Semianalytical Solution for the Transient Response of One-Dimensional Saturated Multilayered Soil Column
Publication: International Journal of Geomechanics
Volume 22, Issue 12
Abstract
A semianalytical solution was obtained in the time domain directly for the one-dimensional transient response of a saturated multilayered soil column under typical boundary conditions based on Biot theory, which could take into account the inertial, viscous, and mechanical couplings of saturated porous soil media. First, one-dimensional wave equations were established by using the nondimensionless method. Then, by decomposing the displacement solution into dynamic and static components, the boundary conditions of the soil column were homogenized. The transfer matrix method was used to obtain the eigenvalue and eigenfunction of homogenized boundary conditions. With the help of undetermined coefficients and orthogonality of eigenfunctions methods, the solution to the problem of nonhomogeneous boundary conditions could be converted to solve the initial value problem of a series of ordinary differential equations. The semianalytical solutions were approached by the precise time-integration method. The proposed method can be used for a soil column under various boundary conditions. Several numerical simulations were carried out to validate this method. Finally, the one-dimensional transient responses of hard–soft double-layered saturated soil under step load was analyzed. The results demonstrate that the rigidity of substratum and different rigidity ratio of hard–soft layers mainly affect the responses over a long period of time.
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Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. To be specific, all data that support all the figures in this paper can be provided from the corresponding author.
Acknowledgments
Financial support from the National Natural Science of Foundation of China (51978247, U2039209, 41874067), Research Initiation Fund Project of Henan University of Technology (31401175), Foundation of Key Laboratory of Soft Soils and Geoenvironmental Engineering (Zhejiang University), and Ministry of Education (2019P03) are gratefully acknowledged.
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© 2022 American Society of Civil Engineers.
History
Received: Mar 10, 2022
Accepted: Jul 4, 2022
Published online: Sep 27, 2022
Published in print: Dec 1, 2022
Discussion open until: Feb 27, 2023
ASCE Technical Topics:
- Boundary conditions
- Boundary value problem
- Continuum mechanics
- Differential equations
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equations (by type)
- Geomechanics
- Geotechnical engineering
- Homogeneity
- Layered soils
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Models (by type)
- Numerical models
- Saturated soils
- Soft soils
- Soil mechanics
- Soil properties
- Soils (by type)
- Solid mechanics
- Transient response
- Wave equations
- Waves (mechanics)
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