Journal of Applied and Computational Mechanics

Dynamic Response of a Step Loaded Cubic Cavity Embedded in a ‎Partially Saturated Poroelastic Half-space by the Boundary ‎Element Method

Document Type : Research Paper

Authors

1 National Research Lobachevsky State University of Nizhny Novgorod, 23 Gagarin av. bld. 6, Nizhny Novgorod, 603950, Russia

2 Department of Mechanics of Materials and Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology,‎ ‎11/12 Gabriela Narutowicza Street, Gdansk, 80-233, Poland

3 Department of Civil and Environmental Engineering and Architecture (DICAAR), University of Cagliari, Via Marengo, 2, 09123 Cagliari, Italy

Abstract

The boundary element method is used to analyze the problem of dynamic loading acting inside a cubic cavity located in a partially saturated poroelastic halfspace. Defining relations of a Biot’s porous medium are used, which are written in Laplace representations for unknown functions of displacements of the skeleton and pore pressures of the fillers. Solutions in time are obtained using the stepped method of numerical inversion of Laplace transforms. Dynamic responses of displacements and pore pressures at points on the surface of the halfspace and the cavity have been constructed. The effect of the values of the saturation coefficient and of the depth of the location of the cavity on dynamic responses has been studied.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Wang, Y., Gao, G.-Y., and Yang, J., Three-dimensional dynamic response of a lined tunnel in a half-space of saturated soil under internal explosive loading, Soil Dynamics and Earthquake Engineering, 101, 2017, 157–161.
[2] Wen, M.-J., Xu, J.-M., Analytical solution for torsional vibration of a pile in saturated soil considering imperfect contact, Gongcheng Lixue, 31(7), 2014, 156–161.
[3] Ozyazicioglu, M., Spherical wave propagation in a poroelastic medium with infinite permeability: Time domain solution, The Scientific World Journal, 2014, 2014, 1–10.
[4] Schanz, M., Poroelastodynamics: Linear models, analytical solutions, and numerical methods, Applied Mechanics Reviews, 62(3), 2009, 1–15.
[5] Karinski, Y.-S., Shershnev, V.-V., Yankelevsky, D.-Z., Analytical solution of the harmonic waves diffraction by a cylindrical lined cavity in poroelastic saturated medium, International Journal for Numerical and Analytical Methods in Geomechanics, 31(5), 2007, 667–689.
[6] Wang, Y., Gao, G.-Y., Lin, J., Gao, M., Dynamic response of cylindrical lining in poroelastic saturated half-space soil induced by internal loading, 6th International Symposium on Environmental Vibration, Shanghai, China, 2013.
[7] Gao, M., Gao, G., Wang, Y., The transient response of cylindrical lining in poroelastic saturated half-space, Guti Lixue Xuebao, 33(2), 2012, 219–226.
[8] Zhou, X.-L., Wang, J.-H., Jiang, L.-F., Dynamic response of a pair of elliptic tunnels embedded in a poroelastic medium, Journal of Sound and Vibration, 325(4–5), 2009, 816–834.
[9] Akhlaghi, T., Nikkar, A., Effect of vertically propagating shear waves on seismic behavior of circular tunnels, The Scientific World Journal, 2014, 2014.
[10] Gao, M., Gao, G.-Y., Li, D.-Y., Transient response of lining structure subjected to sudden internal uniform loading considering effects of coupling mass, Yantu Gongcheng Xuebao, 33(6), 2011, 862–868.
[11] Amorosi, A., Boldini, D., Numerical modelling of the transverse dynamic behaviour of circular tunnels in clayey soils, Soil Dynamics and Earthquake Engineering, 29(6), 2009, 1059–1072.
[12] Rajapakse, R.-K.-N.-D., Senjuntichai, T., An indirect boundary integral equation method for poroelasticity, International Journal for Numerical and Analytical Methods in Geomechanics, 19(9), 1995, 587–614.
[13] Kattis, S.-E., Beskos, D.-E., Cheng, A.-H.-D., 2D dynamic response of unlined and lined tunnels in poroelastic soil to harmonic body waves, Earthquake Engineering and Structural Dynamics, 32(1), 2003, 97–110.
[14] He, C., Zhou, S., Di, H., Xiao, J., A 2.5-D coupled FE-BE model for the dynamic interaction between tunnel and saturated soil, Lixue Xuebao, 49(1), 2017, 126–136.
[15] Yuan, Z., Boström, A., Cai, Y., Cao, Z., Closed-form analytical solution for vibrations from a tunnel embedded in a saturated poroelastic half space, Journal of Engineering Mechanics, 143(9), 2017, 04017079.
[16] Ashayeri, I., Kamalian, M., Jafari, M.K., Gatmiri, B., Analytical 3D transient elastodynamic fundamental solution of unsaturated soils, International Journal for Numerical and Analytical Methods in Geomechanics, 35(17), 2011, 1801–1829.
[17] Li, P., and Schanz, M., Time domain boundary element formulation for partially saturated poroelasticity, Engineering Analysis with Boundary Elements, 37(11), 2013, 1483–1498.
[18] Igumnov, L.A., Petrov, A.N., Belov, A.A., Mironov, A.A., Lyubimov, A.K., Dianov, D.Yu., Numerically-analytically studying fundamental solutions of 3-D dynamics of partially saturated poroelastic bodies, Materials Physics and Mechanics, 42(5), 2019, 596–601.
[19] Igumnov, L.A., Petrov, A.N., Vorobtsov, I.V., The time-step boundary-element scheme on the nodes of the Lobatto method in problems of 3-D dynamic poroelasticity, Materials Physics and Mechanics, 42(1), 2019, 103–111.
[20] Bishop, A. W., The principle of effective stress, Teknisk Ukeblad, 106(39), 1959, 859–863.
[21] Schanz, M., Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach, Springer-Verlag, Berlin Heidelberg, 2001.
[22] Amenitsky, A.V., Belov, A.A., Igumnov, L.A., Karelin I.S., Granichnye integral’nye uravneniya dlya resheniya dinamicheskikh zadach trekhmernoi teorii porouprugosti (Boundary Integral Equations for Analyzing Dynamic Problems of 3-d Porouselasticity (in Russian), Problems of Strength and Plasticity, 71, 2009, 164–171.
[23] Igumnov, L.A., Litvinchuk, S.Yu., Petrov, A.N., Ipatov A.A., Numerically Analytical Modeling the Dynamics of a Prismatic Body of Two- and Three-Component Materials, Advanced Materials, 175, 2016, 505–516.
[24] Bazhenov, V.G., Igumnov, L.A., Metody granichnyh integral’nyh uravnenij i granichnyh elementov v reshenii zadach trekhmernoj dinamicheskoj teorii uprugosti s sopryazhennymi polyami (Boundary Integral Equations and Boundary Element Methods in Treating the Problems of 3D Elastodynamics with Coupled Fields (in Rissian), PhysMathLit, Moscow, 2008.
[25] Goldshteyn, R.V., Metod granichnyh integral’nyh uravnenij – sovremennyj vychislitel’nyj metod prikladnoj mekhaniki (Boundary Integral Equations Method: Numerical Aspects and Application in Mechanics) (in Russian), Mir, Moscow, 1978.
[26] Lachat, J.C., Watson, J.O., Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics, International Journal for Numerical Methods in Engineering, 10(5), 1976, 991–1005.
[27] Igumnov, L.A., Petrov, A.N., Modelirovanie dinamiki chastichno nasyshchennyh porouprugih tel na osnove metoda granichno-vremennyh elementov (Dynamics of partially saturated poroelastic solids by boundary-element method) (in Russian), PNRPU Mechanics Bulletin, 3, 2016, 47–61.
Journal of Applied and Computational Mechanics
Volume 8, Issue 1
January 2022
Pages 331-339