Rock Fracture Process Research Articles

Development of a 3-D Dynamic Fracture Process Analysis code to Simulate Intermediate Loading Rate

For the stimulation solutions for oil and gas wells, the creation of multiple fractures that extend deep into surrounding rock formation is important to improve productivity or injectivity. For this purpose, the application of “not too slow but not too fast dynamic loading rate (hereafter intermediate dynamic loading rate)” has been proposed in the literature, which utilizes solid propellants. While previous researchers have experimentally demonstrated their applicability, our understanding of the detailed mechanism of rock fracturing for such an intermediate dynamic loading rate has not been mature enough. We have self-developed a state-of-the-art 3D combined finite-discrete element simulator that can model the complex dynamic fracture process of rocks. This paper applied the developed code to investigate its applicability to this class of problem characterized by the intermediate dynamic loading rate. NRC (new rock cracker) based on the water vaporized pressure due to the thermit reaction of the non-explosive ingredients was used. Based on the measured pressure as an input to the developed code, the 3D dynamic fracture process analysis (DFPA) was conducted. The involving dynamic fracture process and resultant fracture pattern were discussed. In addition, the required future tasks for more reasonable numerical simulation were also pointed out.

Simulation of the fracturing process in rocks with flaws using a novel continuous-discontinuous technique

Loading induced cracks can emerge from the tips of pre-existing flaws. The overall process involves the interaction of two contacting surfaces in existing flaws, along with the initiation of wing cracks around the tip presenting the tensile failure, and the continuous crack propagation, and this continues until the final coalescence. The present study focuses on a numerical model to investigate the emergence and propagation of cracks, combined with the interaction behavior of crack internal surfaces. Moreover, a convenient and efficient approach to simulate the fracturing process of rocks from continuity to discontinuity is proposed. The numerical model is an integration of the following basic elements: cellular discretization and cellular automaton updating rule; internal interface formulation for the fracture representation; modified potential function for fracture behavior description; crack propagation algorithm; and re-meshing technique. The proposed numerical model is implemented in Cellular Automata Software for engineering Rockmass fracturing process (CASRock), after which it is verified and validated through a comparison between the simulated results and the analytical solution and experimental results.

An Experimental and Numerical Study on Acoustic Emission in the Process of Rock Damage at Different Stress Paths

The study of the damage process of rock under external loads is good guidance for geotechnical construction design. The differences in rock damage processes and damage modes under different stress paths are rarely reported. To explore the effects of stress paths on rock damage processes, uniaxial compression experiments under three stress paths were conducted. Numerical simulation is also used to simulate the rock acoustic emission (AE) and fracture process. The results of the study indicate that the maximum acoustic emission events are at the peak of stress, and fractures are mainly formed at this stage. The peak of AE energy occurs before the peak of AE events. The damage pattern and fragmentation size of the rock are related to the way the stresses are loaded. It is noticed that there is appearance of a quiet period of AE events prior to the production of significant cracks. Minor damage to the rock is accompanied by the generation of bright white spots in the specimen, which is due to the high tensile or shear stress in the units. When the stress in these units exceeds their strength, the units break down and tiny cracks appear. As the external load increased, the cracks developed and penetrated, and the specimen was damaged. Under cyclic loading and unloading, the number of AE events increased significantly compared with the controlled displacement and controlled stress loading methods, and the radius of the AE circle became larger and the energy also increased, which indicates a greater degree of destruction of the rock under cyclic loading and unloading. The results of the study are of reference significance for rock crack propagation and fracture mode influenced by stress conditions and provide some guidance for construction design under different working conditions.

Experimental and Numerical Analysis of Mode I Fracture Process of Rock by Semi-Circular Bend Specimen

The semi-circular bend (SCB) specimen is widely used to measure fracture toughness of brittle materials such as rock. In this work, the stress field, fracture process zone (FPZ), and crack propagation velocity of SCB specimen are analyzed during the fracture process of rock specimens. The FPZ of specimen is obtained by experimental and numerical methods under a three-point bend test. The stress concentration zones of specimen present a heart shape at peak load points. FPZ forms before macro fracture occurs. The macro fracture form inside FPZ in a post-peak region of a load–displacement curve. The crack propagation process of specimen include two stages, namely the rapid crack initial development stage, and the final crack splitting stage. The maximum crack propagation velocity of specimen is about 267 m/s, and the average crack propagation velocity is about 111 m/s.

Comparison between typical numerical models for fluid flow and heat transfer through single rock fractures

Numerical models can explicitly characterize fluid flow and heat transfer processes in rock fractures including randomly distributed asperities and contacts and have been widely used to understand the behaviors of fluid flow and heat transfer in fractured rocks. The differences between three-dimensional and two-dimensional numerical models for single rock fractures were compared in terms of fluid flow and heat transfer behaviors and properties. Both the artificial fractures created by Brazilian tension method and the hypothetical fractures created by duplicating a fracture surface were considered. The results showed that hypothetical fractures and two-dimensional models cannot capture the channeling flow and the non-uniform thermal fronts in artificial fractures, but two-dimensional models can predict the similar streamlines and thermal fronts as hypothetical fractures. The relationship between heat transfer coefficient and flow rate in a single rock fracture can be described by a logarithmic function, and the heat transfer coefficients of two-dimensional and three-dimensional models can be well correlated by an empirical function of fracture surface areas. The comparison between three-dimensional and quasi-three-dimensional models of artificial fractures is also conducted. Both channeling flow and non-uniform thermal fronts from quasi-three-dimensional models became similar to the results of three-dimensional models with increasing numbers of computational elements.

Fracture analysis of rock reconstruction models based on cooling–solidification annealing algorithms

AbstractDue to the heterogeneity and opacity of rocks, it is difficult to visualize the progressive failure process of rock. A novel cooling–solidification annealing algorithm combined with X‐ray computed tomography technology is proposed to study the mechanical behavior (including fracture behavior) of rocks. In this algorithm, the system is annealed in descending order by scale and is constrained by the current scale. Moreover, the gray phase is introduced into the ordinary two‐phase reconstruction system to form a new three‐phase system. The numerical results show that the proposed method can successfully generate a rock model that is statistically equal to natural rock. The analysis of the rock fracture process shows that the initial internal pores and cracks have an important influence on the cracking evolution and failure mode of rock. The proposed method provides a promising means for understanding the mechanical behavior (including fracture behavior) of rocks.

Retaining primary wall roughness for flow in rock fractures and implications on heat transfer and solute transport

Wall roughness is often found to have evident influences on flow-related processes in rock fractures. In this work, we first define the primary wall roughness to have dominating effects on the overall flow, whereas the secondary roughness only generates additional flow resistance and have insignificant impacts on the bulk flow. Accordingly, an effective procedure is presented to quantitatively identify primary and secondary roughness, and the validity of the procedure is tested with flow simulations in a two-dimensional rough fracture. The results show that the reconstructed fracture with only primary roughness can still well resemble the general flow behavior in the original fracture with a steady transmissivity increment of 5% for the Reynolds number from 0.01 to 100. We further examine the effects of both primary and secondary roughness on processes associated with heat transfer and solute transport in fracture flow. It is found that the heat transfer and solute transport behaviors are closely related to the flow behavior under the effect of wall roughness. As the flow velocity increases to cause strong flow inertia, larger eddies can occur to affect the heat transfer and solute transport processes. Although the presence of secondary roughness shows limited effects on the overall transport behaviors, secondary roughness is found to give rise to more irregularly-shaped eddies, which result in different local behaviors. The findings in this study can provide new insights into the roughness effect on fracture flow and associated processes. In addition, the roughness quantification presents a straight-forward evaluation of potential deviations when neglecting small-scale secondary roughness, as is often needed when analyzing larger-scale problems.

Hybrid finite–discrete element modelling of rock fracture process in intact and notched Brazilian disc tests

A hybrid finite–discrete element method is proposed to model the rock fracture behaviour under various loading rates. Three fracture models are proposed to predict the fracture initiation and propagation for modelling the transition from continuum to discontinuum. The modelling transition from continuum to discontinuum makes the hybrid method superior to the traditional continuum-based finite element method and discontinuum-based discrete element method. Moreover, the hybrid method considers the effect of the loading rate by implementing an empirical relationship between the static strengths and the dynamic strengths derived from the dynamic rock fracture experiments. Then, the Brazilian tensile strength tests are modelled to calibrate the proposed method under various loading rate, and demonstrate its ability in modelling the dynamic rock behaviours. The Notched Brazilian Disc tests are modelled to illustrate the capabilities of the proposed method in modelling different fracture modes. The hybrid finite element method has well modelled the stress propagation, fracture initiation and propagation, even the pure mode I, pure mode II and mixed-mode I–II fractures. It is concluded that the hybrid finite element method is superior to the continuum-based finite element method and discontinuum-based discrete element method in modelling the fracture behaviours of rock under various loading rates.

Mechanism study of preventing crack propagation of fractured rockunder dynamic loads

To deeply understanding dynamic fracture properties and preventing crack propagation of fractured rock mass under dynamic loads, impact experiments were conducted using TWSRC (tunnel with single radial crack) samples, and sandstone were selected as the raw material to manufacture fractured rock samples. The crack initiation, propagation and obstructing behavior were measured by using a drop hammer impact test device and crack propagation gauge measuring system. The mechanism of preventing crack propagation and failure behavior during dynamic fracturing process was focused, and then the corresponding numerical simulation was conducted by using the finite difference code, which can be used to accurately estimate the experiment result. The results indicate that the whole dynamic fracturing process of fractured rock under dynamic loads is composed of the cyclic process of crack initiation, high-speed crack propagation, slowly deceleration, preventing crack propagation. In addition, the period of crack obstruction was approximate the microsecond level. The ratio of transgranular (TG) fracture at the crack obstruction point of fractured rock was smaller than that of the crack initiation point, and the ratio of TG fracture of green sandstone during the dynamic fracturing process was larger than that of black sandstone. The fracture energy for crack initiation again after crack obstruction was much less than the fracture energy required for the initial initiation of pre-existing crack.

Mechanical response and energy dissipation characteristics of granite under low velocity cyclic impact

In the process of metal ore blasting mining, the surrounding rock in the middle and far area will still be affected by the stress wave generated by the explosion, resulting in the damage and strength reduction of surrounding rock. The fracture process of rock under cyclic impact load is a process of energy absorption and dissipation. The research on the mechanical properties and energy dissipation law of surrounding rock under low velocity cyclic impact has a good reference for the research on the damage law of rock under weak impact environment. In this paper, the granite samples collected from Sanshandao Gold Mine in Laizhou City, Shandong Province were subjected to cyclic impact tests by using a 50 mm diameter split Hopkinson pressure bar (SHPB) test device. The stress-strain evolution law and energy dissipation law of the specimen in the process of damage and fracture are mainly studied. The results show that the dynamic process of a large number of void defects (such as voids, dislocations, microcracks, etc.) in granite under cyclic impact load is strengthened, and the damaged core is formed and propagated, leading to tensile fracture; With the accumulation of strain energy, the damage situation intensifies, and then affects the stress propagation, so that the ratio of incident energy to reflected energy increases linearly with the accumulation of strain energy, and the ratio of transmitted energy also decreases linearly.

Modelling Rock Fracture Induced By Hydraulic Pulses

Soft cyclic hydraulic fracturing has become an effective technology used in subsurface energy extraction which utilises cyclic hydraulic flow pressure to fracture rock. This new technique induces fatigue of rock to reduce the breakdown pressure and potentially the associated risk of seismicity. To control the fracturing process and achieve desirable fracture networks for enhanced permeability, the rock response under cyclic hydraulic stimulation needs to be understood. However, the mechanism for cyclic stimulation-induced fatigue of rock is rather unclear and to date there is no implementation of fatigue degradation in modelling the rock response under hydraulic cyclic loading. This makes accurate prediction of rock fracture under cyclic hydraulic pressure impossible. This paper develops a numerical method to model rock fracture induced by hydraulic pulses with consideration of rock fatigue. The fatigue degradation is based on S–N curves (S for cyclic stress and N for cycles to failure) and implemented into the constitutive relationship for fracture of rock using in-house FORTRAN scripts and ABAQUS solver. The cohesive crack model is used to simulate discrete crack propagation in the rock which is coupled with hydraulic flow and pore pressure capability. The developed numerical model is validated via experimental results of pulsating hydraulic fracturing of the rock. The effects of flow rate and frequency of cyclic injection on borehole pressure development are investigated. A new loading strategy for pulsating hydraulic fracturing is proposed. It has been found that hydraulic pulses can reduce the breakdown pressure of rock by 10–18% upon 10–4000 cycles. Using the new loading strategy, a slow and steady rock fracture process is obtained while the failure pressure is reduced.

A novel true triaxial test system for microwave-induced fracturing of hard rocks

This study introduces a test system for microwave-induced fracturing of hard rocks under true triaxial stress. The test system comprises a true triaxial stress loading system, an open-ended microwave-induced fracturing system, a data acquisition system, an acoustic emission (AE) monitoring system, and an auxiliary specimen loading system. Microwave-induced surface and borehole fracturing tests under true triaxial stress were fulfilled for the first time, which overcomes the problem of microwave leakage in the coupling loading of true triaxial stress and microwave. By developing the dynamic monitoring system, the thermal response and fracture evolution were obtained during microwave irradiation. The monitoring system includes the infrared thermometry technique for monitoring rock surface temperature, the distributed optic fiber sensing technique for monitoring temperature in borehole in rock, the AE technique and two-dimensional digital speckle correlation technique for monitoring the evolution of thermal damage and the rock fracturing process. To validate the advantages of the test system and investigate the characteristics of microwave-induced fracturing of hard rocks, the study demonstrates the experimental methods and results for microwave-induced surface and borehole fracturing under true triaxial stress. The results show that thermal cracking presented intermittent characteristics (calm–active–calm) during microwave-induced surface and borehole fracturing of basalt. In addition, true triaxial stress can inhibit the development and distribution of thermal cracks during microwave-induced surface fracturing. When microwave-induced borehole fracturing occurs, it promotes the distribution of thermal cracks in rock, but inhibits the width of cracks. The results also prove the reliability of the test system.

Simulation of the rock meso-fracturing process adopting local multiscale high-resolution modeling

The continuum mesoscopic model-based methods are popular in rock fracturing process simulation, because of their powerful trans-scale failure characterization capability. However, for high-resolution characterization of cracks, large-scale global uniform meso-scale elements may lead to serious computational time-space burden. This study is aimed at developing a local multiscale high-resolution modeling (LMHM) strategy, which adopts a high-resolution mesh only in the region of interest instead of a global uniform mesoscopic mesh. Then, based on the statistical meso-damage mechanical method (SMDMM), the meso-fracturing process simulation of rock is achieved. The simulation results of several numerical examples show that the advantages of LMHM are that it can save a lot of computational cost, and avoid calculation waste effectively in treating local fracturing of rock. The simulated failure patterns adopting LMHM are consistent with those of global uniform mesh modeling and physical tests. Meanwhile, the local high-precision stress field of the model can be obtained. It is shown that combination of the SMDMM and LMHM presented in this study is an efficient strategy for modeling the trans-scale progressive failure process of rock.

Accurate moment tensor inversion of acoustic emissions and its application to Brazilian splitting test

The efficiency of three inversions for accurate moment tensors: (1) the standard least-squares inversion, (2) the weighted least-squares inversion, and (3) the shear-tensile-compressive (STC) source inversion, is tested on acoustic emissions (AEs) produced during the Brazilian splitting test. A comparison of plots of the P/T axes of the focal mechanisms reveals that the double-couple part of the moment tensors is well constrained for all three inversions. By contrast, diamond source-type plots show that the non-double-couple components of the retrieved moment tensors are more sensitive to errors due to neglecting inhomogeneities and anisotropy in the rock sample, near-field terms and other wave phenomena effects. The weighted inversion and the STC inversion work better than the standard least-squares method and yield less scattered results. If moment tensors of AEs contain significant non-double-couple components of moment tensors produced by non-shear fracturing, the STC inversion proved to be most accurate. The retrieved moment tensors are well consistent with the expected fracture mechanism of AEs in the Brazilian splitting specimen and provide a further guidance for studying rock fracture processes.

Mechanical responses and fracture mechanism of rock with different free surfaces under the chisel pick cutting

With the increasing demand of the shipping infrastructure projects such as ports and waterways, it is urgent to improve the rock cutting ability and applicable range of trailing suction hopper dredgers. A rock breaking method using free surfaces to assist the draghead is proposed. Verified by experimental results, a series of numerical investigations were carried out to analyze the rock fracturing and cutting process. The rock cutting model by single chisel pick is developed using the LS-DYNA with a rock damage constitutive model, and the results are consistent well with the experimental data. The results show that the cutting force fluctuates with time, the large periodic fluctuations indicate the formation of large chips, and the short fluctuation period means the formation of small fragments. Moreover, with the assistance of free surface, the rock is not limited by the sidewall friction, and the cracks of rock are more likely to expand forward, thereby forming larger chips. Besides, it is found that the slit position and size play important roles in the rock fracture process. Based on all cutting performance parameters, the optimal slit position range is 25–35 mm, the optimal slit depth is 10 mm, which is half of the cutting depth, and the reasonable range of slit width should be 2–5 mm. Finally, a novel saw blades and chisel pick combined cutting method for rock is designed for further engineering application.

Fractures: Tension and Shear

The paper applies the observation cycle to rock fracturing processes. Specifically, it repeats the observation cycle by going from the large (field) scale to increasingly detailed laboratory scales. With this, it is possible to determine that what appear to be tensile or shear fractures on the large scale are produced through a combination of tensile and shear mechanisms on the smaller scale. This involves observations with a variety of techniques that are briefly described. What is also emphasized is that observation has to go hand in hand with abstraction, i.e., modeling to help understand the observed phenomena. The paper, therefore, makes two contributions—a better understanding of rock fracturing processes and showing the importance of the observation cycle in a scientific process.

Temporal evolution of a shear-type rock fracture process zone (FPZ) along continuous, sequential and spontaneously well-separated laboratory instabilities—from intact rock to thick gouged fault

SUMMARY The development of shear-type fault analogues from intact rock at the laboratory scale provides a unique opportunity for investigating tectonic-scale phenomena through the lens of geophysics. The transition from rock fracture creation to laboratory fault slip must exist. We observe three spontaneously temporally well-separated mechanical instabilities attributed to the continuous evolution of a shear-type rock fracture between two artificial flaws. Their separation is validated with rapid mechanical stress drops and stabilizations, periodical acoustic emission (AE) behaviours (AE event number and AE moment release rate) and b-value drops. One instability occurs near the stress peak and corresponds to fracture incipience where fault development is mostly identified via optical observations; the other two instabilities are in the post-stress-peak domain and correspond to the fault nucleation and slip stages, respectively, with distinguishable AE releases from the fault region. The macroscale fracture has been created at the moment of rapid-stress drop for the second instability; off-fault damage, increasing gouge powder generation and slip acceleration can be identified within the fault slip stage. AE behaviour throughout fault nucleation shows a reversal of the Omori–Utsu (O–U) law. AEs attributed to the fault slip display regular O–U law decay and the distinction between the AE behaviour for fault nucleation and fault slip is pronounced. These observations and analyses can provide further understanding on the analogue relationship between a laboratory loading-induced fault and a natural fault.

Do intraplate and plate boundary fault systems evolve in a similar way with repeated slip events?

As repeated slip events occur on a fault, energy is partly dissipated through rock fracturing and frictional processes in the fault zone and partly radiated to the surface as seismic energy. Numerous field studies have shown that the core of intraplate faults is wider on average with increasing total displacement (and hence slip events). In this study we compile data on the fault core thickness, total displacement and internal structure (e.g., fault core composition, host rock juxtaposition, slip direction, fault type, and/or the number of fault core strands) of plate boundary faults to compare to intraplate faults (within the interior of tectonic plates). Fault core thickness data show that plate boundary faults are anomalously narrow by comparison to intraplate faults and that they remain narrow regardless of how much total displacement they have experienced or the local structure of the fault. By examining the scaling relations between seismic moment, average displacement and surface rupture length for plate boundary and intraplate fault ruptures, we find that for a given value of displacement in an individual earthquake, plate boundary fault earthquakes typically have a greater seismic moment (and hence earthquake magnitude) than intraplate events. We infer that narrow plate boundary faults do not process intact rock as much during seismic events as intraplate faults. Thus, plate boundary faults dissipate less energy than intraplate faults during earthquakes meaning that for a given value of average displacement, more energy is radiated to the surface manifested as higher magnitude earthquakes. By contrast, intraplate faults dissipate more energy and get wider as fault slip increases, generating complex zones of damage in the surrounding rock and propagating through linkage with neighbouring structures. The more complex the fault geometry, the more energy has to be consumed at depth during an earthquake and the less energy reaches the surface.

Modelling of dynamic rock fracture process using the finite-discrete element method with a novel and efficient contact activation scheme

Within the framework of combined finite-discrete element method (FDEM), we propose a novel and efficient semi-adaptive contact activation approach (semi-ACAA). The semi-ACAA adaptively activates contact calculations for continuum solid elements around the cohesive element which has just been subjected to shear softening while its softening function has just satisfied a prescribed threshold. The semi-ACAA is implemented in a three-dimensional (3D) FDEM code parallelized based on general-purpose graphic processing units (GPGPU) to model dynamic fracture processes of marbles in dynamic Brazilian tensile strength (BTS) and uniaxial compressive strength (UCS) tests. The semi-ACAA not only overcomes spurious fracturing mode associated with FDEM simulations using ACAA but also is more physically sound and computationally efficient compared with brute-force contact activation approach (BCAA), which has been prevalent in FDEMs with intrinsic cohesive zone model (ICZM)-based cohesive elements. Furthermore, it is proven that the spurious fracturing mode is caused by unphysical movements of mesh due to missing contacts during the shear softening of cohesive elements instead of the sudden activation of contact force calculations as indicated in some literature. Finally, a series of simulations of the dynamic BTS and UCS tests conducted by split Hopkinson pressure bar (SHPB) facility reveals that, if the threshold is set to around unity, not only the spurious fracturing mode can be overcome but also the modelling precision of stress waves in intact rocks can be improved. The speed-up times of semi-ACAA compared with BCAA are between 1.23 and 13.5 depending on the intensity of shear cracking in the simulations including mixed-mode cracking. Since the proposed semi-ACAA is simple and can be easily implemented into any FDEM codes with ICZM-based cohesive elements, it is expected to accelerate future developments and applications of FDEM with ICZM-based cohesive elements in rock dynamics such as drilling and blasting.

Using the characteristics of infrared radiation b-value during the rock fracture process to offer a precursor for serious failure

The Infrared Radiation (IR) on the surface of a rock being loaded will change significantly during its failure process. To effectively monitor and predict rock failure by the IR method, in this paper, the Infrared Radiation Variation Temperature Field (IRVTF) of rock under uniaxial compression was identified. It was found that some IRVTF thermal images were characterized by obvious temperature rise in the later stage of rock loading. The temperature distribution characteristics of IRVTF were analyzed. It was observed that the temperature of the IRVTF exhibited the logarithmic linear distribution within the selected statistical temperature range, with an average coefficient of correlation greater than 0.96. On this basis, the index of “Infrared Radiation b-value (bIR-value)” of rock under uniaxial compression was defined for the first time, and the threshold for identifying its sudden change was proposed. It was found that the sudden changes of bIR-value could be observed with the generation of large-scale micro-cracks. The average amplitude of the bIR-value at first sudden change for all samples was 16.58 times of the mean amplitude before the sudden change on average, which indicated the significance of the bIR-value sudden change. The first sudden change of the bIR-value was 22.5 s ahead of the peak stress on average, which could be used as a precursor of rock failure and instability. The findings of the research can help with the monitoring and early warning of surrounding rock instability in mines, tunnels, and other geotechnical projects.