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提出一种砂土剪切带的两相平衡模型,此模型可看作一种新颖的分岔解。把剪切带考虑作高应变相,剪切带外部其它区域考虑作低应变相。在跨越两相界面处,考虑了变形梯度和应力的不连续性,以及拖曳力和位移的连续性,并且强加了Maxwell关系。推导出砂土在平面应变载荷下的控制方程,并且此分析归结为寻找使控制方程得到唯一一组物理上可以接受的实数解的载荷的最小值。Maxwell应力、剪切带内部和外部的应力应变、剪切带倾角等均可确定,并与实验所观察到的结果相一致。
A two-phase equilibrium model of sand-soil shear zone is proposed, which can be regarded as a novel bifurcation solution. The shear zone is considered as a high strain phase and the rest of the shear zone is considered as a low strain phase. At the interface across the two phases, the discontinuities in deformation gradients and stresses, as well as the continuity of drag and displacement, are considered, and the Maxwell relationship is imposed. The governing equations for sand under plane-strain loading are derived and this analysis comes down to finding the minimum value of the load that gives the governing equations a unique set of physically acceptable real solutions. Maxwell stress, stress and strain inside and outside the shear band, shear band inclination and so on can all be determined and are consistent with the experimental observations.