First-order perturbation approximation for rock elastic moduli in transversely isotropic media

Seismic anisotropy is a relatively common seismic wave phenomenon in laminated sedimentary rocks such as shale and it can be used to investigate mechanical properties of such rocks and other geological materials. Young’s modulus and Poisson’s ratio are the most common mechanical properties determined in various rock engineering practices. Approximate and explicit equations are proposed for determining Young’s modulus and Poisson’s ratio in anisotropic rocks, in which the symmetry plane and symmetry axis of the anisotropy are derived from the constitutive equation of transversely isotropic rock. These equations are based on the media decomposition principle and seismic wave perturbation theory and their accuracy is tested on two sets of laboratory data. A strong correlation is found for Young’s modulus in two principal directions and for Poisson’s ratio along the symmetry plane. Further, there is an underprediction of Poisson’s ratio along the symmetry axis, although the overall behavior follows the trend of the measured data. Tests on a real dataset show that it is necessary to account for anisotropy when characterizing rock mechanical properties of shale. The approximate equations can effectively estimate anisotropic Young’s modulus and Poisson’s ratio, both of which are critical rock mechanical data input for hydraulic fracturing engineering.     

Brittleness characteristics of tight oil siltstones

Rock brittleness directly affects reservoir fracturing and its evaluation is essential for establishing fracturing conditions prior to reservoir reforming. Dynamic and static brittleness data were collected from siltstones of the Qingshankou Formation in Songliao Basin. The brittle–plastic transition was investigated based on the stress–strain relation. The results suggest that the brittleness indices calculated by static elastic parameters are negatively correlated with the stress drop coefficient and the brittleness index B₂, defined as the average of the normalized Young’s modulus and Poisson’s ratio, is strongly correlated with the stress drop. The brittleness index B₂, Young’s modulus, and Poisson’s ratio correlate with the brittle minerals content; that is, quartz, carbonates, and pyrite. We also investigated the correlation between pore fluid and porosity and dynamic brittle characteristic based on index B₂. Pore fluid increases the plasticity of rock and reduces brittleness; moreover, with increasing porosity, rock brittleness decreases. The gas-saturated siltstone brittleness index is higher than that in oil- or water-saturated siltstone; the difference in the brittleness indices of oil- and water-saturated siltstone is very small. By comparing the rock mechanics and ultrasonic experiments, we find that the brittleness index obtained from the rock mechanics experiments is smaller than that obtained from the ultrasonic experiments; nevertheless, both decrease with increasing porosity as well as their differences. Ultrasonic waves propagate through the rock specimens without affecting them, whereas rock mechanics experiments are destructive and induce microcracking and porosity increases; consequently, the brittleness of low-porosity rocks is affected by the formation of internal microcrack systems.     

State of in-situ stress in different rocks

According to the regression analysis of measured stress data in magmatite, sedimentary and metamorphic rock all over the world, it is found that the stress state in the three rocks is different and closely related to its formation. The relationships among the stress and depth and the Young’s modulus of rock are also discussed and the results show that stress can increase with the Young’s modulus.     

Mechanical behavior of magma reservoir envelopes: Elasticity of the olivine tholeiite solidus

A study of the elasticity of the solidus of igneous rocks provides a means of evaluating several high temperature mechanical characteristics of the zone that forms the transition region between solid rock and rock with a small fraction of partial melt — that is, the magma reservoirenvelope. This type of study has been performed for Hawaiian olivine tholeiite, by employing the theoretical treatment ofWalsh (1969). The effective aggregate bulk modulus (K*), aggregate rigidity (μ*), aggregate Young’s modulus (E*) and the aggregate Poisson’s ratio (n*) have been used to characterize the range in elastic behavior expected for this partially molten envelope. The details of mineralogy, mineral crystal chemistry and microstructure for a tholeiitic basalt from a deep-ponded flow unit (the Boiling Pots), as well as the geometry of melt pocket aspect ratios have been used to provide a basis for computing the elasticity for a shallow reservoir solidus. For a broad range in modal mineralogy, the internal 0–1% melt represents a transition region from an aggregate elasticity controlled by mineral composition, to an elastic behavior dominated by the melt phase (evaluated at a melt pocket aspect ratio ofε=0.001). For vesicular rocks in a low pressure environment, the internal 0–1% melt represents a transition from porosity-controlled elasticity to melt-controlled elasticity, evaluated at a prevalent aspect ratio ofε=0.001, and over the porosity range Φ=0.0?0.20 (20%). Thin melt films found to separate plagioclase microlites (0.0001=ε) are capable of effecting a 94.7% reduction in Young’s modulus, E*, over the 0–1% melt range, and suggest that the reservoir envelope may be critically weakened by rather small volume fractions of liquid, if dispersed in such narrow packets.     

The influence of thermal and cyclic stressing on the strength of rocks from Mount St. Helens, Washington

Stratovolcanoes and lava domes are particularly susceptible to sector collapse resulting from wholesale rock failure as a consequence of decreasing rock strength. Here, we provide insights into the influence of thermal and cyclic stressing on the strength and mechanical properties of volcanic rocks. Specifically, this laboratory study examines the properties of samples from Mount St. Helens; chosen because its strength and stability have played a key role in its history, influencing the character of the infamous 1980 eruption. We find that thermal stressing exerts different effects on the strengths of different volcanic units; increasing the heterogeneity of rocks in situ. Increasing the uniaxial compressive stress generates cracking, the timing and magnitude of which was monitored via acoustic emission (AE) output during our experiments. AEs accelerated in the approach to failure, sometimes following the pattern predicted by the failure forecast method (Kilburn 2003). Crack damage during the experiments was tracked using the evolving static Young’s modulus and Poisson’s ratio, which represent the quasi-static deformation in volcanic edifices more accurately than dynamic elastic moduli which are usually implemented in volcanic models. Cyclic loading of these rocks resulted in a lower failure strength, confirming that volcanic rocks may be weakened by repeated inflation and deflation of the volcanic edifice. Additionally, volcanic rocks in this study undergo significant elastic hysteresis; in some instances, a material may fail at a stress lower than the peak stress which has previously been endured. Thus, a volcanic dome repeatedly inflated and deflated may progressively weaken, possibly inducing failure without necessarily exceeding earlier conditions.     

Correlating P-wave Velocity with the Physico-Mechanical Properties of Different Rocks

In mining and civil engineering projects, physico-mechanical properties of the rock affect both the project design and the construction operation. Determination of various physico-mechanical properties of rocks is expensive and time consuming, and sometimes it is very difficult to get cores to perform direct tests to evaluate the rock mass. The purpose of this work is to investigate the relationships between the different physico-mechanical properties of the various rock types with the P-wave velocity. Measurement of P-wave velocity is relatively cheap, non-destructive and easy to carry out. In this study, representative rock mass samples of igneous, sedimentary, and metamorphic rocks were collected from the different locations of India to obtain an empirical relation between P-wave velocity and uniaxial compressive strength, tensile strength, punch shear, density, slake durability index, Young’s modulus, Poisson’s ratio, impact strength index and Schmidt hammer rebound number. A very strong correlation was found between the P-wave velocity and different physico-mechanical properties of various rock types with very high coefficients of determination. To check the sensitivity of the empirical equations, Students t test was also performed, which confirmed the validity of the proposed correlations.     

Velocity and Density Heterogeneities of the Tien-Shan Lithosphere

—The Tien-Shan orogene is a region in which the earth’s crust undergoes considerable thickening and tangential compression. Under these conditions the lithosphere heterogeneities (composi tion, rheological) create the prerequisites for the development of various phenomena of tectonic layering (lateral shearing, different deformation of layers). To study the distribution of velocity, density and other elastic parameters, the results from a seismic tomography study on P-wave as well as S-wave velocities were used. Using empirical as well as theoretical formulas on the relationship between velocity, density and silica content in rocks, their distribution in the Tien-Shan’s lithosphere has been calculated. In addition, other elastic parameters, such as Young’s modulus, shear modulus, Poisson’s ratio and coefficient of general compressions have been determined. Zoning of different types of crust was carried out for the region investigated. The characteristics of the "crust-mantle" transition have been investi gated. Large blocks with different types of the earth’s crust were distinguished. Layers with inverse values of velocity, density and shear and Young modulus are revealed in the Tien-Shan lithosphere. All of the above described features open new ways to solve geodynamics problems.     

Burial stress and elastic strain of carbonate rocks

Burial stress on a sediment or sedimentary rock is relevant for predicting compaction or failure caused by changes in, e.g., pore pressure in the subsurface. For this purpose, the stress is conventionally expressed in terms of its effect: “the effective stress” defined as the consequent elastic strain multiplied by the rock frame modulus. We cannot measure the strain directly in the subsurface, but from the data on bulk density and P‐wave velocity, we can estimate the rock frame modulus and Biot's coefficient and then calculate the “effective vertical stress” as the total vertical stress minus the product of pore pressure and Biot's coefficient. We can now calculate the elastic strain by dividing “effective stress” with the rock frame modulus. By this procedure, the degree of elastic deformation at a given time and depth can be directly expressed. This facilitates the discussion of the deformation mechanisms. The principle is illustrated by comparing carbonate sediments and sedimentary rocks from the North Sea Basin and three oceanic settings: a relatively shallow water setting dominated by coarse carbonate packstones and grainstones and two deep water settings dominated by fine‐grained carbonate mudstones and wackestones.     

钻孔体应变与面应变观测井孔耦合系数的计算

钻孔应变观测系统（岩石、 膨胀水泥和应变仪钢筒）存在显著的井孔耦合效应,只有确定这一耦合系数,才能得到地壳岩石的真实应变值,从而实现不同测点数据的可比性．本文根据双衬套理论及弹性力学理论,建立了三维空间应力作用下体应变与面应变观测力学模型,并进一步推导各自井孔耦合系数计算式,发现两组系数与井孔的受力状况密切相关,分别与不同力源引起的应变信号相对应．亦即应力比（钻孔轴向应力与平面应力之比）不同,耦合系数也不一样,体应变随应力比的增大而下降,面应变则上升. 本文结果还表明平面应力作用下的耦合系数与外加应力无关,只与观测系统本身有关,故数值保持恒定. 此外,文中对其影响因素也进行了分析,结果表明,体应变和面应变的井孔耦合系数均随岩石弹性模量和泊松系数的增大而增大,且前者的幅度较大,井孔耦合材料水泥对二者影响均很小．      

State of in-situ stress in different rocks

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Physical properties,vitrinite reflectance,and microstructure of coal,Taiyuan Formation,Qinshui Basin,China

In this study, we experimentally established the relationship between physical properties, vitrinite reflectance, and microstructure of coal, Taiyuan Formation, Qinshui Basin, China using representative coal samples collected from three different mines via the rock mechanics testing system (MTS). We analyzed the organic macerals, vitrinite reflectance, and microstructure of 11 coal samples using petrography and scanning electron microscopy (SEM). The experimental results suggest that (1) the elastic parameters can be described by linear equations, (2) both P-and S-wave velocities display anisotropy, (3) the anisotropy negatively correlates with vitrinite reflectance, and (4) the acoustic velocities and Young’s modulus are negatively correlated with the volume of micropores. The derived empirical equations can be used in the forward modeling and seismic inversion of physical properties of coal for improving the coal-bed methane (CBM) reservoir characterization.     

岩石模量与应变振幅关系的实验研究及理论解释

地球介质的非线性弹性造成了岩石动态和静态弹性模量在数值上的差异。本文用超声波速度测量得到岩石的动模量，用含有小循环的加卸载实验得到小循环模量，用大循环的应力、应变曲线斜率得到静模量，用测点的应力、应变之比得到杨氏模量。通过改变小循环的应变振幅来研究模量与应变振幅的关系，进而比较用不同测量方法得到的模量值的差异。结果表明，动模量值最大，小循环模量值次之，大循环静模量值再次之，而杨氏模量最小。岩石非线性模量既是所受应变水平的函数，也是应变振幅的函数，模量随应变振幅的增加以指数形式下降，随应变水平增加以指数形式上升。最后简要介绍了P-M模型的基本概念，用岩石中微裂缝具有不同的分布密度，不同的打开和关闭压力来解释模量与应变振幅的关系。     

Permeability Evolution and Rock Brittle Failure

This paper reports an experimental study of the evolution of permeability during rock brittle failure and a theoretical analysis of rock critical stress level. It is assumed that the rock is a strain-softening medium whose strength can be described by Weibull’s distribution. Based on the two-dimensional renormalization group theory, it is found that the stress level λ_c (the ratio of the stress at the critical point to the peak stress) depends mainly on the homogeneity index or shape parameter m in the Weibull’s distribution for the rock. Experimental results show that the evolution of permeability is closely related to rock deformation stages: the permeability has a rapid increase with the growth of cracks and their surface areas (i.e., onset of fracture coalescence point), and reaches the maximum at rock failure. Both the experimental and analytical results show that this point of rapid increase in permeability on the permeability-pressure curve corresponds to the critical point on the stress-strain curve; for rock compression, the stress at this point is approximately 80% of the peak strength. Thus, monitoring the evolution of permeability may provide a new means of identifying the critical point of rock brittle fracture.     

Effects of pore fluids on quasi-static shear modulus caused by pore-scale interfacial phenomena

It is evident from the laboratory experiments that shear moduli of different porous isotropic rocks may show softening behaviour upon saturation. The shear softening means that the shear modulus of dry samples is higher than of saturated samples. Shear softening was observed both at low (seismic) frequencies and high (ultrasonic) frequencies. Shear softening is stronger at seismic frequencies than at ultrasonic frequencies, where the softening is compensated by hardening due to unrelaxed squirt flow. It contradicts to Gassmann's theory suggesting that the relaxed shear modulus of isotropic rock should not depend upon fluid saturation, provided that no chemical reaction between the solid frame and the pore fluid. Several researchers demonstrated that the shear softening effect is reversible during re-saturation of rock samples, suggesting no permanent chemical reaction between the solid frame and the pore fluid. Therefore, it is extremely difficult to explain this fluid–rock interaction mechanism theoretically, because it does not contradict to the assumptions of Gassmann's theory, but contradicts to its conclusions. We argue that the observed shear softening of partially saturated rocks by different pore fluids is related to pore-scale interfacial phenomena effects, typically neglected by the rock physics models. These interface phenomena effects are dependent on surface tension between immiscible fluids, rock wettability, aperture distribution of microcracks, compressibility of microcracks, porosity of microcracks, elastic properties of rock mineral, fluid saturation, effective stress and wave amplitude. Derived equations allow to estimate effects of pore fluids and saturation on the shear modulus and mechanical strength of rocks.     

Experiment Study and Interpretation on Relation between Modulus of Rock and Strain Amplitude

INTRODUCTIONThe modulus of rock is one of the basic elastic parameters of the earth’s medium. Under theassumption of linear elastic theory and Poisson medium,other parameters can be calculated fromit .But the real earth mediumis nonlinear elastic and has not a simple linear relationship between stressand strain.This causes relatively big differences betweenthe dynamic andthe static modulus of rock.In nonlinear elastic theory,the Young’s modulusEis replaced bythe nonlinear elastic modul…     

Study on anisotropy of Longmaxi shale using hydraulic fracturing experiment

Hydraulic fracturing reservoir reconstruction technology is crucial in the development of shale gas exploitation techniques.Large quantities of high-pressure fluids injected into shale reservoirs significantly alter compressional(P)and shear(S)wave velocities,rock mechanical parameters,and anisotropic characteristics.In this study,differentiated hydraulic fracturing petrophysical experiments were carried out on Longmaxi Formation shale under pseudo-triaxial stress loading conditions.The effects of stress loading methods,and water-rock physical and chemical reactions on P-and S-wave velocities and rock mechanical parameters were compared.The experimental results showed that isotropic stress loading may increase the P-and Swave velocities and Young’s modulus of dry shale kldnsample.Furthermore,it may lead to a weakening of the corresponding anisotropy.In contrast,differential stress loading was able to improve the anisotropy of Young’s modulus and accelerate the decrease in the compressive strength of shale in the vertical bedding direction.The water-rock physical and chemical reactions prompted by hydraulic fracturing was found to"soften"shale samples and reduce Young’s modulus.The influence of this"soften"effect on the compressional and shear wave velocities of shale was negligible,whilst there was a significant decrease in the anisotropy characteristics of Thomsen parameters,Young’s modulus,and Poisson’s ratio.The negative linear relationship between the Poisson’s ratios of the shale samples was also observed to lose sensitivity to stress loading,as a result of the"soften"effect of fracturing fluid on shale.The results of this study provide a reliable reference point and data support for future research on the mechanical properties of Longmaxi shale rocks.     

岩石损伤模量分析

从能量的角度出发定义损伤变量,通过应力-应变曲线卸载段有效应力与总应力之间的假定关系,确定损伤模量的计算方法。在单轴和三轴条件下,对岩石损伤相关参数进行统计研究,重点对损伤模量进行计算和对比分析。结果表明,单轴及低围压下损伤模量基本呈逐渐减小的趋势,而随着围压的增大,损伤模量呈先减小后保持动态稳定的趋势。损伤变量的计算充分考虑到围压的影响,可进一步增进对岩石损伤的认识。     

引潮力作用下饱和地质岩体的力学响应

本文应用孔隙弹性理论,探讨了引潮力作用下饱和地质岩体的力学响应.首先通过引潮力作用下饱和岩体的自由能表达式,得到岩体孔压与应力、应力与应变之间的关系;然后从引潮力作用下饱和岩体的平衡微分方程出发,结合流-固耦合理论,分析了饱水岩体应变与引潮位之间的关系;最后推导出饱和岩体的两大力学物理量--孔压和潮汐应力(平均应力)与引潮位之间的物理关系.模型表明:饱和岩体孔压与引潮位成反比,平均潮汐应力与引潮位成正比;比例系数不仅与岩体骨架的Lame系数有关,而且与Biot模量有关.将模型应用于会理川-18井水位变化分析,估计出水位响应系数D,并以此为基础,求得岩体孔压、潮汐应力与引潮位的相关系数(A和C)及Skempton系数B.最后对比分析了耦合条件下与不考虑耦合时得到的各参数之间的差异,分析表明:对饱和地质岩体而言,应力、孔压对引潮力的响应是流-固耦合作用的产物;研究其力学响应时必须充分考虑耦合效应.模型的建立,为研究引潮力作用下井-承压含水层系统力学、水动力学、与地震有关的断层力学以及引潮力触发机制的定量研究提供了基础.     

Rock anelasticity by complex modulus apparatus

Summary An attempt has been made to study the mechanical response of rocks to stress waves using the Complex Modulus Apparatus. Natural resonant frequencies and the half-power relative band widths are determined experimentally in the frequency range 50–5000 c/s for a few igneous, metamorphic and sedimentary rock samples. Elastic and anelastic parameters, like the real part of the elastic modulus, loss factor, complex modulus of elasticity and percentage anelasticity, are evaluated and the interrelationships between them shown. Data on four synthetic materials like perspex, ebonite and laminated sheeting are reported besides the results on different rock types.RM-9/73.     

共轭地震与地壳介质内摩擦系数的测定

安德逊理论表明地震的共轭破裂现象可以用库仑准则解释,断层面夹角与地下岩石内摩擦系数之间存在简单的定量关系。基于本文提出的通过共轭地震计算介质内摩擦系数的方法,对国内外19个具有X形或不完整的X形（L形）共轭破裂特征的地震进行系统性分析,与震源机制、区域应力轴方向等资料进行对比,确定共轭断层面,进而确定共轭面夹角并计算岩石的内摩擦系数。研究结果进一步证实了天然地震的共轭破裂与实验室岩石破裂具有较好的一致性,给出了库仑准则与安德逊理论在大尺度下也成立的证据,表明通过共轭角确定地下介质的内摩擦系数是对地下介质特性认知的有益补充。