Axisymmetric elastic field in layered non-homogeneous and transversely isotropic geo-materials due to surface traction
This paper examines the axisymmetric problem of layered and non-homogeneous geo-material halfspaces with transverse isotropy. The halfspace is subjected to normal traction over a circular area of the boundary surface. A n-layered halfspace system approximates the arbitrary variation of the elastic p...
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| Published in | Computers and geotechnics Vol. 155; p. 105226 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.03.2023
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| Abstract | This paper examines the axisymmetric problem of layered and non-homogeneous geo-material halfspaces with transverse isotropy. The halfspace is subjected to normal traction over a circular area of the boundary surface. A n-layered halfspace system approximates the arbitrary variation of the elastic parameters of non-homogeneous geo-materials with depth. The two-dimensional Fourier integral transforms in the cylindrical coordinate system and the backward transfer matrix method are used for the mathematical formulation and derivation. The solutions of the displacement, stress and strain fields are explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form. Numerical results indicate that there is no problem in the evaluation of the solutions of non-homogeneous halfspaces with arbitrarily variable elastic parameters and the inhomogeneity and transverse isotropy of layered geo-materials have significant effect on the elastic fields. |
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| AbstractList | This paper examines the axisymmetric problem of layered and non-homogeneous geo-material halfspaces with transverse isotropy. The halfspace is subjected to normal traction over a circular area of the boundary surface. A n-layered halfspace system approximates the arbitrary variation of the elastic parameters of non-homogeneous geo-materials with depth. The two-dimensional Fourier integral transforms in the cylindrical coordinate system and the backward transfer matrix method are used for the mathematical formulation and derivation. The solutions of the displacement, stress and strain fields are explicitly expressed in the matrix form in terms of classical improper Hankel transform integrals. The kernel functions of the Hankel transform integrals are explicitly expressed in the forms of backward transfer matrix. The singular terms associated with the improper Hankel transform integrals are analytically isolated and expressed in the exact closed-form. Numerical results indicate that there is no problem in the evaluation of the solutions of non-homogeneous halfspaces with arbitrarily variable elastic parameters and the inhomogeneity and transverse isotropy of layered geo-materials have significant effect on the elastic fields. |
| ArticleNumber | 105226 |
| Author | Yue, Zhongqi Quentin Du, Xiuli Xiao, Sha |
| Author_xml | – sequence: 1 givenname: Sha surname: Xiao fullname: Xiao, Sha organization: Key Laboratory of Urban Security and Disaster Engineering of China Ministry of Education, Beijing University of Technology, Beijing 100124, China – sequence: 2 givenname: Xiuli surname: Du fullname: Du, Xiuli organization: Key Laboratory of Urban Security and Disaster Engineering of China Ministry of Education, Beijing University of Technology, Beijing 100124, China – sequence: 3 givenname: Zhongqi Quentin surname: Yue fullname: Yue, Zhongqi Quentin email: yueqzq@hku.hk organization: Department of Civil Engineering, The University of Hong Kong, Hong Kong, China |
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| CitedBy_id | crossref_primary_10_1016_j_enganabound_2024_106098 crossref_primary_10_1016_j_compgeo_2024_106762 crossref_primary_10_1016_j_enganabound_2023_02_009 crossref_primary_10_1016_j_mechrescom_2024_104308 crossref_primary_10_1007_s10659_024_10090_9 crossref_primary_10_1016_j_enganabound_2023_08_011 |
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| Keywords | Transverse isotropy Elasticity Closed-form solution Layered and non-homogeneous geo-materials Surface traction |
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| SubjectTerms | Closed-form solution Elasticity Layered and non-homogeneous geo-materials Surface traction Transverse isotropy |
| Title | Axisymmetric elastic field in layered non-homogeneous and transversely isotropic geo-materials due to surface traction |
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