Stability Of Rock Engineering Research Articles

Cracking evolution and failure mechanism of brittle rocks containing pre-existing flaws under compression-dominating stresses: Insight from numerical approach

Comprehending the cracking evolution and failure mechanism of flawed rocks under compression-dominating stresses is essential to evaluating the stability of rock engineering. In this work, a newly developed geometry-constraint-based non-ordinary state-based peridynamic (GC-NOSBPD) theory that can eliminate the numerical oscillation is applied to predict the development of new cracks of flawed rocks under compression-dominating stresses. The failure of bonds between particles is judged by the bond-associated stress-based fracture criteria. The cracking evolution trajectories of semi-disc and disc specimens containing flaws are traced. The effects of flaw inclination angle on the cracking trajectories are analyzed. The cracking evolution paths of rock-like specimens with two flaws under uniaxial and biaxial compression are molded. The effects of confining stress on the growth of new cracks are investigated. The confining stress restrains the propagation of tensile cracks, but it is easy to promote the growth of shear cracks. The concentration and transfer effects of stress can plainly revel the failure mechanism of flawed rocks. The present numerical method is reasonable to predict the tensile and shear failure modes of flawed specimens under compression-dominating stresses.

A knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes

Accurate identification and effective support of key blocks are crucial for ensuring the stability and safety of rock slopes. The number of structural planes and rock blocks were reduced in previous studies. This impairs the ability to characterize complex rock slopes accurately and inhibits the identification of key blocks. In this paper, a knowledge-data dually driven paradigm for accurate identification of key blocks in complex rock slopes is proposed. Our basic idea is to integrate key block theory into data-driven models based on finely characterizing structural features to identify key blocks in complex rock slopes accurately. The proposed novel paradigm consists of (1) representing rock slopes as graph-structured data based on complex systems theory, (2) identifying key nodes in the graph-structured data using graph deep learning, and (3) mapping the key nodes of graph-structured data to corresponding key blocks in the rock slope. Verification experiments and real-case applications are conducted by the proposed method. The verification results demonstrate excellent model performance, strong generalization capability, and effective classification results. Moreover, the real case application is conducted on the northern slope of the Yanqianshan Iron Mine. The results show that the proposed method can accurately identify key blocks in complex rock slopes, which can provide a decision-making basis and rational recommendations for effective support and instability prevention of rock slopes, thereby ensuring the stability of rock engineering and the safety of life and property.

Study on crack propagation characteristics of rocks with different lateral pressure based on joint monitoring of DIC and AE

During the process of rock failure, the characteristics of crack propagation affect the fracture characteristics and macroscopic mechanical behavior of rocks, indirectly affecting the safety and stability of rock engineering. In order to study the evolution characteristics of cracks during rock failure under different lateral pressure, based on an improved digital image correlation (DIC) and acoustic emission (AE) signal recognition method, a visual biaxial servo loading device was developed to conduct biaxial compression tests on mudstone with prefabricated cracks of the same inclination angle. The research results indicate that the stages of crack propagation include microcracks propagation, crack tip formation, stable macroscopic cracks propagation, and unstable macroscopic cracks propagation. As the lateral pressure increased, the initiation frequency of cracks decreased, the quantity of propagation decreased, and the propagation path shortened, indirectly increasing the bearing strength of rocks. The initiation stress, peak stress, and elastic modulus of pre-cracked rocks with lateral pressure ≤ 2 MPa were lower than those of pre-cracked rocks with lateral pressure > 3 MPa, with the minimum reduction amplitude of 14.1%, 21.2%, and 12.6%, respectively. As the lateral pressure decreased, the dispersion of the AE main frequency distribution increased and accelerated its downward expansion. The surface temperature curves of rocks were prone to fluctuations and rapid upward evolution characteristics corresponding to crack tip formation and crack propagation, respectively. The research results provide theoretical and engineering references for the mining of weak coal seams.

Dynamic response mechanism of the hole subjected to the 3D point source disturbance in an isotropic formation

Accurate estimation of the effects of dynamic disturbances on stress concentration is crucial for the stability of rock engineering and the corresponding analytical approaches are needed. This study presents an analytical approach to calculate the relative stress distribution with a point source inside and outside a hole using the linear theory of elasticity. The Helmholtz potentials and Sommerfeld integral are employed to describe the displacement and stress components, and then formulate the equilibrium equations to solve the equivalent stress distribution around the hole. Numerical examples demonstrate the impact of model parameters on the equivalent stress, such as frequency, hole radius, source location, etc. It is found that sometimes high frequencies can make the equivalent stress greater far from the source than that close to the source. Additionally, when the ratio of the distance between the source and the hole axis to the hole radius exceeds ten, the equivalent stress distribution around the hole remains nearly constant. This approach can be used for the design and assessment of underground engineering structures' stability under dynamic disturbances.

Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression

The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress–strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress–strain curves of the fissured sandstone specimens.

A Connectivity Metrics-Based Approach for the Prediction of Stress-Dependent Fracture Permeability

Rapid and accurate assessment of fracture permeability is critical for subsurface resource and energy development as well as rock engineering stability. Fracture permeability deviates from the classical cubic law under the effect of roughness, geological stress, as well as mining-induced stress. Conventional laboratory tests and numerical simulations are commonly costly and time-consuming, whereas the use of a connectivity metric based on percolation theory can quickly predict fracture permeability, but with relatively low accuracy. For this reason, we selected two static connectivity metrics with the highest and lowest prediction accuracy in previous studies, respectively, and proposed to revise and use them for fracture permeability estimation, considering the effect of isolated large-aperture regions within the fractures under increasing normal stress. Several hundred fractures with different fractal dimensions and mismatch lengths were numerically generated and deformed, and their permeability was calculated by the local cubic law (LCL). Based on the dataset, the connectivity metrics were counted using the revised approach, and the results show that, regardless of the connectivity metrics, the new model greatly improves the accuracy of permeability prediction compared to the pre-improved model, by at least 8% for different cutoff aperture thresholds.

Predicting dynamic compressive strength of frozen-thawed rocks by characteristic impedance and data-driven methods

In cold regions, the dynamic compressive strength (DCS) of rock damaged by freeze-thaw weathering significantly influences the stability of rock engineering. Nevertheless, testing the dynamic strength under freeze-thaw weathering conditions is often both time-consuming and expensive. Therefore, this study considers the effect of characteristic impedance on DCS and aims to quickly determine the DCS of frozen-thawed rocks through the application of machine-learning techniques. Initially, a database of DCS for frozen-thawed rocks, comprising 216 rock specimens, was compiled. Three external load parameters (freeze-thaw cycle number, confining pressure, and impact pressure) and two rock parameters (characteristic impedance and porosity) were selected as input variables, with DCS as the predicted target. This research optimized the kernel scale, penalty factor, and insensitive loss coefficient of the support vector regression (SVR) model using five swarm intelligent optimization algorithms, leading to the development of five hybrid models. In addition, a statistical DCS prediction equation using multiple linear regression techniques was developed. The performance of the prediction models was comprehensively evaluated using two error indexes and two trend indexes. A sensitivity analysis based on the cosine amplitude method has also been conducted. The results demonstrate that the proposed hybrid SVR-based models consistently provided accurate DCS predictions. Among these models, the SVR model optimized with the chameleon swarm algorithm exhibited the best performance, with metrics indicating its effectiveness, including root mean square error (RMSE) = 3.9675, mean absolute error (MAE) = 2.9673, coefficient of determination (R2) = 0.98631, and variance accounted for (VAF) = 98.634. This suggests that the chameleon swarm algorithm yielded the most optimal results for enhancing SVR models. Notably, impact pressure and characteristic impedance emerged as the two most influential parameters in DCS prediction. This research is anticipated to serve as a reliable reference for estimating the DCS of rocks subjected to freeze-thaw weathering.

Mode I Microscopic Cracking Process of Granite Considering the Criticality of Failure

AbstractRock failure under tensile loading conditions is significant for rock engineering stability and underground energy development. However, a comprehensive understanding of the rock cracking process and the corresponding failure pattern at microscale remains unclear. Therefore, the cracking process and the damage evolution of rock and their underlying mechanisms were systematically investigated. In this study, the fracture behavior of granite was examined by performing mode I fracture tests. For extensive analysis of the cracking process, the cracks were captured in real‐time by scanning electron microscope, and the two fracture toughnesses of the double‐K model were evaluated. Subsequently, fracture morphologies of the post‐failure specimens were analyzed to further investigate the cracking mechanisms. The experimental results indicated the following: (a) the propagated direction of cracks was controlled by the fracture toughness of mineral grains and grain boundaries; and (b) the ratio of the two fracture toughnesses was correlated with fracture tortuosity. Furthermore, two damage modes of granite were found: catastrophic failure and non‐catastrophic failure modes. The former showed precursory behavior prior to catastrophic failure, while the latter did not. The underlying mechanisms of damage modes were revealed as follows: (a) the increased degree of heterogeneity caused by mineral composition complexity led to the early arrival of precursors; and (b) the occurrence of catastrophic or non‐catastrophic failure mode was determined by the difference in grain‐scale heterogeneity. Our results found at microscale also have implications for understanding the macroscopic failure process of rocks.

The modification of Mohr-Coulomb criteria based on shape function and determination method of undetermined parameters

Rock strength criteria is a key step to estimate the stability of rock engineering, especially, the effect of intermediate principal stress on rock failure should be considered in formation at great depth. However, the mostly used Mohr-Coulomb criterion don't consider the effect of intermediate principal stress, besides, most rock mechanics laboratories do not have the ability to do true triaxial strength, the strength parameters in poly-axial strength criteria are difficult to be determined. In order to solve these problems, based on the least absolute deviation method, the square of the correlation coefficient, absolute difference and mean difference are adopted to verify the fitting effect of 10 strength criteria on 32 groups of true triaxial strength data. On this basis, the elliptical Lode angle shape function, hyperbolic Lode angle shape function, and the Lode angle shape function based on spatial slip plane are used to establish the modified MC strength criteria, which not only meets the requirements of smoothness and convexness, but also can be used widely in many geomaterials. Besides, strength parameters of the established criteria can be decided by conventional triaxial strength experiment, and the prediction accuracy of the modified MC strength criteria for the 32 groups of true triaxial strength data is better than or close to the lowest fitting error of the existing poly-axial strength criteria.

Mechanical behaviour and spatial fracture characteristics of granite containing weak inclusions under uniaxial loading revealed by 3D DIC and AE monitoring: The influence of extension length of planar inclusions

The destabilisation failure characteristics of weakly filled rock masses are important influencing factors in rock engineering stability control. To investigate the changes in the mechanical behaviour and spatial fracture characteristics of granite in the presence of both planar and circular weak inclusions, two experimental non-destructive monitoring methods, 3D DIC and AE, were used together. This paper summarises the experimental results and investigates the effect of the extension length of the planar inclusions on the mechanical behaviour and spatial fracture characteristics. The results show that the presence of planar weak inclusions leads to the appearance of “plasticity” before the peak stress, the weakening of “brittleness” and the enhancement of “ductility” after the peak stress, and the increase of extension length will weaken the resistance to deformation and the overall load carrying capacity. When the extension length of planar inclusions varies, there are three main modes of specimen failure: “X” shear failure; crushing and crumbling failure; overall shear failure. The distribution of AE parameters is dominated by the proportion of low-amplitude hit signals, with a wide range of energy distribution, but the concentration in low-amplitude energy and slightly longer signal duration. The correlations of energy-amplitude, count-amplitude, and duration-amplitude are different and similar. The fracture area of the specimen and the spatial location of the fracture event concentration distribution overlap, with the planar inclusions serving as the weak surface, and the fracture event showing the distribution trend of the planar weak inclusions serving as the central area.

Modeling of the Three-Dimensional Point Cloud Based on the Binocular Stereovision and Structure Identification

Abstract The existence of weak planes affects the stability of rock engineering, especially the failure modes of the surrounding rocks. Therefore, investigation of the structural planes of rock mass and the extraction of discontinuities is important for rock mechanics. In this work, the LenaCV binocular stereovision system was studied and applied to establish three-dimensional (3D) surface models. Calibration of the binocular camera parameters, optimal distance discussion, and 3D modeling optimization were conducted. The optimal measuring distance and the intrinsic parameters suitable for the LenaCV stereovision were discussed. Finally, the 3D reconstruction of two case studies was carried out and the 3D point cloud modeling was established. The structural discontinuity mapping in rock faces was also carried out. The feasibility of the binocular stereovision system, as well as the optimum baseline distance, was discussed and verified. The study results can provide a new platform for the economic investigation of 3D rock mass structures and provide a new approach for the efficient extraction of rock mass discontinuities.

Experimental study on the spatial fracture behaviour of red sandstone containing weak inclusions with non-unitary geometric features under uniaxial compression

The failure of weakly filled rock masses is an important factor in the safety and stability of rock engineering. To investigate the spatial fracture behaviour of red sandstone with non-unitary geometric weakly filled joints, uniaxial compression experiments were carried out. The 3D DIC and acoustic emission (AE) technology were used to obtain the three-dimensional spatial deformation information and AE parameters of specimens containing both planar and circular weak inclusions, respectively. The main results are as follows: (1) The results show that the ductility of planar weak inclusions has a certain deterioration effect on the bearing capacity of the specimens, and the extent of this deterioration effect is not constant. (2) When the ductile length of the planar weak inclusions increases, the three-dimensional spatial displacement and strain fields of the specimens are divided by the planar weak inclusions, showing different degrees of deformation behaviour and different distribution patterns in the upper and lower parts. (3) The three-dimensional spatial fracture characteristics of specimens with different ductile lengths of planar weak inclusions will be dominated by the ductility, and the main failure mode of the specimen will gradually evolve from shear failure to splitting failure. The “guiding effect” of circular hole weak inclusions on the main crack is no longer evident when the ductility of planar weak inclusions is at its maximum. (4) The growth trend of the cumulative AE counts can be divided into four stages, and the stage characteristics are significantly influenced by the ductile length of the planar weak inclusions; different failure modes show different AE signal distribution characteristics. In addition, the key points of stability control of rock masses containing weak inclusions in practical engineering are discussed.

Mechanical behaviour of rock containing a persistent joint under uniaxial compression at different strain rates

Understanding the mechanical behaviour of jointed rock during seismic events is crucial for ensuring the stability of rock engineering. A series of uniaxial compression tests were conducted on granite specimens containing a persistent joint at strain rates (10−5–0.05/s). Acoustic emissions (AEs) were monitored to detect the rock fracturing, and the strain field on the specimen surface was measured by the digital image correlation technique. Three failure patterns of specimens were observed: rock splitting, joint slipping and mixed rock splitting–joint slipping. The shapes of typical strain–stress curves for the three patterns are different, but they are all characterised by multiple stress drops indicating significant rock fractures. When significant fractures occur, the frequency range of AEs expends and the dominant frequency of AEs becomes much larger. The specimen strength is affected by the strain rate, but this effect differs for different failure patterns of specimens. The joint inclination could influence the mode and profile of fractures near the joint, and the specimen strength and joint stiffness significantly decrease with increasing joint angle. This study could help better understand the behaviour of jointed rocks subjected to seismic loads.

Anisotropic behavior of the seepage-stress coupling mechanical model of coal pillars of underground reservoirs

Coal pillar dams are an important component of the water storage bodies of underground reservoirs. Influenced by the overlying rock pressure and water seepage, the stability of the coal pillar dam is one of the key factors affecting the stability of underground reservoirs. In this paper, an anisotropic seepage mechanical model of a coal pillar dam under plane strain was established to study the seepage stress coupling mechanism of underground reservoir No. 4 in the Daliuta Coal Mine using the COMSOL Multiphysics code. The stress field and seepage field of the coal pillar dam body were analyzed, and the influence of the principal direction of the mechanical properties of the coal pillar on the stress field, seepage field, and damaged areas of the coal pillar and goaf were discussed. According to the results, the anisotropy of the coal pillar dam body is one of the most significant factors when the principal direction of mechanical properties is θ = 45° or θ = 135°. The coal pillar damage area reaches a maximum value accounting for nearly 50%. The shear stress of the coal pillar reaches 4.69 MPa, which attains the maximum value when the principal direction angle is 90°. With increasing depth, the damaged area of the coal pillar gradually expands in the scenario of θ = 0°. When the depth increases to 160 m, the coal pillar undergoes penetration failure. In conclusion, the principal direction is the main factor affecting the stress field, seepage field displacement field, and energy evolution of the model. The anisotropy model of the equivalent continuum can account for the influence of the coal pillar structure surface, which could provide an analytical model for the stability of rock engineering.

Experimental investigation on crack coalescence and strength loss of rock-like materials containing two parallel water-filled flaws under freeze–thaw

The freezing of water-bearing flaws has a much more serious threat on the stability of fractured rock slopes, because saturated flaws provide more liquid water for frost expansion and thus induces frost cracking. The freeze–thaw collapse of alpine mountains is mainly caused by the frost cracking of rock bridges between flaws. In this research, the frost propagation and coalescence process of two parallel water-filled flaws was investigated by experiment, by considering the effects of flaw angle and bridge angle. It indicates that the maximum frost heaving pressure in these elliptical flaws is more than 4 MPa, which is large enough to drive flaws propagation and cause bridge cracking. A considerable uniaxial compressive strength (UCS) loss occurs after freeze–thaw cycles when the flaw or bridge angle is close to the inherent rupture angle of intact samples, because the loading rupture coincides with new frost heaving cracks. Therefore, more attentions should be paid on these flawed rocks with flaw or bridge angles equal to the rupture angle, which is easier to rupture and fall down from the mountains. In addition, the unidirectional freezing mode is more conducive to drive the flaw propagation than the uniform freezing mode, because the frost heaving pressure under unidirectional freezing is much larger due to the ice plug effect, which means that the solid ice is like a plug blocking the mouth of cracks and preventing the water flowing outside. This study can provide a better understanding of the frost propagation of water filled flaws in rock masses and the stability of rock engineering under freeze–thaw in cold regions.

Subcritical crack growth and fracture behavior of rocks and long-term strength estimation

Understanding the potential subcritical fracture behavior is very essential to assess the perennial stability of rock engineering. The purpose of this study is to reveal the fracture characteristics and subcritical crack propagation of rocks with different lithologies, emphasizing that the influence of time-dependent fractures on the long-term strength of rocks cannot be ignored. The fracture toughness, KI-V curves and subcritical growth index of five types of rocks were obtained by the double-torsion (DT) technique. Subcritical fracture propagation exists in the rock as the stress intensity level is between K0 and KIC, and the ratio of the two values is between 0.73 and 0.83. Using a three-dimensional digital image correlation (3D-DIC) technique and a plane mirror, the evolution of tensile strain and crack propagation process on the bottom surface of specimens were observed successfully. The granite and basalt showed a faster growth rate of subcritical crack propagation, with fracture rate ranging from 10-2.5 to 10-6.9 m/s. The long-term strength of rocks was estimated based on the tensile strength, fracture toughness, SCI and A values. In a short term, basalts with the highest tensile strength have the highest long-term strength, while granites show the highest long-term strength when the time-to-failure exceeds 408.2 years. Therefore, the time-dependent cracking behavior of rock engineering must be considered when assessing the long-term stability.

Simulation Study on Crack Initiation and Energy Mechanisms of Rock-like Samples with Non-Parallel Overlapping Flaws under Uniaxial Compression

Non-parallel overlapping flaws widely exist in engineering rock mass. Understanding their crack initiation and energy evolution characteristics is of great significance to ensure the stability of rock engineering. Based on the existing experiments, the influence of flaw inclination angles (β) on the crack initiation and energy evolution characteristics of rock samples with non-parallel overlapping flaws was studied by numerical simulation. The results show that (1) the uniaxial compressive strength, elastic modulus and crack initiation stress increase with the increase of flaw angle. (2) The boundary energy, strain energy and dissipated energy under peak stress increase with the increase of flaw angle; the dissipated energy increases the most. (3) With the increase of flaw angle, the tension stress zone is transferred to the flaw tip, and the zone is reduced gradually; the maximum tensile stress and the tension stress concentration decrease. (4) In the crack initiation stage, the influence of a lower flaw inclination angle (β ≤ 60°) on the lateral displacement field of the sample is higher than that of a high flaw inclination angle (β = 75°).

Dynamic fracture analysis of sandstone specimens containing different inclusions

Infilling materials are commonly distributed in natural rocks, which play a key role in the stability of rock engineering. To reveal the enhancing mechanism of inclusions, dynamic uniaxial compressive tests were carried out on sandstone specimens containing double elliptical flaws using a split Hopkinson pressure bar (SHPB) system and the digital image correlation (DIC) technique, and three inclusion conditions (R1, R2 and R3) and three flaw inclination angles (0°, 45° and 90°) were taken into consideration. The results indicate that the inclusions (R2 and R3) with a similar wave impedance to sandstone matrix can maximally enhance the dynamic strength of flawed specimens by 46.82% and 42.83%, respectively. The crack initiation and propagation behavior were significantly changed after the flaws were filled with different types of inclusions. The dominant crack in the bridge area can be identified by strain histories and stress intensity factors (SIFs) at the inner inclusion tips. The findings are projected to deepen the understanding of interaction mechanism of rock matrix and inclusions.

Study on Mechanical Properties and Acoustic Emission Characteristics of Sandstone under Freezing and Thawing

The cyclic freezing-thawing action in cold regions leads to the deterioration of rock damage, resulting in local damage and further threatening the safety of engineering. In order to study the degradation characteristics of green sandstone and yellow sandstone under freeze-thaw cycles from macroscopic and microscopic aspects, the sandstone of a mining area in Inner Mongolia was used as experimental material. The freeze-thaw cycles were divided into 20 times, 30 times, and 40 times. NMR images and mechanical test results of two different rock samples were analyzed by binarization, NMR, and mechanical test. The test results show that, except that the mass change is less than that of yellow sandstone, the physical index degradation degree of green sandstone is higher than that of yellow sandstone, and the frost resistance is less than that of yellow sandstone. The change of acoustic emission event rate of green sandstone is mainly in the elastic deformation stage and stable crack propagation stage, and the change of acoustic emission event rate of yellow sandstone is concentrated in the crack closure stage. In the loading process, the energy release trends of the two sandstones are similar; the 30 freeze-thaw cycles are the boundary of brittle-plastic transformation of green sandstone, and the increase of cumulative energy is the most obvious. The research results provide a theoretical basis for studying the rock failure mechanism and improving the stability of rock engineering in cold regions.

Dynamic mechanical properties and wave propagation of composite rock-mortar specimens based on SHPB tests

Filled inclusions in rock discontinuities play a key role in the mechanical characteristics of the rock and thereby influence the stability of rock engineering. In this study, a series of impact tests were performed using a split Hopkinson pressure bar system with high-speed photography to investigate the effect of interlayer strength on the wave propagation and fracturing process in composite rock-mortar specimens. The results indicate that the transmission coefficient, nominal dynamic strength, interlayer closure, and specific normal stiffness generally increase linearly with increasing interlayer stiffness. The cement mortar layer can serve as a buffer during the deformation of composite specimens. The digital images show that tensile cracks are typically initiated at the rock-mortar interface, propagate along the loading direction, and eventually result in a tensile failure regardless of the interlayer properties. However, when a relatively weaker layer is sandwiched between the rock matrix, an increasing amount of cement mortar is violently ejected and slight slabbing occurs near the rock-mortar interface.