非饱和土拟二维平面应变固结问题的解析计算方法

doi:10.16285/j.rsm.2019.0200

岩土力学 ›› 2020, Vol. 41 ›› Issue (2): 453-460.doi: 10.16285/j.rsm.2019.0200

非饱和土拟二维平面应变固结问题的解析计算方法

程涛^{1, 2}，晏克勤¹，胡仁杰¹，郑俊杰²，张欢^{1, 3}，陈合龙¹，江志杰^{1, 3}，刘强^{1, 3}

1. 湖北理工学院土木建筑工程学院，湖北黄石 435003；2. 华中科技大学岩土与地下工程研究所，湖北武汉 430074； 3. 三峡大学土木与建筑学院，湖北宜昌 443002

收稿日期:2019-01-28 修回日期:2019-08-19 出版日期:2020-02-11 发布日期:2020-02-08
作者简介:程涛，男，1975年生，博士，教授，主要从事岩土本构关系、尾矿混合土力学及资源化、岩土工程多场耦合数值分析等方面的研究。
基金资助:
湖北省优秀中青年科技创新团队项目（No. T201823）；国家自然科学基金面上项目（No. 51478201）；湖北省教育厅重点项目（No. D20134401）；湖北省自科基金面上项目（No. 2012FKC14201）；湖北理工学院重点科研项目（No. 13xjz03A）。

Analytical method for quasi-two-dimensional plane strain consolidation problem of unsaturated soil

CHENG Tao^{1, 2}, YAN Ke-qin¹, HU Ren-jie¹, ZHENG Jun-jie², ZHANG Huan^{1, 3}, CHEN He-long¹, JIANG Zhi-jie^{1, 3}, LIU Qiang¹, ³

1. School of Civil Engineering, Hubei Polytechnic University, Huangshi, Hubei 435003, China; 2. Institute of Geotechnical & Underground Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China; 3. College of Civil Engineering & Architecture, China Three Gorges University, Yichang, Hubei 443002, China

Received:2019-01-28 Revised:2019-08-19 Online:2020-02-11 Published:2020-02-08
Supported by:
This work was supported by the Foundation for Innovative Research Team of Hubei Province(T201823), the General Program of National Natural Science Foundation of China (51478201), the Scientific Research Foundation of Hubei Provincial Education Department (D2013440), the General Program of Natural Science Foundation of Hubei Province (2012FKC14201) and the Key Program of Hubei Polytechnic University (13xjz03A).

摘要/Abstract

摘要： 基于Fredlund非饱和土一维固结理论，建立了二维平面应变条件下的固结方程组，并得到了单层非饱和土平面应变条件下的解析解。基于相关理论，假设体变系数和渗透系数都为常量，同时考虑到瞬时加载条件下，沿着土体深度方向上产生均匀或者线性分布的初始超孔隙压力，建立了二阶二元偏微分方程组。求解时，引入函数方法来降低方程的阶数，然后通过分离变量法获得方程的通解。在此基础上，结合一个针对单面排水条件下二维平面应变问题案例，通过与数值解对比，验证了所提方法的正确性。并采用所提方法计算获得了二维平面下超孔隙水压力、气压力沿垂直和水平方向消散的等时线，通过计算对比，分析了不同线性分布情况下，初始超孔隙压力对固结消散过程的影响。研究结果表明：初始超孔隙压力的不同分布对超孔隙气压力消散的影响几乎可以忽略，而对超孔隙水压力消散的影响更大。

关键词: 非饱和土, 二维固结, 平面应变, 解析解, 初始超孔隙压力

Abstract: Based on the one-dimensional consolidation theory of unsaturated soil developed by Fredlund, the consolidation equations under two-dimensional plane strain are established, and the analytical solution of single-layer unsaturated soil under plane strain is obtained. Based on relevant theories, it is assumed that the volume change and the permeability coefficients are both constant, and the second-order binary partial differential equations are established, considering uniform or linear distribution of initial super-porosity pressure along the depth of the soil under the condition of instantaneous loading. To solve the equations, we first introduce the function method to reduce the order of the equation, and then obtain the general solution of the equation by variable separation method. Based on the solution, a case of two-dimensional plane strain problem under single-sided drainage conditions is investigated, and the correctness of the method is verified by numerical solution. The isochronal line of excess pore water and gas pressures dissipated in the vertical and horizontal directions in the two-dimensional plane is calculated by the proposed method. The influence of initial excess pore pressure on the consolidation and dissipation processes under different linear distributions is analyzed by calculation and comparison. The results show that the different distribution of initial excess pore pressure has an almost negligible effect on the dissipation of excess pore gas pressure, and has a great influence on the dissipation of excess pore water pressure.

Key words: unsaturated soil, two-dimensional consolidation, plane strain, analytical solution, initial excess pore pressure

中图分类号:

TU 432

程涛, 晏克勤, 胡仁杰, 郑俊杰, 张欢, 陈合龙, 江志杰, 刘强, . 非饱和土拟二维平面应变固结问题的解析计算方法[J]. 岩土力学, 2020, 41(2): 453-460.

CHENG Tao, YAN Ke-qin, HU Ren-jie, ZHENG Jun-jie, ZHANG Huan, CHEN He-long, JIANG Zhi-jie, LIU Qiang, . Analytical method for quasi-two-dimensional plane strain consolidation problem of unsaturated soil[J]. Rock and Soil Mechanics, 2020, 41(2): 453-460.

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非饱和土拟二维平面应变固结问题的解析计算方法

Analytical method for quasi-two-dimensional plane strain consolidation problem of unsaturated soil

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