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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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

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	Articles by authors
	LIU Guangxiu1
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	DANG Faning1
	WANG Xu1
	LI Yugen2

Cite this article:

LIU Guangxiu1,2,DANG Faning1, et al. Analytical solution of active earth pressure under ultimate stress state conditions[J]. , 2024, 43(11): 2832-2845.

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