常吸力下非饱和土柱孔扩张弹塑性解及饱和度响应

Elasto-plastic solution and saturation response of cylindrical cavity expansion in unsaturated soil under constant suction

摘要:

为研究非饱和土中常吸力条件下圆孔扩张的应力-应变特性及饱和度响应,基于非饱和土临界状态模型(UCSM)和考虑水力滞回的土水特征曲线(SWCC),引入常吸力下饱和度随孔隙比非线性变化模型,推导非饱和土中柱孔扩张问题的排水半解析解。根据柱孔周围土单元平衡微分方程,考虑边界条件,引入辅助坐标将问题转化为以3个主应力分量、孔隙比和饱和度为基本未知量的一阶微分方程组进行求解。本解答充分考虑基质吸力和超固结比对柱孔扩张响应的影响,探究扩张过程中柱孔周围土体的应力分布和体积变化,以及扩张过程中饱和度的演化规律。结果表明:非饱和土常吸力柱孔扩张过程中,呈现吸力硬化特性,且吸力硬化特性随着吸力增大而趋于稳定；孔壁及周围土体饱和度在扩张过程中变化显著,且受吸力大小的影响较大；当吸力较低时,饱和度主要受含水量变化的影响；当吸力较高时,饱和度主要受孔隙比变化的影响。本文的解答可以很好地捕捉非饱和土体不同应力历史和水力状态下的饱和度响应,可为非饱和土中静力触探试验等原位试验的解释提供指导。

Abstract:

The stress-strain characteristics and saturation response of cavity expansion under constant suction in unsaturated soil were investigated. The semi-analytical drained solutions were derived for cylindrical cavity expansion in unsaturated soil based on the unsaturated critical state model (UCSM), the soil-water characteristic curve (SWCC) considering hydraulic hysteresis, and the nonlinear model of saturation varying with void ratio under constant suction. According to the equilibrium differential equations of soil elements around the cylindrical cavity, an auxiliary coordinate was introduced considering boundary conditions, and the problem was solved by first-order differential equations with three principal stress components, void ratio, and saturation as basic unknowns. The solutions fully considered the influence of matric suction and over-consolidation ratio on the expansion response, and explored the stress distribution and volume change in soil around the cylindrical cavity, as well as the saturation evolution law during the expansion process. Results show that the soil exhibited the characteristics of suction hardening during the cylindrical expansion under constant suction and the suction hardening phenomenon tended to be stable with the increase in suction. The saturation of soil at and around the cavity wall changed significantly during the expansion process and was greatly affected by suction. For soil with lower suction, the saturation was mainly affected by the water content change. While for soil with higher suction, the saturation was mainly affected by the void ratio change. This solution can well capture the saturation response of unsaturated soil under different stress histories and hydraulic states, which can provide guidance for the interpretation of in-situ tests such as cone penetration tests in unsaturated soil.