The shape of granular materials is one of the effective parameters in determining mechanical behavior. This property affects the fracture strength, compressibility, maximum friction angle and the distribution of contact stresses. So far, laboratory studies on the effect of shape on the behavior of granular materials have focused mostly on comparing the results of angular and rounded grains. Due to the distribution of different shapes in natural grain materials, experimental studies of the effect of sphericity index are of great importance. On the other hand, it is necessary to investigate the grain shape on the compression model parameters comprehensively. Therefore, based on the energy conservation equation and the use of statistical Weibull and fractal theory, the compressibility model of granular materials under uniaxial loading conditions is obtained by taking into account the quantitative parameters related to the shape of grain. Then, in order to evaluate the analytical model, three stages of laboratory tests are performed. In the first stage, uniaxial loading tests are performed on four different shapes of concrete grains of the same size under the same conditions. In the second stage, similar experiments are performed on angular granite grains to check the applicability of the model to natural materials with different shapes. In the third stage, the sleeper loading modeling is performed on granite grains of real ballast dimensions. The results of large-scale tests are compared with the compressibility model obtained from the results of small-scale tests. Finally, an empirical relationship is proposed to determine the amount of breakage factor based on the energy applied to the grains. The results show that the empirical relationship in combination with the analytical solution can accurately predict the stress-breakage-void ratio behavior of granular materials at each loading step.

粒状材料的形状是确定机械性能的有效参数之一。该特性影响断裂强度、可压缩性、最大摩擦角和接触应力的分布。到目前为止，关于形状对颗粒材料行为影响的实验室研究主要集中在比较有角和圆形颗粒的结果。由于天然颗粒材料中存在不同形状的分布，因此对球形指数影响的实验研究具有重要意义。另一方面，有必要对压缩模型参数的晶粒形状进行综合研究。因此，基于能量守恒方程并利用统计威布尔和分形理论，通过考虑与颗粒形状相关的定量参数，得到了颗粒材料在单轴加载条件下的压缩率模型。然后，为了评估分析模型，进行了三个阶段的实验室测试。第一阶段，在相同条件下对四种不同形状、尺寸相同的混凝土颗粒进行单轴加载试验。在第二阶段，对角花岗岩颗粒进行了类似的实验，以检查模型对不同形状的天然材料的适用性。在第三阶段，对实际道碴尺寸的花岗岩颗粒进行轨枕加载建模。将大尺度试验的结果与小尺度试验结果得到的可压缩性模型进行比较。最后，提出了一种经验关系式来确定基于施加到晶粒上的能量的破碎因子的量。结果表明，经验关系式结合解析解可以准确预测颗粒材料在每个加载步骤的应力-破损-空隙率行为。