Deformation Due to Inclined Loads in Thermoporoelastic Half Space
Subject Areas : EngineeringR Kumar 1 , S Kumar 2 , M.G Gorla 3
1 - Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India
2 - Department of Mathematics, Govt. Degree College Chowari (Chamba), Himachal Pradesh, India
3 - Department of Mathematics, Himachal Pradesh University, Shimla-171005, India
Keywords: Inclined load, Time and frequency domain, Laplace and fourier transform,
Abstract :
The present investigation is concerned with the deformation of thermoporoelastic half space with incompressible fluid as a result of inclined load of arbitrary orientation. The inclined load is assumed to be linear combination of normal load and tangential load. The Laplace and Fourier transform technique are used to solve the problem. The concentrated force, uniformly distributed force and a moving force in time and frequency domain are taken to illustrate the utility of the approach. The transformed components of displacement, stress, pore pressure and temperature change are obtained and inverted by using a numerical inversion techniques. The variations of resulting quantities are depicted graphically. A particular case has also been deduced.
[1] Fillunger P., 1913, Der auftrieb in talsperren, Osterr Wochenschrift Offentl Baudienst 19:532-556.
[2] Terzaghi K.V., 1923, Die berechnug der durchlassigkeitsziffer des tones aus dem verlauf der hydromechanischen spannungserscheinungen, Sitzungsber Akad Wiss Wien, Math Naturwiss KI , Abt, IIa 132:125-138.
[3] Terzaghi K.V., 1925, Erdbaumechanik auf Bodenphysikalischer Grundlage, Leipzig-wien, Franz Deuticke.
[4] Terzaghi K.V., 1933, Auftrieb und kapillardruck an betonierten talsperren, Die Wasserwirtschaft 26: 397-399.
[5] Biot M.A., 1941, General theory of three dimensional consolidation, Journal of Applied Physics 12(2): 155-161.
[6] Biot M.A., 1956, Theory of propagation of elastic waves in fluid saturated porous solid I-low frequency range, Journal of the Acoustical Society of America 28:168-178.
[7] Biot M.A., 1956, Theory of propagation of elastic waves in fluid saturated porous solid II-higher frequency range, Journal of the Acoustical Society of America 28:179-191.
[8] Rice J.R. ,Cleary M.P.,1976, Some basic stress diffusion solution for fluid saturated elastic porous media with compressible constituents, Reviews of Geophysics and Space Physics 14:227-241.
[9] Schiffman R. L., 1971, A Thermoelastic Theory of Consolidation, in Environmental and Geophysical Heat Transfer, American Society of Mechanical Engineers, New York.
[10] Bowen R. M., 1982, Compressible porous media models by use of the theory of mixtures, International Journal of Engineering Science 20: 697-735.
[11] Noorishad J., Tsang C.F., Witherspoon P. A., 1984, Coupled thermohydraulic-mechanical phenomena in saturated fractured porous rocks: Numerical approach, Journal of Geophysical Research 89:10365-10373.
[12] McTigue D.F., 1986, Thermal response of fluid-saturated porous rock, Journal of Geophysical Research 91(B9): 9533-9542.
[13] Kurashige M., 1989, A thermoelastic theory of fluid-filled porous materials, International Journal of Solids and Structures 25:1039-1052.
[14] Abousleiman Y., Ekbote S., 2005, Solutions for the inclined borehole in a porothermoelastic transversely isotropic medium, ASME Journal Applied Mechanics 72: 102-114.
[15] Bai B., 2006, Fluctuation responses of porous media subjected to cyclic thermal loading, Computers and geotechnics 33:396-403.
[16] Bai B., Li T., 2009, Solution for cylindrical cavity in saturated thermoporoelastic medium, Acta Mechanica Solida Sinica 22(1):85-92.
[17] Jabbari M., Dehbani H., 2010, An exact solution for classic coupled thermoelasticity in axisymmetric cylinder, Journal of Solid Mechanics 2(2):129-143.
[18] Ganbin L., Kanghe X., Rongyue Z., 2010, Thermo-elastodynamic response of a spherical cavity in a saturated poroelastic medium, Applied Mathematical Modeling 34:2213-2222.
[19] Gatmiri B., Maghoul P., Duhamel D.,2010, Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains, International Journal of Solid and Structure 47:595-610.
[20] Li X., Chen W., Wang H., 2010, General study state solutions for transversely isotropic thermoporoelastic media in three dimensions and its application, European Journal of Mechanics - A/Solids 29(3): 317-326.
[21] Jabbari M., Dehbani H., 2011, An exact solution for quasi-static poro- thermoelasticity in spherical coordinate, Iranian Journal of Mechanical Engineering 12(1): 86-108.
[22] Liu G., Ding S.,YE R., Liu X., 2011, Relaxation effect of a saturated porous media using the two dimensional generalized thermoelastic theory, Transport in Porous Media 86:283-303.
[23] Belotserkovets b. A., Prevost J. H., 2011, Thermoporoelastic response of fluid-saturated porous sphere: An analytical solution, International Journal of Engineering Science 49(12): 1415-1423.
[24] Bai B., 2013, Thermal response of saturated porous spherical body containing a cavity under several boundary conditions, Journal of Thermal Stresses 36(11): 1217-1232.
[25] Apostolakis G., Dargus G.F., 2013, Mixed variation principal for dynamic response of thermoelastic and poroelastic continua, International Journal of Solid and Structure 50(5): 642-650.
[26] Hou P.F., Zhao M., Jiann-Wen J.U., 2013, The three dimensional green’s function for transversely isotropic thermoporoelastic biomaterial, Journal of Applied Geophysics 95: 36-46.
[27] Jabbari M., Hashemitaheri M., Mojahedin A., Eslami M.R., 2014, Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials, Journal of Thermal Stresses 37:202-220.
[28] Liu M., Chain C., 2015, A micromechanical analysis of the fracture properties of saturated porous media, International Journal of Solid and Structure 63:32-38.
[29] He S.M., Liu W., Wang J., 2015, Dynamic simulation of landslide based on thermoporoelastic approach, Computers and Geosciences 75: 24-32.
[30] Nguyen H.T., Wong H., Fabbri A., Georgin J.F., Prudhomme E., 2015, Analytical study of freezing behaviour of a cavity in thermoporoelastic medium, Computers and Geotechnics 67: 33-45.
[31] Wu D., Yu L., Wang Y., Zhao B., Gao Y., 2015, A refined theory of axisymmetric thermoporoelastic circular cylinder, European Journal of Mechanics - A/Solids 53:187-195.
[32] Kumar R., Ailawalia P., 2005, Moving inclined load at boundary surface, Applied Mathematics and Mechanics 26: 476-485.
[33] Kumar R., Ailawalia P., 2005, Interaction due to inclined load at micropolar elastic half-space with voids, International Journal of Applied Mechanics and Engineering 10:109-122.
[34] Kumar R., Rani L., 2005, Deformation due inclined load in thermoelastic half-space with voids, Archives of Mechanics 57:7-24.
[35] Sharma K., 2011, Analysis of deformation due to inclined load in generalized thermodiffusive elastic medium, International Journal of Engineering, Science and Technology 3(2): 117-129.
[36] Ostsemin A.A., Utkin P.B., 2012, Stress-strain state of a inclined elliptical defect in a plate under biaxial loading, Journal of Applied Mechanics and Technical Physics 53(2): 246-257.
[37] Bogomolov A. N., 2013 , Ushakov A. N., Stress-strain state of an elastic half plane under a system of inclined piecewise-linear loads, Soil Mechanics and Foundation Engineering 50(2): 43-49.
[38] Jabbari M., Dehbani H., 2009, An exact solution for classic coupled thermoporoelasticity in cylindrical coordinate, Journal of Solid Mechanics 1(4): 343-357.
[39] Kumar R., Ailawalia P., 2005, Elastodynamics of inclined loads in micropolar cubic crystal, Mechanics and Mechanical Engineering 9(2): 57-75.