Analytical Model for Vertical Dynamic Interaction between Circular Raft and Saturated Soils
Publication: International Journal of Geomechanics
Volume 21, Issue 4
Abstract
The raft–soil dynamic interaction problem is of great significance in the fields of marine geotechnical engineering and traffic engineering. This paper develops an analytical model to study the dynamic response of an elastic raft embedded in saturated soil bonded to a rigid base. The model combines the classical theory of elastic thin plate and the analytical layer element method (ALEM). The raft was divided into finite circular elements that are governed by the elastic thin plate theory. Fundamental solutions for the layered saturated soils with compressible constituents were obtained by employing ALEM. By considering the compatible conditions at the interface, the dynamic behavior of the elastic raft was investigated. The present method was verified by comparing with existing solutions. The influences of the vibration frequency, embedded depth of the raft, raft–soil stiffness ratio and the layer property of soil were studied in the numerical analysis. The present model is capable of simulating the dynamic response of the elastic raft resting on the surface or embedded in layered saturated soils, and can also be employed to analyze general raft–soil interaction problems encountered in practical engineering.
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Acknowledgments
The authors acknowledge the support of the Scientific Research Foundation (Zhejiang Sci-Tech University, No. 19052148-Y) and the National Natural Science Foundation of China (Nos. 52078458 and 51908225). The support from Prof. Z.Y. Ai at Tongji University on the development of ALEM is highly appreciated.
Notation
The following symbols are used in this paper:
Definitions for Variables in Numerical Calculation
- a
- radius of raft;
- b
- parameter accounting for the internal friction;
- flexural rigidity of raft;
- E
- elastic modulus of soil;
- Ep
- elastic modulus of raft;
- g
- gravity acceleration;
- H
- thickness of soil;
- h
- embedment of raft;
- ht
- thickness of raft;
- h*
- reinforced depth of soil;
- k
- permeability of soil;
- m
- density-like parameter;
- n
- porosity of soil;
- P
- vertical load applied on the rigid disk;
- vertical displacement for an elastic raft on elastic half-space;
- α, M
- compressible parameters of soil constituents;
- stiffness ratio of raft–soil;
- Δ
- vertical displacement of the rigid disk;
- η0
- viscosity of the pore fluid;
- λ
- Lame's constant of soil;
- μ
- shear modulus of soil;
- μp
- Poisson's ratio of raft;
- ν
- Poisson's ratio of soil;
- ρ
- density of soil;
- ρf
- density of pore fluid;
- ρp
- density of raft;
- ρ0 = ρpht/ρa
- mass ratio of raft–soil; and
- ω
- circular frequency.
Dimensionless Variables in Numerical Calculation
- b
- η0/k;
- ;
- h/a;
- ;
- M/μ;
- m
- ρf/n;
- m/ρ;
- p0/μ;
- w/a;
- ;
- δ
- ;
- η0
- nρfg;
- λ /μ; and
- ρf/ρ.
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© 2021 American Society of Civil Engineers.
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Received: Mar 6, 2020
Accepted: Oct 27, 2020
Published online: Jan 29, 2021
Published in print: Apr 1, 2021
Discussion open until: Jun 29, 2021
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