Rock Deformation Research Articles

A Brittle Constitutive Law for Long‐Term Tectonic Modeling Based on Sub‐Critical Crack Growth

AbstractAdequate representations of brittle deformation (fracturing and faulting) are essential ingredients of long‐term tectonic simulations. Such models commonly rely on Mohr‐Coulomb plasticity coupled with prescribed softening of cohesion and/or friction with accumulated plastic strain. This approach captures fundamental properties of brittle failure, but is overly sensitive to empirical softening parameters that cannot be determined experimentally. Here we design a brittle constitutive law that captures key processes of brittle deformation, and can be straightforwardly implemented in standard geodynamic models. In our Sub‐Critically‐Altered Maxwell (SCAM) flow law, brittle failure begins with the accumulation of distributed brittle damage, which represents the sub‐critical lengthening of tensile micro‐cracks prompted by slip on pre‐existing shear defects. Damage progressively and permanently weakens the rock's elastic moduli, until cracks catastrophically interact and coalesce up to macroscopic failure. The model's micromechanical parameters can be fully calibrated against rock deformation experiments, alleviating the need for ad‐hoc softening parameters. Upon implementing the SCAM flow law in 2‐D plane strain simulations of rock deformation experiments, we find that it can produce Coulomb‐oriented shear bands which originate as damage bands. SCAM models can also be used to extrapolate rock strength from laboratory to tectonic strain rates, and nuance the use of Byerlee's law as an upper bound on lithosphere stresses. We further show that SCAM models can be upscaled to simulate tectonic deformation of a 10‐km thick brittle plate over millions of years. These features make the SCAM rheology a promising tool to further investigate the complexity of brittle behavior across scales.

Integrated early warning and reinforcement support system for soft rock tunnels: A novel approach utilizing catastrophe theory and energy transfer laws

The initial support strength of deep-buried soft rock tunnels during excavation is often inadequate, and the timing of reinforcement support is inappropriate. This inadequacy leads to significant deformations in the tunnel, causing the energy released by the surrounding rock to exceed the energy that the support system can absorb, ultimately resulting in tunnel collapse. Tunnel deformation monitoring and anchorage support, when combined with energy transfer laws, are thus imperative for studying collapse prediction, the timing of reinforcement support, and parameters of the reinforcement support system of the surrounding rock. In this paper, a novel approach for early warning and support control in tunnel construction facing large deformations is introduced, and a predictive model for surrounding rock instability utilizing catastrophe theory and energy transfer laws is developed. By analyzing the correlations of rock deformation and energy dissipation, the timing of anchor reinforcement support was determined using function fitting techniques. Further, an energy transfer model under reinforced anchoring support was established, and the energy absorption parameters of the support body were determined. Also, the support parameter design scheme was proposed. The results indicate that the early warning and reinforcement support scheme proposed in this paper reduces the release of potential energy by 35.71 %; decreases the number of steps needed to reduce kinetic energy to zero by 66.67 %; reduces the total dissipated energy in joint shear by 33.68 %; increases the total stored strain energy in the material by 5.70 %; and reduces the total dissipated work in plastic deformation by 26.15 %. Additionally, this plan effectively controls the originally predicted large deformation area of the meter level to within 350 mm.

ON THE INFLUENCE OF EXOGENEOUS PROCESSES ON THE RESULTS OF MEASURING MOVEMENTS OF GEODESIC MARKINGS

The influence of exogenous processes on geodetic marks is multifactorial, and in modern observation practice there is no clear scientifically based system of engineering and geodetic forecasting of neotectonics influence on the results of repeated high-precision leveling, on the basis of which it would be possible to solve the issues of stability of depth, soil and rock leveling marks, as well as modeling the mechanism of influence of exogenous processes on the results of repeated leveling. Therefore, the study of their influence is an urgent task. The study is aimed at determining the influence of exogenous processes on the results of measurements of geodetic marks displacements during observations at local geodynamic polygons in the Kryvyi Rih region. The work performed has shown that the temperature factor is periodic in nature and therefore its influence on the stability of the reps also naturally varies over time: it changes linearly in the time interval March-May and September-November, sinusoidally in June-August, if divided into separate parts. Although, in general, the temperature change can be described as a sinusoid. A linear correlation has been established, but it should be noted that it can be broken by the imposition of a stronger factor that determines the dynamics of the movement of the rappers. There is no clear connection between temperature changes Δt and exceedances Δh in the time interval May-July. The intensive increase in temperature corresponds to the lowering of soil references, which is inconsistent with the general theory of their stability. The phase shift is more than two months, which indicates the influence of another, stronger factor than temperature on the stability of soil references. Periodic changes in atmospheric temperature cause thermal deformations of rocks, which, due to differences in thermal properties and temperature conditions of rocks, have a complex differentiated structure in space and time, which is manifested in heterogeneous vertical displacements of the references underlying these rocks. The revealed regularities of the temperature factor and the instability of the references caused by this factor made it possible to predict its value and recommend a scheme of time periods for field measurements in repeated cycles.

Effect mechanism of seepage force on the hydraulic fracture propagation

The flow of fluid through the porous matrix of a reservoir rock applies a seepage force to the solid rock matrix. Although the seepage force exerted by fluid flow through the porous matrix of a reservoir rock has a notable influence on rock deformation and failure, its effect on hydraulic fracture (HF) propagation remains ambiguous. Therefore, in this study, we improved a traditional fluid–solid coupling method by incorporating the role of seepage force during the fracturing fluid seepage, using the discrete element method. First, we validated the simulation results of the improved method by comparing them with an analytical solution of the seepage force and published experimental results. Next, we conducted numerical simulations in both homogeneous and heterogeneous sandstone formations to investigate the influence of seepage force on HF propagation. Our results indicate that fluid viscosity has a greater impact on the magnitude and extent of seepage force compared to injection rate, and that lower viscosity and injection rate correspond to shorter hydraulic fracture lengths. Furthermore, seepage force influences the direction of HF propagation, causing HFs to deflect towards the side of the reservoir with weaker cementation and higher permeability.

A study on the reasonable width of narrow coal pillars in the section of hard primary roof hewing along the air excavation roadway

AbstractAiming at the reasonable width of the narrow coal pillar of a fully mechanized caving face and the safety support of roadway, taking the coal pillar in the section between 110503 and 110505 face of the Yushuling Coal mine as the research background, a model of the hard basic roof fracture structure of fully mechanized caving face is established through theoretical analysis, and the roadway with narrow coal pillar is analyzed mechanically. Combined with the geological conditions of the working face, it is concluded that the low‐stress area is less than 3.29 m. When the internal stress field of the low‐stress environment is considered in the roadway layout, the influence of mining and the essential roof hardness should be considered. The reasonable size of the narrow coal pillar is 3 ~ 6 m, thinking that the load borne by the coal pillar is less than the ultimate strength of the coal pillar. The limit equilibrium theory calculates that the reasonable width of a coal pillar is at least 4 m. The stress and displacement of coal pillars with different widths of 3, 4, 5 and 6 m are analyzed by numerical simulation, and the 4 m narrow coal pillars are simulated and verified. Field industrial tests show that coal pillar and roadway surrounding rock deformation are small under asymmetric surrounding rock control. The research results have been successfully applied to engineering practice and can provide a reference for the research method of narrow coal pillar width under a hard basic roof.

Stability control of goaf‐driven roadway surrounding rock under interchange remaining coal pillar in close distance coal seams

AbstractThe roadway surrounding rock stability under the influence of interchange remaining coal pillar in close distance coal seams is one of the key factors affecting the coal mines safe and efficient mining. To reduce the roadway deformation, theoretical analysis, numerical simulation, and on‐site verification were used to study the influence of geological, mining, and support factors on the stability of the floor roadway surrounding rock. A design method for strengthening the roadway surrounding rock support was proposed. The results showed that the coal seam depth, the distribution characteristics of the remaining coal pillar load, the starting point position of stress recovery in the upper coal seam goaf and the lower coal seam goaf lateral load had a significant influence on the lower coal seam stress. The peak stress in the lower coal seam increased linearly with the increase of the coal seam depth, the remaining coal pillar, and the lower coal seam goaf lateral peak stress. The remaining coal pillar influence area width increased linearly and exponentially with the increase of the remaining coal pillar width and the distance between the starting point of stress recovery in goaf and the coal pillar edge, respectively. The peak stress and shear strength of the narrow coal pillar decreased exponentially with the increase of the spacing between bolts or cables. The roadway surrounding rock deformation decreased exponentially with the increase of the distance between the strengthening support area and the remaining coal pillar edge. For the Baigou coalmine, a design scheme for bolt strengthening support parameters has been proposed. The roadway surrounding rock deformation tended to stabilize after 21 days, with deformation values of 264 and 488 mm for the roof and floor, and two sides, respectively.

Study on Support Technology of Truss Anchor Cable Beam in Deep Soft Rock Roadway Excavation

Aiming at the difficult problem of soft rock roadway support in deep mine, the support mode of "truss anchor beam" is proposed, and the support mode technology of truss anchor beam in deep soft rock roadway driving is studied by FLAC simulation software. Combined with the measured displacement of coal and rock around underground roadway under this support mode, it is concluded that the truss anchor beam support mode can introduce the high stress of shallow coal and rock around roadway into deep area, thus effectively controlling the deformation of coal and rock around roadway and ensuring safe and efficient production of mine.

Kinematics of the Clarke River Shear Zone (northeastern Australia) and implications for the tectonic evolution of the Tasmanides

The Clarke River Shear Zone marks the boundary between the Thomson and Mossman orogens in the northeastern Tasmanides. To better understand the kinematic history of this east-northeast-trending shear zone, and its role during the tectonic history of eastern Gondwana, we investigated rock deformation along a segment of the Clarke River Shear Zone. Based on field observations, interpretation of aeromagnetic data and microstructural analysis, we show that the Clarke River Shear Zone experienced at least three phases of reactivation. Gently plunging stretching lineation and kinematic indicators, such as steeply plunging asymmetric folds and asymmetric porphyroclasts, correspond to an early phase of sinistral strike-slip ductile shearing. Subsequent general dextral shear deformation is suggested based on the presence of S-tectonites, symmetric porphyroclasts and kinematic indicators with dominant dextral and subordinate sinistral shear senses. This phase, which occurred under amphibolite-facies metamorphic conditions, was contemporaneous with the emplacement of the Craigie Tonalite, for which we obtained a new zircon U–Pb crystallisation age of 410.3 ± 1 Ma. A later reactivation phase along the Clarke River Shear Zone, under brittle conditions, is indicated by the presence of cataclasite zones and chlorite–epidote alteration. Based on our findings, and regional information on the tectono-magmatic evolution of northeastern Queensland, we suggest that the Clarke River Shear Zone was possibly a sinistral transform fault during the Silurian. During the Devonian, it is possible that deformation along the Clarke River Shear Zone was related to the transition between the non-retreating subduction zone in the north, and the highly mobile (retreating) plate boundary farther south. However, the dextral kinematic component associated with this deformation is not fully explained. Brittle deformation, likely associated with dextral transpression during the Carboniferous, marked the last stage of activity along the Clarke River Shear Zone.

Deformation and Failure Evolution Law and Support Optimization of Gob-Side Entry in Weakly Cemented Soft Rock under the Influence of Fault

Under the condition of weakly cemented soft rock in Western China, the surrounding rock deformation of gob-side entry is obvious, especially under the influence of fault, and the problem of surrounding rock control becomes increasingly prominent. To solve this issue, this paper firstly studied and obtained the evolution law of the ground pressure appearance of the gob-side entry in the fault area, then put forward the concept of surrounding rock control in the fault area of the gob-side entry, put forward a targeted pressure relief + increase preload + passive reinforcement parallel to the roadway surrounding rock strengthening control scheme, and carried out field applications. The results show that the roof subsidence and mining side heave of the roadway in the fault area increase significantly, accompanied by the characteristics of broken cables, the length of the broken cable is 0.2 m–0.6 m, and the breaking process is divided into multiple breaks. The stress evolution of gob-side entry in fault area presents a stage characteristic of “rapid growth-stable.” The surrounding rock control effect is improved under the bolt cable high pre-tightening support, and the roadway deformation is effectively controlled under the pressure relief + active + passive support, with a good application effect.

Study on Pretightening Loss Effect of Bolt Support in Deep Soft Rock Roadway

The magnitude of pretension force serves as an important indicator of the effectiveness of anchor bolt active support and is one of the significant factors influencing the stability of tunnel surrounding rock. Therefore, in practical engineering, it is crucial to establish the relationship between pretension torque and pretension force. However, current research in this field has some limitations. With a specific mine in western China as the engineering background, this paper first analyzed the influence factors of surrounding rock deformation and failure, established a mechanical model for pretension structure of anchor bolt support, and derived the quantitative relationship between pretension torque and pretension force based on hypothetical conditions. Finally, it proposed the loss effect of anchor bolt support and modified the pretightening loss coefficient for engineering application. The research results show that the actual pretightening force of anchor support is lower due to the influence of deep soft coal seam, which leads to failure of coal pillar under mining stress. The loss effect of surrounding rock on pretightening force was represented by a coefficient k, and the modified value of the coefficient was calculated as 0.19∼0.43. By applying the modified relationship between pretightening torque and pretightening force, it was found that the actual pretightening torque of 300 Nm applied to 11307 return air roadway effectively controlled surrounding rock deformation and failure, with coal pillar displacement less than 120 mm.

Experimental study of mechanical properties of artificial dam for coal mine underground reservoir under cyclic loading and unloading

This study investigates the stability of an artificial dam used in an underground reservoir in a coal mine under periodic weighting imposed by overlying rock strata. For this purpose, cyclic loading and unloading tests with different stress amplitudes were designed. Differences in the mechanical performance of the artificial dam with and without overlying strata were analyzed using a uniaxial compression test. The mechanical properties of the structure under constant-amplitude cyclic loading and unloading were characterized. Further, the law of influence of stress amplitude on stability was discussed. A formula for predicting the mechanical performance of the artificial dam with its overlying rocks (hereafter referred to as the complex) was finally derived and was suitable for clarifying the law of damage in the complex under cyclic loading and unloading. The results showed that the complex had changed the internal structure of rocks. The strength and deformation of the complex were intermediate to that of either single structure. All three underwent brittle failure. During the constant-amplitude loading and unloading tests, the hysteresis loop could be divided into three phases, namely, sparse, dense, and sparse again, with a shift in the turning point in rock deformation memory effect. As the stress amplitude increased during the test, the damping ratio of the specimens decreased, and the area of the hysteresis loop increased non-linearly. The dynamic elastic modulus decreased first and then increased. The confidence interval for the formula fitted based on the test results was above 97%. Damage to the complex caused by constant-amplitude loading and unloading could be divided into three stages. An increase in peak stress served as a catalyst for the evolution of small cracks within the specimens into median and large cracks, thereby accelerating the damage process.

Fatigue Damage of Rubber Concrete Backfill at Arch Springing Influence on Surrounding Rock Deformation in Tunnel Engineering

The backfill area of tunnel projects may deform or collapse due to the cyclic disturbance of groundwater and train loads. Hence, the anti-deformation and crack resistance performance of backfill materials under cyclic disturbance is critical to engineering safety. In this paper, concrete was produced by mixing 0.85 mm, 1–3 mm and 3–6 mm rubber particles instead of 10% sand, and tested to discuss the effect of rubber particle size on the deterioration of concrete material properties (compressive characteristics and energy dissipation) after bearing cyclic loading. The stress–strain curve and various parameters obtained through the uniaxial compression test and cyclic load test were used to explore the optimal grain size that can be applied to the tunnel engineering backfill area, and numerical simulation was adopted to calculate the deformation of the surrounding rock and the structural stress of different backfill materials. Research shows that the increase in particle size lessens the compressive strength, deformation resistance and cracking resistance of specimens, but after the cyclic loading test, the concrete material deterioration analysis indicates that rubber concrete has lesser and more stable losses compared to ordinary concrete, so the optimum rubber particle size is 0.85 mm. Numerical calculations show that RC-1 reduces the arch top displacement by 0.4 mm, increases the arch bottom displacement by 0.6 mm and increases the maximum principal stress by 11.5% compared to OC. Therefore, rubber concrete can ensure the strength and stability requirements of tunnel structures, which can provide a reference for similar projects.

Research on Double-Layer Support Control for Large Deformation of Weak Surrounding Rock in Xiejiapo Tunnel

Double-layer primary support is proposed to control the deformation of surrounding rock in tunnels within weak geological conditions, where engineering challenges such as large deformations, tunnel faces, and arch collapse are encountered. This approach is based on the principle of combined resistance and release. A combined approach of numerical modeling and on-site surveillance was utilized to analyze the displacement and stress state of the tunnel support structure at different construction stages of primary support for the second layer, using Xiejiapo Tunnel as an engineering case. The findings indicate that the implementation of two-layer primary support can mitigate the progression of large deformations effectively in weak surrounding rock; the sooner the primary support for the second layer is applied, the better the deformation control, and the later the application takes place, the more effectively the tension in the surrounding rock is diminished, whereby the self-supporting capacity of surrounding rock comes into its own. The force of the shotcrete is reduced. Considering the structural deformation and stress state, as well as combination of resistance and release, it is best to implement the primary support for the second layer 10 feet behind the primary support for the first layer.

Mesoscopic precursor anomaly characteristics of red sandstone under uniaxial compression after cyclic high-temperatures

The deformation and failure characteristics of rock caused by periodic changes of temperature are not only significantly different from that under normal temperature, but also significantly different from that produced by a single high-temperature event. Here, using a three-dimensional digital image correlation (3D-DIC) integrated test system, mechanical and micro-damage tests of red sandstone are performed under cycles of high-temperature and natural-cooling with a temperature range of 25°C to 300°C and the number of cycles varying between 0 and 25. Macroscopic, mesoscopic and microscopic characteristics such as rock strength, deformation, strain field and fracture morphology are examined and their evolution with the number of heating-cooling cycles is discussed. Using the time-history evolution of the differentiation rate of the precursor anomaly (En), the characteristic coefficient (K) and the damage variable (DF), three kinds of characteristic time points are put forward to quantify the incubation and development time of precursor abnormal characteristics and are used to divide the whole process of deformation and failure. These time points are the precursor abnormal differentiation time (PADT) tE, the precursor abnormal startup time (PAST) tK, and the precursor abnormal failure time (PAFT) tD. Test results show that: (1) The action of cyclic high-temperature natural-cooling not only shows the strengthening effect of temperature, but also shows the strengthening effect of a certain number of cycles. (2) The evolution sequence of the three precursor abnormal characteristic moments is PADT, PAST and PAFT in turn, and this sequence can intuitively describe the whole complex process of rock deformation and failure, and there are wave peaks in the evolution curve with the number of high-temperature cycle. (3) The effect of high temperature (i.e., 300°C) cyclic heating on rock properties is similar to the threshold effect of a single high-temperature heating event.

Experimental study on the damage characteristics of cyclic disturbance and acoustic emission characteristics of different types of sandstones under high stress in deep mines

AbstractThree sandstone specimens common in rock engineering were selected to study the differences in the mechanical properties of rocks with different lithologies. The development and expansion of the internal cracks in the specimens were observed by combining the simulation system with the acoustic emission system. Through the combination of dynamic and static stresses, the deformation and damage of rocks under deep rock excavation and blasting were simulated. As the results show, the acoustic emission events of specimens with different lithologies under combined static and dynamic cyclic loading can be roughly divided into three phases: weakening, stabilizing, and surging periods. In addition, the acoustic emission characteristics of specimens with different lithologies show general consistency in different compression phases. The degree of fragmentation of specimens increases with the applied stress level; therefore, the stress level is one of the important factors influencing the damage pattern of specimens. The acoustic emission system was used to simulate the deformation and damage of rocks subjected to deep rock body excavation and engineering blasting. Cyclic dynamic perturbations under sinusoidal waves with a frequency of 5 Hz, a loading rate of 0.1 mm/min, a cyclic amplitude of 5 MPa, and a loading rate of 0.1 mm/min were applied to the three rock samples during the experiments. Among them, the fine‐grained sandstones are the most sensitive to the sinusoidal cyclic perturbation, followed by the muddy siltstone and the medium‐grained sandstones. On this basis, the acoustic emission energy release characteristics were analyzed, and the waveform characteristics in the damage evolution of the specimen under dynamic perturbation were studied by extracting the key points and searching for the main frequency eigenvalues.

An Ultrasonic Rock Bolt Sensing Technology (I): Methodology and Laboratory Studies

Rock bolts play a critical role in ground support in mining, tunneling and construction. Being able to obtain timely information on rock bolt load condition and deformation could help immensely in safeguarding workers’ safety, optimization of ground support system, and ensuring stability and longevity of underground structures. The objective of this work was to develop a practical ultrasonic rock bolt sensing technology for monitoring axial load and deformation of a full-bodied rock bolt in both elastic and plastic deformation regimes. To this end, empirical mathematical models involving simultaneous use of times of flight of longitudinal and shear ultrasonic waves propagating along the axial direction of the rock bolt were developed, sensors were designed and fabricated, and laboratory studies were conducted. The results showed that the technology was able to measure load change, provide early detection of yield, and measure both plastic and total elongations of the rock bolt undergoing a pull test. Additionally, sectional load and elongation information could be obtained by applying the technology to rock bolts divided into sections by drilled holes along their shanks, therefore, providing the capability to assess the condition of grouted bolts at different depths within a rock mass. This work has laid the groundwork for the deployment of the technology in the field.

Experimental study on the thermal response of rocks to stress change and its significance

SUMMARY Bedrock temperature contains effective information about changes in the crustal stress. A new method of detecting crustal stress change by bedrock temperature (DSCT) has been proposed. Understanding the stress-induced temperature response characteristics of loaded rocks is fundamental for applying DSCT. In this study, temperature observation experiments of different rocks and water-saturated sandstones subjected to tiered cyclic loading were conducted to investigate the temperature–stress relationship throughout the whole rock deformation and failure process. Through experiments, some valuable results are obtained: (i) temperature changes synchronously with stress and has a very strong linear correlation with it; (ii) the magnitude of temperature response to stress (TRS) is approximately 1 mK MPa−1, ranging from strong to weak are sandstone, marble, diorite and basalt, respectively. The differences in TRS of various rocks are determined by their major rock-forming minerals, textures and structures; (iii) the evolution of TRS experiences three stages: the TRS rises rapidly in the compression stage, slowly in the acoustic emission quiet period and a significant increase in TRS before rock failure is observed on marble, sandstone and basalt, consistent with the abnormal bedrock temperature rise preceding earthquakes; (iv) the TRS of water-saturated sandstones is higher compared to the dry ones, and the abnormal sharp increase in TRS before rock failure is also more significant in the former. These findings mentioned above promote the understanding of thermal anomalies preceding earthquakes.

Mechanism and deterioration pattern of sandstone surrounding rock voiding at bottom of heavy-haul railway tunnel

This study combines laboratory experiments and discrete element simulation methods to analyze the mechanism and deterioration patterns of sandstone surrounding rock voiding the bottom of a heavy-haul railway tunnel. It is based on previously acquired measurement data from optical fiber grating sensors installed in the Taihangshan Mountain Tunnel of the Wari Railway. By incorporating rock particle wastage rate results, a method for calculating the peak strength and elastic modulus attenuation of surrounding rock is proposed. Research indicates that the operation of heavy-haul trains leads to an instantaneous increase in the dynamic water pressure on the bottom rock ranging 144.4–390.0%, resulting in high-speed water flow eroding the rock. After 1–2 years of operation, the bottom water and soil pressures increase by 526.5% and 390.0%, respectively. Focusing on sandstone surrounding rock with high observability, laboratory experiments were conducted to monitor the degradation stages of infiltration, particle loss, and voiding of rock under the action of dynamic water flow. The impact of water flow on the “cone-shaped” bottom rock deformation was also clarified. The extent of rock deterioration and voiding was determined using miniature water and soil pressure sensors in conjunction with discrete element numerical simulations. The measured rock particle loss was used as a criterion. Finally, a fitting approach is derived to calculate the peak strength and elastic modulus attenuation of surrounding rock, gaining insight into and providing a reference for the maintenance and disposal measures for the bottom operation of heavy-haul railway tunnels.

Numerical investigation study on tensile-shear failure behavior of rock bolts in inclined strata mining tunnels

In response to the problem of severe deformation and failure of the surrounding rock of the mining tunnels in inclined strata, a tensile-shear failure numerical model of rock bolts was adopted to analyze the rock bolts failure behavior and the surrounding rock mechanical response, and explore the influence of different factors on rock bolts failure. The results indicate that: (1) As angle between the rock bolt and the interface decreases, the shear force of increases, and the rock bolt is easier to fracture. The maximum displacement is 250.2 mm of fractured position. A new evaluation index of shear axis ratio was proposed. The larger the shear axis ratio, the rock bolt is easier to fracture. The shear axis ratio at the interface has increased by 95 % compared to the non interface. (2) The plastic zone and the surrounding rock deformation exhibit the same inclination trend as the strata. In final state, the maximum deformation is 297.7 mm at the bottom and top position perpendicular to the rock bolts at the interface. At the moment of rock bolts fracture, the interface displacement of surrounding rock immediately increased by about 10 mm. And the stress in the surrounding rock decreased about 1 MPa. The weakening effect of surrounding rock stress shifts with the change of rock bolt fracture position. The stress at the arch waist decreases by 44 %, the stress at the arch crown decreases by 25 %. When the fracture of the rock bolts at the arch crown and arch waist ends, the stress at the side wall begin to decrease by 40 %. (3) As the inclination angle increases, the deformation of the surrounding rock and the number of rock bolt failures increase. The range of the plastic zone in the surrounding rock gradually increases, and the degree of rock bolts asymmetric fracture more aggravated. As the diameter of the rock bolt increases, the fractured number of the rock bolts and range of plastic zone decreases.

New approach for predicting time-dependent deformation of shale rock: a modified fractional-order creep constitutive model

New approach for predicting time-dependent deformation of shale rock: a modified fractional-order creep constitutive model