Precise Model for Predicting Excess Pore-Water Pressure of Layered Soils Induced by Thermal-Mechanical Loads
Publication: Journal of Engineering Mechanics
Volume 145, Issue 1
Abstract
This paper proposes a precise model to investigate the time-dependent response of excess pore-water pressure in stratified saturated soil induced by coupling effects from temperature and mechanical load based on the Laplace–Hankel transform and the precise integration method (PIM). First, the partial differential equations for the thermal consolidation problem are transformed into the ordinary equations by the integral transform techniques. By combining the adjacent layer elements and considering the boundary conditions, the extended precise integration solutions to the thermal consolidation problem in the transformed domain are deduced. By applying the corresponding integral inverse transforms, state variables in the physical domain are obtained. The existing analytical solutions and model test results validate the presented model. Additionally, numerical examples explore the influence of temperature load, Young’s modulus, and permeability coefficient on the thermal consolidation behavior. Numerical results reveal that (1) thermal load has a significant influence on the peak values of excess pore-water pressure and gives rise to the Mandel-Cryer effect; (2) due to the slower velocity of heat conduction than of pore-water penetration, the dissipation time of excess pore-water pressure caused by thermal-mechanical loads lags behind that of the mechanical load; and (3) the layering behavior of soils has significant effects on the distribution of excess pore-water pressure and the consolidation process.
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Acknowledgments
The authors acknowledge funding from the National Natural Science Foundation of China (Grant Nos. 51708494 and 51679211) and the China Postdoctoral Science Foundation (Grant No. 2017M611994).
References
Abate, J., and P. P. Valko. 2004. “Multi-precision Laplace transform inversion.” Int. J. Numer. Methods Eng. 60 (5): 979–993. https://doi.org/10.1002/nme.995.
Abousleiman, Y., and S. Ekbote. 2005. “Solutions for the inclined borehole in a porothermoelastic transversely isotropic medium.” J. Appl. Mech. 72 (1): 102–114. https://doi.org/10.1115/1.1825433.
Abousleiman, Y., S. Hoang, and C. Liu. 2014. “Anisotropic porothermoelastic solution and hydro-thermal effects on fracture width in hydraulic fracturing.” Int. J. Numer. Anal. Methods Geomech. 38 (5): 493–517. https://doi.org/10.1002/nag.2216.
Ai, Z. Y., and L. J. Wang. 2015a. “Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source.” Int. J. Numer. Anal. Methods Geomech. 39 (17): 1912–1931. https://doi.org/10.1002/nag.2381.
Ai, Z. Y., and L. J. Wang. 2015b. “Time-dependent analysis of 3D thermo-mechanical behavior of a layered half-space with anisotropic thermal diffusivity.” Acta Mech. 226 (9): 2939–2954. https://doi.org/10.1007/s00707-015-1360-0.
Ai, Z. Y., Q. L. Wu, and L. J. Wang. 2016. “Axisymmetric coupled thermo-mechanical response of multilayered elastic medium.” Meccanica 51 (6): 1405–1417. https://doi.org/10.1007/s11012-015-0295-9.
Ai, Z. Y., Z. Q. Yue, L. G. Tham, and M. Yang. 2002. “Extended Sneddon and Muki solutions for multilayered elastic materials.” Int. J. Eng. Sci. 40 (13): 1453–1483. https://doi.org/10.1016/S0020-7225(02)00022-8.
Ai, Z. Y., and W. Z. Zeng. 2012. “Analytical layer-element method for non-axisymmetric consolidation of multilayered soils.” Int. J. Numer. Anal. Methods Geomech. 36 (5): 533–545. https://doi.org/10.1002/nag.1000.
Bai, B. 2006. “Thermal consolidation of layered porous half-space to variable thermal loading.” Appl. Math. Mech. 27 (11): 1531–1539. https://doi.org/10.1007/s10483-006-1111-1.
Bai, M., and Y. Abousleiman. 1997. “Thermoporoelastic coupling with application to consolidation.” Int. J. Numer. Anal. Methods Geomech. 21 (2): 121–132. https://doi.org/10.1002/(SICI)1096-9853(199702)21:2%3C121::AID-NAG861%3E3.0.CO;2-W.
Bai, B., and T. Li. 2013. “Irreversible consolidation problem of a saturated porothermoelastic spherical body with a spherical cavity.” Appl. Math. Modell. 37 (4): 1973–1982. https://doi.org/10.1016/j.apm.2012.05.003.
Biot, M. A. 1941. “General theory of three-dimensional consolidation.” J. Appl. Phys. 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Biot, M. A. 1956. “Thermoelasticity and irreversible thermodynamics.” J. Appl. Phys. 27 (3): 240–253. https://doi.org/10.1063/1.1722351.
Booker, J. R., and C. Savvidou. 1984. “Consolidation around a spherical heat source.” Int. J. Solids Struct. 20 (11–12): 1079–1090. https://doi.org/10.1016/0020-7683(84)90091-X.
Booker, J. R., and J. C. Small. 1987. “A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms.” Int. J. Numer. Anal. Methods Geomech. 11 (4): 363–380. https://doi.org/10.1002/nag.1610110405.
Britto, A. M., C. Savvidou, D. V. Maddocks, M. J. Gunn, and J. R. Booker. 1989. “Numerical and centrifuge modelling of coupled heat flow and consolidation around hot cylinders buried in clay.” Géotechnique 39 (1): 13–25. https://doi.org/10.1680/geot.1989.39.1.13.
Chai, H. Y., K. K. Phoon, C. F. Wei, and Y. F. Lu. 2011. “Analysis of effects of active sources on observed phase velocity based on the thin layer method.” J. Appl. Geophys. 73 (1): 49–58. https://doi.org/10.1016/j.jappgeo.2010.11.005.
Chen, G. J. 2004. “Consolidation of multilayered half space with anisotropic permeability and compressible constituents.” Int. J. Solids Struct. 41 (16–17): 4567–4586. https://doi.org/10.1016/j.ijsolstr.2004.03.019.
Cheng, A. H. D., and J. A. Liggett. 1984. “Boundary integral equation method for linear porous-elasticity with applications to soil consolidation.” Int. J. Numer. Methods Eng. 20 (2): 255–278. https://doi.org/10.1002/nme.1620200206.
Costa, A. M., C. O. Cardoso, C. S. Amaral, and A. Andueza. 2002. “Soil-structure interaction of heated pipeline buried in soft clay.” In Proc., IPC2002 4th Int. Pipeline Conf.—ASME. Calgary, AB, Canada: Canadian Energy Pipeline Association.
Coussy, O. 1989. “A general theory of thermoporoelastoplasticity for saturated porous materials.” Transp. Porous Media 4 (3): 281–293. https://doi.org/10.1007/BF00138040.
Coussy, O. 2004. Poromechanics. Chichester, UK: Wiley.
Delage, P., N. Sultan, and Y. J. Cui. 2000. “On the thermal consolidation of Boom clay.” Can. Geotech. J. 37 (2): 343–354. https://doi.org/10.1139/t99-105.
El-Zein, A. 2006. “Laplace boundary element model for the thermoelastic consolidation of multilayered media.” Int. J. Geomech. 6 (2): 136–140. https://doi.org/10.1061/(ASCE)1532-3641(2006)6:2(136).
Gao, Q., W. X. Zhong, and W. P. Howson. 2004. “A precise method for solving wave propagation problems in layered anisotropic media.” Wave Motion 40 (3): 191–207. https://doi.org/10.1016/j.wavemoti.2003.09.002.
Giraud, A., F. Homand, and G. Rousset. 1998. “Thermoelastic and thermoplastic response of a double-layer porous space containing a decaying heat source.” Int. J. Numer. Anal. Methods Geomech. 22 (2): 133–149. https://doi.org/10.1002/(SICI)1096-9853(199802)22:2%3C133::AID-NAG915%3E3.0.CO;2-B.
Hueckel, T., B. Francois, and L. Laloui. 2009. “Explaining thermal failure in saturated clays.” Géotechnique 59 (3): 197–212. https://doi.org/10.1680/geot.2009.59.3.197.
Jia, Y., Y. Wileveau, K. Su, G. Duveau, and J. F. Shao. 2007. “Thermo-hydro-mechanical modelling of an in situ heating experiment.” Géotechnique 57 (10): 845–855. https://doi.org/10.1680/geot.2007.57.10.845.
Jones, S., and H. Hunt. 2011. “Effect of inclined soil layers on surface vibration from underground railways using the thin-layer method.” J. Eng. Mech. 137 (12): 887–900. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000292.
Kausel, E. 1994. “Thin-layer method: Formulation in the time domain.” Int. J. Numer. Methods Eng. 37 (6): 927–941. https://doi.org/10.1002/nme.1620370604.
Kausel, E., and J. M. Roësset. 1981. “Stiffness matrices for layered soils.” Bull. Seismol. Soc. Am. 71 (6): 1743–1761.
Kurashige, M. 1989. “A thermoelastic theory of fluid-filled porous materials.” Int. J. Solids Struct. 25 (9): 1039–1052. https://doi.org/10.1016/0020-7683(89)90020-6.
Lewis, R. W., C. E. Majorana, and B. A. Schrefler. 1986. “A coupled finite element model for the consolidation of nonisothermal elastoplastic porous media.” Transp. Porous Media 1 (2): 155–178. https://doi.org/10.1007/BF00714690.
Lu, J. C. C., and F. Lin. 2010. “Thermal consolidation of a poroelastic full space subjected to a decaying point heat source.” In Vol. 1233 of Proc., 2nd Int. ISCM and the 12th Int. EPMESC Conf., 407–412. College Park, MD: AIP Conference Proceedings.
Lu, Z., H. Yao, and G. Liu. 2010. “Thermomechanical response of a poroelastic half-space soil medium subjected to time harmonic loads.” Comput. Geotech. 37 (3): 343–350. https://doi.org/10.1016/j.compgeo.2009.11.007.
Luco, J. E., and R. J. Apsel. 1983. “On the Green’s functions for a layered half-space. Part I.” Bull. Seismol. Soc. Am. 73 (4): 909–929.
Mctigue, D. F. 1986. “Thermoelastic response of fluid-saturated porous rock.” J. Geophys. Res. Atmos. 91 (B9): 9533–9542. https://doi.org/10.1029/JB091iB09p09533.
Mei, G. X., J. H. Yin, J. M. Zai, Z. Z. Yin, X. L. Ding, G. F. Zhu, and L. M. Chu. 2004. “Consolidation analysis of a cross-anisotropic homogeneous elastic soil using a finite layer numerical method.” Int. J. Numer. Anal. Methods Geomech. 28 (2): 111–129. https://doi.org/10.1002/nag.324.
Mei, C. C., and P. A. Tyvand. 1988. “Thermal consolidation of thick and soft soil layer.” J. Eng. Mech. 114 (6): 990–1010. https://doi.org/10.1061/(ASCE)0733-9399(1988)114:6(990).
Nair, R., Y. Abousleiman, and M. Zaman. 2004. “A finite element porothermoelastic model for dual-porosity media.” Int. J. Numer. Anal. Methods Geomech. 28 (9): 875–898. https://doi.org/10.1002/nag.336.
Pak, R. Y. S., and B. B. Guzina. 2002. “Three-dimensional Green’s functions for a multilayered half-space in displacement potentials.” J. Eng. Mech. 128 (4): 449–461. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:4(449).
Pan, E. 1989. “Static response of a transversely isotropic and layered half-space to general surface loads.” Phys. Earth Planet. Inter. 54 (3–4): 353–363. https://doi.org/10.1016/0031-9201(89)90252-5.
Pan, E. 1990. “Thermoelastic deformation of a transversely isotropic and layered half-space by surface loads and internal sources.” Phys. Earth Planet. Inter. 60 (1): 254–264. https://doi.org/10.1016/0031-9201(90)90266-Z.
Pan, E. 1997. “Static Green’s functions in multilayered half spaces.” Appl. Math. Modell. 21 (8): 509–521. https://doi.org/10.1016/S0307-904X(97)00053-X.
Pan, E. 1999. “Green’s functions in layered poroelastic half-spaces.” Int. J. Numer. Anal. Methods Geomech. 23 (13): 1631–1653. https://doi.org/10.1002/(SICI)1096-9853(199911)23:13%3C1631::AID-NAG60%3E3.0.CO;2-Q.
Rajapakse, R. K. N. D., and T. Senjuntichai. 1993. “Fundamental solutions for a poroelastic half-space with compressible constituents.” J. Appl. Mech. 60 (4): 847–856. https://doi.org/10.1115/1.2900993.
Rokhlin, S. I., and L. Wang. 2002. “Stable recursive algorithm for elastic wave propagation in layered anisotropic media: Stiffness matrix method.” J. Acoust. Soc. Am. 112 (3): 822–834. https://doi.org/10.1121/1.1497365.
Rotta Loria, A. F., and L. Laloui. 2017. “Thermally induced group effects among energy piles.” Géotechnique 67 (5): 374–393. https://doi.org/10.1680/jgeot.16.P.039.
Savvidou, C., and J. R. Booker. 1988. “Consolidation around a spherical heat source with a decaying power output.” Comput. Geotech. 5 (3): 227–244. https://doi.org/10.1016/0266-352X(88)90004-3.
Savvidou, C., and J. R. Booker. 1991. “Consolidation of a deep homogeneous clay stratum subjected to a surface temperature change.” In Proc., 9th Asian Regional Conf. on Soil Mechanics and Foundation Engineering, 425–428. Bangkok, Thailand: Southeast Asian Geotechnical Society.
Schiffman, R. L. 1971. “A thermoelastic theory of consolidation.” In Environmental and Geophysical Heat Transfer, 78–84. New York: ASME.
Selvadurai, A. P. S. 2007. “The analytical method in geomechanics.” Appl. Mech. Rev. 60 (3): 87–106. https://doi.org/10.1115/1.2730845.
Selvadurai, A. P. S., and T. S. Nguyen. 1997. “Scoping analyses of the coupled thermal-hydrological-mechanical behaviour of the rock mass around a nuclear fuel waste repository.” Eng. Geol. 47 (4): 379–400. https://doi.org/10.1016/S0013-7952(96)00100-7.
Selvadurai, A. P. S., and A. P. Suvorov 2014. “Thermo-poromechanics of a fluid-filled cavity in a fluid-saturated geomaterial.” Proc. R. Soc. A 470(2163): 20130634. https://doi.org/10.1098/rspa.2013.0634.
Senjuntichai, T., and R. K. N. D. Rajapakse. 1995. “Exact stiffness method for quasi-statics of a multi-layered poroelastic medium.” Int. J. Solids Struct. 32 (11): 1535–1553. https://doi.org/10.1016/0020-7683(94)00190-8.
Singh, S. J., and S. Rani. 2006. “Plane strain deformation of a multi-layered poroelastic half-space by surface loads.” J. Earth Syst. Sci. 115 (6): 685–694. https://doi.org/10.1007/s12040-006-0001-3.
Small, J. C., and J. R. Booker. 1984. “Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—Strip loadings.” Int. J. Numer. Methods Eng. 20 (6): 1025–1037. https://doi.org/10.1002/nme.1620200606.
Small, J. C., and J. R. Booker. 1986. “The behaviour of layered soil or rock containing a decaying heat source.” Int. J. Numer. Anal. Methods Geomech. 10 (5): 501–519. https://doi.org/10.1002/nag.1610100504.
Smith, D. W., and J. R. Booker. 1996. “Boundary element analysis of linear thermoelastic consolidation.” Int. J. Numer. Anal. Methods Geomech. 20 (7): 457–488. https://doi.org/10.1002/(SICI)1096-9853(199607)20:7%3C457::AID-NAG805%3E3.0.CO;2-H.
Sneddon, I. N. 1972. The use of integral transform. New York: McGraw-Hill.
Suvorov, A. P., and A. P. S. Selvadurai. 2009. “THM processes in a fluid-saturated poroelastic geomaterial: Comparison of analytical results and computational estimates.” In Proc., 3rd CANUS Rock Mechanics Symp. Toronto, Canada: Canadian Association of Rock Mechanics.
Torabi, M., K. Zhang, G. Yang, J. Wang, and P. Wu. 2015. “Heat transfer and entropy generation analyses in a channel partially filled with porous media using local thermal non-equilibrium model.” Energy 82: 922–938. https://doi.org/10.1016/j.energy.2015.01.102.
Wang, L. J., and Z. Y. Ai. 2015. “Plane strain and three-dimensional analyses for thermo-mechanical behavior of multilayered transversely isotropic materials.” Int. J. Mech. Sci. 103: 199–211. https://doi.org/10.1016/j.ijmecsci.2015.09.006.
Wang, J. G., and S. S. Fang. 2003. “State space solution of non-axisymmetric Biot’s consolidation problems for multilayered poroelastic media.” Int. J. Eng. Sci. 41 (15): 1799–1813. https://doi.org/10.1016/S0020-7225(03)00062-4.
Wang, L., and S. I. Rokhlin. 2001. “Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media.” Ultrasonics 39 (6): 413–424. https://doi.org/10.1016/S0041-624X(01)00082-8.
Yue, Z. Q. 2015. “Yue’s solution of classical elasticity in n-layered solids: Part 1, mathematical formulation.” Front. Struct. Civ. Eng. 9 (3): 215–249. https://doi.org/10.1007/s11709-015-0298-6.
Yue, Z. Q., and A. P. S. Selvadurai. 1995. “Contact problem for saturated poroelastic solid.” J. Eng. Mech. 121 (4): 502–512. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:4(502).
Yue, Z. Q., A. P. S. Selvadurai, and K. T. Law. 1994. “Excess pore pressure in a poroelastic seabed saturated with a compressible fluid.” Can. Geotech. J. 31 (6): 989–1003. https://doi.org/10.1139/t94-113.
Zhong, W. X. 2004. “On precise integration method.” J. Comput. Appl. Math. 163 (1): 59–78. https://doi.org/10.1016/j.cam.2003.08.053.
Zhong, W. X., J. H. Lin, and Q. Gao. 2004. “The precise computation for wave propagation in stratified materials.” Int. J. Numer. Methods Eng. 60 (1): 11–25. https://doi.org/10.1002/nme.952.
Zhong, Y., and L. T. Geng. 2009. “Thermal stresses of asphalt pavement under dependence of material characteristics on reference temperature.” Mech. Time-Depend. Mater. 13 (1): 81–91. https://doi.org/10.1007/s11043-008-9073-6.
Zhou, Y., R. K. N. D. Rajapakse, and J. Graham. 1998. “A coupled thermoporoelastic model with thermo-osmosis and thermal-filtration.” Int. J. Solids Struct. 35 (34–35): 4659–4683. https://doi.org/10.1016/S0020-7683(98)00089-4.
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Journal of Engineering Mechanics
Volume 145 • Issue 1 • January 2019
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©2018 American Society of Civil Engineers.
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Received: Jan 9, 2018
Accepted: Jun 18, 2018
Published online: Oct 16, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 16, 2019
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