基于相似性原理超固结土不排水扩张半解析解

在实际工程中，土体往往因卸载、再加载等复杂应力路径而处于超固结状态，而现有的圆孔扩张问题的计算模型往往不能反映超固结土中剪胀、软化等一些特殊性质。为了解决这一问题，基于相似性原理和统一硬化（UH）模型，结合相关联的流动法则和大变形理论，采用相似求解技术求解了超固结土不排水扩张问题的半解析解答。通过理想化算例分析了圆孔扩张挤土产生的应力和孔压响应，并通过分析不同超固结比OCR的土体应力路径的变化规律，讨论了UH模型的适用性。结果表明：对于轻超固结土，空腔周围土体孔压在塑性区沿径向单调递减，随着OCR增大，塑性区内孔压分布呈现出“S”形的趋势，孔壁附近的孔压逐渐减小，孔壁周围甚至出现负孔压。随着OCR增大，压力?扩张曲线收敛变慢。在扩孔过程中正常固结土一直处于剪缩硬化阶段。而对于超固结土，土体则经历了临界状态→剪胀硬化阶段→临界（特征）状态→剪缩硬化阶段。该研究成果不仅丰富了相似求解技术的应用，而且为超固结土中桩基承载力、隧道围岩变形预测和原位测试参数等岩土工程问题的计算提供了理论依据。

A semi-analytical solution for cavity undrained expansion in over-consolidated soils based on similarity transform theory

Soils are often in an over-consolidated state due to complex stress paths such as unloading and reloading in practical engineering and the existing models for the cavity expansion problem fail to reflect the dilatancy and softening characteristics of over-consolidated soils. To this end, a semi-analytical solution for cavity undrained expansion in over-consolidated soils based on UH model was solved by using similarity solving technique in combination with associated flow rule and large strain theory. The response of stress and excess pore-water pressure caused by compaction effect was analyzed and the applicability of UH model was discussed by analyzing the variation of soil stress path with different over-consolidation ratios (OCR). The results, including the stress distributions curves, the expansion-pressure curves, effective stress path and yield locus variation curves and the evolution of the potential strength during cavity expansion, shows that: (1) For the lightly over-consolidated, the excess pore-water pressure decreases monotonously along the radial direction in the plastic zone in which the pressure curve presents a "S" shaped trend and decreases gradually around the cavity, particularly negative pore pressure appears around the pore wall, with the increase of OCR. (2) With the increase of OCR, the convergence of pressure-expansion curves becomes slower. (3) In the process of the cavity expansion, the normally consolidated soil is always in the stage of contraction and hardening. While for the over-consolidated, it goes through critical state to dilatancy and hardening stage to critical state to shear contraction and hardening one. This paper not only enriches the application of similarity solving technique, but also provides a reference for calculation of bearing capacity of pile foundation in over-consolidated soil, prediction for surrounding rock deformation of tunnels and determination of in-situ test parameters.