基于弹性理论的有限位移条件下挡土墙上土压力解析

Analysis of earth pressure on retaining walls with limited displacement based on elastic theory

经典土压力理论都是通过研究弹性半空间体内的应力状态,根据土的极限平衡条件和楔体的静力平衡条件而得出的。因土具有蠕变及固结特性,所以产生主动土压力和被动土压力的时机都是暂时的,从长久角度来看,因蠕变及固结现象作用在挡土墙上的土压力也都是非极限平衡条件(有限位移)下的土压力。为计算有限位移条件下作用在挡土墙上的土压力,依据线弹性本构理论建立了有限位移条件下挡土墙上的土压力计算式,引入Duncan-Chang非线性弹性模型中的切线模量来反映土体模量随围压的变化,并推导出发生朗肯主动土压力、静止土压力、主应力方向偏转、朗肯被动土压力的界限应变,依据这4个界限应变将作用在挡土墙上的土压力分为5个状态分区,即主动破坏状态区、有限位移主动土压力状态区、主应力反转前有限位移被动土压力状态区、主应力反转后有限位移被动土压力状态区和被动破坏状态区。通过将所提公式的计算结果与模型试验结果对比分析,得出如下结论:当挡土墙产生水平平动位移、绕墙脚的转动位移和水平平动+绕墙脚转动组合位移时,土压力分布均呈非线性分布,且不同位移下土压力随墙深度的计算值与实测值基本一致,说明提出的有限位移条件下土压力的计算式能够很好地应用在实际工程的挡土墙设计中。

The classical earth pressure theories were established by studying the stress state in an elastic half-space body based on the limit equilibrium condition of soil and the static equilibrium of the wedge.Due to the creep and consolidation characteristics of soil,the active and passive earth pressures have time-dependent features.From a long-term perspective,the earth pressure acting on retaining walls due to the creep and consolidation of soil is under non-limit equilibrium conditions(limited displacement).A calculation formula for calculating the earth pressure acting on the retaining wall under limited displacement is established in this study based on the linear elastic constitution theory.The tangent modulus in Duncan-Chang nonlinear elastic model is introduced to reflect the change of soil modulus with confining pressure,and the boundary strains of Rankine active earth pressure,earth pressure at rest,principal stress direction deflection and Rankine passive earth pressure are derived.According to the four boundary strains,the earth pressure acting on the retaining wall is divided into five state zones as active failure state zone,active earth pressure state zone with limited displacement,passive earth pressure state zone with limited displacement before principal stress deflection,passive earth pressure state zone with limited displacement after principal stress deflection and passive failure state zone.By comparing and analyzing the calculation results by the proposed formula with the model test results,it is concluded that the earth pressure distribution of the wall is always non-linear when the retaining wall moves in a mode of translation displacement(T mode),rotation displacement around the wall base(RB mode)or translation+rotation displacement around the wall base(RBT mode),and that the calculated values of the earth pressure along the wall depth under different displacements are basically consistent with the measured values,which indicates that the proposed can be well applied to the design of retaining walls in practical engineering.