A Study on the Peak Strength of Brittle Rocks

Summary A study on the peak strength of brittle rock materials having random strength distributions was carried out using the re-normalization group theory approach. A major advantage of the approach is that it is scale invariant, and therefore, one can relate the micro-fractures with macro-fractures of rocks at the critical state. The stress transfer from the broken sub-sections to the unbroken sub-sections is defined by a conditional probability. The critical probability P ^* and the relation between the peak strength and the mean strength of the elements have been obtained theoretically. On the other hand, the whole process of rock brittle fracture has also been simulated numerically from micro-fracture to macro-fracture by using the Rock Failure Process Analysis (RFPA) code. The peak strengths obtained by the numerical model agree fairly well with those obtained by the re-normalisation group theory. Due to the stress transfer from the broken subsections to the unbroken subsections, the peak strength is considerably less than the mean strength of the elements. Received October 24, 2000; accepted February 26, 2002 Published online September 2, 2002     

Role of Crystal Interlocking on the Strength of Brittle Rocks

Results of an experimental programme on heterogeneous rock-like specimens of dental plaster confirm the pronounced role of tensile microcracks on brittle failure. Microbuckling of very small rock-columns formed amid closely located tensile cracks was observed as the key incident connecting stable phenomenon of tensile cracking to unstable phenomenon of shearing and subsequent macroscopic failure. Using the classical beam and buckling theories and considering geometry of the problem a new failure criterion is proposed. As a novel attempt, this new failure criterion relates the compressive strength of rock to three basic microstructural properties, i.e. degree of crystal interlocking, average Young modulus and average tensile strength of rock forming minerals.     

P-(507)萃淋树脂分离富集发射光谱测定矿石中15个微量稀土元素

萃淋树脂作为一种化学分离手段,国外七十年代已有报导。上海最近合成的P_(507)萃淋树脂,具有溶剂萃取和离子交换的双重优点,该树脂对稀土元素有良好的萃取性能,柱上分离周期短而简便,是目前较好的稀土分离试剂之一。本文研究了P_(507)萃淋树脂分离富集稀土元素的条件,采用大色散率的光栅摄谱仪,着重选择了对稀土元素有较高灵敏度的缓冲剂,在柱上色层制备的总稀土氯化物中测定15个微量稀土分量。拟定的     

基于小波包分析的岩石声发射测量地应力

根据目前岩石声发射确定Kaiser点存在的问题采用小波包分析研究方法,在单轴加载岩石声发射试验的基础上,首先提出了基于小波包变换的Kaiser点信号的信噪分离方法,其次确定了Kaiser点信号的频率范围,最后利用小波包分析对岩石声发射信号的能量分布特征进行研究,得到了砂岩Kaiser点信号的特征频带。结果表明,小波包分析是处理岩石声发射Kaiser点信号的一种有效的方法,进而为AE法测量地应力确定Kaiser点奠定了一定的试验基础。     

New Observations on the Brittle Failure Process of Simulated Crystalline Rocks

A biaxial testing program has been performed to study the process of brittle failure in crystalline rocks. Dental plaster has been selected as a model material, and mixing with different ratios of distilled water, different types of common minerals of crystalline rocks have been simulated in the form of brick-like small elements. These elements have been interlocked together according to four systematic patterns and final specimens with 180 × 180 × 76 mm dimensions have been obtained. Details of different types of cracks observed during loading process, effects of mechanical, geometrical and confining pressure on the cracking intensity, the influence of different types of heterogeneity on the macroscopic properties of a system of interlocked elements, and the sequence of events during the failure process are presented in this paper. Based on these observations, a revised mechanism for brittle failure is proposed.     

Linear Elastic and Cohesive Fracture Analysis to Model Hydraulic Fracture in Brittle and Ductile Rocks

Hydraulic fracturing technology is being widely used within the oil and gas industry for both waste injection and unconventional gas production wells. It is essential to predict the behavior of hydraulic fractures accurately based on understanding the fundamental mechanism(s). The prevailing approach for hydraulic fracture modeling continues to rely on computational methods based on Linear Elastic Fracture Mechanics (LEFM). Generally, these methods give reasonable predictions for hard rock hydraulic fracture processes, but still have inherent limitations, especially when fluid injection is performed in soft rock/sand or other non-conventional formations. These methods typically give very conservative predictions on fracture geometry and inaccurate estimation of required fracture pressure. One of the reasons the LEFM-based methods fail to give accurate predictions for these materials is that the fracture process zone ahead of the crack tip and softening effect should not be neglected in ductile rock fracture analysis. A 3D pore pressure cohesive zone model has been developed and applied to predict hydraulic fracturing under fluid injection. The cohesive zone method is a numerical tool developed to model crack initiation and growth in quasi-brittle materials considering the material softening effect. The pore pressure cohesive zone model has been applied to investigate the hydraulic fracture with different rock properties. The hydraulic fracture predictions of a three-layer water injection case have been compared using the pore pressure cohesive zone model with revised parameters, LEFM-based pseudo 3D model, a Perkins-Kern–Nordgren (PKN) model, and an analytical solution. Based on the size of the fracture process zone and its effect on crack extension in ductile rock, the fundamental mechanical difference of LEFM and cohesive fracture mechanics-based methods is discussed. An effective fracture toughness method has been proposed to consider the fracture process zone effect on the ductile rock fracture.     

声发射预报地震的岩体力学分析

岩体受压破坏是由于岩体内裂纹扩展及新的宏观裂纹产生不断积累的结果,大规模岩体受压破坏前会发生局部岩体的先前断裂破坏。裂纹起裂、快速扩展和止裂会产生声发射现象,局部岩体断裂破坏会产生强烈的声发射现象,通过对岩体声发射的监测分析可以预报受压岩体破坏的时间。因此,通过对地壳岩体声发射的监测分析,可以进行地震的短期和临震预报。通过对岩体受压应力分布规律的分析,得出通过监测地壳浅部地应力和地形变预报地震是没有实际意义的结论。     

发射光谱法测定岩石中十五个痕量稀土元素

岩石中稀土元素的配分可作为地壳、地幔演化的标志,尤其是元素Eu,就是地质时代和物质来源的指示剂。因此,岩石中痕量稀土元素的测定越来越引起地质工作者的关注。     

脆性岩石变形机制与渗透率关系研究

为研究脆性岩石变形机制与渗透率- 应变的关系,根据脆性岩石应力- 应变和渗透率- 应变关系曲线分析指出：脆性 岩石经压密、弹性变形和非稳定破裂后,内部微裂隙出现丛集式发展,且不断合并、贯通,导致微观结构发生明显变化, 使渗透率在临界破坏点处急剧增大;当岩石宏观破坏后,内部结构面上的岩桥或凸起体部分被剪断或磨平,使得岩石强度 随变形突然下降,此时渗透率到达峰值。结合重整化群理论分析表明,脆性岩石在应力- 应变曲线拐点处应变和渗透率峰 值点处应变对应、临界破坏点处应变和渗透率急剧增大点处应变对应。通过试验研究和实例统计分析,验证了结论的合理性。     

A Criterion for Brittle Failure of Rocks Using the Theory of Critical Distances

This paper presents a new analytical criterion for brittle failure of rocks and heavily over-consolidated soils. Griffith’s model of a randomly oriented defect under a biaxial stress state is used to keep the criterion simple. The Griffith’s criterion is improved because the maximum tensile strength is not evaluated at the boundary of the defect but at a certain distance from the boundary, known as half of the critical distance. This fracture criterion is known as the point method, and is part of the theory of critical distances, which is utilised in fracture mechanics. The proposed failure criterion has two parameters: the inherent tensile strength, σ ₀, and the ratio of the half-length of the initial crack/flaw to the critical distance, a/L. These parameters are difficult to measure but they may be correlated with the uniaxial compressive and tensile strengths, σ _c and σ _t. The proposed criterion is able to reproduce the common range of strength ratios for rocks and heavily overconsolidated soils (σ _c/σ _t = 3–50) and the influence of several microstructural rock properties, such as texture and porosity. Good agreement with laboratory tests reported in the literature is found for tensile and low-confining stresses.     

Numerical Modeling of Pore Pressure Influence on Fracture Evolution in Brittle Heterogeneous Rocks

Rock is a heterogeneous geological material. When rock is subjected to internal hydraulic pressure and external mechanical loading, the fluid flow properties will be altered by closing, opening, or other interaction of pre-existing weaknesses or by induced new fractures. Meanwhile, the pore pressure can influence the fracture behavior on both a local and global scale. A finite element model that can consider the coupled effects of seepage, damage and stress field in heterogeneous rock is described. First, two series of numerical tests in relatively homogeneous and heterogeneous rocks were performed to investigate the influence of pore pressure magnitude and gradient on initiation and propagation of tensile fractures. Second, to examine the initiation of hydraulic fractures and their subsequent propagation, a series of numerical simulations of the behavior of two injection holes inside a saturated rock mass are carried out. The rock is subjected to different initial in situ stress ratios and to an internal injection (pore) pressure at the two injection holes. Numerically, simulated results indicate that tensile fracture is strongly influenced by both pore pressure magnitude and pore pressure gradient. In addition, the heterogeneity of rock, the initial in situ stress ratio (K), the distance between two injection holes, and the difference of the pore pressure in the two injection holes all play important roles in the initiation and propagation of hydraulic fractures. At relatively close spacing and when the two principal stresses are of similar magnitude, the proximity of adjacent injection holes can cause fracturing to occur in a direction perpendicular to the maximum principal stress.     

Experimental Calibration of ISRM Suggested Fracture Toughness Measurement Techniques in Selected Brittle Rocks

Summary A wide variety of specimen types and methods are employed in fracture toughness measurement of rocks, which result in scattered values for the same rock type. In order to provide some consistency to the values, the International Society for Rock Mechanics (ISRM) recommended three suggested methods using core based specimens, the Chevron Bend (CB) test, the Short Rod (SR) test and the Cracked Chevron Notch Brazilian Disc (CCNBD) test. This standardization helped obtain more consistent values but still a variation of 20–30% was observed in the values of fracture toughness obtained with the CB and SR methods. The values obtained with the CCNBD method were found to be consistently lower (30–50%) than those of the other two methods (CB and SR). Many reasons have been offered to explain this deviation. These include size of the specimen, anisotropy of rock, a dimensionless parameter in the fracture toughness calculation equation for the CCNBD test, etc. A comprehensive test program was initiated to identify the cause of these discrepancies between the CB and CCNBD methods. Three brittle rock types were selected for the study and more than 200 tests were conducted to measure the values of fracture toughness. A rigorous statistical analysis was carried out to determine the confidence level and find the significance of the test results. It was found that the CB and CCNBD methods were very comparable provided the correct equation for fracture toughness calculation was used for the CCNBD method and the size of the specimens was selected carefully. The error in the ISRM 1995 formula of fracture toughness for the CCNBD method could be the major factor responsible for the consistently lower values obtained with the method.     

岩石声发射技术的应用现状

介绍了我国内外岩石声发射技术在测定地应力、钻进监测、岩石力学与岩石破碎学研究、坑道岩体稳定性监测等方面的应用现状及发展趋势。     

Class I and Class II Rocks: Implication of Self-sustaining Fracturing in Brittle Compression

Tests to determine the complete stress–strain curve of rocks indicate whether the rocks can be classified a Class I or Class II. Class II rocks exhibits the potential for self-sustained failure in the post-peak region. The purpose of the research described in this paper was to investigate whether or not this self-sustained failure characteristic is related to the fragmentation of the rock. The aim of the research was, therefore, to determine possible relationships between fragmentation and various properties of several rocks types, including the influence of the Class II characteristic. Fragmentation of rock depends on its self-sustaining failure behaviour and the energy available in the post-peak region to shatter the rock. The correlation of static and dynamic rock properties with size of fragments resulting from compression tests demonstrate clear relationships of Class II rocks, but the same cannot be said for Class I rocks. Analyses of test results show that fragmentation increases with an increase in rock strength, and is explosive for Class II rocks. Probability density distributions were constructed to show the overall comparison of fragment sizes produced during failure of Class II and Class rocks. The calculated probability of passing at X₅₀ and X₁₀ sieve sizes show that Class II rocks as a group are more finely fragmented. It can therefore be concluded that, when breaking rocks under the same steady loading conditions, Class II rocks will show greater fragmentation than Class I rocks.     

声发射测量地应力方法中Kaiser点确定方法的优选与分析

准确确定Kaiser点是研究声发射测量地应力的关键.通过对模拟岩心的水泥块进行单轴受压破坏过程的声发射试验,得到了试件在试验过程中的应力-应变曲线、应力、声发射强度、声发射累积数与时间的关系图.分别对试样用突变点法、最大曲率法、双切线法、重加载法（抹录不尽现象、两次加载相减法）、多方面综合判定法以及声发射强度信号的统计分析法进行了分析.从不同的方面认识了试样的Kaiser点的特性,总结并分析了确定Kaiser点的方法以及各自的适应性,并进行了优选.研究表明,试验确定了试样的物理特性,各种方法都能从不同角度和机理上解释Kaiser点现象,综合判定法能相对更加全面、准确地确定Kaiser点.     

Onset of Hydraulic Fracture Initiation Monitored by Acoustic Emission and Volumetric Deformation Measurements

In this paper, the results of laboratory studies of fracture initiation, early propagation and breakdown are reported. Three experiments were conducted on a low permeability sandstone block, loaded in a polyaxial test frame, to representative effective in situ stress conditions. The blocks were instrumented with acoustic emission (AE) and volumetric deformation sensors. In two experiments, fluids of different viscosity were injected into the wellbore, fluid injection was interrupted soon after the breakdown pressure had been reached. This allowed us to investigate hydraulic fracture initiation. In the third test, fracture initiation criteria were applied to stop hydraulic fracture propagation significantly earlier, prior to breakdown, and as it propagated a short distance from the wellbore. The analysis of AE results shows an increase in AE activity and a change in the AE spatial correlation, during the fracture initiation. This early stage of fracturing correlates strongly with the onset of rock volumetric deformation, and is confirmed by the analysis of ultrasonic transmission monitoring. The rock microstructure, after the test, was investigated by analysis of scanning electron microscope images. These indicated the development of leak-off zone near the wellbore and a dry hydraulic fracture at the farther distance from the wellbore.