横观各向同性饱和介质非轴对称动力响应分离变量解Separation of variables solution of non-axisymmetrical dynamic response of transversely isotropic saturated porous media

首先将横观各向同性饱和弹性多孔介质非轴对称问题的Bio t波动方程,变换为适宜于进行分离变量法求解的形式;然后在非轴对称简谐激励下,用分离变量法得到Bio t方程的一般解,即用分离变量法求得了多孔介质位移和应力分量的解析表达式;并给出了半空间横观各向同性饱和弹性多孔介质在表面竖向简谐荷载作用下表面竖向位移的数值分析结果,得出载荷对30倍受载半径以外的区域几乎无影响的结论。同时表明了本文的分析方法是切实可行的。     

移动荷载作用下饱和土地基中的波动特性分析

基于Biot波动方程,经过Fourier变换和逆Fourier变换后可获得波数-频率域以及时间-空间域的解析解。通过数值分析的手段研究了移动荷载作用下饱和多孔弹性地基中波的传播特性。重点就弥散曲线、多谱勒效应、波的成分和动力响应频率等几个特性进行了分析,发现饱和土地基由于比弹性地基多了一项流体介质,波动特性明显差异于弹性介质。     

Complex variable function method for the scattering of plane waves by an arbitrary hole in a porous medium

Based on the complex variable function method, a new approach for solving the scattering of plane elastic waves by a hole with an arbitrary configuration embedded in an infinite poroelastic medium is developed in the paper. The poroelastic medium is described by Biot's theory. By introducing three potentials, the governing equations for Biot's theory are reduced to three Helmholtz equations for the three potentials. The series solutions of the Helmholtz equations are obtained by the wave function expansion method. Through the conformal mapping method, the arbitrary hole in the physical plane is mapped into a unit circle in the image plane. Integration of the boundary conditions along the unit circle in the image plane yields the algebraic equations for the coefficients of the series solutions. Numerical solution of the resulting algebraic equations yields the displacements, the stresses and the pore pressure for the porous medium. In order to demonstrate the proposed approach, some numerical results are given in the paper.     

Validation of a 2-D semi-coupled numerical model for fluid–structure–seabed interaction

A 2-D semi-coupled model PORO-WSSI 2D (also be referred as FSSI-CAS 2D) for the Fluid-Structure-Seabed Interaction (FSSI) has been developed by employing RANS equations for wave motion in fluid domain, VARANS equations for porous flow in porous structures; and taking the dynamic Biot's equations (known as "u − p" approximation) for soil as the governing equations. The finite difference two-step projection method and the forward time difference method are adopted to solve the RANS, VARANS equations; and the finite element method is adopted to solve the "u − p" approximation. A data exchange port is developed to couple the RANS, VARANS equations and the dynamic Biot's equations together. The analytical solution proposed by Hsu and Jeng (1994) and some experiments conducted in wave flume or geotechnical centrifuge in which various waves involved are used to validate the developed semi-coupled numerical model. The sandy bed involved in these experiments is poro-elastic or poro-elastoplastic. The inclusion of the interaction between fluid, marine structures and poro-elastoplastic seabed foundation is a special point and highlight in this paper, which is essentially different with other previous coupled models The excellent agreement between the numerical results and the experiment data indicates that the developed coupled model is highly reliablefor the FSSI problem.     

Wave-current-induced soil response in marine sediments

This letter presents a new analytical approximation for wave (current)-induced dynamic soil response in marine sediments. In the model, the third-order approximation for wave-current interactions is employed for the flow model, while Biot's dynamic poro-elastic model is used to simulate the porous flow in a seabed. The newly analytical solution is validated with the field observations. Based on the solution, effects of currents and wave-nonlinearity on soil response are examined and a parametric study will be carried out to examine the influence of currents on the liquefaction potential.     

On the propagation of waves through porous solids

This note reexamines Biot's model for the propagation of acoustic waves in a material such as cohensionless sand, infused with a fluid, within the context of mixture theory. Instead of the standard entropy equation that is used in mixture theory, an inequality for the viscous dissipation is employed here due to a conceptual difficulty that one encounters in applying the standard equation to a mixture of sand and a fluid. The wave equations are reformulated by taking the velocity field, instead of the displacement, for the fluid as a primary quantity. By recognizing and thereby exploiting the dependence of the stored energy of the sand on the pore fluid pressure and choosing an appropriate form for the rate of dissipation, a set of governing equations are obtained which are equivalent to those derived by Biot [J. Acoust. Soc. Am. 28(1956) 168, 179; J. Appl. Phys. 33(1962) 1482]. A differential equation for the pore fluid pressure is derived and the effects of drag and virtual mass are dealt with in a unified fashion. The procedure allows us to develop generalizations to Biot's equations in a rational manner.     

Numerical analysis of Biot's consolidation process by radial point interpolation method

An algorithm is proposed to solve Biot's consolidation problem using meshless method called a radial point interpolation method (radial PIM). The radial PIM is advantageous over the meshless methods based on moving least-square (MLS) method in implementation of essential boundary condition and over the original PIM with polynomial basis in avoiding singularity when shape functions are constructed. Two variables in Biot's consolidation theory, displacement and excess pore water pressure, are spatially approximated by the same shape functions through the radial PIM technique. Fully implicit integration scheme is proposed in time domain to avoid spurious ripple effect. Some examples with structured and unstructured nodes are studied and compared with closed-form solution or finite element method solutions.     

On a 2D hydro-mechanical lattice approach for modelling hydraulic fracture

A 2D lattice approach to describe hydraulic fracturing is presented. The interaction of fluid pressure and mechanical response is described by Biot's theory. The lattice model is applied to the analysis of a thick-walled cylinder, for which an analytical solution for the elastic response is derived. The numerical results obtained with the lattice model agree well with the analytical solution. Furthermore, the coupled lattice approach is applied to the fracture analysis of the thick-walled cylinder. It is shown that the proposed lattice approach provides results that are independent of the mesh size. Moreover, a strong geometrical size effect on nominal strength is observed which lies between analytically derived lower and upper bounds. This size effect decreases with increasing Biot's coefficient.     

A quasi-static stability analysis for Biot's equation and standard dissipative systems

In this paper, an extended version of Biot's differential equation is considered in order to discuss the quasi-static stability of a response for a solid in the framework of generalized standard materials. The same equation also holds for gradient theories since the gradients of arbitrary order of the state variables and of their rates can be introduced in the expression of the energy and of the dissipation potentials. The stability of a quasi-static response of a system governed by Biot's equations is discussed. Two approaches are considered, by direct estimates and by linearizations. The approach by direct estimates can be applied in visco-plasticity as well as in plasticity. A sufficient condition of stability is proposed and based upon the positivity of the second variation of energy along the considered response. This is an extension of the criterion of second variation, well known in elastic buckling, into the study of the stability of a response. The linearization approach is available only for smooth dissipation potentials, i.e. for the study of visco-elastic solids and leads to a result on asymptotic stability. The paper is illustrated by a simple example.     

Dynamic characterization of poroelastic materials

This paper presents a method, based on measurement of material dynamic-complex stiffness, of determining the coefficients appearing in Biot's equations for poroelastic materials. This method is relatively simple to employ and has several self-checking features. Results are presented and compared with theoretical predictions for material systems based on polyurethane foam, wool felt and sand solid phases with fluid phases of water, air and silicone fluid.     

Mach waves produced in the supersonic jet mixing layer by shock/vortex interaction

The noise emission of free jets has been extensively investigated for many decades. At subsonic jet velocities, coherent structures of the mixing layer move at subsonic speed and emit sound waves. Free jets blowing at supersonic speeds, however, can emit weak shock waves, called Mach waves. At supersonic speeds, two cases must be distinguished: the structures move either subsonically or supersonically relative to the inside and/or outside speed of sound. In the case of supersonic movement, the Mach waves exist inside as well as outside the jet. At subsonic speeds, no Mach waves appear. Although numerous theories have been established to find the origin of the Mach waves, to the authors’ best knowledge, the mechanism of the Mach wave formation has not yet been clearly explained. Recently another theory of Mach waves in supersonic jets was developed, as described herein, which outlines the causes for the Mach wave production and stability as well as their dynamics. The theory’s principle is that the Mach waves are initiated by vortices which move downstream at three speeds w, \({w}'\) and \({w}''\) inside of the mixing layer. These three types of vortices and Mach waves are described in a comprehensive manner by the theory and are called the “w-, \({w}'\)- and \({w}''\)-vortices” and “w-, \({w}'\)- and \({w}''\)-Mach waves,” respectively.     

Wave propagation in a pre-stressed highly elastic body: two exact solutions for Boussinesq problems

Two problems of wave propagation induced by surface loads in a compressible neo-Hookean half-space, initially at rest under a uniform pre-stress, are considered. One problem concerns a plane-strain situation, the other, one of axial symmetry. An accepted general procedure, that of superposing infinitesimal deformations upon the possibly large deformations due to pre-stress, is carried out completely in terms of tractable exact solutions for both the surface behavior and the full field, and analytical expressions for all wave speeds.

The results show that for a tensile pre-stress above a critical value, a negative Poisson effect occurs; for compressive pre-stresses, Rayleigh waves disappear at a critical value. Indeed, all wave speeds in the deformed configuration (effective wave speeds), as well as the solutions, for both problems are clearly sensitive to material properties and to both the magnitude and nature (compressive or tensile) of the pre-stress. In particular, the constraint imposed by plane strain appears to enhance this sensitivity.     

航行气垫船激励浮冰响应的模型实验研究

基于弹性薄板振动微分方程和相似理论,建立了气垫船在浮冰上运动的原型系统与模型系统参数之间的相似对应关系. 导出了浮冰层自由振动波形传播的相速度和群速度计算公式,明确了相速度的极小值和浅水波传播速度即为气垫船的第一、第二临界速度. 根据研制的高精度非接触式激光位移测量系统,在变水深拖曳水槽中, 开展了不同速度移动气垫载荷激励薄膜变形响应的系列实验,证实了存在使薄膜变形达到最大的移动气垫载荷临界速度. 第一临界速度使气垫载荷之后的薄膜产生最大的下陷变形,第二临界速度使气垫载荷之前的薄膜产生最大的上凸变形. 通过实验结果进一步分析了气垫速度、高度、压力及水深等参数对薄膜变形和临界速度的影响,揭示了移动气垫载荷激励薄膜变形响应的聚能共振增幅机理,为利用气垫船实施有效破冰提供了依据.      

A review of wave celerity in frictionless and axisymmetrical steel-lined pressure tunnels

Generally applicable approaches for estimating the “quasi-static”, which means without fluid-structure interaction and frequency-dependent water-hammer wave speed in steel-lined pressure tunnels are analyzed. The external constraints and assumptions of these approaches are discussed in detail. The reformulated formulas are then compared to commonly used expressions. Some special cases of wave speed calculation such as unlined pressure tunnels and open-air penstocks are investigated. The quasi-static wave speed is significantly influenced by the state of the backfill concrete and the near-field rock zone (cracked or uncracked). In the case when these two layers are cracked, the quasi-static wave speed is overestimated in between 1% and 8% compared to uncracked concrete and near-field rock layers. Depending on the stiffness of steel liner and penstock, the fluid-structure interaction leads to significant difference in wave speeds values. Compared to the quasi-static case, the fluid-structure interaction approach, applied to steel-lined tunnels, results up to 13% higher wave speed values in the high-frequency range (higher than 600 Hz) and up to 150% lower values for frequencies between 150 and 300 Hz in the considered test case.     

MODEL EXPERIMENT ABOUT RESPONSE OF FLOATING ICE SHEET SUBJECTED TO MOVING AIR CUSHION VEHICLE

基于弹性薄板振动微分方程和相似理论,建立了气垫船在浮冰上运动的原型系统与模型系统参数之间的相似对应关系. 导出了浮冰层自由振动波形传播的相速度和群速度计算公式,明确了相速度的极小值和浅水波传播速度即为气垫船的第一、第二临界速度. 根据研制的高精度非接触式激光位移测量系统,在变水深拖曳水槽中, 开展了不同速度移动气垫载荷激励薄膜变形响应的系列实验,证实了存在使薄膜变形达到最大的移动气垫载荷临界速度. 第一临界速度使气垫载荷之后的薄膜产生最大的下陷变形,第二临界速度使气垫载荷之前的薄膜产生最大的上凸变形. 通过实验结果进一步分析了气垫速度、高度、压力及水深等参数对薄膜变形和临界速度的影响,揭示了移动气垫载荷激励薄膜变形响应的聚能共振增幅机理,为利用气垫船实施有效破冰提供了依据.     

Experimental analysis of sand particles＇ lift-off and incident velocities in wind-blown sand flux

The probability distributions of sand particles' lift-off and incident velocities in a wind-blown sand flux play very important roles in the simulation of the wind-blown sand movement. In this paper, the vertical and the horizontal speeds of sand particles located at 1.0 mm above a sand-bed in a wind-blown sand flux are observed with the aid of Phase Doppler Anemometry (PDA) in a wind tunnel. Based on the experimental data, the probability distributions of not only the vertical lift-off speed but also the lift-off velocity as well as its horizontal component and the incident velocity as well as its vertical and horizontal components can be obtained by the equal distance histogram method. It is found, according to the results of the χ ²-test for these probability distributions, that the probability density functions (pdf's) of the sand particles' lift-off and incident velocities as well as their vertical components are described by the Gamma density function with different peak values and shapes and the downwind incident and lift-off horizontal speeds, respectively, can be described by the lognormal and the Gamma density functions. These pdf's depend on not only the sand particle diameter but also the wind speed.     

强角闪石化橄榄二辉岩的动态拉伸强度实验研究

对强角闪石化橄榄二辉岩的动态拉伸断裂强度进行了实验研究。设计了能在样品中产生持续时间大约为1.5 s拉伸应力脉冲的平板冲击回收实验。通过对回收样品的宏观和微观观察,确定了样品出现拉伸破坏开始阶段以及破坏裂纹的扩展阶段,进而确定了该岩石样品的动态拉伸强度约为265.6~315.3 MPa。同时,基于线弹性近似,导出了在一维应变条件下样品内拉伸应力和作用时间的估算公式。     

Characterisation of underground blast-induced ground motions from large-scale field tests

An in-situ large-scale underground blast test program was conducted to investigate stress wave characteristics inside the medium, at the soil-rock interface and on the soil ground surface. The stress wave measurements were made through a vertical borehole and a horizontal borehole inside the rock mass, and along several horizontal lines arranged at the rock-soil interface and on the soil surface. Three different charge weights of 0.5, 2.5 and 10 t with loading densities of 0.5, 2.5 and 10 kg/m³, respectively, were used in the detonation. The measured stress wave time histories and their characteristic parameters, such as peak particle velocity (PPV) and peak particle acceleration (PPA), as well as the principal frequency (PF) at different locations are presented and analyzed in this paper. The results are also compared with those recorded from small-scale tests in a previous study and those from some other researchers, and the pertinent scale effects are discussed by observing differences of the stress wave intensities between the small-scale and the large-scale tests.Received: 18 November 2002, Accepted: 8 July 2003, Published online: 8 October 2003     

荷载作用下多孔饱和地基的热-水-力耦合动力响应分析

基于广义热弹性理论,结合达西定律,对Biot波动方程进行修正,研究了一个受到荷载作用的多孔饱和地基的热-水-力多场耦合动态响应问题。建立了多孔饱和地基在荷载作用下的热-水-力耦合模型及控制方程,该模型可退化为热弹性耦合模型。采用正则模态法求解,得到了问题的解析解,讨论了热-水-力耦合模型和热弹性耦合模型的区别,分析了荷载频率变化对地基中各物理量的影响。最终给出了无量纲的竖向位移、超孔隙水压力、竖向应力和温度等物理量的分布规律。     

Waves in Nonlocal Elastic Solid with Voids

In this paper, the governing relations and equations are derived for nonlocal elastic solid with voids. The propagation of time harmonic plane waves is investigated in an infinite nonlocal elastic solid material with voids. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent transverse wave may travel with distinct speeds. The sets of coupled waves are found to be dispersive, attenuating and influenced by the presence of voids and nonlocality parameters in the medium. The transverse wave is dispersive but non-attenuating, influenced by the nonlocality and independent of void parameters. Furthermore, the transverse wave is found to face critical frequency, while the coupled waves may face critical frequencies conditionally. Beyond each critical frequency, the respective wave is no more a propagating wave. Reflection phenomenon of an incident coupled longitudinal waves from stress-free boundary surface of a nonlocal elastic solid half-space with voids has also been studied. Using appropriate boundary conditions, the formulae for various reflection coefficients and their respective energy ratios are presented. For a particular model, the effects of non-locality and dissipation parameter (\(\tau \)) have been depicted on phase speeds and attenuation coefficients of propagating waves. The effect of nonlocality on reflection coefficients has also been observed and shown graphically.