Torsional vibration of a pipe pile in transversely isotropic saturated soil

This study considers the torsional vibration of a pipe pile in a transversely isotropic saturated soil layer. Based on Biot＇s poroelastic theory and the constitutive relations of the transversely isotropic medium, the dynamic governing equations of the outer and inner transversely isotropic saturated soil layers are derived. The Laplace transform is used to solve the governing equations of the outer and inner soil layers. The dynamic torsional response of the pipe pile in the frequency domain is derived utilizing 1D elastic theory and the continuous conditions at the interfaces between the pipe pile and the soils. The time domain solution is obtained by Fourier inverse transform. A parametric study is conducted to demonstrate the influence of the anisotropies of the outer and inner soil on the torsional dynamic response of the pipe pile.

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE 〈 1 and RG 〈 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.

Scattering wave field around a cavity with circular cross-section embedded in saturated soil using boundary element method

Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.

Dynamic torsional response of pre-strained end bearing pile embedded in pre-strained isotropic saturated soil medium

The influence of initial strain state on the dynamic response of an end bearing pile embedded in isotropic saturated soil is investigated through the linearized theory of small elastic perturbation superposed on largely stressed bodies. The governing equations for soil, based on Blot＇s poroelasticity theory, are derived in the cylindrical coordinates, and the pile is modeled by using the one-dimensional elastic theory. The analytical solutions of pile impedance, frequency response of both twist angle and time history of velocity response are obtained by using of separation of variables technique. Finally, a parametric study of the influence of initial strains on the torsional impedance, twist angle, and velocity response at the top of the pile is carried out.

Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation

The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel trans- form. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multi- layered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

Recent developments of generalized plasticity models for saturated and unsaturated soils

Soil undergoes both elastic and plastic deformations under different loading conditions. A relatively accurate constitutive model of soil behaviors should be capable of predicting the elastic and plastic deformations properly. Among a large number of elastoplastic constitutive models developed over the last several decades, constitutive models based on generalized plasticity have been successfully utilized in modeling the mechanical behavior of various soils. This paper attempts to present a review of the most recent developments of generalized plasticity models for geotechnical problems. After a brief review of generalized plasticity theories and constitutive models, limitations of the original Pastor-Zienkiewicz model in practical application are summarized. Afterwards, recent achievements in the generalized plasticity models for both saturated and unsaturated soils and their applicability are analyzed, and a general approach for modification of generalized plasticity models is highlighted.

Scattering of elastic wave by a cylindrical shell deeply embeded in saturated soils

The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave （fast compressional wave） by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.

New artificial boundary condition for saturated soil foundations

Anew artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves （S-waves） are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, δra＇ is absorbed by the first artificial boundary. The second type of stress, δrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves （fast-P-waves and slow-P-waves） are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.

Instability of Saturated Soilunder Axial Load

A theoretical description of instability of saturated soil under axial load is presented with a set of equations describing the deformation based on the two phase continuous media theory. It is shown that all parameters of water and soil influence the instability and two types of instability may exist. One of them is dominated by pore pressure softening, while the other by strain softening. Finally, a practical application is discussed.

Solution of a rigid disk on saturated soil considering consolidation and rheology

The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using integral transform techniques, general solutions of Biot consolidation functions and the dual integral equations of a rigid disk on saturated soil were established based on the boundary conditions. These equations can be simplified using Laplace-Hankel and Abel transform methods. The numerical solutions of the integral equations, and the corresponding inversion transform were used to obtain the settlement and contact stresses of the rigid disk. Numerical examples showed that the soil settlement is small if only consolidation is considered, so the soil rheology must be taken into account to calculate the soil settlement. Numerical solution of Hankel inverse transform is also given in this paper.

SPHERICAL WAVE PROPAGATION IN SATURATED SOILS

Based on the generally adopted soil model for engineering, an analytic solution of spherical wave propagation problem in a special case for an equally pressurized spherical cavity in saturated space by Laplace transformation which is compared with that of the same problem in a one-phase elastic space. The influence of fluid on dynamic response of saturated soil is examined. The authors propose an effective way for dynamic analysis of underground structure.

A new equation for dielectric permittivity of saturated soils based on polarization mechanics

Based on polarization mechanisms, such as electronic, ionic and orientational polarizations, a new equation for dielectric permittivity of soil is proposed to interpret the dielectric behavior of a mixture like soil, in terms of polarization process of its components and the interactions between its components. The dielectric permittivity is expressed in terms of a fre-quency-dependent part and a frequency-independent part. These two parts correspond to polarizations occurred at different fre-quency range. It is a new volumetric mixing model with theoretical background. Based on time domain reflectometry (TDR) measurements of saturated soil samples and test data from literature, comparisons of this model with some well established mixing models show that the curves for saturated sand soils and slurries resulted from the new equation, which agree well with TDR measurements, are close to those calculated from Birchak's model.

TORSIONAL VIBRATIONS OF RIGID CIRCULAR PLATE ON TRANSVERSELY ISOTROPIC SATURATED SOIL

An analytical method was presented for the torsional vibrations of a rigid disk resting on transversely isotropic saturated soil. By Hankel transform, the dynamic governing differential equations for transversely isotropic saturated poroelastic medium were solved. Considering the mixed boundary-value conditions, the dual integral equations of torsional vibrations of a rigid circular plate resting on transversely isotropic saturated soil were established. By appropriate transform, the dual integral equations were converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficient, the torsional angular amplitude of the foundation and the contact shear stress were expressed explicitly. Selected examples were presented to analyse the influence of saturated soil＇s anisotropy on the foundation＇s vibrations.

An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils

Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.

DYNAMIC INTERACTION BETWEEN ELASTIC THICK CIRCULAR PLATE AND TRANSVERSELY ISOTROPIC SATURATED SOIL GROUND

A study of the dynamic interaction between foundation and the underlying soil has been presented in a recent paper based on the assumption of saturated ground and elastic circular plate excited by the axisymmetrical harmonic source. However, the assumption may not always be valid. The work is extended to the case of a circular plate resting on transversely isotropic saturated soil and subjected to a non-axisymmetrical harmonic force. The analysis is based on the theory of elastic wave in transversely isotropic saturated poroelastic media established. By the technique of Fourier expansion and Hankel transform, the governing difference equations for transversely isotropic saturated soil are easily solved and the cooresponding Hankel transformed stress and displacement solutions are obtained. Then, under the contact conditions, the problem leads to a pair of dual integral equations which describe the mixed boundary-value problem. Furthermore, the dual integral equations can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure. At the end, a numerical result is presented which indicates that on a certain frequency range, the displacement amplitude of the surface of the foundation increases with the increase of the frequency of the exciting force, and decreases in vibration form with the increase of the distance.

Evolutions of Compaction Bands of Saturated Soils

The development of compaction bands in saturated soils, which is coupling-rate, inertial and pore-pressure-dependent, under axisymmetric loading was discussed, using a simple model and a matching technique at the moving boundary of a band. It is shown that the development of compaction bands is dominated by the coupling-rate and pore-pressure effects of material. The soil strength makes the band shrinking, whilst pore pressure diffusion makes the band expand. Numerical simulations were carried out in this paper.

Study on one—dimensional consolidation of saturated soil with semi—pervious boundaries and under cyclic loading

The variation of effective stress ratio of stratfied soil with semi pervious boundaries and under cyclic loading was analyzed on the basis of Terzaghi's one dimensional consolidation assumptions. A solution by Laplace Transform was obtained for the case when the soil was under time varied loading. With numerical inversion of Laplace Transform, some useful results were obtained for several kinds of commonly encountered loadings. The results can be meaningful in engineering practice.

VERTICAL VIBRATION ANALYSIS OF AXISYMMETRIC SATURATED SOIL

Based on Biot＇s dynamic consolidation equations, by means of Laplace-Hankel transform technology, the integral solutions of stress and displacement in saturated soil with subjacent rock-stratum under axisymmetric arbitrary excitations were derived. Influence of the reflected wave generated by the boundary was revealed. Numerical results indicate that the vibration frequency has some effect on the vertical displacement of satu rated soil. The vertical displacement at the surface of saturated soil lags in phase with the load. Furthermore, the dynamic permeability coefficient of saturated soil has significant effect on the vertical displacement at the initial stage of load applied, but when the load becomes stable, the effect is inapparent.

Development of the Shear Bandsin Saturated Soil

This paper describes the development of shear bands in saturated soil under simple shear using a matching technique at the moving boundary of a shear band, and it is shown that the development of shear bands is affected by the coupling strain rate and pore pressure of material.Some numerical solutions have been presented.

Shear Instability of Saturated Soil Considering the Gradients of Strain and Pore Pressure

The dynamic instability of saturated soil considering the gradients of strain and pore pressure was discussed in this paper.The inertia and the drainage effects were considered and the Perturbation method was used.It is shown that the strain gradient and pore pressure gradient are positive factors for the instability of saturated soil.