竖向分层土被动土压力的计算与分析

Analysis and Calculation of Passive Earth Pressure of Vertical Layered Soil

基于极限平衡理论和相关联流动法则,建立了挡土墙后竖向分层土被动土压力关于滑动面夹角的数学模型,根据滑动土楔的静力平衡关系,得出竖向分层土被动土压力的计算表达式及其分布情况.利用Matlab计算软件作出被动土压力随滑动面夹角变化的函数曲线,根据曲线上极小值点确定被动土压力及其对应的极限破裂角.通过与现有理论计算对比,验证了该方法的合理性与可行性.分析了分层土性质参数及挡土结构几何、物理参数等对被动土压力E_(p)和破裂角θ_(cr)的影响.研究结果表明:经典的朗肯、库仑土压力理论及文献解是该研究方法在单一土层情况下的特例.被动土压力Ep随着墙土摩擦角δ、回填土摩擦角φ_(1)、墙土黏聚力C_(w)、回填土黏聚力C_(1)、回填土重度γ_(1)、填土表面荷载q的增加而增加,随着墙背俯斜角α的增加而降低.破裂角θ_(cr)随着δ、φ_(1)、C_(w)、C_(1)、γ_(1)的增加而降低,随α的增加而增加.回填土范围b对被动土压力Ep和破裂角θ_(cr)的影响受回填层和原土层土的性质共同影响.从工程设计角度,挡土墙背竖直、粗糙更有利于被动土压力的发挥.

Based on the limit equilibrium theory and the associated flow rule,a mathematical model of the passive earth pressure of the vertical layered soil behind the retaining wall with respect to the sliding surface angle was established.According to the static equilibrium relationship of the sliding soil wedge,the calculation expression and distribution of passive earth pressure of vertical layered soil were derived.Then,the function curve of passive earth pressure changing with the angle of sliding surface was made by using Matlab calculation software,and the passive earth pressure and its corresponding limit rupture angle were determined according to the minimum points on the curve.The rationality and feasibility of this method were verified by comparison with existing theoretical calculations.Finally,the influence laws of layered soil property parameters and geometric and physical parameters of retaining structures on passive earth pressure Ep and rupture angleθ_(cr)were analyzed.The results show that the classical Rankine and Coulomb earth pressure theories and literature solutions are special cases of the research method in the case of a single soil layer.The passive earth pressure Ep increases with the increase of wall-soil friction angleδ,backfill soil friction angleφ_(1),wall-soil cohesion C_(w),backfill soil cohesion C_(1),backfill weightγ_(1),and fill surface load q,and decreases with the increase of wall back slope angleα.The rupture angleθ_(cr)decreases with the increase ofδ,φ_(1),C_(w),C_(1),γ_(1),and increases with the increase ofα.The influence of backfill distance b on passive earth pressure Ep and rupture angleθ_(cr)is jointly affected by the properties of backfill layer and original soil layer.Finally,from the perspective of engineering design,the vertical and rough back of the retaining wall is more conducive to the passive earth pressure.