An elliptical disc anchor in a damage‐susceptible poroelastic medium

A flat rigid elliptical anchorage located in a damage‐susceptible fluid‐saturated poroelastic medium is subjected to an in‐plane load, which induces a pure translation in the plane of the anchor. This paper develops computational estimates for the time‐dependent displacement of the disc anchor for the classical problem that involves Biot consolidation and compares the results with situations where the porous skeleton can experience micro‐mechanical damage that leads to an alteration in both its elasticity and fluid transport characteristics. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-axisymmetric Biot consolidation analysis of multi-layered saturated poroelastic materials with anisotropic permeability

To start with, an analytical layer-element (i.e., a symmetric stiffness matrix), which describes the relationship between the generalized displacements and the stress levels of a layer subjected to non-axisymmetric loading, is exactly derived in the transformed domain by the application of a Laplace–Hankel transform with respect to variables t and r, a Fourier expansion with respect to variable θ, and a Laplace transform and its inversion with respect to variable z, based on the governing equations of Biot’s consolidation of multi-layered saturated poroelastic materials with anisotropic permeability. The analytical layer-element experiences considerable improvement in computation efficiency and stability, since it only contains negative exponential functions in its elements. In addition, a global stiffness matrix for multi-layered saturated poroelastic media is obtained by assembling the interrelated layer-elements based on the continuity conditions between adjacent layers. By introducing the boundary conditions and solving the global stiffness matrix, the solutions in the Laplace–Hankel transformed domain are obtained, and the final solutions can be recovered by a numerical inversion of the Laplace–Hankel transform. Finally, numerical examples are presented to verify the theory and to study the effect of the property of anisotropic permeability on vertical displacements and excess pore pressure. The calculation results show that the property of anisotropic permeability has a great influence on the process of consolidation.     

The 3-D non-axisymmetrical Lamb''''s problem in transversely isotropic saturated poroelastic media

The dynamic analysis of saturated poroelastic media is significant in many areas such as seismology, earthquake engineering, soil mechanics and geophysics. In 1956, Biot[1—3] first developed the dynamic equations for saturated poroelastic media. He also discussed systematically the propagation of waves in such two-phase media and further predicted the existence of the slow longitudinal wave. Biots work is consummate while the two formal parameters he introduced are difficult to measure. In t…     

Mesoscale characterization of coupled hydromechanical behavior of a fractured-porous slope in response to free water-surface movement

To better understand the role of groundwater-level changes on rock-slope deformation and damage, a carbonate rock slope (30 m×30 m×15 m) was extensively instrumented for mesoscale hydraulic and mechanical measurements during water-level changes. The slope is naturally drained by a spring that can be artificially closed or opened by a water gate. In this study, a 2-h slope-dewatering experiment was analyzed. Changes in fluid pressure and deformation were simultaneously monitored, both at discontinuities and in the intact rock, using short-base extensometers and pressure gauges as well as tiltmeters fixed at the slope surface. Field data were analyzed with different coupled hydromechanical (HM) codes (ROCMAS, FLAC^3D, and UDEC).

Field data indicate that, in the faults, a 40 kPa pressure fall occurs in 2 min and induces a 0.5–31×10⁻⁶ m normal closure. Pressure fall is slower in the bedding-planes, lasting 120 min, with no normal deformation. No pressure change or deformation is observed in the intact rock. The slope surface displays a complex tilt towards the interior of the slope, with magnitudes ranging from 0.6 to 15×10⁻⁶ rad.

Close agreement with model for both slope surface and internal measurements is obtained when a high variability in slope-element properties is introduced into the models, with normal stiffnesses of k_{n_faults}=10⁻³×k_{n_bedding-planes} and permeabilities of k_{h_faults}=10³×k_{h_bedding-planes}. A nonlinear correlation between hydraulic and mechanical discontinuity properties is proposed and related to discontinuity damage. A parametric study shows that 90% of slope deformation depends on HM effects in a few highly permeable and highly deformable discontinuities located in the basal, saturated part of the slope while the remaining 10% is related to elasto-plastic deformations in the low-permeability discontinuities induced by complex stress/strain transfers from the high-permeability zones. The periodicity and magnitude of free water-surface movements cause 10–20% variations in those local stress/strain accumulations related to the contrasting HM behavior for high- and low-permeability elements of the slope. Finally, surface-tilt monitoring coupled with internal localized pressure/deformation measurements appears to be a promising method for characterizing the HM properties and behavior of a slope, and for detecting its progressive destabilization.     

Vertical dynamic interactions of poroelastic soils and embedded piles considering the effects of pile-soil radial deformations

The paper presents an analytical solution for the vertical dynamic interaction analysis of a poroelastic soil layer and an embedded pile with the consideration of pile-soil radial deformations. The soil is treated a three-dimensional porous continuum and described by the Boer’s poroelastic model, while the pile is treated as a two-dimensional rod with both radial and vertical deformations of which the equation of motion is derived by the Hamilton’s variational principle. Without the introduction of potential functions, first take the volumetric strain of soil skeleton and pore fluid pressure as intermediate variables to deal with the equations of motion for the soil and then use the separation of variables to solve the equations of motion for the soil and the pile. By imposing the boundary and continuity conditions of the pile-soil system, the dynamic impedance in frequency domain and the velocity response in time domain of the pile top are obtained. The present solution is then verified by comparing with the corresponding finite element model computation results and the existing solutions. The effects of the pile-soil parameters on the dynamic characteristic of the pile-soil system are also analyzed. Some significant conclusions are drawn, which can provide useful reference for related engineering practice.     

高速列车荷载作用下路轨系统及饱和地基的动力响应

将在高速移动列车荷载作用下的铁路系统分为上覆路轨系统和下卧土体两部分.对于下卧土体部分,通过Fourier变换求解Biot多孔饱和介质的动力方程.对于路轨系统,将钢轨简化为无限长弹性Euler梁,将枕木简化为连续质量块,同时考虑道渣层的影响.用一系列符合列车几何尺寸的点荷载来模拟列车荷载.在Fourier变换域内,联立路轨系统和下卧土体的动力方程,求解在列车荷载作用下的钢轨位移和加速度、土体位移和加速度及土体孔压的表达式.利用数值积分方法对表达式进行Fourier逆变换,得到钢轨位移和加速度、土体孔压在时域内的表达式.通过算例讨论了荷载移动速度和土体渗透系数对钢轨速度和加速度及土体孔压的影响.结果表明,水相介质的存在和荷载移动速度均对土体动力响应产生很大影响.     

饱和半空间表面无限长梁的沉降变形

采用解析方法研究了饱和半空间表面无限长欧拉梁的沉降变形特性。假定梁与地基的竖向接触应力沿梁截面均匀分布、梁的挠度与梁截面下地基表面的位移均值相等,分别考虑地基表面完全透水及完全不透水情况,基于Fourier及Laplace联合变换获得了问题的解析解,并通过已有研究结果及ABAQUS~(TM)有限元分析模型对比验证了解的正确性。分析结果表明,梁的弯曲刚度、地基的排水及不排水泊松比以及地基表面的透水条件对梁的沉降变形有明显影响。     

切比雪夫方法仿真压电耦合场

仿真压电耦合场已有的方法是FDTD法,具有灵活简单易操作的优点。该方法的局限性是其稳定性受时间间隔和空间间隔的约束,运行时间长。该文提出了一种基于切比雪夫矩阵多项式展开,结合数值积分的方法,仿真压电耦合场。该方法具有高精度,高速度的优点。同时采用复坐标变量完全匹配层作为边界吸收条件,将有限区域仿真拓展到无界空间的仿真。通过一维压电媒质的例子说明算法的可行性和稳定性。     

An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations

This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.