Rock Bridge Research Articles

Cyclic fatigue responses of double fissure-contained marble: Insights from mechanical responses, energy conversion and hysteresis characteristics

The intermittent fissures are widely distributed in rock mass, rock bridge segment among the fissures are crucial to the mechanical properties and stability of rock mass. The static mechanical behaviors of fissure-contained rock were well understood, yet the fatigue mechanical properties were poorly investigated. This work aims to reveal the influence of rock bridge length on rock mechanical responses, energy dissipation and hysteresis characteristics in lab-scale. Marble samples with rock bridge length (RBL) of 10, 20, 30, and 40 mm were prefabricated as parallel pattern, and they are subjected to multi-level fatigue loading paths. Testing results show that the rock bridge between the fissures resists rock deformation and the terminal volumetric strain decreases with increasing RBL. In addition, the hysteresis energy density and damage evolution are influenced by the rock bridge length. The strain energy density development aligns with deformation pattern results. Deterioration in the rock bridge structure causes reduced capacity and higher energy consumption. More energy is required to drive damage progression and crack connectivity in rocks with a larger RBL. Ultimately, two hysteresis indices are introduced to characterize fatigue damage evolution. These indices exhibit nearly opposing trends throughout the loading process. It is proposed that extending the rock bridge length results in a roughly linear trend for both hysteresis indices.

Investigation of scale effects of rock bridges based on Multi-Physical field monitoring

The presence of rock bridges is crucial for ensuring the stability of rock slopes. However, evaluating the mechanical properties of rock bridges solely based on the joint persistence coefficient (K) raises doubts due to potential variations in the scales of rock bridges within a rock mass with a constant K value. In this study, direct shear tests with different scales were carried out on sandstone specimens. Acoustic Emission (AE) and Digital Image Correlation (DIC) techniques were utilized to monitor the damage procession of the specimens. The evolution process of the specimen was divided into stages and three threshold points were determined based on AE parameters. As the scale decreased, the Joint Roughness Coefficient (JRC) increased, the tensile failure increased, and the shear failure decreased. As the normal stress increased, the JRC with the same scale decreased, the tensile failure decreased, and the shear failure increased. The change of fracture mechanism was the primary reason for the strength deterioration with decreasing scales. The decrease of the scale was not conducive to the failure prediction. By improving the rock bridge failure potential (RBP) index, the proposed RBPn index could appropriately characterize scale effects under different normal stresses.

Numerical simulation of failure and micro-cracking behavior of non-persistent rock joint under direct shear

Persistency, as a key geometric parameter of joints, significantly affects shear strength parameters of jointed rock mass. A good understanding of how persistency affects shear behavior of joint is therefore crucial for better evaluation of stability of rock slope. To investigate the failure and micro-cracking behavior of non-persistent rock joint under direct shear, a novel Voronoi generation algorithm is first used to establish an improved grain-based model (GBM) of granite which considers the shape of feldspar. The calibrated model is then used to simulate the direct shear test of numerical models possessing different joint persistency under various normal stresses. The results reveal that the developed micro-cracks generally increase rapidly when the shear strain reaches to a value approximately 50 % of the peak shear strain and the grain boundary tensile micro-crack is dominant among these initiated micro-cracks. Micro-cracks generally initiate at the ends of rock bridge, and then gradually propagate to the central of rock bridge, forming en-echelon fractures. The failure mode of numerical model is closely related to the generated en-echelon fractures. An increase in both joint persistency and normal stress can lead to a shear failure. The finding in this study provides an important basis for understanding the mechanical behavior and failure mechanism of jointed rock mass.

Experimental investigation of failure mechanism of fissure-filled sandstone under hydro-mechanical conditions

Fissure fillings are critical to the hydro-mechanical properties of jointed rock masses in rock engineering. In this study, triaxial seepage tests were performed on standard cylindrical fissure-filled sandstone. The characteristics of stress–strain relationships, absorption and consumption of energy, variations in deformation resistance, and permeability evolution during the experimental process, along with the crack development observed in post-failure computed tomography scan images of the sandstone specimens were analyzed. The results demonstrate that the fillings improve the energy capacity and reduce the damage accumulation of sandstone specimens, with sand-filled specimens performing better than mud-filled specimens, especially at lower bridge angles. The fillings can reduce the depth of crack extension and lessen the influence of prefabricated fissures on sandstone failure, with this effect diminishing as the rock bridge angle increases. Permeability decreases in the pre-peak failure stage as the fillings improve the deformation resistance of the sandstone specimens. In the post-peak failure stage, the fillings and rock debris generated by the sandstone failure move within the developed fractures, causing significant fluctuations in permeability. These findings deepen the understanding of the hydro-mechanical properties of jointed rocks and provide a scientific basis for stability analysis in rock engineering.

Exploring the influence of rock bridge angle on the rock secant modulus.

Rock can undergo shape deformation and damage due to the influence of joint fissures, and the range of damage caused by joints at different rock bridge angles varies. To study the influence of rock bridge angle on the size effect of rock secant modulus, this paper adopts the principle of regression analysis and combines numerical simulation to carry out relevant research. The research results indicate that: (1) As the rock bridge angle increases, the secant modulus gradually decreases, following a power function relationship. (2) As the rock size increases, the secant modulus shows a trend of first decreasing and then stabilizing, following a power function relationship. (3) As the rock bridge angle increases, the characteristic tangent modulus and characteristic size gradually decrease, following a power function relationship. On this basis, we obtained their relationship formulas separately.

Crack propagation process in double-flawed granite under compression using digital image correlation method and numerical simulation

The existence of flaws seriously weakens the rock strength, directly affects the crack expansion morphology, and indirectly affects the slope stability. In this study, uniaxial compression tests were carried out on double-flawed granite to investigate the effects of flaw angle on its compressive strength and crack coalescence based on DIC technology and PFC2D numerical simulation. The result indicates that the UCS values of flawed specimens at angles of 15°, 30°, 45°, and 60° are approximately 25.5–51.7% lower than that of the intact specimen. The failure strength of the double-flawed sample increases with the increase of flaw inclination angle, and the fracture morphology shifts from no expansion to split expansion. When the flaw tip strain of each flaw sample exceeded 0.6%, the stress concentration was generated at the flaw tip, and the sample began to appear macroscopic large cracks. DIC technique can well observe the crack initiation and propagation process, recording inclined shear strain bands at flaw tips, tensile strain bands in the middle of flaws, and tensile shear O-shaped strain ring in rock bridge areas. Numerical simulations using PFC2D software were carried out and showed a good agreement with the physical results. In addition, the effect of structural inclination on specimen failure strength is clearly explained by the theory of compressive damage based on the projected size of flaws. The deformation of rock mass is not a simple material deformation but is composed of material deformation and structural deformation. These experimental and numerical results enhance our understanding of crack initiation and coalescence characteristics, aiding in the analysis of rock structure stability in scenarios such as excavated underground openings, slopes, and tunneling construction, where pre-existing cracks or step-path fractures are pivotal to structural integrity.

Numerical characterization on fracture evolution behavior of pre-flawed sandstone under monotonic and multilevel cyclic loading

This study employed an improved stress corrosion model within a three-dimensional particle flow program to investigate the mechanical and cracking behavior of fractured sandstone samples with varying rock bridge angles under both monotonic loading and multilevel cyclic loading. Firstly, using the experimental results from intact sandstone under uniaxial compression, we calibrated the microscopic mechanical parameters of the parallel bond model. Then, the model was validated using the experimental results of fractured sandstone under monotonic and cyclic loading. Finally, the initiation, propagation, and coalescence behavior of cracks in fractured sandstone samples under the above two loading paths, as well as the evolution process of the stress field, displacement field, and force chain distribution, were discussed in detail. The results show that the stress–strain curves, strength, deformation parameters, and macroscopic failure modes obtained from numerical simulations are consistent with those from laboratory mechanical tests. The mechanical behavior of fractured sandstone is influenced by both the rock bridge angle and the loading path. As the rock bridge angle decreases, the mechanical parameters of the sample show an increasing trend, and the influence of rock bridge angle on the failure mode is reduced. Cracks in the samples all initiate at the tips of pre-existing flaws, and the rock bridge angle affects the crack propagation and coalescence process: for sandstones with smaller rock bridge angles, cracks gradually extend to the sample’s ends; for sandstones with larger rock bridge angles, direct coalescence of cracks at the rock bridge is observed, then extending to the sample’s ends. Compared with monotonic loading, the damage degree of sandstone samples under multilevel cyclic loading is more severe, and even obvious block spalling is observed. The experimental and numerical simulation results are expected to improve the understanding of the mechanical behavior and fracture behavior of fractured rocks under monotonic and multilevel cyclic loading.

Experimental and Simulation Studies on the Effect of Rock Bridges on Rock Failure

Experimental and Simulation Studies on the Effect of Rock Bridges on Rock Failure

Research on triaxial compressive mechanical properties and damage constructive model of post-thawing double-fractured quasi-sandstones with different angles

Joints and fractures lead to different failure mechanisms in rock masses under different environments. The mechanical properties and failure mechanisms of rocks with fissures are key problems in rock mass engineering. Parallel double-fracture quasi-sandstone specimens with different dip angles were prepared and subjected to triaxial compression tests after a single freeze-thaw cycle. Pore development, crack propagation, damage evolution, and failure characteristics were analysed. Combined with the strength distribution theory of microelements and the static elastic modulus theory, a damage constitutive model of double-fracture quasi-sandstone under freeze-thaw cycles and loads was established. This study explored the pore development, fracture propagation, damage evolution, and failure characteristics of fractured sandstone after thawing. The results showed that the compression wave velocity of the thawed specimens decreased, the nuclear magnetic resonance (NMR) T2 curve shifted to the right, and the frost heave force promoted the development of the internal porosity in the specimens. With an increase in the crack dip angle, peak stress, expansion stress, cohesion and internal friction angle, the specimen showed a ‘U’ shaped change trend, compression cracks, and rock bridge penetration rate after failure decreased, and mixed failure of tension and shear gradually changed into shear failure. When the dip angles were 30° and 60°, the double fractured quasi-sandstone had larger total damage and more obvious brittle failure characteristics.

Failure Mechanism and Control Mechanism of Intermittent Jointed Rock Bridge Based on Acoustic Emission (AE) and Digital Image Correlation (DIC).

Deep foundation pit excavation is an important way to develop underground space in congested urban areas. Rock bridges prevent the interconnection of joints and control the deformation and failure of the rock mass caused by excavation for foundation pits. However, few studies have considered the acoustic properties and strain field evolution of rock bridges. To investigate the control mechanisms of rock bridges in intermittent joints, jointed specimens with varying rock bridge length and angle were prepared and subjected to laboratory uniaxial compression tests, employing acoustic emission (AE) and digital image correlation (DIC) techniques. The results indicated a linear and positive correlation between uniaxial compressive strength and length, and a non-linear and negative correlation with angle. Moreover, AE counts and cumulative AE counts increased with loading, suggesting surges due to the propagation and coalescence of wing and macroscopic cracks. Analysis of RA-AF values revealed that shear microcracks dominated the failure, with the ratio of shear microcracks increasing as length decreased and angle increased. Notably, angle exerted a more significant impact on the damage form. As length diminished, the failure plane's transition across the rock bridge shifted from a complex coalescence of shear cracks to a direct merger of only coplanar shear cracks, reducing the number of tensile cracks required for failure initiation. The larger the angle, the higher the degree of coalescence of the rock bridge and, consequently, the fewer tensile cracks required for failure. The decrease of length and the increase of angle make rock mass more fragile. The more inclined the failure mode is to shear failure, the smaller the damage required for failure, and the more prone the areas is to rock mass disaster. These findings can provide theoretical guidance for the deformation and control of deep foundation pits.

A true triaxial experiment investigation of the mechanical and deformation failure behaviors of flawed granite after exposure to high-temperature treatment

Understanding the mechanical and deformation failure behaviors of heated flawed granite under true triaxial stresses is of great significance for evaluating the wellbore stability in developing hot dry rock resources. In this study, true triaxial experiments are conducted on flawed granite specimens of a varying flaw overlapping length lfo with and without high temperature (HT) treatment, with the emphases on the crack development under true triaxial stresses and its correlations with the strength, plastic anisotropy and failure forecast. Investigations demonstrate that HT, σ2 (intermediate principal stress) and lfo, significantly affect the mechanical properties of flawed granite. Due to strong 3D confinement, the loop crack, the secondary transverse crack and the far-field crack are frequently induced in flawed granite, unlike experiments of uniaxial, biaxial and conventional triaxial compression. When increasing lfo, the rock bridge undergoes the stress amplification which tendentiously drives the internal crack coalescence and typically causes a reduced strength. The PSIRs (Plastic Strain Increments Ratios) analysis, first extended to the true-triaxial experimental data, reveals that the 3D stress-induced extensional/shear fracturing from the flaw tips in σ2-direction is the mechanism of the plastic anisotropy generated. Besides, an attempt to anticipate the failure time in the framework of the time‐reversed Omori’s law suggests a poor predictability by using the acoustic emission but a higher-quality forecast (being more precise and less biased) by using the dissipated energy.

Mechanical characteristics and damage model for rock-like specimen with two parallel grout-filled cracks

To investigate the mechanical properties of rock-like specimens with two parallel cracks filled with grout, uniaxial compression tests in combination with digital image correlation (DIC) and acoustic emission (AE) techniques have been performed on grout-filled cracked specimens with different rock bridge dip angles β. Results indicated that with the increase of β, the uniaxial compression strength, cumulated AE count, AE energy, as well as shear crack proportion initially decreases and subsequently increases. The overall AE b-value and the DIC-based maximum principal strain initially increases and subsequently decreases as β increases. The failure mode also varies from tensile to mixed tensile-shear mode. Furthermore, a particle flow code (PFC) model, which considers the grout filling, grout-rock interface, and rock, has been proposed. Numerical results showed that the range of microcracks inclination angle first decrease from 70°−100° to 70°–90° and then increases to 70°–110°. Besides, existence of grout filling and changes of bridge angle leads to significant difference in PFC particle displacement, which can cause the changed of crack initiation positions and failure modes. Finally, a damage model considering stress intensity factor for the grout-filled specimen was established. Both of pre-crack damage and loading damage were considered in this model, and a damage repair factor was proposed to describe effect of grout filling. The results showed that grouting could can effectively suppress stress concentration caused by pre-existing crack, thereby changes the strength of cracked specimen.

Investigation of acoustic events during shear loading of layered rock bridge: particle flow code approach

Investigation of acoustic events during shear loading of layered rock bridge: particle flow code approach

Investigation of the mechanical behavior of rock-like material with two flaws subjected to biaxial compression

The biaxial compression experiments of rock-like materials with two flaws are carried out under different flaw inclination angle, rock bridge ligament angle, lateral stress. The experimental studies show that crack propagation modes of rock-like material are as follows: wing crack through mode (Y mode), shear crack through mode (J mode), mixed crack through mode (wing shear JY mode), longitudinal extension of crack and transverse shear splitting. prefabricated fractured rock specimens have experienced the closing stage of prefabricated fractures, the elastic deformation stage, the generation and expansion of cracks (or plastic strengthening), and the residual loading stage. The peak strength of the specimen is increases with the increase of flaw inclination angle and lateral stress. With the increase of the rock bridge ligament angle, the failure of the rock bridge region changes from the shear crack failure to composite failure of shear crack and the wing type tensile crack failure, and then to the wing crack failure. With the increase of the lateral pressure, the failure of the specimen changes from the wing type tensile crack failure to the wing type and shear crack failure, and then to shear crack failure. The flaw inclination angle mainly changes the form of crack growth but does not effect on the failure modes. The counting number of acoustic emission events at the center of the sample is relative large, indicating that the cacks appear in the part of the rock bridge firstly. With the increasing of loads, the cracks of the rock bridge expanding constantly and connecting finally. The changes of acoustic emission event counts is consistent with the macroscopic damage form obtained from the experiments.

Investigation on uniaxial compression and fracture damage mode of prefabricated parallel double-jointed red sandstone.

As a special type of joint fracture, the fracture evolution characteristics of parallel double joints have important engineering significance for the stability analysis of fractured rock mass. In this work, a new method for calculating stress intensity factor of parallel double-jointed fractures was importantly proposed. Physical uniaxial compression tests were carried out on parallel double jointed red sandstone filled with cement mortar under different geometric parameters, and the macroscopic mechanical properties and failure characteristics of red sandstone are deeply analyzed. The results show that the larger the connectivity rate is, the smaller the peak stress and strain are. The increase of connectivity rate will affect the change rate of transverse strain in the center of rock bridge. The closer the dip angle of the joint is, the lower the peak stress is and the shorter the failure time is. The damage mode of joint tip encroachment affects the lateral displacement of the rock bridge center, and the displacement is always close to the first damage section. The closer the joint tip is to the load, the easier the end-face penetrating cracks occur. The research content can provide basic support for guaranteeing the stability of underground engineering rock mass.

Study of the mechanical properties and propagation mechanisms of non-coplanar and discontinuous joints via numerical simulation experiments

Non-coplanar and discontinuously jointed rock masses are more complex than coplanar and discontinuously jointed rock masses. The mechanical properties and propagation mechanisms of non-coplanar and discontinuous joints were studied via direct shear tests with microscopic numerical simulation experiments. The numerical simulation tests were performed under different normal stresses, joint inclination angles, and shear rates. The numerical experimental results show that the microscale failure of non-coplanar and discontinuously jointed rock masses is mainly caused by tensile cracks. Additionally, when the peak shear stress is reached, the growth rate of cracks increases rapidly, and the number of cracks increases with increasing normal stress. The shear strength of non-coplanar and discontinuously jointed rock masses increases with increasing normal stress. Under the same normal stress, the variation curves of the shear strength of non-coplanar and discontinuously jointed rock masses with respect to the dip angle exhibit an “S”-shaped nonlinear pattern. Rock masses with joint inclination angles of approximately 15° and 65° have minimum and maximum shear strengths, respectively. The joint dip angle has a significant impact on the final failure mode of rock bridges in the rock mass. As the joint dip angle increases, the final failure modes of rock bridges change from “end-to-end” connection to a combination of “head-to-head” and “tail-to-tail” connections. The shear rate has a certain impact on the peak shear stress, but the impact is not significant. The spatial distribution of the tensile force chains changes as shearing progresses, and stress concentration occurs at the tips of the original joints, which is the reason for the development of long tensile cracks in the deeper parts.

Study on the influence of rock bridge angle on the size effect of rock uniaxial compression.

As a basic parameter of rock, the rock bridge angle plays an important role in maintaining the stability of rock masses. To study the size effect of rock bridge angle on the uniaxial compressive strength of rocks, this paper adopts the principle of regression analysis and combines numerical simulation to carry out relevant research. The research results indicate that: (1) the uniaxial compressive strength decreases with the increase of the rock bridge angle, showing a power function relationship; (2) The uniaxial compressive strength decreases with the increase of rock size and tends to stabilize when the rock size is greater than 350 mm, showing a significant size effect. (3) The fluctuation coefficient of compressive strength increases with the increase of rock bridge angle and decreases with the increase of rock size; When the rock size is 350 mm, the fluctuation coefficient is less than 5%; (4) The characteristic compressive strength and characteristic size both increase with the increase of the rock bridge angle.

A comparative study of progressive failure of granite and marble rock bridges under direct shearing

Shear failure of rock bridges is an important process in geological phenomena, including landslides and earthquakes. However, the progressive failure of natural rock bridges has not yet been fully understood. In this work, we carried out direct shearing experiments on both granite and marble rock bridges, and applied acoustic emission (AE) monitoring throughout the experiments. With the mechanical curves and the evolution of AE activity (including AE energy rate and b value), the failure of rock bridges can be divided into three pre-failure phases and one ultimate failure phases. We analyzed the effects of normal stress and lithology on the pre-failure phases. We noted that with the increasing of normal stress, the length of stable cracking phase decreases and the length of unstable cracking phase slightly increases, except for marble rock bridges at high normal stress, which maintains a great proportion of stable cracking phase that possibly results from the great off-fault damage. Increasing normal stress also suppresses the dilation of granite rock bridges, but has a different effect on marble rock bridges, which also suggests the effect of lithology on failure modes.

Failure behaviour of frozen rock with double ice-filled flaws under Brazilian splitting tension

Geotechnical engineering in cold regions frequently involves dealing with frozen fractured rock masses, particularly in the activities of strip mining and tunnel support design, where tensile failure predominates as the main failure mode in stress-driven failures. Seasonal freezing can adversely affect the performance of rock masses. To investigate the tensile characteristics of frozen rock masses, marble specimens with double parallel ice-filled flaws were artificially frozen and subjected to Brazilian splitting experiments at a loading rate of 0.001 mm/s. The influence of the angle of the double coplanar flaws and the rock bridge angle of ice-filled flaws on the tensile behaviours were numerically studied by RFPA3D (3D Rock Failure Process Analysis), a finite element method specifically developed for simulating rock failure. Results showed that as the angle of the double parallel ice-filled flaws increases, tensile strength initially decreases and then increases. Furthermore, in specimens with the double coplanar ice-filled flaws, an increase in the angles of the flaws and rock bridge leads to a gradual decrease in tensile strength. The spatial distribution of ice-filled flaws is a crucial factor that influences the failure mode after split cracking occurs. The ice filling and bonding mechanism controls the tensile strength and cracking behaviour of frozen rock masses. The findings of this study provide valuable insights and serve as a theoretical foundation for designing blasting parameters and disaster prevention in strip mines located in cold regions.

Dynamic mechanical properties and failure mechanisms of rock-like materials containing main and auxiliary holes with various arrangement inclinations and spacing ratios

As a typical rock defect, circular holes significantly influence rock masses, diversifying their failure modes and ultimately weakening their bearing capacities. To study the effects of hole arrangement inclination and spacing ratio on the mechanical properties and failure mechanisms of rock-like specimens, dynamic uniaxial compressive tests were conducted by employing a modified split Hopkinson bar apparatus and digital image correlation. The results reveal a V-shaped trend in the peak stress, Young’s modulus, and absorbed energy proportion as the hole arrangement inclination increases from 0° to 90°. However, the peak strain is insensitive to changes in the hole arrangement inclination and spacing ratio. The hole spacing ratio has no significant effect on the Young’s modulus, but it causes a gradual reduction in the proportion of energy absorbed in the specimens. Moreover, shear and tensile cracks emanating from the main hole dominate the failure mode of specimens with main and auxiliary holes, as demonstrated by the resultant displacement and vertical strain contours. Rock bridges experience shear failure as the hole arrangement inclination increases from 15° to 75°, whereas the rock bridges of specimens with various hole spacing ratios tend to fail owing to tensile cracks. The interaction between main and auxiliary holes with an arrangement inclination of 0° is the weakest, suggesting that tunnel groups should be arranged perpendicularly to the direction of dynamic loading.