Behavior Of Rocks Research Articles

Comparing the performance of machine learning methods in estimating the shear wave transit time in one of the reservoirs in southwest of Iran.

Shear wave transit time is a crucial parameter in petroleum engineering and geomechanical modeling with significant implications for reservoir performance and rock behavior prediction. Without accurate shear wave velocity information, geomechanical models are unable to fully characterize reservoir rock behavior, impacting operations such as hydraulic fracturing, production planning, and well stimulation. While traditional direct measurement methods are accurate but resource-intensive, indirect methods utilizing seismic and petrophysical data, as well as artificial intelligence algorithms, offer viable alternatives for shear wave velocity estimation. Machine learning algorithms have been proposed to predict shear wave velocity. However, until now, a comprehensive comparison has not been made on the common methods of machine learning that had an acceptable performance in previous researches. This research focuses on the prediction of shear wave transit time using prevalent machine learning techniques, along with a comparative analysis of these methods. To predict this parameter, various input features have been employed: compressional wave transit time, density, porosity, depth, Caliper log, and Gamma-ray log. Among the employed methods, the random forest approach demonstrated the most favorable performance, yielding R-squared and RMSE values of 0.9495 and 9.4567, respectively. Furthermore, the artificial neural network, LSBoost, Bayesian, multivariate regression, and support vector machine techniques achieved R-squared values of 0.878, 0.8583, 0.8471, 0.847 and 0.7975, RMSE values of 22.4068, 27.8158, 28.0138, 28.0240 and 37.5822, respectively. Estimation analysis confirmed the statistical reliability of the Random Forest model. The formulated strategies offer a promising framework applicable to shear wave velocity estimation in carbonate reservoirs.

Numerical study of effective parameters on true triaxial test results in rigid type apparatus

Operational parameters in true triaxial loading devices (TTA), such as the loading rod dimensions, friction between the loading platens and sample faces, loading gap, and one-side loading may affect the test results. Knowledge of the effect of each parameter is very important to correctly interpret rock behavior and to optimize these devices. Employing the Flac3D finite difference software, a rigid type true triaxial systemdesigned and builtat Amirkabir University of Iran (AUT-TTA) was simulated andinvestigated in this study. The results indicate that increasing the ratio of the rod cross-section to the loading platen area leads to an increase in the sample confinement, so, more uniform stress distribution occurs in the rock sample. The loading gap reduces strength of the rock specimen and leads to concentration of tensile stresses at the sample edges. The end effect leads to an increase in the stress level and a pseudo-hardening behavior in the samples. Also, the end effect is intensified under one-side loading condition compared to two-side loading. Comparison between results of AUT-TTA numerical simulation and analytical analysis (ideal conditions without considering operational parameters) indicates that the slope of the stress–strain diagram has low sensitivity to operational parameters. The most important operational factor affecting the stress level and dilatation stress is the end effect and other operational parameters have little effect. All parameters lead to an increase in the dilation strain. The clear edge and one-sided loading under low intermediate principal stresses and the end effect under high intermediate principal stresses have the greatest effect on the dilation strain.

Micro-dissolution mechanism and macro-mechanical behavior of red-bed soft rock under dry-wet cycle

The microscopic pore characteristics of rocks have an important influence on their macroscopic mechanical behavior. The micro-pore dissolution mechanism of red-bed soft rock was revealed by the dry-wet cycle method, and its macroscopic mechanical behavior was studied by a series of uniaxial compression tests. The results show that with an increase in the number of dry-wet cycles, the micro-pore dissolution and micro-grain spalling of red-bed soft rock result in its porosity increasing nonlinearly. Under the action of the axial load, the number of micro-fractures increases and evolves from tensile fracture to shear fracture, and the macroscopic failure mode changes from brittle splitting failure to ductile conical failure.

Investigation of the strength behavior and failure modes of layered sedimentary rocks under Brazilian test conditions

As the anisotropic behavior of sandstones and limestone along the Khorramabad-Zal expressway has not been studied, this research aims to examine the impact of layer orientation on the strength characteristics and failure patterns of layered sedimentary rocks using the Brazilian test. For this purpose, a total of 8 rock blocks were gathered from Kashkan sandstones and Sarvak limestones in three different locations along the Khorramabad-Zal highway in western Iran. The core specimens were drilled with 54 mm diameter and parallel to the laminations. Overall 150 disc-shaped specimens were subjected to Brazilian tensile strength (BTS) in ten different anisotropy angles, which refers to the angle between the loading direction and the lamination plane. The findings revealed that the highest and lowest BTS values were obtained at β = 70° and 20° for all three types of rock. After analyzing the samples that experienced the Brazilian test and examining their failure patterns, three primary modes of failure were identified: parallel to the lamination (PL), across the lamination (AL), and curved fracture (CF). Furthermore, the transitional angle, which signifies the point at which the dominant pattern of failure shifts from PL to AL or from PL to CF, was also determined.

Effect of Footing Shape on the Rocking Behavior of Shallow Foundations

Sources such as wind or severe seismic activity often exert extreme lateral loading onto the shallow foundations supporting high-rise structures such as bridge piers, buildings, shear walls, and wind turbine towers. Such loading conditions may cause the foundation to exhibit nonlinear responses such as uplift and bearing capacity mobilization of the supporting soil (i.e., rocking behavior). Previous numerical and experimental studies suggest that while such inelastic behaviors may engender residual deformations in the soil–foundation system, they offer potential benefits to the overall integrity of structures through dissipating energy and reducing inertia forces transmitted to the superstructure, thereby limiting seismic demand on structural elements. This study investigates the effect of footing shape on the rocking performance of shallow foundations in different subgrade densities and initial vertical factor of safety (FSv). To this end, a series of reduced-scale slow cyclic tests under 1 g condition were conducted using a single degree of freedom (SDOF) structure model. The performance of different footing shapes was studied in terms of moment capacity, recentering ratio, rocking stiffness, damping ratio, and settlement. For three foundations with different length-to-width ratios, the results indicate that increasing the safety factor and length-to-width ratio leads to thinner, S-shaped moment–rotation curves, mainly owing to the enhanced recentering capability and the P-δ effect. Moreover, across all foundation types, the repetition of a limited loading cycles with consistent rotation amplitude does not cause stiffness degradation or moment capacity reduction.

Fatigue behavior investigation of artificial rock under cyclic loading by using discrete element method

In numerous engineering projects, such as tunnel construction, underground gas storage in caverns, and the impact of earthquakes, rock materials experience cyclic loading. However, the response of rock materials to cyclic loading, which may vary in terms of waveform, frequency, and amplitude, is not uniform. Consequently, comprehending the mechanical attributes and fatigue behavior of rocks holds significant importance in engineering designs. This study focuses on subjecting a collection of cylindrical concrete specimens, categorized into three groups with distinct mechanical properties, to both monotonic and cyclic loading within a laboratory environment. Three groups of cylindrical concrete samples with different mixing designs are prepared to evaluate the effect of the mechanical strength of the samples on the fatigue response of the rock. In such a way that: The first group (G1) with Uniaxial Compressive Strength (UCS): 19 MPa, the second group (G2) with (UCS): 49 MPa, and the third group (G3) with (UCS): 71 MPa. In addition, the discrete element method is utilized to simulate uniaxial cyclic compression tests under various loading conditions, such as monotonic and cyclic loading. The resulting fracture propagation patterns and geometries are then analyzed. Numerical and experimental results show that the cyclic uniaxial compressive strength, due to the presence of damage and fatigue phenomena, has decreased relative to the monotonic tests. Also the cyclic elastic modulus values (Ec) have decreased by 53 %, 25 %, and 11 % relative to the monotonic elastic modulus (Em) for the three groups of G1, G2, and G3, respectively. The Stress-life (S-N) model is used to express the fatigue behavior of rock, and the final equation for the S-N model is expressed.

Dual-scale 3DEC-GBM Discrete Element Simulation On Mechanical Behavior and Anisotropic Fracture Evolution Mechanism of Rock Induced by True Three-dimensional Stress

Dual-scale 3DEC-GBM Discrete Element Simulation On Mechanical Behavior and Anisotropic Fracture Evolution Mechanism of Rock Induced by True Three-dimensional Stress

Progressive damage and fracture behavior of brittle rock under multi-axial prestress constraint and cyclic impact load coupling

To explore the progressive damage and fracture mechanics characteristics of brittle rock materials under combined dynamic-static loading. Taking account of the coupling effect of the constraint states of uniaxial stress (σ1 ≥ σ2 = σ3 = 0), biaxial stress (σ1 ≥ σ2 > σ3 = 0) and true triaxial stress (σ1 ≥ σ2 ≥ σ3 ≠ 0) and impact load, the strain rate effect and prestress constraint effect of dynamic mechanical characteristics of sandstone are studied. The progressive damage evolution law of sandstone under the coupling of true triaxial stress constraint and cyclic impact load is discussed. The results show that with the increase of axial stress σ1, the dynamic compressive strength and peak strain gradually decrease, and the strain rate gradually increases, resulting in crushing failure under high strain rate. When the axial stress is fixed, the lateral stress constraint reduces the damage degree of sandstone and improves the dynamic compressive strength. With the increase of strain rate, the sample changes from slight splitting failure to inclined shear failure mode. Under the true triaxial stress constraint, the intermediate principal stress σ2 obviously enhances the dynamic compressive strength of sandstone. Under the constraints of triaxial stress, biaxial stress and uniaxial stress, the enhancement effect of dynamic compressive strength and the deformation resistance of sandstone are weakened in turn. Under the coupling of true triaxial stress constraint and high strain rate, sandstone samples show obvious progressive damage evolution effect under repeated impacts, and eventually inclined shear failure occurs, resulting in complete loss of bearing capacity.

Compressive Fracture Behavior and Acoustic Emission Characteristics of Sandstone under Constant Crack Water Pressure

Abstract Engineering rock containing flaws or defects under a large water source is frequently subject to the couple influence of constant crack water pressure and geostress. To investigate the fracture behavior of precracked rock under hydromechanical coupling with constant crack water pressure, compression tests were conducted on red sandstone specimens containing a single crack of different angles using a device to realize the constant crack water pressure during loading, and the failure process of rock specimens was monitored by acoustic emission (AE) technique. The results show that the presence of constant crack water pressure has a significant promotion effect on the development of shear wing cracks, and the promotion effect is influenced by the prefabricated crack angle and water pressure. As the constant crack water pressure increases, the failure mode of the 0° precrack specimen changes from “X”- shear failure to the single oblique shear failure along the shear wing crack direction, the main failure crack of the inclined precracked specimens (precrack angles of 15°, 45°, and 60°) changes from a small acute angle with the prefabricated crack to a direction along the shear wing crack, and irregular cracks occur at the chipped prefabricated crack in the 90° precracked specimen. With an increase in the constant crack water pressure, the average energy for a single hit, cumulative AE energy, and cumulative AE hits decrease, and the proportion of the tensile cracks increases and that of the shear cracks decreases.

Effect of grouting on damage and fracture characteristics of fractured rocks under mode I loading

Grouting is widely used to improve the mechanical properties of fractured rocks, but its impact on the fracture behavior of fractured rocks remains incompletely understood. This research aims to investigate the effects of grouting on the damage and fracture characteristics of fractured rocks under mode I loading. We used epoxy resin and ultrafine cement to grout granite and sandstone centre-cracked Brazilian disc specimens. We conducted Brazilian splitting tests on intact specimens, as well as specimens with and without grouting under mode I loading. Acoustic emission (AE) and digital image correlation (DIC) techniques were utilized to study the effect of grouting on rock fracture behavior. Furthermore, we employed an improved fracture toughness calculation method to evaluate the anti-fracture capacity of grouted specimens. The results show that grouting positively reinforces fractured rocks by increasing the shear crack ratio, mitigating the stress concentration effect at the crack tip, and fostering a more complete and stable development of the fracture process zone (FPZ). Materials with superior strength and bonding properties can effectively improve the mechanical performance of fractured rocks. Notably, epoxy resin significantly boosts the strength, deformation adaptability, and anti-fracture capacity of the specimens, outperforming ultrafine cement in terms of grouting effect. The entropy change of AE energy during the loading process indicates that the rock system undergoes three stages of order-to-disorder-to-order. The second stage and the abrupt changes in entropy value can serve as precursors to rock damage and fracture. This research enriches our understanding of how grouting influences the damage and fracture behavior of fractured rocks, providing valuable insights for risk assessment and disaster prediction in geotechnical grouting engineering.

Grain-based modeling study of time-dependent mechanical behavior of brittle rocks in deep underground caverns based on the stress corrosion model

Failure and instability in deep underground caverns, such as delayed rockburst and time-dependent deformations, are not immediate after excavation. These phenomena are closely linked to the complex stress conditions affecting deformation and fracture mechanisms in brittle rock over time. Therefore, understanding the mesoscopic evolution mechanism of time-dependent deformation and fracture in brittle rocks is crucial. This study conducted single-stage loading and creep experiments on marble in the Jinping I underground powerhouse to investigate the influence of stress levels and stress-strength ratios on time-dependent deformation and fracture using grain-based and parallel-bond stress corrosion models. Results indicate that the long-term stress strength ratio is governed by stress levels. Higher confining pressures have less impact on time-dependent deformation and fracture, resulting in longer failure time or even absence of failure. Conversely, higher stress-strength ratios significantly impact brittle rock, leading to shorter failure time. Increasing confining pressure or stress-strength ratio primarily controls the micro-evolution mechanism of time-dependent fracture in marble through the interaction between tensile and shear cracks. More tensile cracks decrease the number of shear cracks. Under larger load gradients, time-dependent deformations and failure decrease, resulting in longer unstable failure time.

Risk Assessment and Analysis of Rock Burst under High-Temperature Liquid Nitrogen Cooling

Rock burst, an important kind of geological disaster, often occurs in underground construction. Rock burst risk assessment, as an important part of engineering risk assessment, cannot be ignored. Liquid nitrogen fracturing is a new technology used in the geological, oil, and gas industries to enhance productivity. It involves injecting liquid nitrogen into reservoir rocks to induce fractures and increase permeability, effectively reducing rock burst occurrences and facilitating the flow of oil or gas toward the wellbore. The research on rock burst risk assessment technology is the basis of reducing rock burst geological disasters, which has important theoretical and practical significance. This article examines the temperature treatment of two types of rocks at 25 °C, 100 °C, 200 °C, 300 °C, and 400 °C, followed by immersion in a liquid nitrogen tank. The temperature difference between the liquid nitrogen and the rocks may trigger rock bursting. The research focused on analyzing various characteristics of rock samples when exposed to liquid nitrogen. This included studying the stress–strain curve, elastic modulus, strength, cross-section analysis, wave velocity, and other relevant aspects. Under the influence of high temperature and a liquid nitrogen jet, the wave velocity of rocks often changes. The structural characteristics and possible hidden dangers of rocks can be understood more comprehensively through section scanning analysis. The stress–strain curve describes the deformation and failure behavior of rocks under different stress levels, which can help to evaluate their stability and structural performance. The investigation specifically focused on the behavior of rocks subjected to high temperatures and liquid nitrogen. By analyzing the stress–strain curves, researchers were able to identify the precursors and deformation processes that occur before significant deformation or failure. These findings have implications for the mechanical properties and stability of the rocks.

Macro-micro failure and crack coalescence behavior of soft-hard composite rock with three parallel joints under uniaxial compression

Jointed soft-hard composite rock mass is very common in engineering. The existence of joint and the uncoordinated deformation of soft-hard layer make the failure behavior more complicated. In this study, soft-hard composite rock with three parallel joints (two coplanar joints and one out-of-plane parallel joint) were fabricated to carry out uniaxial compression experiment. With the aid of digital imagine correlation (DIC) and acoustic emission (AE) technology, the influence of joint angle, ligament angle and the location of out-of-plane joint on crack propagation behavior of specimen is analyzed. The results show that when the hard layer contains more joints, the rock mass presents more obvious brittleness. The variation of peak strength with ligament angle also depends on the rock layer where the out-of-plane crack is located. Three failure modes and ten crack coalescence modes are summarized, which are affected by joint angle and ligament angle. The transition of crack coalescence between adjacent rock layer is mainly influenced by the space of wing cracks at joint tips. The coalescence of rock bridge in the layer with double joints is affected by ligament angle and the relative strength of layer. When the out-of-plane joint is in the hard layer, the coalescence possibility is greatly reduced.

Experimental research into the dynamic damage characteristics and failure behavior of rock subjected to incremental repeated impact loads

The damage to rocks caused by frequent disturbance loads is a major issue in rock engineering. Understanding the failure behaviors and establishing the dynamic energy-damage model of rock under constant and incremental repeated impact loads are key to the structural safety and stability design of rock mass engineering works. In this work, the split Hopkinson pressure bar (SHPB) system and an ultrasonic measuring system were used to test constant and incremental repeated impact loads on red sandstone. The damage evolution of red sandstone was revealed under constant and incremental repeated impact loads, the energy-damage model of constant and incremental repeated impact loads was established, the crack expansion pattern and fatigue failure properties were studied, and the changing trend of the critical damage amount and the fractal characteristics of block after fatigue failure were investigated. The experimental results show that: the dynamic strength of red sandstone shows an overall decreasing trend with the impact velocity and the number of impacts under constant repeated impact loads. The damage evolution of the specimens follows an inverted S-shaped pattern of development. The critical damage amount is negatively correlated with the impact velocity. As the impact velocity is increased, the crack expansion velocity and main-body block size of the specimens after destruction increase. Under incremental repeated impact loads, the dynamic strength of red sandstone increases with the velocity incremental gradient and the number of impacts, and the damage to the specimens shows an accelerated upwardly concave trend. The critical damage amount and the incremental gradient demonstrate an alternating trend of negative-positive correlations. The crack expansion velocity is gradually accelerated, and the main-body block size of specimens after destruction displays a trend of growing and then reducing with the incremental gradient.

Discrete element analysis of hydraulic stimulation in a slate geothermal reservoir using the ubiquitous foliation model

This study employs the discrete element method for a series of coupled hydro-mechanical analyses aimed at investigating the hydraulic stimulation effect on a slate geothermal reservoir. Initially, a ubiquitous foliation model (UFM) is devised to characterize the mechanical properties of slate. The UFM consists of a foliation model for near-field discontinuity features and a ubiquitous model for far-field anisotropic rock behavior. The devised model undergoes validation through an established benchmark analysis considering isotropic conditions. The analysis is subsequently extended to investigate anisotropic shear response influenced by the foliation. In cases where the anisotropic angle equals 90°, new fractures initiate along the foliation, which leads to a concentrated and severe damage pattern. In contrast, models with the anisotropic angle of 45° and 135° exhibit minor failures due to foliation orientation hindering fracture propagation. Lastly, an anisotropic hydraulic-mechanical analysis is undertaken to assess the hydraulic stimulation influence and its consequential effects on a slate geothermal reservoir. The results indicate that higher injection rates amplify damage to the rock matrix and the propagation of fractures, which are concentrated between open fractures and adjacent foliations.

Study on Rock Mechanics Parameter Prediction Method Based on DTW Similarity and Machine-Learning Algorithms

Rock mechanics parameters are crucial factors for predicting rock behavior in oil and gas reservoirs, optimizing extraction strategies, and ensuring drilling safety. In this study, we propose a random forest (RF)-convolutional neural network (CNN)-long-term short-term memory network (LSTM) fusion model based on the dynamic time warping (DTW) algorithm to construct intelligent prediction models for elastic modulus, Poisson’s ratio, and compressive strength using real-time drilling engineering data. An autoencoder with a sliding window is employed to automatically identify abnormal points or segments in the calculated values of elastic modulus, Poisson’s ratio, and compressive strength obtained from drilled wells. These abnormal values are then corrected using a backpropagation (BP) neural network. Compared to single CNN-LSTM or single RF models, the RF-CNN-LSTM fusion model performs better. It achieves this by effectively combining the strengths of different algorithms in predicting outcomes. The accuracy of the RF-CNN-LSTM fusion model is over 94% when compared to the actual values. Furthermore, the analysis of the relative importance of input parameters reveals that weight on bit (WOB), temperature, displacement, equivalent circulation density (ECD), and mud density are the primary input features for predicting elastic modulus. For predicting Poisson’s ratio, the main input features include WOB, mud density, ECD, temperature, pumping pressure, displacement, and rate of penetration (ROP). Similarly, for predicting compressive strength, the main input features consist of WOB, temperature, displacement, ECD, and mud density. The research findings demonstrate that the rock mechanics parameter prediction models based on the RF-CNN-LSTM algorithm using DTW exhibit high computational accuracy in the B oil field of China. These results are significant for gaining a deeper understanding of the variations in rock mechanics parameters and optimizing drilling decisions.

A fully coupled thermo-hydro-mechanical elastoplastic damage model for fractured rock

A detailed and fully coupled thermo-hydro-mechanical (THM) model for fractured rock is presented. This model distinguishes itself by harmoniously integrating elastoplastic material behaviour with a continuum damage mechanics framework. Solid matrix displacement, pore and fissure water pressures and temperature of the solid are introduced as the primary nodal variables. The ingenuity of this research is embedded in the intricate coupling of THM processes with plastic deformation and damage mechanics in a double porous medium, a venture that significantly broadens the remit of existing methodologies. The model is implemented using finite element method (FEM) and validation is achieved by comparing the FEM results against existing literature numerical outcomes describing linear and elastoplastic continuum damage behaviour of fractured rock. The model also exhibits an extraordinary proficiency in reproducing experimental triaxial test results, using THM components conjoined with elastoplastic bounding surface aspects and inherent hardening effects. It is imperative, nonetheless, to underscore the model's sensitivity to certain material properties, inclusive of strength parameters, leakage coefficients, and permeability attributes. This fully coupled THM model provides a comprehensive and sophisticated tool for investigating the behaviour of fractured rock under various loading conditions. It can help us better understand the physics of fractured rock behaviour and contribute to the development of more accurate and reliable models for engineering applications, such as CO2 injection.

Effects of elastic anisotropic models on the prediction of horizontal stresses and hydraulic fracture geometry

Abstract Stress barriers play a key role in the propagation of hydraulic fractures. They are local maxima in the stress field that constrain vertical fracture propagation. The development of stress barriers is influenced by rock mechanical properties, pore pressure and tectonic stresses. However, stress prediction models are highly sensitive to available geophysical measurements and assumptions made on rock constitutive models. We compare stress estimations performed with elastic isotropic, anisotropic and viscoplastic models using Thomsen's notation ( ɛ , δ , γ ) to quantify anisotropy and its effects on hydraulic fracture geometry. Using a single depth for principal stress calibration, we compare stress distributions and simulate hydraulic fracture geometries along simple vertical and horizontal well sections. Prediction errors stemming from isotropic models along anisotropic intervals increase when tectonic stresses increase. Errors generated by either over- or underestimation of δ increase for tectonically passive environments, while errors generated by either over- or underestimation of ɛ increase for tectonically active environments. Additional corrections, but also uncertainties, can be introduced by considering viscoelastic rock behaviour. Because of stress shadowing and fracture interaction, the risk of stress barrier underestimation is higher when estimating hydraulic fracture geometries along the various stages of horizontal wells.

Dynamic strength and full-field cracking behaviours of pre-cracked rocks under impact loads

The impact loads have a significant influence on the dynamic strength and cracking behaviours of pre-cracked rocks, which plays a key role in the stability and safety of rock engineering. In this study, impact tests were performed by using a split Hopkinson pressure bar (SHPB) in conjunction with the high-speed photography technique. The dynamic strength of pre-cracked rocks under different strain rates and flaw angles was analysed, and the full-field cracking behaviours were elucidated by the evolution of strain localization zones based on the digital image correlation (DIC) analysis. By means of discrete element method (DEM), the impact tests were numerically reproduced to study the strength enhancement and the cracking processes. The results illustrate that the increase in the strain rate and flaw angle would lead to the increasing dynamic strength, the change of tensile and shear crack number is consistent with the strength variation, implying that the microcracking processes has a significant influence on the rate dependency of dynamic strength. As for the cracking behaviours, the strain localization zones would form around the flaw, and the crack branching phenomenon could be witnessed in dynamic tests. Furthermore, the complexity of cracking patterns becomes larger with the increasing strain rate, while the samples with the large flaw angle are difficult to generate strain localization zones and macroscopic cracks. By using a DIC-based method to analyse the crack initiation mechanisms, three types of stress-induced cracks were identified, i.e., mode I, II, and mixed mode I/II cracks. Among these cracks, the mode II cracks are the dominate type of cracks. Based on the mathematical analysis of Griffith model, the combined action of the tangential stress distribution and sliding deformation might be the reason for the crack initiation, and the rate-dependent strength might be induced by the increase of the maximum tangential stress regarding external stress.

Time-dependent behavior of reinforcement rock unit anchored by energy-absorbing bolt for large deformation control in tunneling

The energy-absorbing bolt is designed to counteract both burst-prone and squeezing rock conditions in rock excavation. In this paper, the mechanical contribution of energy-absorbing bolts installed systematically around tunnels excavated in rock masses was investigated based on the assumptions of the reinforced rock unit (RRU) model. The time-dependent behavior of rock with a large deformation problem was simulated using a Nishihara model, while that of an energy-absorbing bolt was simplified by a rheological model connecting a Hookean elastic element and a Saint-Venant element in series. The mechanical model of RRU anchored by an energy-absorbing bolt was established by connecting the rock mass model and the energy-absorbing bolt model in a parallel combination. The closed-form solution presented the time-dependent behavior of RRU under an instantaneously applied tension stress and an linearly increasing load, respectively. The results showed the reinforcement could reduce the time-dependent deformation of the reinforced region of tunnels significantly. A preliminary estimate of NPR-bolt reinforcement for large-deformation controls in the Muzhailing tunnel was carried out using the proposed model. The results showed that the NPR cables could have critical effects in controlling the large deformation of the tunnel.