饱和土不排水柱孔扩张计算的通用半解析解  

Semi-analytical solution for the undrained expansion of a cylindrical cavity in saturated soil

作　　者：刘贯飞 雷胜友[1] LIU Guanfei;LEI Shengyou(School of Highway,Chang’an University,Xi’an 710064,China;China 19th Metallurgical Corporation,Chengdu 610031,China)

机构地区：[1]长安大学公路学院,陕西西安710064 [2]中国十九冶集团有限公司,四川成都610031

出　　处：《水利水运工程学报》2024年第1期138-148,共11页Hydro-Science and Engineering

基　　金：国家自然科学基金资助项目(59479017);铁道部科技研究开发资助项目(2010G003-F)。

摘　　要：基于修正剑桥模型建立的不排水柱孔扩张解答仅适用于正常固结和弱超固结饱和黏土,不适用于严重超固结土和颗粒材料。采用统一状态参数模型(CASM)和Rowe剪胀方程推导土的弹塑性应力应变关系,结合大应变理论并引入辅助变量,用拉格朗日分析法推导了弹塑性土体有效应力和超孔隙水压力的相似解,在此基础上结合弹塑性区的边界条件,最终建立通用的饱和土中不排水柱孔扩张半解析解。计算结果表明,选择合适的间距比和应力-状态参数,所得结果与修正剑桥模型结果一致,并且对严重超固结土的计算结果更加合理;通过修正参数取值,该半解析解可用于更多类别饱和土中的不排水柱孔扩张计算。The existing solution for undrained cylindrical cavity expansion,based on the modified Cam clay model,is limited in its applicability to saturated,normally consolidated,and slightly over-consolidated clays,excluding heavily over-consolidated soils and granular materials.To address this limitation,a general solution is proposed for the expansion of a cylindrical cavity in saturated soil under undrained conditions.The solution utilizes a Unified State Parameter Model(CASM)incorporating Rowe's stress-dilatancy relation to derive the elastoplastic stress-strain relationship of saturated soil.By employing the large deformation theory and introducing an auxiliary variable,expressions for the effective stress and excess pore water pressure of the soil in the elastoplastic zone are derived using the Lagrangian analysis method.A semi-analytical solution for undrained cylindrical cavity expansion is obtained under the elastic-plastic boundary conditions.The results demonstrate that the present solution yields consistent calculations with the modified Cam clay model when appropriate spacing ratio and stress-state parameters are selected,and it provides more reasonable results for heavily over-consolidated soils.Furthermore,the proposed solution can be applied to calculate undrained cylindrical cavity expansion in various types of saturated soils by adjusting the parameter values.

关 键 词：柱孔扩张 统一状态参数模型 不排水 拉格朗日分析法 

分 类 号：TU473[建筑科学—结构工程]