有限无黏性填土刚性挡土墙主动土压力计算

针对经典的Rankine或Coulomb土压力理论不适用于山区挡土墙或邻近既有地下室基坑工程中常常遇到的墙后为有限宽度填土的情况，以墙背和稳定岩质坡面间为有限无黏性填土的刚性挡土墙为研究对象，假定在平面应变条件下，墙体平移使得墙后土体在极限平衡状态时出现通过墙踵的直线形或折线形滑裂面，且其中形成圆弧形土拱，考虑滑动土楔内水平土层间存在的平均剪应力，引入水平层分析法，得到非线性分布的主动土压力表达式。通过与文献中离心机模型试验结果的对比，验证所提方法的合理性，并在此基础上，以三角形和矩形断面有限填土挡土墙为例，探讨墙背倾角、岩质坡面倾角、墙土摩擦角、岩土摩擦角、填土内摩擦角或填土宽度等参数对主动土压力的影响。计算结果表明：该方法合理可行；有限填土时主动土压力沿墙高一般为非线性分布，且其合力作用点的位置一般不在墙高的1/3处；当填土宽度较大时，主动土压力合力大小有可能大于Coulomb土压力理论计算值，而且对于矩形断面有限填土的挡土墙，滑裂面的倾角都小于Coulomb土压力理论值。

Active Earth Pressure Calculation of Rigid Retaining Walls with Limited Granular Backfill Space

The classical Rankine or Coulomb earth pressure theories were established on the basis of the infinite soil behind the retaining walls, so they are inappropriate in estimating the active earth pressure on retaining walls with limited backfill space built in mountainous regions or retaining structures for foundation pit built close to the existing basement. Taking a rigid retaining wall with the granular backfill built adjacent to a stable rock face as a research object, it was assumed that the outward horizontal translation of the wall made the backfill in the limit equilibrium state, the slip surface with the linear type or the mansard appeared through the wall heel. And the soil arch in the backfill took the form of a circle under the plane strain condition. Considering the mean shear stress between level soil layers in the failure wedge, the differential level layer method was introduced to obtain a new formulation for estimating the active earth pressure. In order to verify the accuracy and rationality of the proposed formulation, the predictions from the equation were compared with the centrifuge model test results in the literature. On this basis, taking these retaining walls with triangular-section or rectangular-section backfill as examples, the influences of the inclination angle of wall back, the slope angle, the interface friction angle between the wall and the backfill, the interface friction angle between the rock face and the backfill, the internal friction angle of backfill and the width of backfill on the active earth pressure distribution were investigated. The results show that:for the wall with limited backfill space, the distribution of active earth pressure along the depth is generally nonlinear, and the location of its resultant is possibly higher or lower than one third of the wall height. For the wall with wide backfill, the value of the resultant of active earth pressure is possibly greater than the solution based on the Coulomb theory. In addition, the inclination angle of the slip surface is less than that based on the Coulomb theory for the wall with rectangular-section backfill space.