) 极限应力状态条件下挡土墙的主动土压力的合力是Coulomb土压力合力的外包络线，基于Mohr-Coulomb强度理论，推论出滑动土楔体处于极限平衡状态时内部单元的应力状态为：挡土墙背光滑时( = 0°)，滑动土楔体内部单元为极限应力状态，即为经典的Rankine土压力理论；挡土墙背粗糙( ＞0°)时，滑动土楔体内部单元已进入塑性–破坏应力状态，并随着挡土墙背粗糙度的增加，塑性状态越显著。(4) 极限应力状态条件下的主动土压力为主动土压力的塑性上限解，Coulomb土压力为塑性下限解。最后，通过数值模拟与实例验证本文方法的可行性与合理性。

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	刘光秀1
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	党发宁1
	王旭1
	李玉根2

关键词 ：土力学, 主动土压力, 挡土墙, 主应力迹线, 非线性分布, 极限应力状态

Abstract：To investigate the distribution characteristics of active earth pressure on non-smooth retaining walls and the stress state of soil behind the wall under active limit equilibrium conditions，a method for calculating the active earth pressure of retaining walls under ultimate stress conditions is developed for cohesionless soil. Firstly，it is assumed that in the limiting equilibrium of the sliding wedge，the soil elements on the slip surface，at the wall-soil interface，and within the wedge body all achieve the ultimate stress state. Additionally，the principal stresses within the wedge are assumed to transfer as a circular arc principal stress trace. The sliding soil wedge is then discretized into multiple thin-layer units along the minor principal stress traces. By applying static equilibrium principles，the active earth pressure on retaining walls under ultimate stress conditions is derived through force analysis of these units. Subsequently，the influence of the wall-soil friction angle on the distribution form，magnitude，resultant force action point of active earth pressure，and overturning moment at the base of the retaining wall is analyzed，and comparisons are made with Coulomb?s theory and other earth pressure theories. Theoretical analysis demonstrates that：(1) The active earth pressure exhibits a convex nonlinear distribution with depth，which is significantly influenced by the roughness of the retaining wall's back，characterized by the wall-soil friction angle . When the wall back is smooth( = 0°)，the earth pressure distribution degenerates into Coulomb?s linear distribution. As the wall-soil friction angle increases，the earth pressure distribution curve shifts gradually to the left，with the inflection point on the curve rising，accentuating the nonlinear effect. (2) As the wall-soil friction angle increases，the resultant force of the active earth pressure gradually decreases，while the position of the resultant force?s action point rises due to the influence of nonlinear distribution. The overturning moment at the base of the wall initially decreases and then increases. (3) The resultant force of active earth pressure under ultimate stress conditions is the outer envelope of the Coulomb’s earth pressure resultant force. Based on Mohr-Coulomb strength theory，it is deduced that the stress state of internal units within the sliding soil wedge at limit equilibrium can be described as follows：When the retaining wall back is smooth( = 0°)，internal units of the sliding soil wedge reach ultimate stress conditions，corresponding to the classical Rankine earth pressure theory. When the retaining wall back is rough( ＞0°)，internal units of the sliding soil wedge enter a plastic-failure stress state. As the roughness of the retaining wall back increases，the plasticity becomes more pronounced. (4) The active earth pressure under ultimate stress conditions represents the upper bound plastic solution，while Coulomb?s earth pressure represents the lower bound plastic solution. Finally，the feasibility and rationality of the proposed method are validated through numerical simulations and practical examples.

Key words： soil mechanics active earth pressure retaining wall principal stress trace nonlinear distribution ultimate stress state

引用本文:

刘光秀1，2，党发宁1，王旭1，李玉根2. 基于极限应力状态条件的主动土压力解析[J]. 岩石力学与工程学报, 2024, 43(11): 2832-2845.
LIU Guangxiu1，2，DANG Faning1，WANG Xu1，LI Yugen2. Analytical solution of active earth pressure under ultimate stress state conditions. , 2024, 43(11): 2832-2845.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2024.0329 或 https://rockmech.whrsm.ac.cn/CN/Y2024/V43/I11/2832

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