Exact solutions for one-dimensional thermal consolidation of single-layer saturated soil
-
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。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.
-
[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. -
期刊类型引用(22)
1. 卢汉青，包卫星，陈锐，郭强，尹严. 基于核磁共振技术的冻融板岩损伤特性试验研究. 地下空间与工程学报. 2025(01): 78-86+99 . 
百度学术
2. 贾朝军，庞锐锋，俞隽，雷明锋，李忠. 基于离散元的岩石冻融损伤劣化机制研究. 岩土力学. 2024(02): 588-600 . 百度学术
3. 赵越，司运航，张译丹，赵京禹. 水化-冻融耦合条件下大理岩蠕变损伤本构模型. 吉林大学学报(地球科学版). 2024(01): 231-241 . 百度学术
4. 樊赖宇，吴志军，储昭飞，翁磊，王智洋，刘泉声，陈结. 动态冲击下红砂岩蠕变特性及损伤本构模型. 岩土力学. 2024(06): 1608-1622 . 百度学术
5. 刘文博，张树光，黄翔，刘轶品. 基于蠕变曲线对称的蠕变模型研究及参数敏感性分析. 煤炭科学技术. 2024(07): 48-56 . 百度学术
6. 宋勇军，操警辉，程柯岩，杨慧敏，毕冉，张琨. 砂岩冻结/解冻过程蠕变特性研究. 水文地质工程地质. 2024(06): 93-103 . 百度学术
7. 王波，任永政，田志银，马世纪，王军，黄万朋，王灵. 流变扰动条件下岩石微观损伤试验研究. 煤炭学报. 2024(S2): 852-861 . 百度学术
8. 杨志全，甘进，樊详珑，朱颖彦，杨溢，丁渝池. 岩石冻融损伤机理研究进展及展望. 防灾减灾工程学报. 2023(01): 176-188 . 百度学术
9. 赵志波. 冻融条件下隧道围岩单轴蠕变力学特性试验及本构模型. 黑龙江科技大学学报. 2023(02): 299-305 . 百度学术
10. 苗浩东，任富强. 冻融循环作用下不同含水率砂岩抗拉特性研究. 工矿自动化. 2023(05): 133-138+152 . 百度学术
11. 闫建兵，张小强，宋选民，王开，姜玉龙，岳少飞. 低围压条件下无烟煤三轴蠕变特性试验研究（英文）. Journal of Central South University. 2023(05): 1618-1630 . 百度学术
12. 张卫泽，王琳庆，郭文重，陈雷. 基于Weibull分布的红砂岩三轴蠕变试验及模型研究. 水文地质工程地质. 2023(04): 137-148 . 百度学术
13. 赵越，李磊，闫晗，肖万山，苏艳军. 水化-冻融耦合作用下大理岩单轴蠕变力学特性. 吉林大学学报(地球科学版). 2023(04): 1195-1203 . 百度学术
14. 包卫星，卢汉青，郭强，尹严. 新疆高寒炭质板岩隧道围岩冻融劣化特性研究. 工程地质学报. 2023(04): 1213-1224 . 百度学术
15. 王丹，冯子军，张子翔. 砂岩的三维非线性损伤蠕变特性. 矿业研究与开发. 2023(10): 139-144 . 百度学术
16. 付宏渊，段鑫波，史振宁. 冻融循环下粉砂质泥岩强度劣化特性及细观机理研究. 工程地质学报. 2023(06): 1833-1841 . 百度学术
17. 张进元. 冻融作用下公路块石路基损伤特性研究. 青海交通科技. 2023(06): 131-134 . 百度学术
18. 王璐. 二次损伤岩石的蠕变研究综述. 工程技术研究. 2022(07): 39-42 . 百度学术
19. 唐志强，吉锋，许汉华，冯文凯，何萧. 豫南燕山期花岗岩蠕变特性及非线性蠕变损伤模型. 科学技术与工程. 2022(16): 6421-6429 . 百度学术
20. 尹彦波. 不同应变率下冻融损伤大理岩的动态压缩特性研究. 矿业研究与开发. 2022(08): 139-145 . 百度学术
21. 马志奇，杨小彬，刘腾辉，李志辉. 粒径大小对颗粒堆积体Burgers模型蠕变参数相似试验研究. 矿业科学学报. 2022(06): 730-737 . 百度学术
22. 王飞，高明忠，邱冠豪，汪亦显，周昌台，王之禾. 初始损伤–载荷–冻融作用下红砂岩的孔隙结构及力学特性. 工程科学与技术. 2022(06): 194-203 . 百度学术
其他类型引用(43)
计量
- 文章访问数: 327
- HTML全文浏览量: 13
- PDF下载量: 187
- 被引次数: 65
下载:
