Rock Bridge Research Articles

Tensile mechanical properties and fracture evolution characteristics of sandstone containing parallel pre-cracks under dynamic loading

Parallel cracks have a significant influence on the dynamic tensile failure behavior of rock. The systematic investigation of dynamic tensile mechanical properties and fracture evolution characteristics of fractured rocks are significant for guiding the safe excavation and stability sustaining of rock engineering. Two groups of dynamic Brazilian splitting tests were conducted for the sandstone specimens containing parallel pre-cracks. The influences of crack inclination angle (Group A) and rock bridge length (Group B) on the tensile mechanical properties and fracture evolution characteristics were analyzed. Results showed: the dynamic peak load of pre-cracked specimens is significantly lower than that of intact specimens. The peak load presents a V-shaped evolution trend with the growth of crack inclination angle. Differently, the dynamic peak load increased monotonically with the increasing of rock bridge length. In addition, the crack initiation points move from crack tips to crack walls when the crack inclination angle is increasing. When rock bridge length is large enough, the crack propagation paths are observed near the central axis of specimens. By utilizing the DIC method, six different failure modes are identified to explain the crack initiation and propagation mechanisms under dynamic loading. The tensile-shear fracture modes are mainly presented for specimens with different crack inclinations. Differently, the ultimate failure modes change from tensile-shear mode to tensile mode when the rock bridge length is increasing. In addition, numerical results (ANSYS/LS-DYNA) are in good agreement with the experimental results as a whole, which can verify and explain the experimental results. This study is expected to provide guidance for controlling fractured rock masses.

Tensile behavior of Brazilian disks containing non-persistent joint sets subjected to diametral loading: experimental and numerical investigations

Structural defects are part of the inherent characteristics of rock masses. They can be found in fishers, joints, and beddings and can be divided into persistent or non-persistent ones. The coalescence of non-persistent cracks may lead to the formation of persistent joints under the tensile stress field, leading to rock mass instability. The mechanical behavior of non-persistent jointed disks under tensile stress has important implications for rock structures. In this paper, experimental and Discrete Element Method (DEM) numerical simulation approaches were adopted to investigate the effect of joint continuity factor (the relationship between joint length and rock bridge length), bridge angle, joint spacing, and loading direction in relation to joint angle on the tensile strength and stiffness as well as failure pattern. Cement-mortar-based Brazilian disks containing open non-persistent joints were constructed and subjected to diametral loading and simulated using a two-dimensional Particle Flow Code (PFC2D). The investigations revealed that the tensile strength, stiffness, and failure pattern of Brazilian disks are highly affected by non-persistent pre-existing cracks. The increase of joint continuity factor and loading direction leads to the reduction of both tensile strength and stiffness. However, when spacing increases, tensile strength and stiffens have a minimum at the average spacing, but it was concluded that bridge angle does not affect both parameters. Finally, the results showed that the experimental and numerical approaches are in good agreement, and almost all the parameters affect the failure pattern, and some failure patterns such as step-path failure, splitting, or sliding may occur as a function of non-persistent joint sets.

Drilled-hole number effects on energy and acoustic emission characteristics of brittle coal

Energy accumulation and release are the essence of rock deformation and damage. Thus, investigating the damage mode and energy evolution law of coal specimens containing holes to elucidate the mechanism of borehole pressure relief is important. To examine the effect of the number of drilled holes on the energy and acoustic emission (AE) evolution characteristics of brittle coal, uniaxial compression AE tests were performed using four types of drilled coal specimen. The results revealed that the peak strengths and elastic moduli of the specimens exhibited nonlinear and linear decreasing trends, respectively, with the increase in hole number; however, the peak strain initially decreased and subsequently increased. The failure mode changed from shear splitting to penetration crack damage between rock bridges, accompanied by a hole collapse phenomenon. As the hole number increased, the total and elastic energy exhibited a decreasing trend, whereas the ratios of the elastic and dissipative energy to total energy exhibited a decreasing and an increasing trend, respectively. The AEs of different types of drilled coal specimens had similar evolutionary processes, but their activity exhibited an overall increasing trend with an increase in hole number. The AE fractal characteristics of a drilled coal specimen were calculated based on the G-P algorithm. The AE signal of the specimen exhibited fractal characteristics, and the sudden drop in fractal dimension was considered the precursor of specimen failure. The findings provide a reference for understanding the energy evolution mechanism and advance warning for coal pressure relief.

The effect of flaw geometry and infilling on crack initiation, propagation, and coalescence of a parallel flaw pair in marble

A series of uniaxial compression tests were conducted on unfilled or filled marble specimens with a parallel flaw pair to study the effect of the flaw geometry and infilling on the crack coalescence pattern. Special attention was paid to the crack initiation, propagation, and coalescence processes, which were traced by the CCD camera and digital image correlation (DIC) technique. The experimental results have shown that the appearance of the white patch and strain localization band precedes the initiation of macroscopic crack. The tensile crack evolves from a narrow strain band or white patches with clear boundaries, while the shear crack evolves from a wider strain band or white patch with blurry boundaries. The high-strength fillers suppress the initiation and propagation of the tensile cracks (i.e., T1, T2, and T3) and promote the appearance of the coplanar shear cracks and mixed tensile-shear cracks (i.e., M1, M2, and S1). The variation in the infilling condition leads to the difference in the fundamental crack types, hence resulting in different coalescence patterns for a given flaw geometry. For small rock bridge angles (i.e., β = 30°, 45°), no coalescence and indirect coalescence tends to occur between the open and gypsum-filled flaws, while shear coalescence is prone to occur between the cement- and resin-filled flaws. The coalescence patterns are dominated by the flaw geometry for medium rock bridge angles (i.e., β = 60°, 90°), but the crack coalescence stress and peak strength of specimens are greatly affected by the infilling conditions. For large rock bridge angle (i.e., β = 120°), the increase in the strength of the filler tends to generate straighter wing cracks for the tensile coalescence at the rock bridge and promotes the initiation of mixed tensile-shear cracks for additional coalescence outside the rock bridge.

Numerical Simulation of the Coalescence Behavior of Intermittent Structures with Fissures

To further study the failure behavior of the rock-like materials containing intermittent fissures subjected to uniaxial compression, 3D printing technology was adopted to manufacture specimens with prefabricated kinked and straight fissures (K-S fissure). The order of average peak strength was −45° > −90° > +90° > +45°. The influence of different parameters, including the effective length and inclination angle of branch fissure, on the coalescence pattern was discussed. Results showed that two failure modes were observed: Model I represented tensile-shear composite failure in the rock bridge area, while Model II showed non-coalescence occurring. The effective length parameter presented a relatively larger influence than the inclination angle on the failure behavior. Additionally, Model I was discovered to tend to occur in the rock bridge region when the branch fissure turned anticlockwise. Based on numerical simulation using the Realistic Failure Process Analysis (RFPA2D), a quick damage criterion approach was proposed to estimate the coalescence behavior in the rock bridge, which was beneficial to determine coalescence pattern and failure behavior. Based on the curve fitted by the simulation, the coalescence pattern of cracks initiated from pre-existing intermittent fissures occurs in the tensile-shear composite fracture pattern, while non-coalescence occurs in the rock bridge below the curve.

Influences of the number of non-consecutive joints on the dynamic mechanical properties and failure characteristics of a rock-like material

The dynamic mechanical properties and failure characteristics of jointed rocks are the focus of research in rock engineering. In this study, cement mortar specimens with 0–4 parallel non-consecutive joints were prepared. The split Hopkinson pressure bar (SHPB) was used for dynamic impact testing of prepared specimens. Nuclear magnetic resonance (NMR) was used to detect the pore structure deterioration of the specimens after impact. Finally, the failure characteristics of the specimens were studied by extracting the surface cracks of the specimens. The results show that the number of non-consecutive joints have a significant effect on the dynamic mechanical properties of cement mortar specimens. The increased number of joints will change the stress–strain curve from a single-peak shape to a multi-peak shape and enhance the ductility. The dynamic peak strengths and the proportion of dissipated energy of the specimens decrease with the increase of number of joints, but the magnitude of change decreases gradually. NMR analysis reveals the pore structure alterations of the specimens. After being impacted, the internal pores of the specimens increase significantly, especially the macro-pores and micro-pores. Some micro-pores become meso-pores and macro-pores, and some pores are connected. These changes of microscopic pore structure lead to macroscopic failure of specimens. A quantitative analysis of the porosity of the specimens shows that the rate of change in porosity is in direct proportion to the number of joints, which means that the greater the number of joints, the larger the damage degree of the specimens. The failure characteristics of the specimens indicate that tensile stress mainly dominates the fracture behavior of the specimens, while shear stress has limited damage to the specimens. After the tensile wing cracks start from both tips of the joint, they extend along the rock bridge to the adjacent joint or the end of the specimen. After the wing cracks coalesce, they form a rectangular failure zone. In addition, axial tensile cracks will start near the middle of the first joint and the middle of the last joint, extending to the top and bottom of the specimen, respectively. Slight shear cracks only develop at the joint ends.

The Bologna Interpretation of Rock Bridges

One can only know where a rock bridge is once one measures it. In addition, to measure it, you need the rock mass to fail. This critical problem is ignored by many, and engineers continue to refer to rock bridges as geometrical distances between non-persistent fractures. This paper argues that this rather simplistic approach can lead to non-realistic failure mechanisms. We also raise the critical question of whether the inappropriate functioning of strength equations centred on the measurement of rock bridge percentages could result in misinterpreting the risk of failure. We propose a new interpterion, aptly called the Bologna Interpretation, as an analogy to the Copenhagen Interpretation of quantum mechanics, to highlight the indeterministic nature of rock bridges and to honour the oldest university in Europe (Bologna University). The Bologna Interpretation does not negate the existence of rock bridges. What rock bridges look like, how many there are, and where they are, we do not know; we can assume their existence and account for their contribution to rock mass strength using a potential analogue.

Experimental study on mechanical properties and failure behaviours of new materials for modeling rock bridges

Rock bridges control the stability of rock slopes with intermittent joints. To better understand the evolution of water-induced damage in rock bridges, we developed new, water-sensitive similar materials and investigated their physical, mechanical, and hydraulic properties. The reasonable proportions of the material components required to simulate a rock bridge were systematically determined based on deformation failure modes, shear creep characteristics, deterioration degree, and the brittleness characteristics after water-rock interaction. Sensitivity analysis and contribution rates were used to characterize the effects of different influencing factors on the mechanical properties of similar materials. We found that one similar material specimen, SM-24, exhibited the analogous characteristics of natural rock bridge in shear creep behavior, crack propagation, and ruptured surfaces. Such similar material for modeling rock bridges has the following mechanical characteristics: reproducing the volume-expansion point, showing high deterioration degree and specific brittle failure characteristics after water-rock interaction, and reproducing the identifiable precursor of accelerated creep and stepped fracture morphology subjected to shear creep loading. The bone-binder ratio dominated mechanical properties of similar materials, while physical and hydraulic properties depended mainly on the bentonite content. These findings provide guidelines for reliably producing similar materials that meet the requirements of different geomechanical model tests in solving geotechnical engineering problems considering the water-rock interactions.

Influence of a Rock Bridge on the Shearing Behavior of Nonpersistent Rough Joints: An Experimental Study

Influence of a Rock Bridge on the Shearing Behavior of Nonpersistent Rough Joints: An Experimental Study

Laboratory-Scale Investigation on Shear Behavior of Non-Persistent Joints and Joint Infill Using Lattice-Spring-Based Synthetic Rock Mass Model

Discontinuities mainly control the mechanical behavior of rock mass and cause a significant reduction in the rock mass strength. Joint persistency and joint infill conditions are considered the most significant joint parameters that control the mechanical response of rock mass. In this study, numerical and statistical analyses were performed on pre-cracked specimens with two flaws to investigate the effect of joint persistence parameters on shear strength. In addition, an extensive study was conducted to explore the effect of infilled mineral strength, infill thickness, and infill wall roughness on shear strength. The Lattice-Spring-Based Synthetic Rock Mass (LS-SRM) approach was utilized to perform the numerical models. The results showed that the tensile crack propagation is limited at higher normal stresses as tensile damage is largely suppressed. The increases in rock bridge angle slightly increased the shear strength and caused a change in the failure mechanisms of the rock bridge from tensile to shearing. The results of the models with infilled minerals revealed that infilled minerals mainly controlled the shear strength of specimens when the infill thickness was 4.0 mm or greater. The infill wall roughness had no apparent effect on the shear strength. In contrast, it governed the failure mechanisms; cracks initiated at the asperity of the rough filling wall and propagated through the hosted rock mass.

Influence of intermittent opening density on mechanical behavior and fracture characteristics of 3D-printed rock

To investigate the influence of intermittent opening density on the mechanical behavior and fracture characteristics of rock, sand 3D-printed specimens containing different opening numbers are prepared using quartz silica sand and furan resin adhesive as printing substrates. Uniaxial compression testing is performed on these rock-like specimens. Based on digital image correlation (DIC) technology, a methodology for identifying crack types and evaluating rock damage is proposed to quantify the mechanical mechanism of crack evolution during loading. The experimental results are verified and explained using the rock failure process analysis (RFPA) code. The results show that with increasing intermittent opening density, the stress–strain curves of the specimens are similar. Meanwhile, the increase in intermittent opening density causes the stress field distribution of the specimen to change, which in turn leads to a decrease in the uniaxial compressive strength and elastic modulus. The types of cracks around the opening can be grouped into tensile cracks (T) and shear cracks (S), and the coalescence modes of the rock bridge between the openings can be grouped into shear coalescence (C1) and traction coalescence (C2). As the intermittent opening density increases, the coalescence type between openings changes from C1 to C2, and the overall failure pattern is converted from tensile-shear failure to tensile failure. The damage factor (Df) evolution is closely related to the intermittent opening density of the specimens. A one-way exponential decay correlation between the stress ratio and the damage factor is found. The above study is expected to deepen the understanding of the deformation and fracture mechanism of rock masses with openings and to provide a reference for the application of 3D printing technology in the rock mechanics field.

Shear behaviour of a rock bridge sandwiched between incipient joints under the influence of hydraulic pressures

The rock bridges sandwiched in incipiently jointed rock mass were considered as barriers that block the fluid seepage, and provide certain shear strength reservation. For better revealing the influence of hydraulic pressure on the failure behaviour of rock bridges, direct shear tests were carried out through a newly proposed method on rock samples that contain two parallel incipient joints. By developing the gypsum-silicone pad coupling samples, a conventional triaxial test system was qualified to implement direct shear tests with satisfied sealing capability. The results showed that the rock bridges could be failed through the tensile failure, shear failure and mixed failure mechanism. The hydraulic pressure would facilitate the tensile failure mechanism and induce rougher fracture surfaces; while the normal stress would facilitate the shear failure mechanism and induce less rough fracture. The hydraulic pressure reduced the global shear strength of the rock block through reducing the efficient normal stress applied on the rock bridge area, which was highly dependent on the joint persistence, k. Moreover, because of the iterating occurrence of the hydraulic pressure lag with the fracture propagation, the rock bridge failure stage in the shear stress-shear displacement curves displayed a fluctuation trend.

Mechanical properties and failure law of composite rock containing two coplanar fractures

Composite rocks comprise the rock structures that are commonly used in geotechnical engineering. The fracture configuration has a substantial influence on the mechanical behavior, failure mode, and crack propagation of composite rocks. In this study, we considered a composite rock with two prefabricated coplanar fractures. Through laboratory uniaxial compression tests and using a digital image acquisition system, we systematically studied the effects of different fracture lengths and inclination angles on the mechanical properties and failure characteristics of the rocks. We obtained the following results: 1) during the loading deformation of the rock sample, the peak stress and elastic modulus increased with an increase in the fracture inclination angle and decreased with an increase in the fracture length. The deterioration coefficient k (the ratio of the difference between the peak strength of intact and fractured rock sample to that of intact rock sample) decreased with an increase in the fracture inclination angle and increased with an increase in the fracture length. 2) The failure type of the rock samples was primarily controlled by the fracture inclination angle and material of the two rock types, and the fragmentation degree was primarily controlled by the fracture length. With an increase in the fracture inclination angle, the failure mode of rock sample exhibited the following order of changes leading to failure: a double-Y type (trwo wing and one antiwing cracks appeared on each prefabricated fracture) → double-Z type (two wing cracks appeared on each prefabricated fracture) → Z type (one wing crack appeared on each prefabricated fracture). 3) The type of coalescence of the rock bridge was controlled by the fracture inclination angle and structural plane. The crack positions were primarily affected by the fracture length. 4) At a low fracture inclination angle (α ≤ 30°), the propagation of the microcracks showed aggregated band formation. Above moderate fracture inclination angles (α > 30°), the microcrack aggregation band gradually weakened and expanded in the direction of dispersion.

Lower Bound Limit Analysis of Non-Persistent Jointed Rock Masses Using Mixed Numerical Discretization

The bearing capacity of a non-persistent jointed rock mass containing a rock bridge is investigated by combining the lower bound limit analysis theory, a mixed numerical discrete method, and linear mathematical programming. A mixed numerical discrete method is proposed to divide non-persistent jointed rock masses in which rigid block elements are used to simulate the rock blocks, whereas the finite element method is used to simulate the intact rock bridges. A linear mathematical programming model for the ultimate bearing capacity is constructed and solved using the interior point algorithm. The proposed formulation is validated by application to three rock slopes.

Shear mechanical responses and cracking evolution mechanisms of flawed sandstone containing two circular holes

Shear tests on rectangular plate sandstone containing two pre-existing holes were performed to analyze the shear mechanical responses and cracking evolution mechanisms. With generation of the penetrating fracture surfaces, both shear stress and normal displacement show a dramatic drop. Then, during the shear slipping process, the shear stress increases once again due to wear and shear off of the surface asperities, and three different variation trends of the normal deformation including shear dilation, fluctuation, and shear contraction are respectively identified. The role of ligament length and normal stress on several key indices such as peak shear stress, peak normal displacement and residual shear stress was investigated. Violent AE (acoustic emission) responses occur along with penetration of the fracture surfaces, and in the shear slipping process, AE events continue to occur due to wear of surface asperities, while the increase rate of accumulative AE events declines. Cracks coalesced at the rock bridge and running through the rock matrix form the main failure planes of the samples. From the PFC2D simulation results, the crack clusters first initiate from hole-walls and coalesce at the rock bridge for a small ligament length, while first produce the main failure planes at the right/left rock matrix for a large ligament length. The total number of micro cracks shows a “calm → rapid increase → decreasing growth amplitude” variation during shearing, and the induced cracks become more concentrated for a larger normal stress, implying a cumulative damage of the failure surfaces.

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.

Rate Effect on the Direct Shear Behavior of Granite Rock Bridges at Low to Subseismic Shear Rates

AbstractNatural faults are often heterogeneous with spatially variable cohesion caused by healing processes. Using rock bridges as laboratory analogs, we investigate how cohesion‐healed patches rupture at different shear rates. We performed direct shear experiments on granite rock bridges at shear rates from 1 μm/s to 10 mm/s (low to subseismic shear rates), and quantitatively characterized the failure surface morphology by integrating laser scanning with ArcGIS. The results show a notable dependence of both mechanical and morphological characteristics on shear rate. The failure mode transitions from tensile failure at low shear rates to shear failure at subseismic shear rates. At low shear rates, tensile failure forms curved coalescence patterns and undulating failure surfaces with significant roughness and morphological anisotropy. At subseismic shear rates, straighter shear‐formed coalescence patterns are observed. In addition, the peak shear strength, the roughness and morphological anisotropy increase with increasing shear rate within the subseismic rate regime. We explain the observed rate‐dependent behaviors by the energy and geometric features of micro‐cracking mechanisms. We suggest through the variations in 3D morphological parameters that rate effects should be incorporated into models of fault morphology. In addition, the failure surfaces at all shear rates are asymmetric, with asperities more inclined to the direction of the shear load. We find that this asymmetry results from both the fracture of rock bridges and the further shearing after failure, and it can be used to determine the sense of fault displacement.

Failure Behaviour of Jointed Rock Masses with 3D Nonpenetrating Joints under Uniaxial Compression: Insights from Discrete Element Method Modelling

It is well known that joints or fissures have an important effect on the failure mechanism of natural rocks. Previously, many numerical and experimental papers have been carried out to study the strength anisotropy and failure characteristics of jointed rocks. However, few studies have been carried out on the failure mechanism of nonpersistent jointed rock masses with different persistence, especially for nonpersistent joints in three dimensions. In the present study, the failure characteristics of a 3D nonpersistent jointed rock mass with different inclinations (θ) and persistence (K) are studied by numerical simulation. For the 3D digital elevation model (DEM), the linear parallel bond model (LPBM) and smooth-joint model (S-J) were used to model the rock-like material and joint interface, respectively. The connections between the geometric parameters of joints and peak strength are revealed. For the peak strength, the joint persistence only plays a minor role in specimens with inclinations of 0° and 90°, and its influence on strength is mainly reflected in the specimens with shear failure (θ = 45°, 60°, and 75°). Based on microcrack accumulation and evolution, four typical failure processes (shear failure, split failure, mixed failure, and intact failure) are analysed from the micro perspective. The shear stress evolution process on the 3D nonpersistent joint of the specimen with different inclinations under K1 = 0.42 was monitored by the measurement circle, and it was found that the distribution of shear stress inside the rock bridge is related to the failure mode of the specimen. For the specimens with θ = 0° and 90°, the shear stress had little change, indicating that there is slight shear slip behaviour on the joint surface. When the inclination is 45°, 60°, and 75°, the shear stress changes obviously during loading, indicating that the shear action is strong in this failure mode.

Fracture Evolution Analysis of Rock Bridges in Hard Rock with Nonparallel Joints in True Triaxial Stress States

Fracture Evolution Analysis of Rock Bridges in Hard Rock with Nonparallel Joints in True Triaxial Stress States

Numerical study of dynamic fracture behaviors of rock containing double pre-existing flaws under different confined stress and flaw geometry

In underground rock engineering, flaws can significantly affect both the physical properties and mechanical properties of the rock. The dynamic failure mechanism of sandstone with double pre-existing flaws is systematically analyzed through the parallel bond model in particle flow code. First, the model of the intact sandstone sample is established to verify the rationality of the parameters. Simulations of dynamic compression are then performed on sandstone that contains double pre-existing flaws under different impact velocities and confining pressures. The research results show that sandstone samples with various flaw lengths, rock bridge lengths, rock bridge angles and flaw angles exhibit different failure modes, strength reduction and AE evolution characteristics. Furthermore, by analyzing microforce fields, the cracking type and the crack propagation mechanism of sandstone samples are revealed. The rock bridge angle has a significant impact on the propagation of microcracks and the dynamic failure of the rock mass; while the rock bridge length between the two flaws has little effect on this.