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Collaborating Authors
13th ISRM International Congress of Rock Mechanics
Abstract This paper aims at enriching a homogenization-based anisotropic damage model for hard rocks under complex loading. A new damage criterion is proposed to capture material strain softening. Within the framework of irreversible thermodynamics, we are particularly concerned with two strongly coupled dissipative mechanisms: frictional sliding and damage by microcracking, which usually take place at cracks within cohesive geomaterials under compression. Focusing on the representative elementary volume containing multiple crack families, the free enthalpy of the matrix-cracks system is obtained. Importantly, a back-stress term is involved in the local stress applied to microcracks. This back stress plays the hardening/softening role in the friction criterion which is formulated at local scale. Strain hardening owns to the accumulation of frictional shearing and dilatancy while strain softening is caused by crack growth. The multiscale damage model is used to simulate laboratory tests on the Westerly granite under true triaxial compressions. Introduction When subjected to compressive loads, hard rocks present nonlinear mechanical behaviors and induced material anisotropies. In that process, two main dissipative mechanisms have been largely identified: damage by crack growth and frictional sliding along closed crack faces, which are usually strongly coupled to each other on crack scale. Theoretical investigations have shown that the damage friction coupling analyses allow explaining a large number of experimental phenomena involved in brittle or quasi-brittle materials. Concerning constitutive modeling, the standard Eshelby's solution-based homogenization procedure for heterogeneous materials was recently applied successfully to describing the mechanical and poromechanical behaviors of cracked frictional solids. This paper presents a homogenization-based anisotropic damage model for hard rocks under complex loading. Within the thermodynamic framework, we are particularly concerned with two strongly coupled dissipative mechanisms: frictional sliding and damage by microcracking, which usually take place at cracks in cohesive geomaterials under compression. Focusing on the representative elementary volume containing multiple crack families, the free enthalpy of the matrix-cracks system is obtained. Importantly, a back-stress term is involved in the local stress applied to microcracks. This back stress plays the hardening/softening role in the friction criterion which is formulated at local scale. Strain hardening owns to the cumulation of frictional shearing and dilatancy while strain softening is caused by crack growth. A new damage criterion is proposed to capture strain softening of the material. Finally, the multiscale damage model is used to simulate laboratory tests on the Westerly granite under true triaxial compressions.
- Europe (0.28)
- North America > Canada (0.19)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Igneous Rock > Granite (0.86)
Numerical Modelling of Fold-Related Fractures
Kolo, I. (Masdar Institute of Science and Technology) | Al-Rub, R. K. Abu (Masdar Institute of Science and Technology) | Sousa, R. L. (Masdar Institute of Science and Technology) | Sassi, Mohamed (Masdar Institute of Science and Technology) | Sirat, Manhal (Abu Dhabi Company for Onshore Oil Operations (ADCO))
Abstract Fractures induced by folds are pivotal in hydrocarbon exploration, ground water transport and harnessing of geothermal energy. This is because of the need to predict and understand fracture propagation in reservoirs which have folded rock formations. Despite its prominence, there is a lack of reliable numerical models for simulating fractures resulting from rock folding. This is partially due to the difficulty involved in fracture modelling. As a contribution to fold-fracture modelling, this work applies a coupled plasticity-damage model to rock fracturing and anticlinal folds. Parametric studies on a single folded layer give insight into the fold formation and behaviour. The anisotropic continuum damage model which considers both tension and compression is formulated using the power damage evolution law. For ease in formulation, strain equivalence hypothesis is adopted whereby the strain is the same for both damaged and undamaged configurations. Lubliner plasticity yield criterion is adopted for plastic deformation. The model is coded in Abaqus user subroutine UMAT and is applicable to quasi-brittle materials. Introduction The understanding of fractures in the earth's crust helps in the prediction, evaluation and characterization of fractured reservoirs, whether they are petroleum, geothermal or underground water reservoirs. This is partly because reservoir permeability and stability are dependent on fracture properties (Nelson, 2001). To achieve this, various approaches have been developed to analyze reservoir rock fractures. These could be grouped intodiscrete approaches – where the rock mass is represented by a finite number of well-defined components and continuum approaches – where the mathematical assumption of an infinitesimal element is made (Jing, 2003). Ivanova (Ivanova, 1998) comprehensively studied fracture systems in nature and highlighted folds as one of the major geologic settings that produce fractures. Naturally occurring folds in reservoirs sometimes compound fracture analysis. It might not be clear whether the fractures formed before, during or after rock folding. Fractures formed during the folding process are expected to show stress orientations related to folding and are thus of primary concern in rock folding simulation. It could be argued that there are no numerical models that assuredly simulate rock folding and fracturing simultaneously (Jäger, Schmalholz, Schmid, & Kuhl, 2008). Folds are formed when planar or straight surfaces of the earth become curved or bent due to plastic deformation. The process of folding has two mechanisms: flexure and shear. Flexural folding could be in the form of bending or buckling depending on the compressive force. When the force is parallel to the bedding, buckling occurs; when stresses are applied across layers causing torque, bending occurs. Shear folding occurs due to small displacements along closely spaced planes perpendicular to the bedding. Flexural folding is associated with competent (strong, thick and stiff) rock layers while shear folding is found in incompetent formations (Ivanova, 1998). Fractures resulting from flexural folding are expected to be more pronounced. In this study, fractures due to bending are investigated. Numerical models based on continuum approaches majorly describe material deformation while discrete approaches describe element movement of the system (Bobet et al., 2009). The former will be more appropriate to study the initiation and propagation of fractures due to rock bending. Hence, Finite Element Method (FEM) is adopted.
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Structural Geology > Tectonics > Compressional Tectonics > Fold and Thrust Belt (0.68)
Composite Landslides Affecting Flysch and Neogene Weak Rock Formations Induced by Heavy Rainfalls
Tsiambaos, G. (National Technical University of Athens) | Sabatakakis, N. (University of Patras) | Rondoyanni, Th. (National Technical University of Athens) | Depountis, N. (University of Patras) | Kavoura, K. (University of Patras)
Abstract Some typical landslide phenomena in Western Greece, in terms of the geological composition and structure of the affected materials, induced by heavy rainfalls are thoroughly studied and analyzed. The studied cases involved composite landslides on Flysch and Neogene weak rock materials that constitute the most critical landslide prone geological formations in Greece. The studied cases named Platanos, Platanitis and Karya include representative landslide sites as regards to the geological composition and structure of the displaced formations. Thus:flysch formation includes different lithological units as shales, marls, siltstones, sandstones and conglomerates and is closely related to the Alpine orogenesis, suffering intense past tectonic movements and the Plio-Pleistocene sediments include clayey marls, marlstones and siltstones. The investigated landslides, affecting mainly transportation routes, are closely related to heavy rainfalls induced by extreme meteorological events and are controlled by active fault tectonics. Long term movement monitoring using borehole inclinometers and surface benchmarks showed that landslides control was effective only when the proper stabilization measures were taken. Introduction Landslides represent a major threat to human life, property, infrastructure and natural environment in most regions of the world. They are recognized by the scientific and politic authorities as having a major socio-economic impact and they represent a significant hazard for the population and the properties in particular locations. Landslide hazard expressed as the probability of occurrence within a reference time period and is a function of the spatial and temporal probability (Varnes, 1984; Guzzetti et al. 1999; Lee and Jones, 2004). The spatial probability of landslide initiation (susceptibility) is mainly related to static causal factors (slope inclination, material properties, etc.), while temporal probability is mainly related to dynamic causal factors such as rain input, increased groundwater levels and drainage, earthquakes, etc. (Van Westen et al. 2005). One of the most frequent causes of landslides in the Western part of Greece is a change in groundwater levels, either by natural drainage conditions or by an increase in groundwater due to periods of excessive rainfall. The presence of groundwater affect slope stability by increasing the effective weight of the saturated materials, creating appreciable pore pressure and tending to weaken soft rocks and unconsolidated materials. Other factors such as: variant lithological composition, intense folding and jointing as well as high relief energy favor the manifestation of such phenomena. However, the predominant factors relative to the triggering effects are mainly heavy rainfalls and active fault tectonics. The interrelation between landslide events and precipitation for Western Greece was initially established by Koukis et al. (1996).
- Phanerozoic > Cenozoic > Neogene (0.95)
- Phanerozoic > Cenozoic > Quaternary > Pleistocene (0.56)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock (0.90)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (0.55)
Deep-Seated Structurally Controlled Landslides of Corinth Gulf Rift Zone, Greece: The Case of Panagopoula Landslide
Sabatakakis, N. (University of Patras) | Tsiambaos, G. (National Technical University of Athens) | Rondoyanni, Th. (National Technical University of Athens) | Papanakli, S. (University of Patras) | Kavoura, K. (University of Patras)
Abstract A representative composite fault-related landslide of the Corinth Gulf graben named "Panagopoula" is reported that considered to be one of the most prone to slope instability sites along the main motorway and railway connecting Athens with the city of Patras. The presence of tectonically highly sheared and weathered geological formations, including Alpine basement (mainly flysch) contributes to the site instability, triggered/reactivated by seismic activity and heavy rainfalls. Although a series of remedial measures have been already constructed, the inclinometer readings during the last twenty years time period show a continuous very slow movement which indicates that the landslide is still "active". This fact has resulted to divert the axes of the new motorway and railway through twin tunnels which are under construction. Introduction The spatial and temporal evolution of landslides in the case of structurally complex slopes is lithologically and often structurally controlled while their type and frequency are mainly related to tectonic and lithological anisotropy (Baron et al. 2005; Hradecky et al. 2007). The triggering mechanisms mainly include:excessive rainfall generating high pore pressure and strong earthquakes resulting in dynamic loading conditions at the failure surface. Data such as past earthquakes or the precipitation records are useful to be gathered when a landslide model is examined since they could act as a landslide triggering mechanism. Recording of the movement through surface and inclinometer measurements as well as combination of the above information with historical records of failure could lead to a more accurate estimation of the location of the failure surface and understanding of the landslide mechanism. Slope instability in the southern segment of the Gulf of Corinth, Northern Peloponnesus, Greece, is ubiquitous and ranges from deep-seated bedrock failure to secondary earth flows in recent deposits. In this part of Greece, the periodically induced landslide events triggered by heavy rainfall, earthquake and anthropogenic activity are closely related to active fault tectonics. The Gulf of Corinth is considered as a typical example of a relatively simple asymmetric half-graben with major border faults to the south and a flexure of the northern shore. Panagopoula landslide is located along the trace of a WNW trending normal fault (dipping northwards) (Figure 1). The area is considered to be one of those most prone to slope instability along the E95 motorway and railway connecting Athens with the city of Patras. The paper outlines the significance of active fault tectonics for the development of landslides which could affect the transportation routes. Recent and past inclinometer data are evaluated in order to establish a ground displacement rate through a twenty years' time frame.
- Phanerozoic > Mesozoic (0.70)
- Phanerozoic > Cenozoic > Neogene (0.47)
- Phanerozoic > Cenozoic > Quaternary (0.47)
- Geology > Structural Geology > Tectonics > Plate Tectonics > Earthquake (1.00)
- Geology > Structural Geology > Tectonics > Extensional Tectonics (1.00)
- Geology > Structural Geology > Fault > Dip-Slip Fault > Normal Fault (1.00)
- Transportation > Ground (1.00)
- Energy > Oil & Gas > Upstream (1.00)
Experimental Study on the Damage and Failure Properties of Rock-Like Material with Pre-Existing Double Flaws under Uniaxial Compression
Zhao, Cheng (Tongji University) | Bao, Chong (Tongji University) | Zhao, Chunfeng (Tongji University) | Tian, Jiashen (Tongji University) | Hiroshi, Matsuda (Nagasaki University)
Abstract Based on digital image correlation (DIC) method and self-developed code, the global strain field changing and failure properties of rock-like materials with pre-existing double flaws are experimentally studied under uniaxial compression. By theoretical analysis with linear elastic fracture mechanics (LEFM), the strain approach proves to be practicable to investigate cracking process. Thus, two types of process zone are defined to discuss the specimen's coalescence evolution at different loading stages. Crack initiation, propagation, and coalescence is a process of zone development and nucleation. DIC strain field results are studied on a meso-level using a strain approach. In the shear coalescence mode, the SPZ (shear process zone) in a bridge area coalesces with each other, while the TPZ (tensile process zone) grows independently. In general, the paper tries to establish the link between microscopic mechanical mechanisms and macroscopic mechanical responses in flawed rock. Further research should be done to study the cracking process and its effect on rock strength in detail by the DIC method. Introduction Natural rock contains discontinuities including pores, fractures, inclusions or other defects. The existence of these discontinuities in the rock can decrease the strength and stiffness of the rock and they are a source of initiation of new discontinuities which may in turn propagate and link with other cracks and further decrease the strength and the stiffness of the rock (Sagong & Bobet, 2002). Lots of theoretical, experimental and numerical researches have been done in studying crack initiation, propagation and coalescence in rocks (Hoek & Bieniawski, 1965; Kranz, 1983; Reyes & Einstein, 1991; Park & Bobet, 2009; Gonçalves & Einstein, 2013). But when it comes to multiple pre-flaws, the issue that how the preexisting flaws affect each other becomes complicated and uncertain. The stress field around the tips of flaw can either enhance the impact of single flaw or weaken it. According to the observations have been done before, it is found that the way and function in which these cracks propagate and coalescence depends on the geometric arrangements (Bobet, 1997; Bobet & Einstein, 1998; Wong & Chau, 2001).
- Asia (0.47)
- North America > Canada (0.18)
- Research Report > New Finding (0.67)
- Research Report > Experimental Study (0.53)
- Media > Photography (0.69)
- Energy > Oil & Gas > Upstream (0.50)
Abstract Time-dependent swelling deformation of several shaley rock formations in Ontario is a wellknown phenomenon. In shales and mudstones with a higher salt concentration in the pore fluid than the ambient fluid, the outward gradient generates an osmotic pressure which acts as the driving force for swelling. The swelling phenomenon appears to be related to ion exchange between the rock porewater and the surrounding water. The swelling potential is expressed as the percent swelling strain that occurs per log cycle of time, in either the vertical (perpendicular to bedding) or horizontal (parallel to bedding) directions. In addition, the swelling potential is also noted to be stress dependent. In practice, therefore, the conditions required for swelling are (i) the accessibility to water, and (ii) an outward salt concentration gradient from pore fluid of the rock to the ambient fluid. The relief of in-situ rock stress during excavation serves an initiating mechanism (Lo and Micic, 2010). Introduction Time-dependent swelling deformation of several shaley rock formations in Ontario is a well-known phenomenon. In shales and mudstones with a higher salt concentration in the pore fluid than the ambient fluid, the outward gradient generates an osmotic pressure which acts as the driving force for swelling. Swelling is also controlled by the inter-particle bonding; if the bond strength exceeds the osmotic pressure, swelling will not occur, and vice-versa. The bond strength can be reflected by the calcite content which forms cementation bond between rock particles. The swelling phenomenon appears to be related to ion exchange between the rock porewater and the surrounding water. The swelling potential is expressed as the percent swelling strain that occurs per log cycle of time, in either the vertical (perpendicular to bedding) or horizontal (parallel to bedding) directions. The swelling potential is also noted to be stress dependent. The swelling phenomenon in soils and rocks has received wide treatment in the past by numerous researchers. However, the mechanism and numerical model presented in this paper concentrates on the work done at the University of Western Ontario by Dr. K.Y. Lo and a number of graduate students over the last 30 years. The reader is encouraged to look at the papers in the reference list to follow the evolution of the swelling model for Southern Ontario shales over the last three decades.
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
Abstract One of the most concerns of room and pillar mining system is subsidence of the ground surface due to coal mining particularly in room and pillar mines. Subsidence of ground surface is a result of floor, pillar, or roof failure of the mine. At the same, due to many difficulties associated with surface disposal facilities of coal refuse, some mining companies are trying to use underground space as a disposal storage place. In this study, stability and subsidence analyses of an underground coal mine located in the Illinois Basin are conducted. This room and pillar mine was abandoned and later on was used as a storage place to accommodate the coal fine refuse with slurry backfilling method. The geological stratigrophy and geomechanical properties of the mine floor and roof were collected. Floor and pillar stability analyses were conducted for areas with various extraction ratios. The stability of the mine was evaluated both prior and after slurry backfilling. The floor and pillar stability analyses results of the mine due to moisture exposure after slurry backfilling are discussed. The subsidence potential due to mine failure is also evaluated. Introduction A typical lithology of coal seams in the Illinois Basin consists of weak underclay stratum. The immediate weak underclay causes frequent floor instability problems in Illinois underground coal mines. There are two different stages in assessing floor stability of the mines where slurry backfilling is planned. The first stage is during the mining operation when weak underclay layer squeezes under pillar stress and results in punching or bearing capacity failure. The second stage is after slurry backfilling. During this stage, the slurry material soaks non-durable floor layers and causes strength reduction in floor material. Pillar stability conditions should also be taken into account during both the operational period and after the slurry backfilling.
- Geology > Rock Type > Sedimentary Rock > Organic-Rich Rock > Coal (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
Abstract The characterization of the failure process of induced fractures by hydraulic stimulation is fundamental to understanding the generation and evolution of the discrete fracture network within the reservoir. A more detailed analysis of the fracture mechanism can be a powerful tool for identifying fluid flow paths and proppant placement within the reservoir. For example, during the rupture process the energy release is partitioned into different physical processes for which the relative ratio is changed by the presence of fluids or rotations in the local stress field with relation to the frictional resistance in the fracture plane. Fractures occurring in the same host rock under the same stress conditions are expected to rupture similarly, independent of their size (self-similarity). Changes in the scaling relationships of fractures are indicative of a change in the failure process, host rock or in-situ stress. Correlation of failure process data with reservoir rock properties and the in-situ stress field will help identify regions within the reservoir with characteristic types of failures. Further correlation with hydrocarbon production data can be used to develop efficient treatment plans and production diagnostic tools. In this study we investigate the failure process of ~ 27,000 microseismic (M < -1) fractures induced during a hydraulic fracturing shale completion program in NE British Columbia, Canada by estimating static and dynamic source parameters, such as dynamic and static stress drop, radiated energy, seismic efficiency, moment tensor, fracture plane orientation, slip direction and rupture velocity. On average, the microseismic events have low radiated energy, low dynamic stress and low seismic efficiency, consistent with the obtained slow rupture velocities. Events fail in overshoot mode (slip weakening failure model), with fluids lubricating faults and decreasing friction resistance. Events occurring in deeper formations tend to have faster rupture velocities and are more efficient in radiating energy. Variations in rupture velocity tend to correlate with variation in depth, fault azimuth and elapsed time, reflecting a dominance of the local stress field over other factors. Further identification of spatial and temporal distribution of families of events with similar characteristic rupture behaviors, based on either rock formation, depth, source type, fracture plane orientation, stress drop, pad or proppant stage, may be used as a proxy for specific fracture network development and hydrocarbon production. This information may be used to determine reservoir properties, constrain reservoir geo-mechanical models with measured physical parameters, classify dynamic rupture processes for fracture models and improve fracture treatment designs. These will be the focus of future studies.
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.65)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Horn River Basin > Horn River Shale Formation (0.98)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Horn River Basin > Otter Park Formation (0.94)
- North America > Canada > British Columbia > Western Canada Sedimentary Basin > Horn River Basin > Muskwa Field > Muskwa Formation (0.94)
Abstract In geomechanics, conducting uniaxial or triaxial compression tests require samples to be prepared to a certain length-to-diameter ratio. This ratio is typically defined as 2:1 (length to diameter) and is accepted as a common standard for all materials on which mechanical properties testing is performed. Variations in sample length can cause changes in measured strength properties across multiple material types, such as cement, rock, or soil. Within the oil and gas industry, it is not uncommon to receive samples for technical services work that are slightly under or exactly the length requirement before surface grinding and sample preparation. Many of these samples are discarded from uniaxial and triaxial compression tests and used in another manner; therefore, it is necessary to study the length-to-diameter ratio in efforts to understand the limits and validity of testing samples that are slightly out of the 2:1 ratio. This paper discusses uniaxial compression tests performed using Berea sandstone and a standard cement mixture of 2.54-cm diameter to study changes in rock strength and properties. Compressive strength for each lengthto- diameter ratio over a range of 0.5:1 to 2.2:1 was measured. The investigation was extended to study near-end effects, where the sample length is near, but not exactly twice the diameter. It was discovered that the cement samples conformed reasonably well to the suggested ASTM correction factors. The sandstone did not conform to the correction factors and further analysis is required to develop a correction factor unique to the material. Near end effects, in both the cement and Berea, were found to increase compressive strengths, especially when the L/D of the samples was increased slightly over a 2:1 L/D. Introduction In the oil field, it is customary to receive samples for mechanical properties testing. These sample types range from produced materials, such as cementitious mixtures, to materials obtained through coring from a reservoir, such as sandstone or shale. Each of these types of materials is tested for compressive strength and other properties in labs dedicated to the study of mechanical properties. The information gathered from testing is typically used during modeling and other procedures throughout the field to help determine the best method for drilling, fracturing, cementing, etc. Thus, it is imperative that the values obtained through testing be as accurate as possible.
- North America > United States > Pennsylvania (0.38)
- North America > United States > West Virginia (0.28)
- North America > United States > Ohio (0.28)
- North America > United States > Kentucky (0.28)
- Geology > Geological Subdiscipline > Geomechanics (0.92)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.70)
Abstract We modeled mode I fracture in shale with an equivalent damage zone (CDM), a cohesive zone (CZM) and discontinuous enrichment functions (XFEM). In the Differential Stress Induced Damage model (DSID model) used in the continuum approach the total work input is equal to the sum of the energy released by crack debonding, the energy dissipated by crack opening, and the elastic strain energy stored in the bulk outside of the damage zone. In CZM and XFEM, the overall stiffness of the rock mass in the process zone drops as soon as the fracture starts propagating (unstable fracture propagation), whereas rock elastic properties in the CDM equivalent damage zone evolve smoothly with the displacement imposed at the boundary of the domain. In the CZM and XFEM, fracture propagation stabilizes after a turning point: this point coincides with damage initiation in the DSID model. As a result, the total energy of the rock mass calculated with CDM is about twice as large as in CZM and XFEM. The relative energy components of the rock mass are in the same order of magnitude and follow the same trends in the three models. This numerical study compares the evolution of dissipated energy potentials during mode I fracture propagation, and is expected to provide a basis to predict the amount of energy released by discrete fracture growth vs. damage propagation in the fracture process zone. Introduction In numerical codes, large-scale discontinuities such as hydraulic fractures and faults are usually modeled as separated surfaces or weakly bonded surfaces, or are represented with notch shapes at the macro-scale (Lund, 2007; Adachi et al., 2007). On the contrary, Excavation Damaged Zones are most often modeled with Continuum Damage Mechanics (CDM) models of elasto-plasticity models (Tsang et al., 2005). In Cohesive Zone Models (CZM), fractures propagate along predefined paths, and a governing law (traction-separation law) determines fracture and dissipated energy evolution. In Extended Finite Element Methods (XFEM), the propagation path is not predefined. Discontinuous enrichment functions are added to the shape functions used in standard Finite Element Methods (FEM), in order to account for the presence of fractures (Mohammadi, 2008). CZM and XFEM models are based on fracture mechanics principles: the total energy dissipated during the loading is the energy released to produce new material surfaces within the bulk of the material, and small-scale discontinuities that form the damage process zone around the fracture tip are neglected. Because the initiation and propagation of micro-cracks consume energy, neglecting their effects imply that solid stiffness degradation is neglected, which can lead to underestimating fracture propagation. At the scale of the Representative Elementary Volume, CDM allows modeling micro-crack propagation with a damage variable that is usually defined as a micro-crack density tensor. An attempt to bridge CDM and fracture mechanics was made by Mazars and Pijaudier-Cabot (1996), who assumed that the energy dissipated prior to large scale fracture instability is solely due to the degradation of elastic properties due to the propagation of micro-cracks in a localized zone, which is fully characterised by a material internal length. Mazars and Pijaudier-Cabot assumed that the internal length parameter and the energy release rate marking the transition between smeared damage propagation and discrete fracture propagation are known. This energy equivalence is impractical for the prediction of damage and fractures in shale, which is a sedimentary rock with a complex fabric that involves discontinuities at multiple scales. In this paper, we compare three numerical approaches to predict the forms of energy dissipated during mode I fracture propagation in shale. We explain how we calibrated the mechanical model parameters in the first section. The three following sections present the numerical results obtained with the CDM Differential Stress Induced Damage (DSID) model, the CZM and the XFEM, respectively. We compare the evolution of the relative energy components in the last section of the paper.
- North America > United States > Gulf of Mexico > Central GOM (0.24)
- North America > United States > North Dakota (0.15)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- North America > United States > South Dakota > Williston Basin > Bakken Shale Formation (0.99)
- North America > United States > North Dakota > Williston Basin > Bakken Shale Formation (0.99)
- North America > United States > Montana > Williston Basin > Bakken Shale Formation (0.99)