考虑中主应力影响倾斜填土面朗肯土压力参数的敏感性分析

Sensitivity analysis of parameters of Rankine's earth pressure with inclined surface considering intermediate principal stress

挡土墙后填土面为倾斜时,朗肯土压力理论应用很少。经典的各种土压力理论是基于Mohr-Coulomb强度准则得出的,没有考虑中主应力的影响。首先推导了填土面倾斜时的朗肯主动和被动土压力的计算公式;根据平面应变假设确定了中主应力σ2=ν(σ1+σ3),在此基础上推导了统一强度理论下的材料强度指标计算公式,利用该公式可将Mohr-Coulomb强度准则下的材料强度指标转化为考虑中主应力效应的统一强度理论下的材料强度指标;最后通过一算例采用正交试验设计对反映中主应力影响的中间主剪应力系数、泊松比、填土面倾角、黏聚力、内摩擦角、重度6种因素进行了敏感性分析。结果表明:影响朗肯主动土压力强度的6种因素从大到小分别为:重度、中间主剪应力系数、黏聚力、内摩擦角、倾角、泊松比;影响朗肯被动土压力强度的6种因素从大到小分别为:内摩擦角、中间主剪应力系数、泊松比、黏聚力、倾角、重度;中主应力对朗肯土压力计算结果的影响是一个不可忽视的重要因素。

Up to now the Rankine＇s earth pressure theory has not been widely used under the condition of inclined surface.Generally,the classical earth pressure theories are based on the Mohr-Coulomb criterion and the intermediate principal stress is not taken into account.First,a formula for Rankine＇s active and passive earth pressures with inclined surface as well as that for the intermediate principal stress in the plane strain assumption is derived.Then,the formula for shear strength parameters in the unified strength theory is derived based on the formula for the intermediate principal stress,so the shear strength parameters under the Mohr-Coulomb criterion can be transformed into the shear strength parameters under the unified strength theory.Finally,an example is given to carry out sensitivity analysis of six factors in terms of the design theory of orthogonal tests.The six influential factors are considered including the cohesion,internal friction angle,intermediate principal shear stress parameter,Poisson＇s ratio,angle of inclined surface and unit weight.It is shown that among the influential factors of Rankine＇s active earth pressure,the unit weight is the most important one,followed by the intermediate principal shear stress parameter,the cohesion,the internal friction angle,the angle of inclined surface and the Poisson＇s ratio;among those of Rankine＇s passive earth pressure,the internal friction angle is the most important one,followed by the intermediate principal shear stress parameter,the Poisson＇s ratio,the cohesion,the angle of inclined surface and the unit weight.So the effect of the intermediate principal stress on the calculated results of the Rankine＇s earth pressure is a critical factor.