Abstract
Porous materials can be found in a variety of geophysical and engineering applications. The existence of thermal contact resistance at the interface between bilayered saturated porous strata would result in a significant temperature difference at the interface. An attempt is made to study the thermo-hydro-mechanical coupling dynamic response of bilayered saturated porous strata with thermal contact resistance and elastic wave impedance. The corresponding analytical solutions for the dynamic response of bilayered saturated porous strata under a harmonic thermal load are derived by the operator decomposition method, and their rationality is verified by comparing them with existing solutions. The influences of thermal contact resistance, thermal conductivity ratio, and porosity ratio on the dynamic response of bilayered saturated porous strata are systematically investigated. Outcomes disclose that with the increase of thermal contact resistance, the displacement, pore water pressure and stress decrease gradually, and the temperature jump at the interface between two saturated porous strata increases.
摘要
多孔介质广泛存在于各类地球物理环境和工程应用中。由于双层饱和孔隙地层接触面间接触热阻的存在,接触面间会产生显著的温度差异。本文尝试对考虑接触热阻和弹性波阻抗效应的双层饱和孔隙地层的热-水-力耦合动力响应进行研究。采用算子分解方法求得简谐热力荷载作用下双层饱和孔隙地层的热-水-力耦合动力响应的解析解;通过与现有解的对比验证该解的正确性。此外,对接触热阻、热传递系数、孔隙比对双层饱和孔隙地层热-水-力耦合动力响应的影响开展了系统分析。结果表明,随着接触热阻的增大,位移、孔隙水压力和应力大小都逐渐降低,且温度跃变现象在地层接触面上表现的更为明显。
Similar content being viewed by others
References
WU Wen-bing, YANG Zi-jian, LIU Xin, et al. Horizontal dynamic response of pile in unsaturated soil considering its construction disturbance effect [J]. Ocean Engineering, 2022, 245: 110483. DOI: https://doi.org/10.1016/j.oceaneng.2021.110483.
WU Xun, SHI Jian-yong, LEI Hao, et al. Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills [J]. Journal of Central South University, 2019, 26(11): 3175–3187. DOI: https://doi.org/10.1007/s11771-019-4244-y.
ZHAO Xiao-dong, ZHOU Guo-qing, CHEN Guo-zhou. Triaxial compression strength for artificial frozen clay with thermal gradient [J]. Journal of Central South University, 2013, 20(1): 218–225. DOI: https://doi.org/10.1007/s11771-013-1479-x.
ZHANG Yun-peng, JIANG Guo-sheng, WU Wen-bing, et al. Analytical solution for distributed torsional low strain integrity test for pipe pile [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2022, 46(1): 47–67. DOI: https://doi.org/10.1002/nag.3290.
KRISHNA M V, CHAMKHA A J. Hall and ion slip effects on unsteady MHD convective rotating flow of nanofluids—Application in biomedical engineering [J]. Journal of the Egyptian Mathematical Society, 2020, 28: 1. DOI: https://doi.org/10.1186/s42787-019-0065-2.
KRISHNA M V, SRAVANTHI C S, GORLA R S R. Hall and ion slip effects on MHD rotating flow of ciliary propulsion of microscopic organism through porous media [J]. International Communications in Heat and Mass Transfer, 2020, 112: 104500. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2020.104500.
KRISHNA M V, AHAMMAD N A, CHAMKHA A J. Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface [J]. Case Studies in Thermal Engineering, 2021, 27: 101229. DOI: https://doi.org/10.1016/j.csite.2021.101229.
XU Yun-shan, SUN De-an, ZENG Zhao-tian, et al. Effect of temperature on thermal conductivity of lateritic clays over a wide temperature range [J]. International Journal of Heat and Mass Transfer, 2019, 138: 562–570. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2019.04.077.
XU Yun-shan, ZENG Zhao-tian, SUN De-an, et al. Comparative study on thermal properties of undisturbed and compacted lateritic soils subjected to drying and wetting [J]. Engineering Geology, 2020, 277: 105800. DOI: https://doi.org/10.1016/j.enggeo.2020.105800.
WANG Kui-hua, WU Wen-bing, ZHANG Zhi-qing, et al. Vertical dynamic response of an inhomogeneous viscoelastic pile [J]. Computers and Geotechnics, 2010, 37(4): 536–544. DOI: https://doi.org/10.1016/j.compgeo.2010.03.001.
XIE Kang-he, XIA Chang-qing, AN Ran, et al. A study on the one-dimensional consolidation of double-layered structured soils [J]. Computers and Geotechnics, 2016, 73: 189–198. DOI: https://doi.org/10.1016/j.compgeo.2015.12.007.
LI Chuan-xun, XIE Kang-he, HU An-feng, et al. One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient [J]. Journal of Central South University, 2012, 19(2): 562–571. DOI: https://doi.org/10.1007/s11771-012-1040-3.
ZHANG Yun-peng, WU Wen-bing, ZHANG Hai-kuan, et al. A novel soil-pile interaction model for vertical pile settlement prediction [J]. Applied Mathematical Modelling, 2021, 99: 478–496. DOI: https://doi.org/10.1016/j.apm.2021.07.004.
GUAN Wen-jie, WU Wen-bing, JIANG Guo-sheng, et al. Torsional dynamic response of tapered pile considering compaction effect and stress diffusion effect [J]. Journal of Central South University, 2020, 27(12): 3839–3851. DOI: https://doi.org/10.1007/s11771-020-4503-y.
CUI Peng-lu, LIU Zhong-yu, ZHANG Jia-chao, et al. Analysis of one-dimensional rheological consolidation of double-layered soil with fractional derivative Merchant model and non-Darcian flow described by non-Newtonian index [J]. Journal of Central South University, 2021, 28(1): 284–296. DOI: https://doi.org/10.1007/s11771-021-4602-4.
HUANG Kan, SUN Yi-wei, ZHOU De-quan, et al. Influence of water-rich tunnel by shield tunneling on existing bridge pile foundation in layered soils [J]. Journal of Central South University, 2021, 28(8): 2574–2588. DOI: https://doi.org/10.1007/s11771-021-4787-6.
CHENG Tian-bao, LI Wei-guo, ZHANG Chuan-zeng, et al. Unified thermal shock resistance of ultra-high temperature ceramics under different thermal environments [J]. Journal of Thermal Stresses, 2014, 37(1): 14–33. DOI: https://doi.org/10.1080/01495739.2013.818891.
BIOT M A. Thermoelasticity and irreversible thermodynamics [J]. Journal of Applied Physics, 1956, 27(3): 240–253. DOI: https://doi.org/10.1063/1.1722351.
BAI Bing, LI Tao. Irreversible consolidation problem of a saturated porothermoelastic spherical body with a spherical cavity [J]. Applied Mathematical Modelling, 2013, 37(4): 1973–1982. DOI: https://doi.org/10.1016/j.apm.2012.05.003.
BAI Bing. Thermal response of saturated porous spherical body containing a cavity under several boundary conditions [J]. Journal of Thermal Stresses, 2013, 36(11): 1217–1232. DOI: https://doi.org/10.1080/01495739.2013.788389.
ZHANG Yun-peng, LIU Hao, WU Wen-bing, et al. A 3D analytical model for distributed low strain test and parallel seismic test of pipe piles [J]. Ocean Engineering, 2021, 225: 108828. DOI: https://doi.org/10.1016/j.oceaneng.2021.108828.
LIU Gan-bin, LIU Xiao-hu, YE Rong-hua. The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory [J]. International Journal of Engineering Science, 2010, 48(9): 795–808. DOI: https://doi.org/10.1016/j.ijengsci.2010.04.006.
LORD H W, SHULMAN Y. A generalized dynamical theory of thermoelasticity [J]. Journal of the Mechanics and Physics of Solids, 1967, 15(5): 299–309. DOI: https://doi.org/10.1016/0022-5096(67)90024-5.
GREEN A E, LINDSAY K A. Thermoelasticity [J]. Journal of Elasticity, 1972, 2(1): 1–7. DOI: https://doi.org/10.1007/BF00045689.
HUSSEIN E M. Effect of the porosity on a porous plate saturated with a liquid and subjected to a sudden change in temperature [J]. Acta Mechanica, 2018, 229(6): 2431–2444. DOI: https://doi.org/10.1007/s00707-017-2106-y.
ZHANG Yun-peng, LIU Hao, WU Wen-bing, et al. Interaction model for torsional dynamic response of thin-wall pipe piles embedded in both vertically and radially inhomogeneous soil [J]. International Journal of Geomechanics, 2021, 21(10): 04021185. DOI: https://doi.org/10.1061/(asce)gm.1943-5622.0002165.
LIU Run, WANG Wu-gang, YAN Shu-wang. Finite element analysis on thermal upheaval buckling of submarine burial pipelines with initial imperfection [J]. Journal of Central South University, 2013, 20(1): 236–245. DOI: https://doi.org/10.1007/s11771-013-1481-3.
GAO Jia-jia, DENG Jin-gen, LAN Kai, et al. Porothermoelastic effect on wellbore stability in transversely isotropic medium subjected to local thermal non-equilibrium [J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 96: 66–84. DOI: https://doi.org/10.1016/j.ijrmms.2016.12.007.
HENDY M H, AMIN M M, EZZAT M A. Two-dimensional problem for thermoviscoelastic materials with fractional order heat transfer [J]. Journal of Thermal Stresses, 2019, 42(10): 1298–1315. DOI: https://doi.org/10.1080/01495739.2019.1623734.
WANG Ying-ze, ZHANG Xiao-bing, SONG Xin-nan. A generalized theory of thermoelasticity based on thermomass and its uniqueness theorem [J]. Acta Mechanica, 2014, 225(3): 797–808. DOI: https://doi.org/10.1007/s00707-013-1001-4.
GREEN A E, NAGHDI P M. Thermoelasticity without energy dissipation [J]. Journal of Elasticity, 1993, 31(3): 189–208. DOI: https://doi.org/10.1007/BF00044969.
KUANG Zhen-bang. Variational principles for generalized thermodiffusion theory in pyroelectricity [J]. Acta Mechanica, 2010, 214(3–4): 275–289. DOI: https://doi.org/10.1007/s00707-010-0285-x.
YOUSSEF H M, EL-BARY A A. Thermal shock problem of a generalized thermoelastic layered composite material with variable thermal conductivity [J]. Mathematical Problems in Engineering, 2006: 087940. DOI: https://doi.org/10.1155/MPE/2006/87940.
KHANNA A, KOTOUSOV A. Stress analysis of a crack in a fiber-reinforced layered composite [J]. Composite Structures, 2014, 118: 139–148. DOI: https://doi.org/10.1016/j.compstruct.2014.07.024.
BAI Bing. Thermal consolidation of layered porous half-space to variable thermal loading [J]. Applied Mathematics and Mechanics, 2006, 27(11): 1531–1539. DOI: https://doi.org/10.1007/s10483-006-1111-1.
SHERIEF H H, ANWAR M N. A problem in generalized thermoelasticity for an infinitely long annular cylinder composed of two different materials [J]. Journal of Thermal Stresses, 1989, 12(4): 529–543. DOI: https://doi.org/10.1080/01495738908961982.
ABD EL-LATIEF A M, KHADER S E. Fractional model of thermoelasticity for a half-space overlaid by a thick layer [J]. ZAMM - Journal of Applied Mathematics and Mechanics/Zeitschrift Für Angewandte Mathematik Und Mechanik, 2015, 95(5): 511–518. DOI: https://doi.org/10.1002/zamm.201300174.
WEN Min-jie, XU Jin-ming, XIONG Hou-ren. Thermal diffusion effects in a tunnel with a cylindrical lining and soil system under explosive loading [J]. Mathematical Problems in Engineering, 2019, 2019: 2535980. DOI: https://doi.org/10.1155/2019/2535980.
WEN Min-jie, XU Jin-ming, XIONG Hou-ren. Thermo-hydro-mechanical dynamic response of a cylindrical lined tunnel in a poroelastic medium with fractional thermoelastic theory [J]. Soil Dynamics and Earthquake Engineering, 2020, 130: 105960. DOI: https://doi.org/10.1016/j.soildyn.2019.105960.
LI Li-chen, WU Wen-bing, LIU Hao, et al. DEM analysis of the plugging effect of open-ended pile during the installation process [J]. Ocean Engineering, 2021, 220: 108375. DOI: https://doi.org/10.1016/j.oceaneng.2020.108375.
LIU Y, MIODUCHOWSKI A, RU C Q. Effect of imperfect interface on thermal stresses-assisted matrix cracking in fiber composites [J]. Journal of Thermal Stresses, 2002, 25(6): 585–599. DOI: https://doi.org/10.1080/01495730290074315.
MAHANTY M, CHATTOPADHYAY A, KUMAR P, et al. Effect of initial stress, heterogeneity and anisotropy on the propagation of seismic surface waves [J]. Mechanics of Advanced Materials and Structures, 2020, 27(3): 177–188. DOI: https://doi.org/10.1080/15376494.2018.1472329.
MAHANTY M, KUMAR P, SINGH A K, et al. Dynamic response of an irregular heterogeneous anisotropic poroelastic composite structure due to normal moving load [J]. Acta Mechanica, 2020, 231(6): 2303–2321. DOI: https://doi.org/10.1007/s00707-020-02649-z.
LI Li-chen, LIU Hao, WU Wen-bing, et al. Investigation on the behavior of hybrid pile foundation and its surrounding soil during cyclic lateral loading [J]. Ocean Engineering, 2021, 240: 110006. DOI: https://doi.org/10.1016/j.oceaneng.2021.110006.
WU Wen-bing, LIU Hao, YANG Xiao-yan, et al. New method to calculate apparent phase velocity of open-ended pipe pile [J]. Canadian Geotechnical Journal, 2020, 57(1): 127–138. DOI: https://doi.org/10.1139/cgj-2018-0816.
DUSCHLBAUER D, PETTERMANN H E, BÖHM H J. Heat conduction of a spheroidal inhomogeneity with imperfectly bonded interface [J]. Journal of Applied Physics, 2003, 94(3): 1539–1549. DOI: https://doi.org/10.1063/1.1587886.
CHENG Zhen-qiang, BATRA R C. Thermal effects on laminated composite shells containing interfacial imperfections [J]. Composite Structures, 2001, 52(1): 3–11. DOI: https://doi.org/10.1016/S0263-8223(00)00197-5.
HATAMI-MARBINI H, SHODJA H M. On thermoelastic fields of a multi-phase inhomogeneity system with perfectly/imperfectly bonded interfaces [J]. International Journal of Solids and Structures, 2008, 45(22–23): 5831–5843. DOI: https://doi.org/10.1016/j.ijsolstr.2008.06.018.
WEN Min-jie, XIONG Hou-ren, YUAN Ke-long, et al. Transient responses of a cylindrical lining in a thermoelastic medium based on the discontinuous interfacial model [J]. Journal of Thermal Stresses, 2020, 43(10): 1258–1276. DOI: https://doi.org/10.1080/01495739.2020.1775533.
XUE Zhang-na, YU Ya-jun, TIAN Xiao-geng. Transient responses of bi-layered structure based on generalized thermoelasticity: Interfacial conditions [J]. International Journal of Mechanical Sciences, 2015, 99: 179–186. DOI: https://doi.org/10.1016/j.ijmecsci.2015.05.016.
XUE Zhang-na, YU Ya-jun, LI Chen-lin, et al. Application of fractional order theory of thermoelasticity to a bilayered structure with interfacial conditions [J]. Journal of Thermal Stresses, 2016, 39(9): 1017–1034. DOI: https://doi.org/10.1080/01495739.2016.1192451.
XUE Zhang-na, YU Ya-jun, TIAN Xiao-geng. Transient responses of multi-layered structures with interfacial conditions in the generalized thermoelastic diffusion theory [J]. International Journal of Mechanical Sciences, 2017, 131–132: 63–74. DOI: https://doi.org/10.1016/j.ijmecsci.2017.05.054.
XUE Zhang-na, YU Ya-jun, LI Xiao-ya, et al. Study of a generalized thermoelastic diffusion bi-layered structures with variable thermal conductivity and mass diffusivity [J]. Waves in Random and Complex Media, 2019, 29(1): 34–53. DOI: https://doi.org/10.1080/17455030.2017.1397810.
HE Tian-hu, ZHANG Pei, XU Chi, et al. Transient response analysis of a spherical shell embedded in an infinite thermoelastic medium based on a memory-dependent generalized thermoelasticity [J]. Journal of Thermal Stresses, 2019, 42(8): 943–961. DOI: https://doi.org/10.1080/01495739.2019.1610342.
LU Zheng, YAO Hai-lin, LIU Gan-bin. Thermomechanical response of a poroelastic half-space soil medium subjected to time harmonic loads [J]. Computers and Geotechnics, 2010, 37(3): 343–350. DOI: https://doi.org/10.1016/j.compgeo.2009.11.007.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item
Projects(52108347, 52178371) supported by the National Natural Science Foundation of China; Project(LQ22E080010) supported by the Exploring Youth Project of Zhejiang Natural Science Foundation, China
Contributors
WEN Min-jie provided the concept and edited the draft of manuscript. TIAN Yi conducted the literature review and wrote the first draft of the manuscript. WU Wen-bing provided the concept and funding, and edited the draft of manuscript. WANG Kui-hua edited and revised the draft of manuscript. XIONG Hou-ren edited the draft of manuscript.
Conflict of interest
WEN Min-jie, TIAN Yi, WU Wen-bing, WANG Kui-hua and XIONG Hou-ren declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Wen, Mj., Tian, Y., Wu, Wb. et al. Influence of thermal contact resistance on dynamic response of bilayered saturated porous strata. J. Cent. South Univ. 29, 1823–1839 (2022). https://doi.org/10.1007/s11771-022-5053-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-022-5053-2
Key words
- dynamic response
- bilayered saturated porous strata
- thermal contact resistance
- generalized thermoelastic theory
- elastic wave impedance