Comparing Reservoir and Outcrop Specimens for Mixed Mode I–II Fracture Toughness of a Limestone Rock Formation at Various Conditions

Summary A fracture toughness study was conducted on a limestone rock formation from a petroleum reservoir in Saudi Arabia, and results were compared with those for outcrop specimens from the same geological formation. The objective was to investigate the possibility of using outcrop specimens to estimate the fracture toughness behavior of reservoir rock at in-situ conditions of temperature and confining pressure. The study was made on reservoir specimens from a depth of about 3.5 km, at both ambient and reservoir conditions. Mixed mode I–II fracture toughness at reservoir conditions of high temperature and confining pressure was studied using straight notched Brazilian disk (SNBD) specimens under diametrical compression. Tests were conducted at ambient conditions, at an effective confining pressure (σ₃) of 28 MPa (4000 psi), and at a temperature of 116^°C. The results showed a substantial increase in fracture toughness under confining pressure. Under σ₃=28 MPa, the pure mode-I fracture toughness (K _IC), increased by a factor of about 3.2, and the pure mode-II fracture toughness (K _IIC) increased by a factor of 4.4, compared to those under ambient conditions. On the other hand, K _IC at 116^°C was only 25% more than that at ambient conditions. These results were compared with recent results for outcrop specimens from the same geological formation. The results reveal that outcrop specimens can be successfully used to predict the fracture behavior of reservoir specimens at in-situ conditions, in spite of some differences at ambient conditions. Additionally, fracture toughness envelopes were obtained for reservoir specimens at ambient and high pressure conditions, in both positive and negative regions. Received September 14, 2000; accepted February 22, 2002 Published online September 2, 2002     

Fracture toughness analysis on cracked ring disks of anisotropic rock

Summary  This paper presents a combination of the Boundary Element Method (BEM) and the cracked ring test to determine the mixed-mode (I–II) fracture toughness of anisotropic rocks. The proposed BEM is used to accurately calculate the Stress Intensity Factors (SIFs) of a cracked anisotropic plate. An anisotropic Hualien marble of Taiwan with a distinct foliation was selected to conduct the cracked ring tests. Based on the measurement of the failure load during the test, the mixed-mode (I–II) fracture toughness can be determined. Experimental results show that the radius ratio, inclination and crack angle significantly affect the fracture toughness. The mode-I fracture toughness (K _IC ) is shown to decrease with the increase in hole diameter, whereas the mode-II fracture toughness (K _IIC ) increases with the increase in hole diameter when the crack angle β is equal to 0°. The experimental methods proposed have the advantage that the material is easily prepared, the test procedure is simple, and the cost is low. Correspondence: Chia-Hau Chen, Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, 701 Tainan, Taiwan     

A new approach to numerical method of modelling geological processes and rock engineering problems — continuum to discontinuum and linearity to nonlinearity

Numerical modelling as an efficient method is widely employed in various fields of science and engineering. In rock mechanics and geomechanics, considerable progress has been made in numerical simulation on nonlinear and discontinuum problems. However, there is a tendency in this field that the theoretical framework for nonlinear and discontinuum problems becomes more and more complicated and sometimes becomes less practicable. This paper gives a brief introduction to a newly developed numerical code, RFPA^2D (rock failure process analysis), which is mathematically a linear and continuum mechanics method for numerically processing nonlinear and discontinuum mechanics problems in rock failure. Although it is simple comparing with other numerical methods for nonlinear and discontinuum problems. It allows one to model the observed evolution of the progressive failure leading to collapse in brittle rocks. An important conclusion from the simulation results is that the microscale heterogeneity is the source of macroscale nonlinearity. Examples showing the potential applications are given in this paper. It can be seen that the RFPA^2D has a unique ability to reveal the evolutionary nature of the fracture phenomenon from microfracture scale to global failure, and the great potential exists in modelling mining induced rockbursts and stability of underground openings in greath depth. The capabilities to handle dilation, self-induced faults or even block movement and rotation should also attract applications in the fields of geomechanics as well as rock mechanics.     

Rock interface strength influences fluid-filled fracture propagation pathways in the crust

Rock interface strengths have often been assumed to be zero in numerical and analogue models of fracture propagation and magma intrusion in the crust. Rock strength tests were performed to explore the role that rock interfaces have on the geometry and propagation dynamics of fluid-filled fractures in the crust. We used a 1 kN test machine to study 5 mm thick cuboidal specimens cut from a sandstone-siltstone rock core, where the strata were known to host magma intrusions and the rock interface between the units was intact. By measuring the load required to grow a crack running along the lithological contact between the layers we calculate its fracture toughness K_c. The siltstone had an average K_c of 0.56 ± 0.03 MPa m^1/2 compared to the sandstone at 0.42 ± 0.02 MPa m^1/2. The rock interface had intermediate average fracture toughness to the parent units at 0.45 ± 0.03 MPa m^1/2. These results have important implications on fracture propagation pathways through rocks, as well as for the geometry and propagation dynamics of magma intrusions in the crust.     

Parameters controlling pressure and fracture behaviors in field injectivity tests: A numerical investigation using coupled flow and geomechanics model

Field injectivity tests are widely used in the oil and gas industry to obtain key formation characteristics. The prevailing approaches for injectivity test interpretation rely on traditional analytical models. A number of parameters may affect the test results and lead to interpretation difficulties. Understanding their impacts on pressure response and fracture geometry of the test is essential for accurate test interpretation. In this work, a coupled flow and geomechanics model is developed for numerical simulation of field injectivity tests. The coupled model combines a cohesive zone model for simulating fluid-driven fracture and a poro-elastic/plastic model for simulating formation behavior. The model can capture fracture propagation, fluid flow within the fracture and formation, deformation of the formation, and evolution of pore pressure and stress around the wellbore and fracture during the tests. Numerical simulations are carried out to investigate the impacts of a multitude of parameters on test behaviors. The parameters include rock permeability, the leak-off coefficient of the fracture, rock stiffness, rock toughness, rock strength, plasticity deformation, and injection rate. The sensitivity of pressure response and fracture geometry on each parameter is reported and discussed. The coupled flow and geomechanics model provides additional advantages in the understanding of the fundamental mechanisms of field injectivity tests.     

Numerical Modelling of the Heterogeneous Rock Fracture Process Using Various Test Techniques

Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R–T^2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R–T^2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.     

Physicomechanical properties of cryptocrystalline fluorite from the Suran deposit, southern Urals

Microhardness (H) and fracture toughness (K _1C) have been studied for the main varieties of shock-resistant cryptocrystalline fluorite, a natural ceramic widespread at the Suran deposit. Suran cryptocrystalline fluorite (SCF) is characterized by high fracture toughness (K _1C), which is 2–5 times higher than K _1C of common fluorite monocrystals. The relationship between K _1C and microhardness H is complex and nonlinear. The SCF varieties from the sellaite-fluorite orebody are distinguished by the highest K _1C = 1.9–2.3 MPa m^1/2, which exceeds K _1C = 0.84 MPa m^1/2 of porcelain-like fluorite from the main fluorite orebody. Qualitative and quantitative variations of structural point defects in the studied samples exert a much stronger effect on microhardness than on fracture toughness, which mainly depends on the size of crystallites, their mutual crystallographic orientation, and the structure of intergranular boundaries, i.e., on the parameters seemingly related to recrystallization and/or twinning of fluorite. In general, the nature of the Suran deposit of fluorite ceramic with unusual physicomechanical properties remains a geological puzzle in many respects.     

A comparison of seismic and structural measurements of scaling exponents during tensile subcritical crack growth

The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, K_I, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity K_I/KIC, where K_IC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for K_I < K_IC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.     

Transient solution for a plane‐strain fracture driven by a shear‐thinning,power‐law fluid

This paper analyses the problem of a fluid‐driven fracture propagating in an impermeable, linear elastic rock with finite toughness. The fracture is driven by injection of an incompressible viscous fluid with power‐law rheology. The relation between the fracture opening and the internal fluid pressure and the fracture propagation in mobile equilibrium are described by equations of linear elastic fracture mechanics (LEFM), and the flow of fluid inside the fracture is governed by the lubrication theory. It is shown that for shear‐thinning fracturing fluids, the fracture propagation regime evolves in time from the toughness‐ to the viscosity‐dominated regime. In the former, dissipation in the viscous fluid flow is negligible compared to the dissipation in extending the fracture in the rock, and in the later, the opposite holds. Corresponding self‐similar asymptotic solutions are given by the zero‐viscosity and zero‐toughness (J. Numer. Anal. Meth. Geomech. 2002; 26 :579–604) solutions, respectively. A transient solution in terms of the crack length, the fracture opening, and the net fluid pressure, which describes the fracture evolution from the early‐time (toughness‐dominated) to the large‐time (viscosity‐dominated) asymptote is presented and some of the implications for the practical range of parameters are discussed. Copyright © 2006 John Wiley & Sons, Ltd.     

Buoyancy-driven propagation of an isolated fluid-filled crack in rock: implication for fluid transport in metamorphism

A new model for upward transport of buoyant fluid released during metamorphism is proposed. The model is fluid transport by buoyancy-driven propagation of isolated fluid-filled cracks. The mechanical behavior of a two-dimensional, isolated, vertical, and fluid-filled crack in impermeable rock is investigated using linear fractire mechanics and fluid dynamics. The results show that steady-state crack propagation which causes long-distance transport of the fluid occurs when the vertical cross-sectional area of the crack exceeds a critical value. Propagation velocity and average thickness of the crack under the steady-state propagation regime are expressed explicitly by the following seven parameters: vertical crack length; rigidity, Poisson's ratio, and fracture toughness of the rock; fluid viscosity; density difference between the rock and the fluid; gravitational acceleration. An isolated H₂O-filled crack of vertical length 100 m, for example, propagates upwards in the crust at 0.3 m/s with the average thickness 0.2 mm when the following likely values are assumed: 0.1 mPa s for the H₂O viscosity; 3 MPa m^1/2 for the fracture toughness of the crustal rock. The application of the obtained results to the transport of H₂O released during metamorphism suggests that the number density of isolated cracks propagating in the crust is very low. Since the propagation velocity is high, our model is suitable particularly for fluid transport through hot quartz-rich rock where fluid-filled cracks have geologically short lifetimes.     

地震导致山体变形破裂机制地质力学模拟试验研究

地震导致山体变形破裂是一个复杂的演化过程,文中通过一些典型实例的地质分析,总结归纳了高地震烈度区山体变形破裂失稳有一定代表性的倾外层状体斜坡滑坡型、高陡块(层)状体斜坡崩塌型、软弱基座体斜坡滑坡型等3种典型性地质力学模式。自主创新研制、设计、探索了一套振动条件下地质力学模拟试验的设备模型和方法,并对3种典型性地质力学模型进行机制模拟试验。通过变形破裂演化过程模拟再现试验,从中揭示出一些振动条件下变形破裂的典型迹象和重要证据,充分再现了典型地震失稳机制的形成条件、相关性因素以及演化规律,为进一步研究分析提供科学可靠的试验数据和证据。     

Numerical simulation and evaluation of the fracturing and tight gas production with a new dimensionless fracture conductivity (FCD) model

Hydraulic fracturing is an essential technology for the development of unconventional resources such as tight gas. The evaluation of the fracture performance and productivity is important for the design of fracturing operations. However, the traditional dimensionless fracture conductivity is too simple to be applied in real fracturing operations. In this work, we proposed a new model of dimensionless fracture conductivity (F_CD), which considers the irregular fracture geometry, proppant position and concentration. It was based on the numerical study of the multistage hydraulic fracturing and production in a tight gas horizontal well of the North German Basin. A self-developed full 3D hydraulic fracturing model, FLAC3D^plus, was combined with a sensitive/reliability analysis and robust design optimization tool optiSLang and reservoir simulator TMVOCMP to achieve an automatic history matching as well as simulation of the gas production. With this tool chain, the four fracturing stages were history matched. The simulation results show that all four fractures have different geometry and proppant distribution, which is mainly due to different stress states and injection schedule. The position and concentration of the proppant play important roles for the later production, which is not considered in the traditional dimensionless fracture conductivity F_CD. In comparison, the newly proposed formulation of F_CD could predict the productivity more accurately and is better for the posttreatment evaluation.

     

Fracture Toughness and Fracture Roughness in Anisotropic Granitic Rocks

In this paper we present an experimental approach aimed at assessing the correlation between fracture toughness (K _IC) and fracture roughness of two granitic rocks (Barre and Stanstead granites) exhibiting significant fracture toughness anisotropy. Roughness values have been estimated for fractured surfaces obtained from Chevron Cracked Notch Brazilian Disc samples failed under mode I along three orthogonal planes with respect to their microstructural fabrics. There exists a clear correlation between roughness and toughness within each rock examined along the three planes. Specific orientation of micro-crack alignment could result in preferred out-of-plane propagation of the test-crack irrespective of grain-size distribution. These experimental observations reinforce the hypothesis of the existence of a link among pre-existing petrofabric anisotropy, fracture toughness, fracture roughness, and the evolution and extent of the associated induced fractures within the process zone of granitic rocks along specific directions. This study also highlights the need for employment of pre-failure and advanced post-failure diagnostic techniques in quantifying these inter-relationships.     

On Fröhlich's solution for Boussinesq's problem

The concentration factor introduced by O. K. Fröhlich is visualized as a procedure for examining the pattern of load transfer from surface loads to the interior of a geomaterial. The historical details that led to the introduction of the concentration factor are scant although it is widely used in the area of soil mechanics problems associated with tillage‐induced soil compaction. The purpose of this note is to examine the concentration factor in terms of the geomechanics of an elastic continuum and to identify the precise conditions that are satisfied by the distribution of stresses and strains that accommodate the concentration factor. Copyright © 2013 John Wiley & Sons, Ltd.     

Earthquake source nucleation as self organization process

The theory of an earthquake source nucleation is discussed. Based on the assumption that self organization of damage process takes place in the zone of an earthquake source nucleation the theory incorporates the damage rheology framework of Lyakhovsky et al. and the approach of phenomenology theory of second-order phase transition. Namely, the free energy governing the process of an earthquake source nucleation depends on two collective variables α and φ in addition to the strain tensor ε_ij. The variable α quantifies the fracture of the medium and the variable φ quantifies the interaction effect of cracks. The region Ω_S is associated with a potential source of an earthquake if the damage variable α exceeds the critical value α_cr⁽¹⁾ inside Ω_S. The important feature of a potential source is that interaction of fractures causes acceleration of damage process inside the region of potential source and the material should lose stability primarily in this region. Interaction of fractures results also in occurrence of a residual stress caused by nonuniformity of fracture density. The appearance and development of the potential source result in increase of intensity of damage process not only in the region of potential source but also in a certain neighborhood of the last. It is compatible with such observed effects as acceleration of seismic energy release and growth of correlation length of weak seismicity before large earthquake. Transition of potential source to the stage of avalanche-unstable fracturing is associated with instability generated by explosive increase of interaction of fractures when the damage variable α exceeds the second critical value α_cr⁽²⁾ inside Ω_S.     

A Review of Some Rock Mechanics Issues in Geothermal Reservoir Development

Rock mechanics and geomechanical studies can provide crucial information for economic geothermal reservoir development. Although significant progress has been made in reservoir geomechanics, technical challenges specific to the geothermal area (high temps, data collection, experimentation issues) have prevented widespread use of geomechanics in geothermal reservoir development. However, as the geothermal industry moves to develop more challenging resources using the concept of enhanced geothermal systems (EGS), and to maximize productivity from conventional resources, the need for improved understanding of geomechanical issues and developing specific technologies for geothermal reservoirs has become critical. Rock mechanics research and improved technologies can impact areas related to in-situ stress characterization, initiation and propagation of artificial and natural fractures, and the effects of coupled hydro-thermo-chemo-mechanical processes on fracture permeability and induced seismicity. Rock mechanics/geomechanics research, including experimental and theoretical investigations as well as numerical and analytical solutions, has an important role in optimizing reservoir design and heat extraction strategies for sustainable geothermal energy development. A number of major areas where rock mechanics research can facilitate geothermal systems development are reviewed in this paper with particular emphasis on EGS design and management.     

Dynamic Model of Fracture Normal Behaviour and Application to Prediction of Stress Wave Attenuation Across Fractures

Summary.  The purpose of this paper is to establish a dynamic constitutive model of fracture normal behaviour, based on laboratory tests of artificial fractures cast by cement mortar. A series of tests are systematically carried out under quasi-static (10⁻¹ MPa/s) up to highly dynamic (10³ MPa/s) monotonic loading conditions. The normal stress-fracture closure response is measured at different loading rates. Based on the measured curves, a nonlinear (hyperbolic) dynamic model of fracture normal behaviour, termed as dynamic BB model, is proposed. The dynamic model is modified from the existing BB model of static normal behaviour of fractures by taking into account the loading-rate effect. Two important dynamic parameters of fractures, FSC _d (dynamic fracture stiffness constant, which describes the incremental ratio of dynamic initial stiffness) and FCC _d (dynamic fracture closure constant, which describes the decremental ratio of dynamic maximum allowable closure), are identified. They indicate the quantitative degree of loading-rate effect on fracture normal behaviour subjected to dynamic loads. For practical application, the new model is incorporated into the Universal Distinct Element Code (UDEC) and subsequently, UDEC modelling of normally incident P-wave transmission across single fractures with the dynamic BB model is conducted. Wave transmission coefficient is obtained for various combinations of fracture dynamic parameters, as well as different wave amplitudes and frequencies. The numerical results show that wave transmission coefficient for a fracture with the dynamic BB model is greater than that for a fracture with the static BB model. In addition, a fracture with higher values of FSC _d and FCC _d leads to higher transmission (lower attenuation). Author’s address: J. Zhao, Ecole Polytechnique Federale de Lausanne (EPFL), Rock Mechanics Laboratory, 1015 Lausanne, Switzerland     

两个值得关注的工程地质力学问题

岩体工程地质力学的问世 ,不仅推动了工程地质学科的发展 ,而且提高了解决实际工程问题的能力。在其发展过程中 ,新的研究课题不断地被提了出来。随着这些问题的解决 ,一些重要的理论、方法和技术将形成和逐步走向完善。作者认为以下两个工程地质力学问题值得我们关注 ,即边坡滚石机理和防治和工程地质力学综合集成理论和方法。     

Size and Geometry Effects on Rock Fracture Toughness: Mode I Fracture

In this paper, the effects of specimen size and geometry on the apparent mode I fracture toughness (K _c) of an Iranian white marble (Neyriz) are studied. A number of fracture tests were conducted on center-cracked circular disk (CCCD) specimens with different radii to investigate the size effects on K _c. The experimental results demonstrate that the apparent fracture toughness increases in bigger specimens. In order to explain the experimental results, the modified maximum tangential stress (MMTS) criterion is used, where higher order terms of the Williams’ series expansion are included in the maximum tangential stress criterion. It is shown that the MMTS criterion provides good estimates for the apparent fracture toughness of Neyriz marble, obtained from fracture tests of edge-cracked triangular specimens. It is, therefore, concluded that the proposed criterion is able to account for the size and geometry effects on the fracture resistance of rocks simultaneously.     

Analysis of Cracking in Rock Salt

Summary ?The use of underground mines in salt-rock formations for waste repositories makes the precise analysis of isolation properties of rock salt very important. One of the main mechanisms responsible for a degradation of isolation ability of the rock salt is the generation and development of cracks under influence of mining processes. Various aspects of cracking in salt rocks are studied – both in situ and in laboratory tests – for rocks of the world's largest Verkhnekamskoe potash-ore deposit (Russia). It is shown that not all the discontinuities (fractures) are closed in the course of the creep deformation of rocks. Parameters of cracking are determined for various conditions: age of pillars, mining technology, etc. Different methods – filtration, electrometric, nuclear magnetic resonance, mechanical tests – are used for crack observation and characterisation, both in specimens and in situ. Traditional investigations (partly with specially designed equipment) are accomplished by the testing methods of fracture mechanics for determination of critical values of stress intensity factors K _Ic and K _IIc. The problems and ways of the use of the obtained results in analysis of isolation properties for areas in vicinity of underground mines and/or waste repositories are discussed.