State Space Solution to 3D Multilayered Elastic Soils Based on Order Reduction Method

AI Zhi-yong; CHENG Yi-chong; LIU Peng

doi:10.3879/j.issn.1000-0887.2012.11.003

Volume 33 Issue 11

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AI Zhi-yong, CHENG Yi-chong, LIU Peng. State Space Solution to 3D Multilayered Elastic Soils Based on Order Reduction Method[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1275-1283. doi: 10.3879/j.issn.1000-0887.2012.11.003

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State Space Solution to 3D Multilayered Elastic Soils Based on Order Reduction Method

doi: 10.3879/j.issn.1000-0887.2012.11.003

Department of Geotechnical Engineering, Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Tongji University, Shanghai 200092, P.R.China

Received Date: 2011-04-27
Rev Recd Date: 2012-06-21
Publish Date: 2012-11-15

Abstract

Abstract

Starting with the governing equations in terms of displacements of threedimensional elastic medium, the solutions of displacement components and their first derivatives were obtained by the application of a double Fourier transform and an order reduction method based on the CayleyHamilton theorem. Combining the solutions and the constitutive equations which connected the displacements and stresses, the transfer matrix of a single soil layer was acquired. And then the state space solution of multilayered elastic soils was further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. Numerical analysis based on the present theory was carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratum were compared and discussed.
- state space solution,
- multilayered elastic soils,
- double Fourier transform,
- order reduction method

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References(17)

References

[1]	Mindlin R D. Force at a point in the interior of a semi-infinite solid[J]. Physics, 1936, 7(5): 195-202.
[2]	Muki R. Asymmetric problems of the theory of elasticity for a semi-infinite solid and thick plate[C]Sneddon I N, Hill R. Progress in Soild Mechanics. Amsterdam: North-Holland, 1960: 399-439.
[3]	Sneddon I N. On Muki’s solution of the equations of linear elasticity[J]. International Journal of Engineering Science, 1992, 30(10): 1237-1246.
[4]	Pan E.Static Green’s functions in multilayered half spaces[J]. Applied Mathematical Modelling, 1997, 21(8): 509-521.
[5]	Bufler H.Theory of elasticity of a multilayered medium[J]. Journal of Elasticity, 1971, 1(2): 125-143.
[6]	Bahar L Y.Transfer matrix approach to layered systems[J]. Journal of the Engineering Mechanics Division, 1972, 98(5): 1159-1172.
[7]	Kausel E, Seak S H. Static loads in layered half-spaces[J]. Journal of Applied Mechanics, 1987, 54(2): 403-408.
[8]	Small J C, Booker J R. Finite layer analysis of layered elastic material using a flexibility approach—part 2: circular and rectangular loadings[J]. International Journal for Numerical Methods in Engineering, 1986, 23(5): 959-978.
[9]	Ai Z Y, Yue Z Q, Tham L G,Yang M. Extended Sneddon and Muki solutions for multilayered elastic materials[J]. International Journal of Engineering Science, 2002, 40(13): 1453-1483.
[10]	王林生. 求解成层地基空间轴对称问题的初参数法[J]. 力学学报, 1986, 18(6): 528-537. （WANG Lin-sheng. The initial parameter method for solving three-dimensional axisymmetrical problems of layered foundation[J]. Acta Mechanica Sinica, 1986, 18(6): 528-537. （in Chinese））
[11]	钟阳, 王哲人, 郭大智, 王争宇. 求解多层弹性半空间非轴对称问题的传递矩阵法[J]. 土木工程学报, 1995, 28(1): 66-72.（ZHONG Yang, WANG Zhe-ren, GUO Da-zhi, WANG Zheng-yu. Transfer matrix method for solving non-axisymmetrical problems in multilayered elastic half space[J]. China Civil Engineering Journal, 1995, 28(1): 66-72. （in Chinese))
[12]	艾智勇, 吴超. 三维直角坐标系下分层地基的传递矩阵解[J]. 重庆建筑大学学报, 2008, 30(2): 43-46.（AI Zhi-yong, WU Chao. Transfer matrix solution for multilayered soils in rectangular coordinate system[J]. Journal of Chongqing Jianzhu University, 2008, 30(2): 43-46. （in Chinese))
[13]	岳中琦, 王仁. 多层横观各向同性弹性体静力学问题的解[J]. 北京大学学报(自然科学版), 1988, 24(2): 202-211.（YUE Zhong-qi, WANG Ren. Static solution for transversely isotropic elastic N-layered systems[J]. Acta Scientiarum Naturalium Universitatis Pekinensis, 1988, 24(2): 202-211.（in Chinese））
[14]	王有凯, 龚耀清. 任意荷载作用下层状横观各向同性弹性地基的直角坐标解[J]. 工程力学, 2006, 23(5): 9-13.（WANG You-kai, GONG Yao-qing. Analytical solution of transversely isotropic elastic multilayered subgrade under arbitrary loading in rectangular coordinates[J]. Engineering Mechanics, 2006, 23(5): 9-13.（in Chinese））
[15]	Timoshenko S P, Good J N. Theory of Elasticity[M]. New York: McGraw-Hill, 1970.
[16]	Sneddon I N. The Use of Integral Transform[M]. New York: McGraw-Hill, 1972.
[17]	Pastel E C, Leckie F A. Matrix Methods in Elasto-Mechanics[M]. New York: McGraw-Hill, 1963.