Transient mechanical wave propagation in semi-infinite porous media using a finite element approach

In this study, we propose a numerical investigation in the time domain of the mechanical wave propagation of an impulsional load on semi-infinite soil. The ground is modelled as a porous saturated viscoelastic medium involving complete Biot theory. All the couplings and a hysteretic Rayleigh damping are taken into consideration. An accurate and efficient finite element method using a matrix-free technique and an expert multigrid system are applied. Our results present the displacements of the fluid and solid particles over the surface and in depth. The arrival times of body and surface waves are studied. Particularly, the compressional wave of the second kind is highlighted. The influence of the different couplings and more specifically, the influence of the permeability on the response of the soil are analyzed.     

Analysis of the solid phase stress tensor in multiphase porous media

Conservation equations for mass, momentum, energy, and entropy are formulated for the phases and interfaces of a three‐phase system consisting of a solid and two immiscible fluids. The microscale equations are averaged to the macroscale by integration over a representative elementary volume. Thermodynamic statements for each of the phases and interface entities are also formulated at the microscale and then averaged to the macroscale. This departure from most uses of thermodynamics in macroscale analysis ensures consistency between models and parameters at the two scales. The expressions for the macroscale rates of change of internal energy are obtained by differentiating the derived forms for energy and making use of averaging theorems. These thermodynamic expressions, along with the conservation equations, serve as constraints on the entropy inequality. A linearization of the resulting equations is employed to investigate the theoretical origins of the Biot coefficient that relates the hydrostatic part of the total stress tensor to the normal force applied at the solid surface by the pore fluids. The results here are placed in the context of other formulations and expressions that appear in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Sound speed dispersion characteristics of three types of shallow sediments in the southern yellow sea

To accurately characterize sound speed dispersion of shallow sediments in the Southern Yellow Sea, three types of sediments, i.e., silt, clayey silt, and silty clay, were selected to measure the sound speeds at 25–250?kHz. Over the frequency range, the sound speeds vary approximately from 1,536 to 1,565?m?s^?1 in silt sediment, from 1,511 to 1,527?m?s^?1 in clayey silt sediment, and from 1,456 to 1,466?m?s^?1 in silty clay sediment. The sound speed exhibits a slow increase with frequency in a nearly linear gradient, but these three types of sediments have different sound speed dispersion characteristics. The silt sediment with relatively coarse grains has the most significant sound speed dispersion, while the sound speed dispersions of the two others are relatively weak. Comparison between the measured dispersions and the model predictions shows that the grain-shearing model can match the measured data at most of frequencies. Nevertheless, when the grain bulk modulus was assigned 3.2?×?10¹⁰?Pa according to relevant references, the Biot–Stoll model predictions were higher than the measured values at high frequencies; when it was assigned a relatively small value of 2.8?×?10¹⁰?Pa, the model predictions achieved optimal matching with the measured values.     

Numerical analysis on random wave-induced porous seabed response

Research on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.     

邓肯-张模型参数对比奥随机固结的影响

推导出比奥随机固结有限元方程,将对比奥固结影响显著的邓肯-张模型参数k、C、φ、G模拟为随机场,采用Mont-Carlo法实现随机固结有限元程序,在某一自关距离下研究4个参数的不同变异对比奥随机固结的影响。发现参数的变异对计算结果的均值影响不大;而对计算结果的变异性影响较大:对竖向位移影响显著的是k、φ的随机性,而对侧向位移影响显著的是k、φ、G,参数C的随机性影响较弱。参数G的随机性影响是后天引起的,可以通过提高试验精度,改进分析方法减小随机性。     

高层建筑引发地面沉降模拟预测三维流固全耦合模型

为了准确预测由高层建筑引发土体应力场和渗流场变化而导致的地面沉降,以比奥固结理论为基础,结合土体非线性流变理论,将比奥固结理论中的本构关系拓展到黏弹塑性,并考虑了土体孔隙度、渗透系数及变形参数随有效应力的动态变化关系。以河北省沧州市为例,建立了沧州市高层建筑荷载、地下水渗流与土体变形三维流固全耦合数学模型。在对模型进行识别、验证的基础上,模拟预测了沧州市在地下水停采、仅存在高层建筑荷载的影响下,从2010年12月底到2025年12月底逐年的各含水层组地下水流场变化特征和地面沉降发展趋势。结果表明：沧州市由高层建筑荷载引发的最大地面沉降量为40.57 mm,最大地面沉降速率为2.7 mm/a,位于沧州市区。     

Study of transient poroviscoelastic soil motions by semi-analytical and numerical approaches

In this paper, the authors compare results obtained by semi-analytical and numerical approaches for the dynamic response of a poroviscoelastic soil under transient loads. The behaviour of the medium is governed by complete Biot formalism. The semi-analytical approach is based on Helmholtz decompositions and Fourier transforms, and yields exact solid and fluid displacements in the transformed domain. The numerical approach uses a C++$\mathrm{C}++$ object oriented programming finite element–finite difference code. Both methods give concurring results. Moreover, influence of viscous coupling on the response of the ground and visualization of the compressional wave of the second kind are discussed.     

Low-frequency dilatational wave propagation through fully-saturated poroelastic media

The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems.     

《毕奥理论中3个基本参数的显式解》一文中的真正错误——兼答丁伯阳教授

论述了《西北地震学报》1997年第4期发表的《毕奥理论中3个基本参数的显式解》一中的真正错误所在,与丁伯阳教授1998年第4期《西北地震学报》发表的间《关于《毕奥理论中3个基本参数显式解》一的错误》中所说的错误有所不同,指出丁教授中存在着概念性的错误。     

Practical causal hysteretic damping

A number of experiments indicate that the internal damping corresponding to the energy dissipation of many materials is essentially frequency independent. Accordingly, an analysis model that can express such characteristics (called a hysteretic damping model) in the time domain is needed. Although a great number of investigations into this subject have been carried out, there are a few practical methods. In this paper, a simple hysteretic damping model which satisfies the causality condition is presented using an extension of the complex stiffness transfer method that the author has proposed. Compared with the energy proportional damping model and the Biot model, the applicability and the efficiency of this model to time history response analyses were confirmed well by example problems. Copyright © 2006 John Wiley & Sons, Ltd.