饱和单层土体一维热固结精确解

钮家军; 凌道盛; 王秀凯; 单振东; 赵云

doi:10.11779/CJGE201909016

饱和单层土体一维热固结精确解 English Version

钮家军¹,
凌道盛^1, ,,
王秀凯¹,
单振东²,
赵云^{1, 3}

1. 浙江大学岩土工程研究所,浙江杭州 310058;
2.中国地震局工程力学研究所,黑龙江哈尔滨 150080;
3.河南工业大学土木建筑学院,河南郑州 450001

基金项目: 国家重点研发计划项目（2016YFC0800202）; 国家自然科学基金项目（51578502）

详细信息

作者简介:
钮家军(1993— ),男,博士研究生,主要从事热-水-力耦合现象的解析解研究。E-mail：niu0918@zju.edu.cn。

通讯作者:
凌道盛，E-mail：dsling@zju.edu.cn

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出版历程
- 收稿日期: 2018-11-19
- 发布日期: 2019-09-24

Exact solutions for one-dimensional thermal consolidation of single-layer saturated soil

1. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China;
2. Institute of Engineering Mechanics, China Earthquake Administration, Harbin 150080, China;
3. College of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, China

摘要

摘要: 岩土体在非等温场下的固结响应一直是研究热点。基于考虑渗流的饱和土热固结控制方程,给出了一种三类任意边界条件下,饱和单层土体一维热固结精确解的求解方法。首先,利用函数φ将对温度和超静孔压的求解转换为对函数ϕ的求解,采用分离变量法,结合边界条件得到微分方程的特征函数。然后,将非齐次边界条件齐次化,利用微分方程的特征函数,采用系数变易法,给出非齐次边界条件下的精确级数解。最后,通过算例揭示土体边界的透水条件及温度变化对土体热固结响应影响显著。
- 饱和单层土 /
- 热固结 /
- 精确解 /
- 非齐次边界条件
Abstract: The consolidation under the non-isothermal field has long been the research focus. Based on the governing equations which take seepage flow into consideration, a new method to obtain exact solutions for one-dimensional thermal consolidation of single-layer saturated soil with three types of arbitrary boundary conditions is proposed. Firstly, the aim to solve temperature and excess pore pressure is transformed to solve the function ϕ by introducing the function φ. The eigenfunctions of differential equations are achieved with boundary conditions by the method of separation of variables. The nonhomogeneous boundary conditions are then transformed into homogeneous ones. The series form exact solutions are put forward according to the method of undetermined coefficients and eigenfunctions of differential equations. Finally, the conclusions that the seepage and temperature boundary play an important role in the thermal consolidation of the soil are reached by case studies.
- single-layer saturated soil /
- thermal consolidation /
- exact solution /
- nonhomogeneous boundary condition

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参考文献(16)

[1]	BIOT M A.General theory of three‐dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2): 155-164.
[2]	BIOT M A.Thermoelasticity and irreversible thermodynamics[J]. Journal of Applied Physics, 1956, 27(3): 240-253.
[3]	BOOKER J R, SAVVIDOU C.Consolidation around a point heat source[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 1985, 9(2): 173-184.
[4]	SMITH D W, BOOKER J R.Boundary element analysis of linear thermoelastic consolidation[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 1996, 20(7): 457-488.
[5]	ZHOU Y, RAJAPAKSE R K N D, GRAHAM J. A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration[J]. International Journal of Solids & Structures, 1998, 35(34/35): 4659-4683.
[6]	BOOKER J R, SAVVIDOU C.Consolidation around a spherical heat source[J]. International Journal of Solids & Structures, 1984, 20(11/12): 1079-1090.
[7]	MCTIGUE D F.Thermoelastic response of fluid-saturated porous rock[J]. Journal of Geophysical Research, 1986, 91(B9): 9533-9542.
[8]	GIRAUD A, ROUSSET G.Thermoelastic and thermoplastic response of a porous space submitted to a decaying heat source[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2010, 19(7): 475-495.
[9]	BLOND E, SCHMITT N, FRANÇOIS H. Response of saturated porous media to cyclic thermal loading[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 2010, 27(11): 883-904.
[10]	BAI M, ABOUSLEIMAN Y.Thermoporoelastic coupling with application to consolidation[J]. International Journal for Numerical & Analytical Methods in Geomechanics, 1997, 21(2): 121-132.
[11]	白冰. 岩土颗粒介质非等温一维热固结特性研究[J]. 工程力学, 2005, 22(5): 186-191. (BAI Bai.One-dimensional thermal consolidation characteristics of geotechnical media under non-isothermal condition[J]. Engineering Mechanics, 2005, 22(5): 186-191. (in Chinese))
[12]	BAI B.Fluctuation responses of saturated porous media subjected to cyclic thermal loading[J]. Computers & Geotechnics, 2006, 33(8): 396-403.
[13]	白冰. 循环温度荷载作用下饱和多孔介质热-水-力耦合响应[J]. 工程力学, 2007, 24(5): 87-92. (BAI Bai.Thermo-Hydro-Mechanical responses of saturated porous media under cyclic thermal loading[J]. Engineering Mechanics, 2007, 24(5): 87-92. (in Chinese))
[14]	BAI B.Thermal consolidation of layered porous half-space to variable thermal loading[J]. Applied Mathematics and Mechanics (English Edition), 2006, 11(27): 1531-1539.
[15]	王路君, 艾智勇. 衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法[J]. 力学学报, 2017, 49(2): 324-334. (WANG Lu-jun, AI Zhi-yong.Epim for thermal consolidation problems of saturated porous media subjected to a decaying heat source[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 324-334.(in Chinese))
[16]	SMITH D W.Boundary element analysis of heat flow and consolidation for geotechnical applications[D]. Sydney: University of Sydney, 1990.

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