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.     

Effects of Grain Size on the Initiation and Propagation Thresholds of Stress-induced Brittle Fractures

Summary The microstructure of rock is known to influence its strength and deformation characteristics. This paper presents the results of a laboratory investigation into the effects of grain size on the initiation and propagation thresholds of stress-induced brittle fracturing in crystalline rocks with similar mineralogical compositions, but with three different grain sizes. Strain gauge and acoustic emission measurements were used to aid in the identification and characterization of the different stages of crack development in uniaxial compression. Results indicate that grain size had only a minor effect on the stress at which new cracks initiated. Crack initiation thresholds were found to be more dependent on the strength of the constituent minerals. Grain size did have a significant effect, however, in controlling the behaviour of the cracks once they began to propagate. The evidence suggests that longer grain boundaries and larger intergranular cracks, resulting from increased grain size, provide longer paths of weakness for growing cracks to propagate along. This promoted degradation of material strength once the longer cracks began to coalesce and interact. Thus, rock strength was found to decrease with increasing grain size, not by inducing crack initiation at lower stresses, but through a process where longer cracks propagating along longer planes of weakness coalesced at lower stresses.     

Fatigue Behavior of Granite Subjected to Cyclic Loading Under Triaxial Compression Condition

A series of laboratory tests were performed to examine the fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. In these tests, the influences of volumetric change and residual strain on the deformation modulus of granite under triaxial cyclic compression were investigated. It is shown that the fatigue behavior of granite varies with the tendency for volumetric change in triaxial cyclic compression tests. In the stress–strain space, there are three domains for fatigue behavior of rock subjected to cyclic loading, namely the volumetric compaction, volumetric dilation with strain-hardening behavior, and volumetric dilation with strain-softening behavior domains. In the different domains, the microscopic mechanisms for rock deformation are different. It was also found that the stress level corresponding to the transition from volumetric compaction to volumetric dilation could be considered as the threshold for fatigue failure. The potential of fatigue deformation was compared with that of plastic deformation. The comparison shows that rocks exhibit higher resistances to volumetric deformation under cyclic loading than under plastic loading. The influence of residual strain on the fatigue behavior of rock was also investigated. It was found that the axial residual strain could be a better option to describe the fatigue behavior of rock than the loading cycle number. A constitutive model for the fatigue behavior of rock subjected to cyclic loading is proposed according to the test results and discussion. In the model, the axial residual strain is considered as an internal state variable. The influences of confining pressure and peak deviatoric stress on the deformation modulus are considered in a term named the equivalent stress. Comparison of test results with model predictions shows that the proposed model is capable of describing the prepeak fatigue behavior of rock subjected to cyclic loading.     

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.     

Modeling of Crack Initiation, Propagation and Coalescence in Uniaxial Compression

Summary ?Cracks that initiate from pre-existing discontinuities can link with other cracks or with other discontinuities and produce failure in a rock mass. The Displacement Discontinuity Method (DDM), FROCK, is used in this investigation to model experimental observations on pre-cracked specimens of gypsum. In these experiments two fractures, which were either both open or closed, were placed through the thickness of the specimens, and detailed observations of the cracking process were performed as the specimens were loaded in uniaxial compression. The following aspects are studied for both open and closed fractures: 1) crack initiation stress; 2) direction and propagation of the new cracks; 3) type of coalescence and stress at which it occurs. Modeling is done considering the actual size of the specimens. Relations between the direction of initiation for each type of crack, the orientation of the initial fractures, and the type and coalescence are established. In addition, comparisons between results from experiments and predictions from the model are presented. The numerical results are in agreement with the experiments.     

Application of Leeb Hardness Test in Prediction of Dynamic Elastic Constants of Sedimentary and Igneous Rocks

Geotechnical and Geological Engineering - The Leeb hardness test is a non-destructive and portable technique that can be used both in the laboratory and in-field applications. The main purpose of...     

Study on Mechanical and Permeability Characteristics of Containing Gas Coal-Rock Under Conventional Triaxial Compression

Geotechnical and Geological Engineering - In this paper, the mechanical and permeability experiments of containing-gas raw coal and sandstone samples under conventional triaxial compression were...     

ESR定年：一种确定脆性断层活动年龄的方法原理与应用

在浅层低温环境中，脆性断层活动难以生成新的变质矿物，断层的准确活动年龄就难以确定。但在浅层断层活动中，往往伴生有同期生成的石英脉，对石英脉采用热活化电子自旋共振(ESR)测年，能够确定石英脉的生成年龄，从而能提供断层活动的年龄。如果断层带中发育有多期石英脉，通过测定还能提供断层多次活动的年龄。以雪峰山2条断裂带为例，使用ESR定年方法获得了202.3~60.6 Ma的地质年龄，并探讨了2条断裂带的演化与区域构造活动的关系，最后对ESR测年的可信性与使用条件进行了讨论。     

关于用室内三轴(CD)试验方法确定基床系数的探讨

根据基床系数的理论结合现场平板载荷试验方法结果,对用室内三轴(CD)试验测定基床系数测定结果的处理方法进行分析。     

A Review of the Influence of Microscopic Characteristics on the Progressively Brittle Failure of Foliated Rocks Subjected to Compression Loading

Geotechnical and Geological Engineering - The progressively brittle failure of foliated rocks involving the initiation, propagation, and aggregation modes is closely related to the microscopic...