提出一种基于弹性力学平面问题傅里叶级数的长方形岩石劈裂应力解析方法。为了与该傅里叶级数解析方法比较，建立了相同劈裂载荷条件下长方形岩石三维有限元模型，分析了劈裂试件的应力分布，以及试件宽长比、垫条宽度对劈裂试件应力分布的影响。结果表明，两种方法的分析结果一致，劈裂试件的最大拉应力未出现在试件中心，而是出现在试件x=0 对称轴上靠近边界的某一点；最大拉应力随着垫条宽度2c 和试件宽长比b/a 的增加而减小；正方形试件的最大拉应力大于圆柱形试件的最大拉应力。通过类岩石材料劈裂实验，证明了该傅里叶级数解析方法描述的长方形岩石劈裂应力分布规律与实验结果相符。
The stress distribution of rectangular rock under split loads is an important research topic of rock mechanics. The formula of rectangular specimen tensile stress under splitting loads can be deduced by the Fourier series solution of the elastic plane problem. To compare the theoretical solution and the finite element solution, a dimensional finite element model of the rectangular specimen is built under the same loading conditions. The stress distribution and the impact of the width of spacer and the width to length ratio are analyzed. It is shown that results of the theoretical solution and the finite element solution are consistent. The maximum tensile stress does not appear in the center of the specimen but in a certain point with coordinates. The maximum tensile stress decreases with the increasing of the width of spacer and the width to length ratio b/a. The tensile stress distribution patterns of cylindrical specimen and square specimen are consistent, but the tensile stress of the square specimen is greater than that of the cylindrical specimen. It is proved that the splitting stress distribution of rectangular rock obtained by the Fourier series analysis method is consistent with the rock-like material splitting experimental results.
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