基于Rankine模型的墙体位移–土压力近似计算

Calculation of displacement-dependent lateral earth pressure based on Rankine earth pressure model

墙体位移是影响土压力的核心要素。根据Rankine土压力模型,以试样在单剪试验中的剪切过程近似模拟墙后土体由静止进入极限状态的历程,构建土体剪应变与墙体位移在等极限应变条件下的几何方程和基于点应力状态的剪应力与土压力平衡方程,结合以双曲线表达且与几何方程相匹配的剪应变–剪应力理想非线弹塑性物理模型,建立综合反映土体变形与强度特性及初始应力状态影响的墙体位移–土压力函数关系,讨论极限状态下墙体位移的主要影响因素。分析表明:静止与被动(或主动)状态之间的墙体位移–土压力曲线是土体应力–应变特性的宏观体现,两者随变形的增加呈现出相似的变化规律;主动(或被动)状态下的墙体位移随土体极限剪应变、滑移区范围的增加而增大,随静止土压力系数的降低而减小(或增大);工程设计常用力学指标下的粗细粒土进入主动状态时,墙体位移与墙高之比为0.6‰~15.0‰,被动时为-0.5%^-5.9%,理论分析与相关文献模型试验结果吻合。

The magnitude of the lateral earth pressure against wall depends on the wall movement. The soil behind a wall approaching the active or passive earth pressure state from initial state is considered as the shearing process of soil sample in the simple shear test. The geometric relationship between the shear strain of soil and the wall displacement,the equilibrium equation between the earth pressure and the shear stress of soil,and the constitutive relationship between the shear strain and the shear stress of soil were used to derive the expression of the wall displacement with lateral earth pressure. The wall displacement reaching the limit state of earth pressure increases with the ultimate shear strain of soil and the scope of failure zone. The required displacement decreases with k_0（rest earth pressure coefficient） from the initial to the active state,but increases with k_0 from the initial to the passive state. The relationship between the wall movement and the lateral earth pressure macroscopically describes soil stress-strain behavior. The calculated displacement required to reach the active state for the cohesionless and cohesive soils are about 0.6‰–15.0‰ of H,and to reach passive state which are about-0.5%–-5.9% of H,where H is the height of the wall. The estimated wall displacement-earth pressure curves agree reasonably with the model test results from the relevant literatures.