结构性黄土排水柱孔扩张问题弹塑性解析

为研究黄土地区原位测试、沉桩扩孔以及劈裂注浆等岩土工程问题,基于结构性黄土修正剑桥模型,在严格遵循平均有效应力与偏应力定义前提下,针对排水柱孔扩张问题导出严密解。在孔周弹性区采用小变形理论求得土体应力与位移解析解,在孔周塑性区采用大变形理论,并借助中间变量将圆孔扩张问题转化为基于拉格朗日描述的一阶常微分方程组的初值问题,结合孔周弹塑性边界条件,导出塑性区土体有效应力分量与比容的半解析半数值严格解。结果表明:得出的退化解与已有解析解完全吻合,并且考虑土体结构性的计算结果与黄土地区开展的原位试验结果也较接近,从而验证了该分析方法与计算结果的合理性;结构性对土体塑性区半径、塑性区应力与比容影响显著,考虑结构性影响能够提高土体强度,在超固结比较大时也能减小土体软化程度。该解答不仅能为静压桩的桩侧阻力、劈裂注浆压力与原位试验参数等计算提供参考,还能为该类工程的简化计算提供理论验证依据。

Elastic-plastic solution for drained cylindrical cavity expansion in structured loess

To investigate geotechnical engineering problems such as in-situ soil testing,driven piles and splitting grouting in loess areas,a rigorous semi-analytical solution is derived for drained expansion of a cylindrical cavity under the premise of strict adherence to the definitions of mean effective stress and deviatoric stress,based on the modified Cam-clay model of structured loess. The analytical solutions of the stress and displacement in the elastic zone around the cavity are obtained by using the small deformation theory,and with the aid of the large strain theory and an auxiliary variable,the problem of cavity expansion is transformed into an initial value problem of a system of first-order ordinary differential equations in terms of the Lagrangian scheme in the plastic zone around the cavity. The rigorous semi-analytical solutions of the components of the effective stress and the specific volume are derived based on the elastic-plastic boundary conditions. The results show that the degenerate solutions developed are in good agreement with the existing analytical solutions and the calculation results considering the soil structure are close to in situ test results in the loess area,indicating the rationality of the analysis method and calculation results. The soil structure has a significant effect on the plastic zone radius,the stress component and the specific volume of the plastic zone. The strength of the soil can be increased by taking into account the effects of the soil structure. The degree of softening of the soil can be reduced when the over-consolidation ratio is relatively large. The developed solution can not only provide a reference for the calculation of the lateral resistance of driven piles,splitting grouting pressure and in-situ test parameters,but also provide theoretical verification basis for the simplified calculation of such kind of engineering.