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Time-dependent interaction between superstructure, raft and layered cross-anisotropic viscoelastic saturated soils. (English) Zbl 1485.74066

Summary: By introducing the elastic-viscoelastic correspondence principle and the integral transform technique, the extended precise integral solution to Biot’s consolidation equation is derived for cross-anisotropic viscoelastic saturated soils based on the Merchant model. A displacement-time solution for a slowly changing load is obtained based on the above solution in the Laplace transformed domain, which is taken as the kernel function for the boundary element method (BEM). The Mindlin plate model is established by 8-node isoparametric finite element method (FEM), and the substructure condensation technique is employed to couple the stiffness matrices of the superstructure and the plate. With the BEM-FEM coupling method, a semi-analytical and semi-numerical solution is proposed for the interaction between layered cross-anisotropic viscoelastic saturated soils and raft foundation considering the stiffness contributions of the superstructure. Numerical examples are performed to study the influences of viscoelastic parameters, cross-anisotropic parameters, raft thickness and superstructure stiffness on the time-dependent behavior of the settlement and bending moment for the raft.

MSC:

74L10 Soil and rock mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74K20 Plates
74D05 Linear constitutive equations for materials with memory
74S15 Boundary element methods applied to problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
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References:

[1] Fraser, R. A.; Wardle, L. J., Numerical-analysis of rectangular rafts on layered foundations, Geotechnique, 26, 4, 613-630 (1976)
[2] Small, J. C.; Zhang, B. Q., Finite layer analysis of the behavior of a raft on a consolidating soil, Int. J. Numer. Anal. Methods Geomech., 18, 4, 237-251 (1994)
[3] Melerski, E. S., Numerical modelling of elastic interaction between circular rafts and cross-anisotropic media, Comput. Struct., 64, 1-4, 567-578 (1997) · Zbl 0919.73276
[4] Sadecka, L., A finite/infinite element analysis of thick plate on a layered foundation, Comput. Struct., 76, 5, 603-610 (2000)
[5] Wang, Y. H.; Cheung, Y. K., Plate on cross-anisotropic foundation analyzed by the finite element method, Comput. Geotech., 28, 1, 37-54 (2001)
[6] Wang, Y. H.; Tham, L. G.; Tsui, Y.; Yue, Z. Q., Plate on layered foundation analyzed by a semi-analytical and semi-numerical method, Comput. Geotech., 30, 5, 409-418 (2003)
[7] Katebi, A. A.; Khojasteh, A.; Rahimian, M.; Pak, R. Y.S, Axisymmetric interaction of a rigid disc with a transversely isotropic half-space, Int. J. Numer. Anal. Methods Geomech., 34, 12, 1211-1236 (2010) · Zbl 1273.74356
[8] Chen, S. L.; Abousleiman, Y., Time-dependent behaviour of a rigid foundation on a transversely isotropic soil layer, Int. J. Numer. Anal. Methods Geomech., 34, 9, 937-952 (2010) · Zbl 1273.74215
[9] Ai, Z. Y.; Cheng, Y. C.; Cao, G. J., A quasistatic analysis of a plate on consolidating layered soils by analytical layer-element/finite element method coupling, Int. J. Numer. Anal. Methods Geomech., 38, 13, 1362-1380 (2014)
[10] Ai, Z. Y.; Hu, Y. D., A coupled BEM-ALEM approach for analysis of elastic thin plates on multilayered soil with anisotropic permeability, Eng. Anal. Bound. Elem., 53, 40-45 (2015) · Zbl 1403.74141
[11] Ai, Z. Y.; Zhang, Y. F., The analysis of a rigid rectangular plate on a transversely isotropic multilayered medium, Appl. Math. Model., 39, 20, 6085-6102 (2015) · Zbl 1443.74009
[12] Ai, Z. Y.; Cao, Z.; Mu, J. J.; Shi, B. K., Elastic thin plate resting on saturated multilayered soils with anisotropic permeability and elastic superstrata, Int. J. Geomech., 18, 10, Article 04018137 pp. (2018)
[13] Meyerhof, G. G., The settlement analysis of building frames, Struct. Eng., 25, 9, 369-409 (1947)
[14] Meyerhof, G. G., Some recent foundation research and its application to design, Struct. Eng., 31, 6, 151-167 (1953)
[15] Zhang, B. Q.; Small, J. C., Finite Layer Analysis of Soil-Raft-Structure Interaction, 587-590 (1994), XIII CIMSTF: XIII CIMSTF New Delhi, India
[16] Almeida, V. S.; de Paiva, J. B., A mixed BEM-FEM formulation for layered soil-superstructure interaction, Eng. Anal. Bound. Elem., 28, 9, 1111-1121 (2004) · Zbl 1130.74455
[17] Haddadin, J. M., Mats and combined footings-analysis by the finite element method, Proc. ACI, 68, 12, 945-949 (1971)
[18] Hain, S. J.; Lee, I. K., Rational analysis of raft foundation, J.e Geotechn. Eng. Div. ASCE, 100, GT7, 843-860 (1974)
[19] Vlladkar, M. N.; Ranjan, G.; Sharma, R. P., Soil-structure interaction in the time domain, Comput. Struct., 46, 3, 429-442 (1993) · Zbl 0825.73604
[20] Nasri, V.; Magnan, J. P., Effect of soil consolidation on space frame-raft-soil interaction, J. Struct. Eng., 123, 11, 1528-1534 (1997)
[21] Wang, J.; Chen, J.; Pei, J., Interaction between superstructure and layered visco-elastic foundation considering consolidation and rheology of soil, J. Build. Struct., 23, 4, 59-64 (2002), in Chinese
[22] Sneddon, I. N., The Use of Integral Transform (1972), McGraw-Hill: McGraw-Hill New York · Zbl 0237.44001
[23] Ai, Z. Y.; Cheng, Y. C., Extended precise integration method for consolidation of transversely isotropic poroelastic layered media, Comput. Math. Appl., 68, 12, 1806-1818 (2014) · Zbl 1369.74083
[24] Lee, E. H., Stress analysis in visco-elastic bodies, Q. Appl. Math., 13, 183-190 (1955) · Zbl 0066.18901
[25] Mandal, J. J.; Ghosh, D. P., Prediction of elastic settlement of rectangular raft foundation—A coupled FE-BE approach, Int. J. Numer. Anal. Methods Geomech., 23, 3, 263-273 (1999) · Zbl 0955.74065
[26] Khojasteh, A.; Rahimian, M.; Eskandari, M., Three-dimensional dynamic Green’s functions in transversely isotropic tri-materials, Appl. Math. Model., 37, 5, 3164-3180 (2013) · Zbl 1351.74029
[27] Singh, S. J.; Kumar, R.; Rani, S., Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading, J. Earth Syst. Sci., 118, 5, 563-574 (2009)
[28] Gibson, R. E.; Lo, K. Y., A theory of consolidation for soils exhibiting secondary compression, Acta Polytech. Scand., 296: (1961), Chapter 10
[29] Liu, X. Z.; Zhu, H. H., Back analysis on staged construction in transversely isotropic viscoelastic soil and its application to geotechnical engineering, Chin. J. Geotech. Eng., 24, 1, 89-92 (2002), in Chinese
[30] Cheung, Y. K.; Zienkiewicz, O. C., Plates and tanks on elastic foundation—An application of finite element method, Int. J. Solids Struct., 1, 4, 451-461 (1965)
[31] Zienkiewicz, O. C.; Taylor, R. L., The Finite Element Method (4th) (1991), McGraw-Hill: McGraw-Hill London
[32] Mandel, J., Consolidation Des Sols, Geotechnique, 3, 7, 287-299 (1953)
[33] Cryer, C. W., A comparison of the three-dimensional consolidation theories of Biot and Terzaghi, Q. J. Mech. Appl. Math., 16, 4, 401-412 (1963) · Zbl 0121.21502
[34] Ai, Z. Y.; Zhao, Y. Z.; Song, X. Y.; Mu, J. J., Multi-dimensional consolidation analysis of transversely isotropic viscoelastic saturated soils, Eng. Geol., 253, 1-13 (2019)
[35] Cheng, Y. C.; Ai, Z. Y., Consolidation analysis of transversely isotropic layered saturated soils in the Cartesian coordinate system by extended precise integration method, Appl. Math. Model., 40, 4, 2692-2704 (2016) · Zbl 1452.76232
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