非饱和土干缩开裂分析的近场动力学模拟  

Peridynamics for Moisture Diffusion and Crack Propagation in Unsaturated Soil Desiccation

作　　者：刘攀勇 顾鑫[1] 章青[1] LIU Panyong;GU Xin;ZHANG Qing(College of Mechanics and Engineering Science,Hohai University,Nanjing 211100,P.R.China)

机构地区：[1]河海大学力学与工程科学学院,南京211100

出　　处：《应用数学和力学》2024年第7期823-834,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12172121,12002118,11932006);湖南省水利科技项目(XSKJ2023059-16);上海市青年科技英才扬帆计划(21YF1419000)。

摘　　要：非饱和土失水收缩变形是一种水力耦合现象,其诱发的开裂问题严重削弱了土体的水力和力学特性,造成各种潜在的自然灾害.相对于饱和土体,非饱和土的失水收缩机制更为复杂,受到广泛关注.为此,提出了一种考虑水-力耦合作用效应的键型近场动力学(PD)模型,探究由于水分变化引起的非饱和土体变形开裂特征.在该模型中,非饱和土扩散方程由近场动力学微分算子进行重构,键型近场动力学运动方程采用改进的微弹性模量.然后提出了一种显-隐式混合算法,扩散方程采用显式差分格式求解,运动方程采用隐式整体格式求解,有效避免了两类方程在同一显式格式下时间步不协调的问题.通过非饱和土块干燥收缩变形和三维土盘干燥开裂的算例分析,验证了模型和算法的有效性.研究结果表明,所建立的模型和算法能较好地捕捉非饱和土失水收缩开裂的过程.Unsaturated soil desiccation cracking is a coupled hydro-mechanical problem.It seriously weakens the hydraulic and mechanical characteristics of soil,causing various natural disasters potentially.For the unsat-urated soil,the mechanism of moisture diffusion and deformation is more complicated compared with saturated soil,attracting wide attention.Thus,a coupled hydro-mechanical bond-based peridynamic(BB PD)model was proposed to explore the moisture diffusion and crack propagation in unsaturated soil.Specifically,the moisture diffusion equation for unsaturated soil was recast with the peridynamic differential operator,and an improved micro-modulus was adopted to revise the bond force density in the BB PD.In addition,a hybrid algorithm com-bining the explicit difference scheme for solving the diffusion equation and the implicit scheme for solving the motion equation was adopted,to avoid the incongruity of time steps for two types equations under the same ex-plicit scheme.The validity of the proposed model and algorithm was verified by the examples on the desiccation of an unsaturated soil block and the desiccation cracking of a 3D unsaturated soil plate.The results show the potential of peridynamics in capturing desiccation cracks of unsaturated soil.

关 键 词：非饱和土 水-力耦合 干缩开裂 近场动力学 

分 类 号：P642.3[天文地球—工程地质学]