Micromechanics-based stress-dilatancy relationship for granular materials
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摘要: 从微观力学角度出发,基于真应力张量推导了散体中平均接触力与平均接触位移的计算公式,并通过宏-微观能量守恒得到了考虑散体各向异性组构及其演化的应力-剪胀关系；详细分析了剪胀参数的物理意义及对剪胀性的影响,并与经典的剑桥流动法则、Rowe剪胀方程以及室内试验结果进行了比较分析。研究结果表明,提出的应力-剪胀关系宏微观物理意义明确,考虑了材料密实状态和微观各向异性组构及其演化对应力-剪胀关系的影响,可以很好地模拟散粒体的初始剪胀（缩）行为,并可反映峰值应力比滞后于最大剪胀比的现象。同时提出的应力-剪胀方程还可以描述材料在相变点处应力比不等于临界应力比的现象,与已有室内试验结果一致,能够较好地预测散体材料三轴条件下的各向异性应力-剪胀关系。Abstract: From the perspective of micromechanics, the formulas for the average contact force and contact displacement in the granular are derived based on the true stress tensor, then the stress-shear dilatancy relationship considering the fabric anisotropy and its evolution is obtained through the macro-micro energy conservation. In addition, the physical meaning of dilatancy parameters and their influence on dilatancy are analyzed. Finally, the proposed formulation is compared with the classical Cambridge flow law, Rowe dilatancy equation and test results to calibrate its reasonableness and applicability. The proposed stress-dilatancy relationship with clear physical meaning can describe the initial dilatancy (contraction) behavior for granular materials, considering the anisotropic evolution of fabric and the influence of the density on the dilatancy. Moreover, the proposed stress-dilatancy equation can reflect that the stress ratio at the phase transition point is less than the critical stress ratio and the peak stress ratio emerges behind the maximum dilatancy ratio. It is in good agreement with the test results and can better predict the anisotropic stress-dilatancy relationship of granular materials.
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图 5 不同流动法则下应力比-剪胀比关系对比图
Figure 5. Comparison of different stress-dilatancy relationships
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图 6 Ottawa砂应力-剪胀关系的试验结果与预测结果对比图
Figure 6. Comparison of predicted and test results for Ottawa sand
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