基于砂土状态和细观特征的剪切带倾角公式

剪切带扩展方向的确定是岩土体渐进破坏分析的关键.系统收集国内外文献中各类砂土剪切带倾角的平面应变试验结果，将其与现有的剪切带倾角计算方法的结果进行对比，发现现有方法的计算值与试验值偏离较大，计算误差不可忽略.提出考虑砂土颗粒形状、密实度和有效平均正应力等影响因素的剪切带倾角经验公式，表征各类砂土破裂发展方向，定量描述土体状态对剪切带倾角的影响.提出的公式适用于各类砂土的剪切带倾角计算，公式各参数物理意义明确，且均可由常规物性试验和室内单元体试验测得.研究表明，由提出的公式得到的理论值与试验值偏差基本在-5°~5°，平均误差、标准误差和均方误差等统计指标约为现有其他方法的1/3，且不同密实度或有效平均正应力下的倾角变化规律与试验结果一致.
Abstract: The determination of shear band propagation direction is the key to the progressive failure analysis of rock and soil mass. The plane strain test results for inclination angles of shear band in various sands reported in literatures at home and abroad were collected systematically. Comparison of the calculated values of existing methods with experimental measurements showed that the calculated values seriously deviated from the test values and the errors cannot be neglected. A new empirical formula for inclination angle of shear band considering the influence of sand particle shape, density and effective mean normal stress was proposed to characterize the rupture direction of various sands and to quantitatively describe the influence of soil state on inclination angle. The formula is suitable for various sands, and all parameters determined by common phsical property tests and laboratory tests have explicit physical meaning. Results showed that the errors between the test values and the calculated values obtained from the proposed empirical formula were smaller than 5° and the statistical indices, such as the average, standard error and mean square error, are 1/3 of the results of the existing methods. In addition, the predicted variations of shear band inclination angles with different effective mean normal stresses or densities are in good agreement with the test results.