Dynamic Response of a Circular Tunnel Embedded in a Saturated Poroelastic Medium due to a Moving Load

2006 ◽  
Vol 128 (6) ◽  
pp. 750-756 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Porous Medium ◽  
Dynamic Response ◽  
Closed Form ◽  
Pore Pressure ◽  
Fourier Transformation ◽  
Moving Load ◽  
Wave Number ◽  
Circular Tunnel ◽  
Soil Response ◽  
General Solutions

Dynamic response of a circular tunnel embedded in a porous medium and subjected to a moving axisymmetric ring load is investigated in this paper. In this study, two scalar potentials and two vectorial potentials are introduced to represent the displacements for the solid skeleton and the pore fluid. Based on Biot’s theory and applying the Fourier transformation on time variable, a set of frequency domain governing equations for the potentials are obtained. Performing the Fourier transformation on the axial coordinate, closed-form general solutions for the potentials with arbitrary constants are obtained. Using the closed-form general solutions and boundary conditions along the tunnel surface, the arbitrary constants involved in the potentials are calculated. Representations for the displacements, the stresses and the pore pressure are derived in terms of the closed-form potentials. Analytical inversion of the Fourier transformation with respect to frequency and numerical inversion of the Fourier transformation with respect to the axial wave number lead to numerical solutions for the displacements, the stresses and the pore pressure in the porous medium. Numerical results demonstrate the soil response due to a high speed load is quite different from those due to a static load or a lower speed load. These differences become more pronounced when the velocity of moving load approaches the velocities of elastic waves of a porous medium.

An Analytical Solution for Wave-Induced Soil Response and Seabed Liquefaction

2010 ◽  
Author(s):  
Xiang-Lian Zhou ◽  
Jian-Hua Wang ◽  
Yun-Feng Xu
Keyword(s):  
Shear Modulus ◽  
Pore Pressure ◽  
Effective Stress ◽  
Fourier Transformation ◽  
Saturated Porous Medium ◽  
Helmholtz Equations ◽  
Soil Response ◽  
Depth Increase ◽  
Vertical Effective Stress ◽  
Wave Induced

In this study, an analytical method to solve the wave-induced pore pressure and effective stress in a saturated porous seabed is proposed. The seabed is considered as a saturated porous medium and characterized by Biot’s theory. The displacements of the solid skeleton and pore pressure are expressed in terms of two scalar potentials and one vector potential. Then, the Biot’s dynamic equations can be solved by using the Fourier transformation and reducing to Helmholtz equations that the potentials satisfy. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinate. Numerical results show that the permeability and shear modulus of the porous seabed has obvious influence on the response of the seabed. The vertical effective stress and attenuation velocity of pore pressure along seabed depth increase as permeability k increases. The liquefaction may be occur at the surface of seabed when shear modulus decreasing.

Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell

1969 ◽  
Vol 39 (3) ◽  
pp. 477-495 ◽  
Author(s):  
R. A. Wooding
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Hyperbolic Equations ◽  
Saturated Porous Medium ◽  
Mean Amplitude ◽  
Wave Number ◽  
Two Fluids ◽  
Averaged Equations ◽  
The Mean ◽  
Hele Shaw Cell

Waves at an unstable horizontal interface between two fluids moving vertically through a saturated porous medium are observed to grow rapidly to become fingers (i.e. the amplitude greatly exceeds the wavelength). For a diffusing interface, in experiments using a Hele-Shaw cell, the mean amplitude taken over many fingers grows approximately as (time)2, followed by a transition to a growth proportional to time. Correspondingly, the mean wave-number decreases approximately as (time)−½. Because of the rapid increase in amplitude, longitudinal dispersion ultimately becomes negligible relative to wave growth. To represent the observed quantities at large time, the transport equation is suitably weighted and averaged over the horizontal plane. Hyperbolic equations result, and the ascending and descending zones containing the fronts of the fingers are replaced by discontinuities. These averaged equations form an unclosed set, but closure is achieved by assuming a law for the mean wave-number based on similarity. It is found that the mean amplitude is fairly insensitive to changes in wave-number. Numerical solutions of the averaged equations give more detailed information about the growth behaviour, in excellent agreement with the similarity results and with the Hele-Shaw experiments.

scholarly journals Spectral analysis of multiple cracked beam subjected to moving load

2014 ◽  
Vol 36 (4) ◽  
pp. 245-254
Author(s):  
N. T. Khiem ◽  
P. T. Hang
Keyword(s):  
Dynamic Response ◽  
Moving Load ◽  
Time History ◽  
Theoretical Development ◽  
Multiple Cracks ◽  
Spectral Approach ◽  
Cracked Beam ◽  
Time History Response ◽  
Numerical Case Study

In present paper, the spectral approach is proposed for analysis of multiple cracked beam subjected to general moving load that allows us to obtain explicitly dynamic response of the beam in frequency domain. The obtained frequency response is straightforward to calculate time history response by using the FFT algorithm and provides a novel tool to investigate effect of position and depth of multiple cracks on the dynamic response. The analysis is important to develop the spectral method for identification of multiple cracked beam by using its response to moving load. The theoretical development is illustrated and validated by numerical case study.

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