基于率态模型的颗粒材料剪切强度理论

Shear strength theory of granular materials based on rate-state model

颗粒材料在工程中非常普遍,发展精确的颗粒材料强度理论是其得以应用的基础和关键.本文基于颗粒接触微观模型,考虑剪应变由接触颗粒的滑移和颗粒自身旋转共同作用的结果,建立了剪切带上的应变分量关系.结合经典的摩擦率态模型,以能量原理为基础,构建了颗粒材料剪切强度的耦合演化模型,该模型可用于分析颗粒材料系统的内摩擦系数随剪切变形的全过程演化状态.为了验证所得模型的合理性,使用平均粒径为0.15 mm的规则球状玻璃珠分别进行了等竖向压力变剪切速率和等剪切速率变竖向压力的直剪实验.实验结果表明,颗粒材料系统内摩擦系数随剪切位移的变化规律与本文推导的理论模型预测完全一致,从而验证了本文所提出模型的合理性.通过进一步对模型参数进行详细分析,研究了剪切速率和竖向压力对模型参数及材料强度的影响.结果表明,颗粒材料系统的剪切强度并非严格遵守库仑强度理论,剪胀角对剪切强度会产生明显的影响;颗粒材料竖向应力的增大会使其在剪切破坏前经历更大的变形,提高颗粒材料系统的韧性.本文提出的模型可以综合考虑更多的强度影响因素,提高了模型的准确性,进一步丰富了颗粒材料强度分析理论.

Granular materials are very common in engineering applications.Thus,it is essential to develop an accurate strength theory for their description.In this paper,we establish a relationship between the strain components in the shear band based on the microscopic particle contact model.More specifically,we consider the shear strain caused by both the slip and the rotation of the particles.From the principle of energy,a coupled evolution model of the shear strength of granular materials was constructed.This model can be used to analyze the entire evolution process of the internal friction coefficient in granular materials with shear deformation.To verify the model,we used materials composed of glass beads with an average particle size of 0.15 mm.We conducted the shear tests under both constant normal stress and constant shear rate.The experimental results showed that the variation of the internal friction coefficient with shear displacement was consistent with the prediction of our theoretical model.The influences of shear rate and normal stress on the strength were studied by further detailing the model parameters.More specifically,we demonstrated that the shear strength of the granular material system did not strictly follow the Coulomb strength theory,and the dilatancy angle had a significant effect on the shear strength.The increase of normal stress in granular materials resulted in larger deformations before failure.Hence the toughness of granular material was significantly enhanced.The proposed model allowed to comprehensively consider more influencing factors of strength,improve the accuracy of the model,and further enrich the strength analysis theory of granular materials.