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目前砂土中球孔弹塑性扩张解无法合理考虑砂土的峰值强度和剪胀特性,因而其解答与实际情况存在一定偏差。为得出剪胀性砂土中球孔扩张问题的合理解答,采用砂土临界状态模型考虑球孔扩张过程中砂土剪胀特性和峰值强度对球孔扩张机制的影响,基于相关联流动法则推导了球孔扩张问题的弹塑性本构张量,进而在塑性区采用大变形理论并引入辅助变量,将球孔扩张问题归结为基于拉格朗日描述的一阶偏微分方程组的初值问题。在此基础上,结合孔周弹塑性边界条件求解得出了剪胀性砂土中球孔扩张问题的严格解答。通过与基于修正剑桥模型的球孔扩张解答相对比,研究了砂土峰值强度和剪胀特性对孔周土体应力状态和位移的影响规律。结果表明,基于砂土临界状态模型的弹塑性解答不仅可以合理反映球孔扩张过程过程中剪胀性砂土的峰值强度和剪胀特性,而且可退化为非剪胀性土体中的球孔扩张解答,因而可以更加广泛地应用于静力触探、静压沉桩等岩土工程问题中。
At present, the elastic-plastic expansive solution of the ball holes in sand can not reasonably consider the peak strength and dilatancy characteristics of sand so there is a certain deviation between the solution and the actual situation. In order to get a reasonable solution to the problem of ball hole expansion in dilapidated sand, the influence of the dilatancy of sand and the peak intensity on the expansion mechanism of the ball hole during the expansion of the ball hole are considered based on the criticality model of sand. Based on the associated flow rule The elasto-plastic constitutive tensor of the ball-hole expansion problem is deduced, and then the large deformation theory is introduced into the plastic zone and the auxiliary variables are introduced. The problem of spherical-hole expansion is attributed to the initial value of the first-order partial differential equations based on Lagrange’s description problem. On this basis, a rigorous solution to the problem of spherical cavity expansion in dilatable sand is obtained by solving the elastic-plastic boundary conditions around the hole. By comparing with the solution based on the modified Cambridge model, the influence of peak strength and dilatancy on the stress state and displacement of soils is studied. The results show that the elastic-plastic solution based on the critical state model of sand and soil can not only reflect the peak strength and dilatancy of dilatant sand during the expansion process of spherical pores, but also degenerate into the sphere of non-dilatancy soil Expansion of the solution, which can be more widely used in static probe, static pressure pile and other geotechnical problems.