Random Search Method of Fracture Surface for Seismic Stability of Reinforced Retaining Wall
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摘要: 为确定加筋土挡墙破裂面的位置，基于水平条分法提出了一种多线段破裂面表现形式. 将加筋土挡墙破裂面视为由多条线段组成，各条线段在一个平面内以不同的长度和角度相互连接；根据地震作用下水平土条的力学平衡条件，推导出与破裂面参数相关的筋材拉力计算式；将筋材总拉力作为目标函数，采用两层循环方式进行求解计算，外层为墙后填土水平表面破裂点位置循环，内层为随机角度循环；对比每次外层循环计算所得筋材总拉力，取最大值所对应的破裂面为所求加筋土挡墙临界破裂面. 通过算例对比验证了多线段破裂面计算方法的合理性，并对加筋土挡墙稳定性影响因素进行分析. 研究结果表明：以角度随机方式产生多线段破裂面的计算方法无需进行数学优化可得到合理结果，加筋土挡墙破裂面位置比对数螺旋破裂面更接近临空面；填土内摩擦角的增大使得筋材总拉力与筋材长度减小，能够增强加筋土挡墙的内部稳定性.Abstract: In order to determine the fracture surface location of the reinforced retaining wall, a polyline fracture surfaceform was proposed based on the horizontal slice method. The fracture surface of the reinforced retaining wall is viewed to be composed of several line segments, one connected with another in a plane at different lengths and angles. According to the mechanical equilibrium of horizontal soil strip under seismic action, the calculation formula of reinforcement forces related to fracture surface parameters is derived. The total force of the reinforcement is taken as the objective function, and the calculation is run in a way of a two-layer cycle. The outer layer is a cycle of the fracture point position of the horizontal filling behind the wall, and the inner layer is a random angular cycle. By comparing the total forces of reinforcement calculated in each outer cycle, the fracture surface corresponding to the maximum value is the critical fracture surface of the reinforced retaining wall. A calculation example is used to verify the calculation method of the polyline fracture surface, and the influential factors on the stability of the reinforced retaining wall are analyzed. The results show that the calculation method in which the polyline fracture surface is generated by the random angular method can obtain reasonable results without mathematical optimization, and the fracture surface location of the reinforced retaining wall is closer to the free face than the logarithmic spiral fracture surface. The increase in the internal friction angle of the fill reduces the total tensile force and the length of the reinforcement, which can enhance the internal stability of the reinforced retaining wall.
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图 5
${{{L_{\rm{c}}}} / H}$ 与$\varphi $ 关系的比较Figure 5. Comparison of relationship between
${{{L_{\rm{c}}}} / H}$ and$\varphi $ 
图 7 多线段破裂面与对数螺旋破裂面位置的比较
Figure 7. Position comparison of polyline fracture surfaces and logarithmic spiral fracture surfaces
图 8
$\alpha $ 不同时K随$\varphi $ 的变化规律Figure 8. Trend of K changing with
$\varphi $ under different$\alpha $ 
图 9
$\alpha $ 不同时${{{L_{\rm{c}}}} / H}$ 随$\varphi $ 的变化规律Figure 9. Trend of
${{{L_c}} / H}$ changing with$\varphi $ under different$\alpha $ -
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