Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.

Petrologic composition model of the upper crust in Bohai Bay basin,China,based on Lamé impedances

Seismic attributes, such as P- and S-wave velocity, Poisson＇s ratio, and acoustic impedances, all generally can be used for distinguishing different rock types. The nonuniqueness can be largely reduced using Lame impedances instead of acoustic impedances as additional constraints. We have followed this method to constitute a petrologic composition model of the upper crust in the Bohai Bay basin, China. We briefly review the seismic parameters used for discrimination of rock types and focus our attention on the sensitivity of different combinations of parameters to determine the composition of materials. Corrections for pressure and temperature are performed in order to compare elastic wave velocities and densities measured at room temperature and surface pressure in laboratory with those for representative rock parameters. In a second step, we find the rock classes in the tested area by contrasting known data to laboratory measurements on a variety of rock samples extracted in the area. The basic field data are P-wave velocity values collected along a seismic profile conducted in the Bozhong Depression. The different rock types belonging to a particular rock class are finally constrained by the seismic velocities, Poisson＇s ratio, density, acoustic impedance, and Lame imoedance related to the topmost 10 km of the Bohai Bav crust.

A methodology to determine the elastic properties of anisotropic rocks from a single uniaxial compression test

This paper introduces a new methodology to measure the elastic constants of transversely isotropic rocks from a single uniaxial compression test.We first give the mathematical proof that a uniaxial compression test provides only four independent strain equations.As a result,the exact determination of all five independent elastic constants from only one test is not possible.An approximate determination of the Young’s moduli and the Poisson’s ratios is however practical and efficient when adding the Saint-Venant relation as the fifth equation.Explicit formulae are then developed to calculate both secant and tangent definitions of the five elastic constants from a minimum of four strain measurements.The results of this new methodology applied on three granitic samples demonstrate a significant stress-induced nonlinear behavior,where the tangent moduli increase by a factor of three to four when the rock is loaded up to 20 MPa.The static elastic constants obtained from the uniaxial compression test are also found to be significantly smaller than the dynamic ones obtained from the ultrasonic measurements.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

硅和镁质量分数对Al-Si-Mg合金机械力学性能参数影响的计算分析

基于第一性原理,利用CASTEP模块,通过虚拟晶体近似的方法建模,采用GGA+PBE泛函关联函数,研究了Al-Si7-Mg X(X=0.1~0.5)、Al-Si X-Mg0.3(X=6~9)合金中的Si、Mg质量分数的变化对机械力学性能参数的影响。研究表明,随着研究组元质量分数的增加,晶格常数有所减小,最大值与最小值相差约0.265%;弹性常数C_(11)、C_(12)、C_(44)满足结构稳定性条件;体积模量B、剪切模量G、杨氏模量E、泊松比u随着A356中Si、Mg质量分数变化而变化;Mg质量分数的变化对剪切模量G、杨氏模量E的影响比Si质量分数的变化更敏感。计算结果与现有实验数据对比表明,计算结果接近实验数据,第一性原理计算Al-Si-Mg合金材料参数可行。

Petrophysical properties and their influencing factors of carbonates in the fourth member of Sinian Dengying Formation, Sichuan Basin, SW China

Based on the measurements of petrological, petrophysical and elastic properties of the samples of different sedimentary facies in the fourth member of Sinian Dengying Formation (Deng 4 Member) in the Sichuan Basin, the diagenetic processes of reservoirs of different sedimentary facies and their controls on the petrophysical properties were discussed. The results show that cracks and mineral composition jointly control the petrophysical properties, and both are significantly influenced by sedimentary environment and diagenesis. The microbial dolomite of mound-shoal facies mainly experienced multi-stage dolomitization, penecontemporaneous dissolution, tectonic rupture and hydrothermal/organic acid dissolution processes, giving rise to cracks and dissolved pores. The grannular dolomite of inter-mound-shoal bottomland or dolomitic lagoon facies mainly underwent mechanical compaction, burial dolomitization and tectonic-hydrothermal action, creating cracks and intercrystalline pores. The diagenesis related to crack development increases the pressure- and saturation-dependent effects of samples, leading to significant decrease in the compressional wave impedance and Poisson's ratio. Dolomitization changes the properties of mineral particles, resulting in a Poisson's ratio close to dolomite. The muddy, siliceous and calcareous sediments in the low-energy environment lead to the decrease of impedance and the differential change of Poisson's ratio (significantly increased or decreased). The samples with both cracks and dissolved pores show high P-wave velocity dispersion characteristics, and the P-wave velocity dispersion of samples with only fractures or pores is the lowest.

应用L_(p)拟范数稀疏约束的纵横波速比直接反演

纵横波速比(vP/vS)是识别气藏、描述储层特征和判别岩性的重要解释工具。目前主要是通过反射系数近似方程反演得到纵、横波速度,再进一步计算纵横波速比,但是这种间接计算方法会产生累积误差。为了直接从叠前地震数据反演纵横波速比,文中提出了一种新的广义弹性阻抗方程,再进一步推导出一个与纵横波速比、纵波速度、密度相关的纵波反射系数近似方程。为了得到精度较高的反演结果,基于推导出的反射系数近似方程,提出一种基于Lp拟范数稀疏约束的叠前地震反演方法,并通过交替方向乘子算法求解。将提出的直接反演方法应用于理论模型和实际数据,并与间接反演方法相对比,结果表明该直接反演方法的反演结果精度较高,对含气储层的边界刻画更清晰。

地震横波建模技术及其在深水天然气田储层预测中的应用

深水区缺少横波资料,在叠前反演的建模环节中,一般通过线性关系或者相控将纵波模型转换为横波模型,但实现过程受人为因素影响较大,反演结果无法完整、可靠地表征地层特点和储层分布。为此,结合生产需求,提出基于远道地震数据提取三维空间的泊松比信息,作为纵、横波数据之间的转换关系,进而获得泊松比约束的横波低频模型。具体步骤为:(1)优选对岩性敏感的地震波入射角;(2)反演泊松比弹性阻抗PEI;(3)建立横波低频模型。在白云深水区的勘探实践表明,由于初始模型更好地反映了地层岩性背景,减少了反演结果的异常值,2号砂体的平面分布与气/水边界吻合,与实钻结果一致,落实了储层分布,扩大了天然气探明储量,取得了较好的经济效益。

循环加卸载下不同冲击损伤砂岩的力学特性研究

针对地下岩体工程在开挖掘进后因循环扰动导致围岩劣化和失稳问题,以冲击损伤砂岩为研究对象,开展三轴循环加卸载试验,研究循环加卸载条件下冲击损伤岩石的性能劣化和破坏规律。研究结果表明,冲击损伤越大的砂岩试样,在临近峰值强度时,其轴向应变会出现急速增长的现象;砂岩的塑性应变随循环次数的增加不断累积,在裂纹不稳定发展阶段,塑性应变大幅度增长;在弹性模量方面,研究发现同一循环等级下,砂岩试样的冲击损伤越大,其对应的割线弹性模量越小,抵抗变形的能力越弱;关于泊松比的研究发现,三种不同冲击损伤砂岩试样在试验过程中都表现出相似的变化趋势,先加速上升,然后缓慢增加,最后急剧增长。但损伤度越大的砂岩试样在试验后期表现出更明显的扩容现象,泊松比增加也更为显著。

Analysis of the geometrical dependence of auxetic behavior in reentrant structures by finite elements

Materials with a negative Poisson＇s ratio（PR）are called auxetics;they are characterized by expansion/contraction when tensioned/compressed.Given this counterintuitive behavior,they present very particular characteristics and mechanical behavior.Geometrical models have been developed to justify and artificiall reproduce such materials＇ auxetic behavior.The focus of this study is the exploration of a reentrant model by analyzing the variation in the PR of reentrant structures as a function of geometrical and base material parameters.It is shown that,even in the presence of protruding ribs,there may not be auxetic behavior,and this depends on the geometry of each reentrant structure.Values determined for these parameters can be helpful as approximate reference data in the design and fabrication of auxetic lattices using reentrant geometries.

Experimental Study for Improving the Toughness of Harden Cement Using Carbon Fiber

Many measures, such as water injection, acid fracturing, thermal recovery, have been taken in the oilfield development. These can easily induce brittle fracture of set cement. Most of all, there are greater potential for fractures in set cement in slim holes. Therefore, it is necessary to improve the toughness of the cement mantle. Results obtained from experiments show that carbon fiber, with a concentration of 0.12%-0.19% in cement and a length of 700 to 1,400μm, plays an important role in improving cement quality. Addition of carbon fiber can improve the bending strength of set cement by up to 30%. At the same time, the increase in fiber concentration can lower the elastic modulus and increase the Poisson＇s ratio of set cement. Thin-section analysis shows that fiber can effectively prevent the propagation of fractures and enhance the plasticity of the matrix and the ability to prevent fracture.

Anisotropic Constitutive Modeling of Compressible Biological Tissue

The anisotropic continuum stored energy density (ACSED) functional is applied for accurate constitutive modeling of biological tissues and finite element implementation without the isochoric—volumetric split, the anisotropic—isotropic split, or the anisotropic invariant split. Related stress and elasticity tensors in the reference and current configurations are worked out. A new kinematic model is derived based on the tangent Poisson’s ratio as a cubic polynomial function of stretch. The ACSED model, along with the kinematic model, accurately fits uniaxial extension test data for compressible human skin, bovine articular cartilage, and human aorta samples.

材料力学性能参数的动态视觉测量研究

为了对材料在拉伸变形状态下弹性模量、泊松比等力学性能参数进行动态的视觉测量,基于数字图像相关技术和随机采样一致性原理,提出了一种针对材料在拉伸变形状态下的应变、弹性模量和泊松比等多种力学性能参数的动态测量和计算方法。首先,利用数字图像相关技术,测量出了材料变形试件点对间的位移、应力及线应变值;其次,基于随机采样一致性原理,自动确定了材料的弹性区间;在变形试件的弹性区间内,运用最小二乘拟合法准确获取了材料的弹性模量和泊松比;最后,常温环境下,对两种金属材料进行拉伸实验,实时计算和显示了试件的变形情况以及试验机拉伸过程中的参数变化量。实验结果表明:采用该方法可以准确地对材料弹性模量和泊松比进行动态视觉测量,且弹性模量测量精度平均可达0.86%,泊松比测量精度平均可达0.97%。研究结果表明:该力学性能参数的动态测量和计算方法基本可以满足工业检测行业材料性能参数的测量精度标准。

岩石动静力学参数的试验研究

在三轴应力下对砂、泥岩等岩芯（干岩样）进行了岩石力学参数的动、静态同步测试，并对动静态弹性参数进行了线性回归。结果表明：岩石的动静态杨氏模量之间存在较好的相关性，而动静态泊松比之间的关系不明显，该项研究为岩石的声学性质在石油工程中的应用提供了实验依据。

砂岩高温后的力学特性

对焦作砂岩在常温及经历100℃～1 200℃温度作用后的力学特性进行试验研究,详细分析加温后砂岩的表观形态、峰值应力、峰值应变、弹性模量、泊松比以及应力–应变全过程曲线等的变化情况,并对砂岩的高温劣化机制作初步探讨。研究表明,高温使砂岩的表观形态发生改变;在400℃以内,温度对砂岩的力学性能影响不大,加温对砂岩的某些力学指标有一定的增强作用;但经历的温度超过400℃后,随受热温度升高砂岩的力学性能发生劣化,砂岩的峰值应力和弹性模量均有不同幅度的降低,而800℃前砂岩的峰值应变随温度的升高而大幅增加;砂岩的变形大体随经历温度的升高而增大;600℃前砂岩的泊松比随经历温度的升高而减少,而后呈上升趋势。温度引起的热应力作用、矿物组分和微结构变化导致砂岩力学性质发生改变与高温劣化。

自密实堆石混凝土力学性能的试验研究

以试验为基础讨论堆石混凝土的力学性能,试验试样直接从自密实堆石混凝土大型试块中切割取样,其尺寸为1 500 mm×500 mm×500 mm。强度试验确定堆石混凝土的立方体抗压强度、棱柱体抗弯强度、棱柱体轴心抗压强度及其力学特征;控制自密实混凝土的自流动距离在1 500 mm范围内,可形成不低于自密实混凝土配制强度的堆石混凝土;堆石混凝土棱柱体轴心受压应力–应变关系曲线基本接近直线,其比例极限和强度极限接近,只有微小的塑性变形,破坏呈突发式纵向劈裂;试样断口形态表明:堆石混凝土中的块石与自密实混凝土界面具有较好的黏结性。

基于弹性阻抗反演理论的泊松比反演方法研究

实际应用中泊松比主要通过间接反演的方式获取,其累积误差明显,针对这一不足,基于弹性阻抗反演理论,在总结出常用弹性阻抗方程的通用表达式和岩性参数通用提取方法的基础上,推导出了一种新的AVO近似式,进而提出一种包含有泊松比参数项的新的弹性阻抗方程。模型试验与实际应用结果表明,利用新的弹性阻抗方程进行弹性阻抗反演直接得到泊松比的方法与传统利用纵、横波速度转化计算间接得到泊松比的方法相比,减少了误差的累积并且稳定性和抗噪性均得到了提高,泊松比精度更高。

矸石膏体充填体控制地表沉陷力学性能试验研究

针对膏体充填体在煤矿采空区特殊环境下(高温、高湿、高应力、高密闭)所表现出的力学特性,运用现场取芯、室内试验等方法开展了矸石膏体充填体力学性能研究,揭示了充填膏体力学特性(抗拉强度、单轴压缩强度、弹性模量、泊松比)随时间的变化规律,并运用最小二乘法建立了各力学参数与时间的回归方程。结果表明,采空区特定的环境条件有助于充填体内部各化学物质的充分反应,使充填体胶凝性增强,且充填膏体在承载时抗变形能力强,能够很好控制地表沉陷。