Flaws In Rock Research Articles

Numerical modeling of crack propagation from open and closed flaws in rock

The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (KII) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of KII can be effectively eliminated when the non-singular stress (T-stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T-stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions.

Mechanical behaviors and failure mechanism of flawed sandstone containing infillings under freeze-thaw cycles and uniaxial compression

The flawed rock masses with joints, fissures, and other defects in cold regions engineering are affected by freeze–thaw (F-T) cycles. Substantial efforts have been focused on the mechanical properties and failure characteristics of flawed rock masses under F-T cycles. However, only a few laboratory tests have considered the effect of fillers in the rock flaws under F-T cycles. In the present work, F-T cycling and uniaxial compression tests are conducted on intact sandstone, flawed sandstone containing infillings, and flawed sandstone without infillings to further investigate the effects of fillers and the number of F-T cycles on the mechanical behaviors and failure mechanism of flawed sandstone containing infillings. The experimental results indicate that filling the flaws can effectively inhibit mass loss and pore growth of flawed sandstone specimens in the early stages of F-T cycles. Fillers can effectively reduce the stress concentration at the flaws and improve the strength of flawed specimens. In the early stages of F-T cycles, crack propagation caused by uneven stress and deformation at the flaws leads to the failure of the specimen. As the number of F-T cycles increases, the peak stresses of the specimens are gradually decreased, and the reduction of the cementation strength between rock particles causes particle loss and cracking failure in the specimens. The failure characteristics of flawed specimens containing infillings are significantly different from those of other two types of specimens. Based on the test phenomena, a deterioration failure mode for F-T failure of flawed specimens containing infillings is proposed.

Experimental study of crack evolution in prefabricated double-fissure red sandstone based on acoustic emission location

The development of micro-cracks during damage to rocks affects the propagation of macroscopic cracks on the surface. To explore the crack evolution among pre-existing flaws in rocks, based on the acoustic emission (AE) source location results, the paper analysed the influences of micro-crack development on failure mode. By analyzing AE characteristic parameters, the main controlling factors affecting the development of micro-fractures are determined. The results show that: (1) the development of micro-cracks in rock samples presents a trend of having a high-energy fracture point, the low-energy and small fracture region, the extensive fracture region, and a macroscopic fracture zone. (2) The difference in rock failure mode arises from the influence of rock bridge on the number, location, and extension direction of high-energy fractures, which results in the difference in the formation of main damage zone in rock samples. (3) The total number of micro-cracks, the proportion of shear cracks, and mixed-mode cracks gradually increase with the increase of the rock bridge inclination angle, leading to the gradual evolution of rock samples from simple tensile failure mode to complex crack penetration mode. The variation of the rock bridge inclination angle affects the stress direction of the rock particles at a microscopic level, while it affects the direction of macroscopic crack propagation at a macroscopic level.

Simulating three dimensional hydraulic fracture propagation using displacement correlation method

The TOUGH-FEMM simulator is used to investigate the interaction of multiple simultaneous hydraulic fractures. In TOUGH-FEMM simulator, rock deformation is modeled using the hybrid Finite Element-Meshfree Method (FEMM) and fluid flow is simulated through the Transport Of Unsaturated Groundwater and Heat (TOUGH2) simulator. The stress intensity factors are calculated by using the Displacement Correlation Method (DCM). The equivalent mode I stress intensity factor is used for determining fracture propagation criterion and direction. Successfully creating multiple hydraulic fractures in horizontal wells is critical for unconventional gas production economically. These previous works focussed on the propagation of fractures which are parallel initially. However, because of inevitable error in practical engineering and natural flaws in rock, the initial fractures might be inclined. The overall objective of the current work is to study the influence of initial fracture orientation on the simultaneous hydraulic fracturing of a horizontal well. The results of the present work show that initial fracture orientation has significant effect on the fracture propagation direction and final fracture contour. Different fracture contours will result in distinct fracture network, which will greatly affect the reservoir permeability.

A Study on Crack Initiation and Propagation in Rock with Pre-existing Flaw Under Uniaxial Compression

A study for crack initiation and propagation in rock with a pre-existing flaw is carried under uniaxial compression. The aim is to understand the influence of crack initiation stress and peak stress for narrow flaws in rock by conducting laboratory experiments and subsequent numerical simulations. Specimens are prepared using Gypsum material with the incorporation of flaws at varying flaw angles from 15° to 75° having three different strengths. The results of the crack initiation and peak stresses for different flaw angles along with crack growth patterns are observed. Numerical simulations using ABAQUS adopting extended finite element and cohesive zone model is attempted to capture the crack initiation and propagation in rock specimens. For closed crack condition, the numerical model considers frictional behaviour across the flaw surface and model could capture the crack initiation and peak stresses along with propagated crack patterns irrespective of the material strengths. Both laboratory and numerical studies reveal that the crack initiation stress and peak stress gets initiated sooner for the flaw having 45° when compared to all other angles which are in contrast to open flaw conditions. Also at this angle, a stable curvilinear wing cracks are observed irrespective of the material strengths. In laboratory experiments, pre-dominant wing cracks are observed for a material having high strengths that influence the final pattern in specimens while in numerical analysis, all the specimens shows clear visible wing crack propagation and leads to failure of the material.

Effect of Hydraulic Pressure and Tectonic Stress on Fracture Initiation in Rock Flaws

This study examines the effects of hydraulic pressure and tectonic stress on fracture initiation in rock flaws by using the finite element method. A square domain with double flaws is analyzed under vertical load, different horizontal loads (modeling tectonic stresses), and various hydraulic pressures.

Fracture evolution and failure behaviour of marble specimens containing rectangular cavities under uniaxial loading

To analyse the fracture coalescence behaviour around hole-like flaws in rock, rectangular cuboid marble specimens containing a single rectangular cavity or two rectangular cavities with different layouts were tested under uniaxial compression. Failure characteristics of specimens and strain concentration regime (SCR) evolution on specimen surfaces were measured by means of acoustic emission (AE) and digital image correlation (DIC) techniques respectively. Numerical simulations were further conducted on specimens with the same specimen and cavity dimensions using the discrete element method (DEM), and the inclination angle between centroids of two cavities with respect to the horizontal direction was varied to investigate its influence on failure modes and mechanical properties of specimens. Results showed that both cavity number and layout have a significant influence on mechanical behaviour of marble specimens. The existence of two cavities leads to more degradation of mechanical properties than a single cavity. For specimens with two cavities, the strength first decreases and subsequently increases with increasing inclination angle, and the specimen with two vertically aligned cavities has the maximum strength. Four failure modes were observed in specimens, namely splitting failure, shear failure, mixed tensile/shear failure, and surface spalling. In addition, absorbed energy per unit volume e was introduced to characterise the fragmentation of different groups of specimens. Specimens containing cavities absorbed less energy per unit volume, and thus were less fragmented after failure.

Numerical simulation of propagation and coalescence of flaws in rock materials under compressive loads using the extended non-ordinary state-based peridynamics

The maximum tensile stress criterion and the Mohr-Coulomb criterion are incorporated into the extended non-ordinary state-based peridynamics (NOSB-PD) to simulate the initiation, propagation and coalescence of the pre-existing flaws in rocks subjected to compressive loads. Wing cracks, oblique secondary cracks, quasi-coplanar secondary cracks and anti-wing cracks can be modeled and distinguished using the proposed numerical method. In the present study, a four-point beam in bending with two notches as a benchmark example is firstly conducted to verify the ability, accuracy and numerical convergence of the proposed numerical method. Then, the numerical samples of rock materials containing the one single pre-existing flaw with various lengths under uniaxial compression are modeled. Four significant factors, i.e. the axial stress versus axial strain curves, the peak strength, the ultimate failure mode and crack coalescence process, are obtained from the present numerical simulation. The effect of the flaw length on the propagation of cracks is investigated. Next, sandstone samples containing three pre-existing flaws with different ligament angles under uniaxial compression are also simulated. The effect of ligament angle on the propagation and coalescence of cracks is studied. Finally, rock-like samples containing two parallel pre-existing flaws subjected to biaxial compressive loads with confining stresses of 2.5, 5.0, 7.5 and 10.0MPa are simulated. The effect of the confining stresses on the initiation, propagation and coalescence of flaws is investigated. The present numerical results are in good agreement with the previous experimental ones.

Influence of crack surface friction on crack initiation and propagation: A numerical investigation based on extended finite element method

Rock strengths are directly influenced by the open or closed flaws widely distributed in rock masses. Extensive studies have been conducted on the propagations of open flaws in rocks. However, few concerns are paid on the propagation of closed flaws, the influence of the surface friction on the initiation and propagation of closed flaws should be investigated systematically. In present article, the crack initiation and propagation in rock like material subjected to compressive loads have been investigated. The effects of crack surface friction on crack initiation and propagation have been quantified with the help from extended finite element method which is efficient and accurate. Based on the analysis on stress distribution and propagation patterns, following results are obtained: Firstly, minor effects are exerted by crack surface friction on the stress distribution around the flaws when the flaws inclination angle is 30° and 45°. However, as the inclination angle increases to 60°, the effects are much more significant. Secondly, as the inclination angle ranges from 30° to 60°, the most favorable angle for crack propagation is 45°. Thirdly, the initiation location and angle of the wing cracks will not be influenced by the frictions. However, the propagation length will be greatly influenced by the friction and the inclination angle.

Numerical Study on Coalescence of Pre-Existing Flaw Pairs in Rock-Like Material

The present numerical study, which is an extension of our previous numerical analysis on cracking processes of a single pre-existing flaw, focuses on the coalescence of two pre-existing parallel open flaws in rock subjected to a uniaxial compressive loading. To facilitate a systematic investigation, the arrangements of the flaw pair are classified into 11 categories. Simulations engaging AUTODYN are conducted on each category. The numerical results are compared with some published physical experimental test results. Eleven typical coalescence patterns are obtained, which are in good agreement with the experimental results, which include two coalescence patterns obtained in flaw pair arrangements (II) and (VIII″) not being reported in previous studies. The information gathered in the simulations helps identify the type (tensile/shear) of each crack segment involved in the coalescence. Most of the coalescence cracks initiate at or around the flaw tips, except those in flaw pair arrangements (II) and (IX′) with a very short ligament length, in which the coalescence cracks initiate on the flaw surfaces away from the flaw tip regions. Based on the numerical simulation results, the properties of the 11 coalescence patterns are obtained. Except those in flaw pair arrangements (II) and (IX′), the other coalescence patterns can be interpreted with respect to the basic crack types—tensile wing crack, horsetail crack and anti-wing crack. In addition, based on the type of crack segments involved in coalescence, namely tensile and shear, the coalescence can be classified into T mode (tensile mode), S mode (shear mode) and TS mode (mixed tensile–shear mode).

Numerical study on coalescence of two pre-existing coplanar flaws in rock

Crack propagation and coalescence processes are the fundamental mechanisms leading to progressive failure processes in rock masses, in which parallel non-persistent rock joints are commonly involved. The coalescence behavior of the latter, which are represented as pre-existing coplanar flaws (cracks), is numerically investigated in the present study. By using AUTODYN as the numerical tool, the present study systematically simulates the coalescence of two pre-existing coplanar flaws in rock under compression. The cumulative damage failure criterion is adopted in the numerical models to simulate the cumulative damage process in the crack initiation and propagation. The crack types (shear or tensile) are identified by analyzing the mechanics information associated with the crack initiation and propagation processes. The simulation results, which are generally in a good accordance with physical experimental results, indicate that the ligament length and the flaw inclination angle have a great influence on the coalescence pattern. The coalescence pattern is relatively simple for the flaw arrangements with a short ligament length, which becomes more complicated for those with a long ligament length. The coalescence trajectory is composed of shear cracks only when the flaw inclination angle is small (such as β⩽30°). When the pre-existing flaws are steep (such as β⩾75°), the coalescence trajectory is composed of tensile cracks as well as shear cracks. When the inclination angle is close to the failure angle of the corresponding intact rock material, and the ligament length is not long (such as L⩽2a), the direct shear coalescence is the more favorable coalescence pattern. In the special case that the two pre-existing flaws are vertical, the model will have a direct tensile coalescence pattern when the ligament length is short (L⩽a), while the coalescence between the two inner flaw tips is not easy to achieve if the ligament length is long (L⩾2a).

Shock Events in the Solar System: The Message from Minerals in Terrestrial Planets and Asteroids

Impacts are central to the origin and evolution of planets of the Solar System. The shapes of craters, which can reach up to 1,000 km in diameter on the Moon, provide critical information on the large-scale dynamics of the impact and related shock. Minerals formed at high pressure and temperature found in shocked terrestrial rocks and meteorites give additional and complementary insights on the shock process at a smaller scale, typically from a few micrometers to a few millimeters. Local flaws in rocks, such as voids and mineral interfaces, are the preferential sites for the formation of high-pressure melts and minerals. Calculations based on the physics of shocks and the thermodynamics and kinetics of mineral transformations provide orders of magnitude for the duration, transient pressure, and prevailing temperature conditions of shock events. Case studies on shocked terrestrial and extraterrestrial materials illustrate the links between these parameters and impact duration. Many of the high-pressure mineral phases of olivine, pyroxenes, feldspars, silica, phosphates, titanium oxide, and carbon have been discovered in these heavily shocked rocks and provide unique opportunities to study the high-pressure minerals that exist in the deep Earth.

Influence of flaws on joint spacing and saturation: Results of one‐dimensional mechanical modeling

In bedded sedimentary or mechanically anisotropic rocks, joints often occur in laterally persistent, parallel sets with distinctive spacing attributes. Three of those attributes include a positively skewed distribution of joint spacings, a positive correlation between median spacing and mechanical layer thickness, and the tendency for rocks to appear saturated with joints and to show a ratio of layer thickness to median joint spacing near one. We identify total applied strain, mechanical interaction, joint propagation velocity, and flaws as key variables in the progressive jointing process, and we use a one‐dimensional model of mechanically interacting joints to characterize the specific influence on joint spacing, of the number, sizes, and size distributions of flaws in rock. For a given flaw size distribution, the mode flaw size has no effect on spacing distribution shape, median spacing, or saturation. Layers with fewer flaws approach saturation more slowly and reach it with fewer joints and larger median joint spacing. The joint spacing distributions in these layers have variance and skewness that may be 1–3 orders of magnitude larger than in layers with greater numbers of flaws. Flaw size range affects the rate at which a jointing layer approaches saturation but not the number of joints at saturation. Resulting spacing distributions are similar, although narrow flaw size ranges tend to promote greater numbers of closely spaced joints. The skewness of a flaw size distribution affects the rate at which layers approach saturation, as well as the shape of the resulting joint spacing distribution at saturation. Negatively skewed flaw size distributions promote close joint spacing and create spacing distributions with greater variance and skewness.