Time-Dependent Poromechanical Responses of Saturated Cylinders

The uniaxial, hydrostatic, and triaxial tests of saturated cylindrical rock samples are very common in a rock mechanics laboratory. The conventional solution for the mechanical responses of the sample under such testing conditions (an axial load and a confining pressure) is trivial within the elastic range. For saturated samples, however, these elastic solutions can only be applied to the drained or undrained cases, and there has been a lack of transient analyses of cylindrical samples under such tests, taking into account the pore fluid pressure buildup and the coupling effects, especially for samples with low permeability. In this paper, poroelasticity is employed to develop the solution for saturated cylindrical samples subjected to an axial load and a confining pressure. Significant poroelastic effects on the tests were observed through the analyses of a uniaxial test and a triaxial test based on the proposed poroelastic solution. Without consideration of the poroelastic effects, erroneous interpretations of the testing results can be expected.     

Microporodynamics of Bones: Prediction of the “Frenkel–Biot” Slow Compressional Wave

Understanding of ultrasonic wave propagation in bones is essential for further development of related techniques in clinical practice. As any other saturated porous medium, bone is characterized by different forms of longitudinal wave propagation, either undrained waves or fast and (Frenkel–Biot) slow compressional waves. We here study the wave propagation in the framework of poromicromechanics. A continuum micromechanics model allows for the prediction of the anisotropic poroelastic properties, Biot’s coefficients, and moduli, from tissue-specific composition data, on the basis of tissue-independent (“universal”) elastic properties of the elementary components of all bones. These poroelastic properties enter the governing equations for wave propagation in anisotropic porous media. They allow for the prediction of undrained, fast and slow waves, as is verified by comparison of model results with experimental findings.     

Forced Vertical Vibration of Circular Plate in Multilayered Poroelastic Medium

This paper considers the vertical vibrations of an elastic circular plate in a multilayered poroelastic half space. The plate is subjected to axisymmetric time–harmonic vertical loading and its response is governed by the classical thin-plate theory. The contact surface between the plate and the multilayered half space is assumed to be smooth and either fully permeable or impermeable. The half space under consideration consists of a number of layers with different thicknesses and material properties and is governed by Biot’s poroelastodynamic theory. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Contact stress and pore pressure jump are established in terms of generalized coordinates through the solution of flexibility equations based on the influence functions corresponding to vertical and pore pressure loading. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results are presented to portray the influence of various parameters on dynamic interaction between an elastic plate and a multilayered poroelastic half space.     

Analytical Model for Concrete Confined with Fiber Reinforced Polymer Composite

An analytical model to predict the behavior of concrete confined with fiber reinforced plastic (FRP) composites subjected to axial compressive loads was developed. First, a constitutive model for plain concrete was formulated from past experimental results obtained from triaxial compression tests of concrete, in which concrete specimens were maintained under constant confining stresses. This was an orthotropic constitutive model based on the concept of equivalent uniaxial strain. Subsequently, in the analytical model for FRP confined concrete, the proposed constitutive model for concrete materials was incorporated. The FRP was assumed to be a linear elastic material. Force equilibrium and strain compatibility between the concrete and the FRP as well were satisfied. When the proposed model was applied to FRP confined concrete, the model overestimated the axial stress. To rectify this, a subsequent maximum strength criterion was introduced to control the maximum strength in the postpeak region when confining stress was continuously increased. The proposed analytical model with the addition of the subsequent maximum strength criterion is in good agreement with the experimental results.     

Mixture Theory for a Fluid-Saturated Isotropic Elastic Matrix

The theory for a fluid saturated linearly isotropic elastic matrix is still the basis for many geophysical applications, and commonly adopts Biot’s symmetric stress–strain laws for the matrix stress and fluid pressure. These involve a shear modulus and three elastic moduli governing the mixture and constituent compressions, in contrast to four compression moduli if Biot’s invalid potential energy argument is not applied. We now show that an energy argument applied to undrained loading also leads to three compression moduli, but distinct from those derived by Biot (Biot symmetry). However, there are two distinct solutions of this energy balance, corresponding to the Voigt and Reuss limits of the analogous theory of a linear two-phase elastic composite, whereas a unique undrained modulus not at either limit would be expected. It is proposed that an energy contribution is lost due to the idealised assumptions made for undrained loading, which therefore does not determine a further restriction, so that there are four independent compression moduli. The general and restricted combinations of the total pressure and fluid pressure (effective stress) governing the matrix compression are then presented, together with the alternative forms of the partial differential equations governing the deformation and flow.     

Dynamic Axial Load Transfer from Elastic Bar to Poroelastic Medium

The time-harmonic response of a cylindrical elastic bar (pile) partially embedded in a homogeneous poroelastic medium and subjected to a vertical load is considered. The bar is modeled using 1D elastic theory valid for long bars in the low-frequency range, and the porous medium using Biot's 3D elastodynamic theory. The bar is bonded to the surrounding medium along the contact surface. The problem is formulated by decomposing the bar∕porous medium system into a fictitious bar and an extended porous medium. A Fredholm's integral equation of the second kind governs the distribution of axial force in the fictitious bar. The integral equation involves kernels that are displacement and strain influence functions of a poroelastic half-space subjected to a buried, uniform vertical patch load. The governing integral equation is solved by applying numerical quadrature. The solutions for axial displacement and axial force of the bar, and the pore pressure are also derived. Selected numerical results for vertical impedance, axial force, and pore pressure profiles are presented to portray the influence of bar stiffness and length∕radius ratio, frequency of excitation, and poroelastic properties.     

Effective elastic response of two-phase composites

We present finite element analyses of the overall elastic properties of two-phase composites as a function of the shape, concentration and spatial distribution of the reinforcement. The analyses of the geometrical effects of constituent phases on the overall elastic moduli have been carried out within the context of axisymmetric and plane strain unit cell formulations. In most calculations, the phases are taken to be isotropic and linear elastic, and the interface perfectly bonded. These finite element results are compared with available analytical results for a variety of geometrical arrangements of the constituent phases of the composites. Computations which predict the effective elastic properties for the limiting case where all the reinforcing particles fracture are carried out. The competition between stiffening due to reinforcement and increased compliance due to cracking of the reinforcement is evaluated for metallic, ceramic and intermetallic matrices with brittle reinforcements, and the numerical results are compared with analytical solutions. The paper also includes discussions of the role of thermal residual stresses in influencing apparent initial moduli and the effects of interfacial compliance on the stress distribution within the reinforcement.     

Effects of Weakly Nonlinear Water Waves on Soft Poroelastic Bed with Finite Thickness

Since porous material is usually of a finite thickness in nature, the effects of periodically nonlinear water waves propagating over a soft poroelastic bed with finite thickness are hence noticed and studied in this work. The water waves are simulated by potential theory while the porous bed is governed by Biot’s theory of poroelasticity herein. The conventional Stokes expansion of water waves based on a one-parameter perturbation expansion fails to solve the soft poroelastic bed problem; therefore, the boundary layer correction approach combined with a two-parameter perturbation expansion is proposed, which enables us to solve the problem of soft poroelastic bed with finite thickness. The results are compared to the similar problem with an infinite-thickness porous bed. The boundary effects of the impervious rock are significant on wave-induced pore water pressure and effective stresses, but are of very little significance on wave profiles at the free surface and the porous bed surface. However, the rigid boundary is insignificant to the pore water pressure and effective stresses when the thickness of porous bed is larger than about one wavelength.     

Characterization of Cemented Sand in Triaxial Compression

This work aims at studying the stress-strain-strength behavior of an artificially cemented sandy soil produced through the addition of portland cement. An analysis of the mechanical behavior of the soil is performed from the interpretation of results from unconfined compression tests, drained triaxial compression tests with local strain measurements, and scanning electron microscopy, in which the influence of both the degree of cementation and the initial mean effective stress was investigated. For cemented sandy soils, it was concluded that the unconfined compression resistance is a direct measurement of the degree of cementation. Consequently, the triaxial shear strength can be expressed as a function of only two variables: (1) the internal shear angle of the nonstructured material; and (2) the unconfined compression resistance. In addition, a logarithmic formulation is adopted to express the relationship between static deformation moduli and axial strain amplitude in axisymmetric conditions. Data from other reported investigation programs give to the proposed correlations a broader acceptance to general geotechnical applications.     

On mechanics of crack growth and its effects on the overall response of brittle porous solids

This paper is concerned with crack growth in brittle porous solids under compression and its effects on the overall response of the material. As a mathematical model, we consider an elastic solid containing a zig-zag array of circular holes with a pair of edge cracks (two-dimensional problem), and solve this problem by using a theory which gives numerical results as accurate as desired. Based on the analytical results, we discuss the crack growth process and estimate the effective Young's moduli as well as the stress-strain relation for porous solids. Our computations show that the cracks emanating from the poles of the circular holes extend in the axial direction and grow—in most cases in a stable manner, but for certain cases in an unstable manner during an intermediate loading state—as the overall applied uniaxial compression increases, reaching a certain limiting maximum length. This maximum crack length strongly depends on the ratio of the hole radius to the hole spacing in the loading direction. The effective Young's modulus in the direction of the crack growth is basically determined by the initial porosity, and is little affected by the crack length or its growth regime, i.e. whether stable or unstable. We find that the overall axial stress-strain curve remains monotonie, exhibiting no peak stress or strain softening, as cracks extend in the axial direction and reach their limiting length with increasing axial stress.     

Dynamic Stress Concentrations in Lined Twin Tunnels within Fluid-Saturated Soil

An exact analysis for three-dimensional dynamic interaction of monochromatic seismic plane waves with two lined circular parallel tunnels within a boundless fluid-saturated porous elastic medium is presented. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to obtain a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two identical tunnels, lined with concrete and embedded within water-saturated soils of distinct frame properties (i.e., soft or stiff soils), are insonified by plane fast compressional or shear waves at end-on incidence. The basic dynamic field quantities such as the hoop and axial stress amplitudes are evaluated and discussed for representative values of the parameters characterizing the system. The effects of formation material type, angle of incidence, incident wave frequency, and the proximity of the two tunnels on the liner stresses are examined. Particular attention is paid to the influence of bonding and drainage conditions at the liner/soil interface on the dynamic stress concentrations. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.     

砂岩单轴循环加卸载试验及声发射特征研究

通过对砂岩进行循环加载试验,揭示了砂岩在循环加卸载过程中的强度变化及声发射特性。试验利用电液伺服岩石三轴试验机和SDAES数字声发射检测仪采集系统,对两组砂岩试样分别进行单轴抗压、单轴循环加卸载试验。试验结果表明岩样在经过循环加卸载后试样的单轴抗压强度略有增大,循环加卸载过程中在伴随着岩样内部原始天然裂隙的压密、新生裂纹的产生、扩展和贯通的同时,也伴随着声发射不断产生。声发射事件在砂岩再次加载应力到达上次加载最大应力前极少发生,达到上次加载最大应力以后则大量发生,说明砂岩岩样在循环加卸在作用下存在声发射的Kaiser效应,而无Felicity效应产生。     

A general approach for predicting the drawing fracture load and limit drawing ratio of an axisymmetric drawing process

Based on Hill’s theory of plasticity and the Swift diffuse instability criterion, new theoretical models are proposed for predicting the drawing fracture load and limit drawing ratio (LDR) of an axisymmetric cup drawing. These models take into account the influence of triaxial stress state, anisotropy, strain hardening, bending, and tool geometry. By introducing both conventional and modified Hollomon’s equations, the influences of these variables on the constitutive relation of sheet steels are also analyzed. It is shown that the theoretical predictions of the drawing fracture load are in good agreement with experimental results for a wide range of sheet steels currently used in the automotive industry. Specific tool geometries are found to decrease the drawing fracture load and the LDR, because of increased triaxial stress states and bending effects at the critical section of the workpiece. The optimum punch-profile radius is found to be between 5.0 and 7.0 times the thickness of the sheet. Additionally, the role of both the anisotropy and strain-hardening properties of the sheet steels in determining the drawing fracture load and the LDR are, subsequently, discussed.     

A Self-Consistent Approach for Necking Correction in Tensile Specimens With Rectangular Cross-Section Using a Novel Mirror Fixture

True stress?Ctrue strain cannot be computed beyond necking, unless the effects of necking on the geometry of the tensile specimen and the stress state are accurately quantified. Necking produces a triaxial stress state that does not reflect the true uniaxial flow stress of the material. Therefore, the true stress must be multiplied by a correction factor to correct for the effect of the triaxial stresses and obtain the true uniaxial flow stress. While necking effects are easily quantified for specimens with circular cross-sections, specimens with rectangular cross-sections can exhibit complex necking geometry. In this paper, the necking behavior of pure Sn and Sn-3.5Ag-0.7Cu solders was studied to: (1) quantify necking geometry in rectangular specimens using a novel mirror fixture and a high speed camera during tests conducted at 10^?3 to 30?s^?1, and (2) develop a self-consistent method of necking correction that incorporates strain rate effects and can be applied to many materials.     

Effects of misalignment on the pre-macroyield region of the uniaxial stress-strain curve

Some bending usually occurs in uniaxial testing systems due to small unavoidable misalignment. The resulting elastic strain gradient can lead to significant differences between axial strain and extreme surface bending strains, especially at small strains. A three-point microstrain measurement around a cylindrical sample permits evaluation of the extreme strains and of the precision of alignment. A three-point, parallel-plate capacitance strain gage having a linear output with displacement was designed to evaluate bending of tensile samples in the microstrain range. The resolution of the gage was 3 parts in 10,000 at plate separations of 0.010 in. Varying misalignment resulted in extreme elastic bending strains at the sample surface of the order of tens to hundreds of micro-in. per in. larger than the axial strain. Analysis of the mechanics of bending in uniaxial loading demonstrated that: 1) the average applied stress divided by the average elastic strain always gives a unique number, Young's modulus, and 2) the average microplastic strain is not uniquely related to the average applied stress, but rather depends upon precision of alignment. The influence of bending on the determination of the average stress at which microplastic flow initiates is discussed, and a method for making meaningful comparisons of plastic microstrain data generated with significant misalignment is suggested.     

Defining Yield from Bender Element Measurements in Triaxial Stress Probe Experiments

This paper describes the elastic response of a block sample of compressible Chicago glacial clay under a variety of stresses and its relationship with the deformation characteristics at relatively large strains. The elastic shear stiffness was obtained from bender element tests during consolidation and shearing in drained triaxial stress probe tests. An empirical correlation was established based on the elastic shear stiffness in a preyield condition. By comparing the empirical correlation with the measured elastic shear stiffness in the stress region during probing, the changes of elastic shear stiffness were investigated. The departure of elastic shear stiffness from values computed by the empirical relation based on K0 loading directly relates to the yielding characteristics of the clay. The large-scale change of soil structure at yielding alters the well-established relationship between the elastic shear stiffness and stresses in the preyield condition. The mechanical yielding response of clays can be detected based on the systematic analysis of the elastic shear wave velocities.     

加卸载下原煤力学特性及渗透演化规律

基于自主研发的煤岩热流固耦合试验系统,在考虑实际开采方式的条件下,进行轴压升高和围压降低的加卸载试验,分析研究不同加卸载速率下原煤的力学特性和渗透演化规律.结果表明:加卸载过程中,轴向应力的加载速率越大,峰值应力附近的曲线平台越长,峰值应力、轴向应变和环向应变也越大,体应变则越小.不同加卸载速率比下含瓦斯煤变形模量均先迅速减小后缓慢减小,到破坏时再迅速降低,而后逐渐保持稳定趋势;在相同轴向应变时,加卸载速率比越小,煤样的变形模量越大.加卸载过程中,煤样的偏应力、渗透率与应变的关系可分为三个阶段:初始压密与弹性阶段、屈服破坏阶段和破坏后阶段.加卸载速率比越小,煤样达到峰值应力时,含瓦斯煤的渗透率和体积变形越大.