Rock Creep Research Articles

Fractional Derivative-based Burger Creep Model for Soft Rocks and its Verification Using Tunnel Monitoring Results and Experimental Data

AbstractConsidering the creep behavior of soft and weak rocks is critical for analyzing the long-term stability of underground constructions. This paper introduces a novel creep constitutive model to characterize the creep behavior of rocks under uniaxial and triaxial stress states. The fractional derivative Abel dashpot was used to improve the Burger model, and a viscoplastic component was added in series with the modified Burgers model to replicate the tertiary phase of rock creep. The effectiveness of the model was verified using creep test data from various soft rocks and monitoring measurements from a tunnel excavated in heavily jointed weak rock masses. Furthermore, a sensitivity analysis was carried out to assess the impact of the model parameters on creep deformation, and a comparative study was performed to evaluate the efficacy of the suggested model in modeling the accelerated stage of rock creep compared with some existing models. The strong agreement observed between the calculated results and both the creep test data and tunnel monitoring measurements underscores the accuracy and validity of the proposed model. The comparative analysis further revealed that the proposed model offers the highest fitting efficiency for describing the tertiary stage of rock creep. These findings suggest that the model effectively captures the creep behavior of rocks and precisely represents the entire creep process.

Experimental study on the mechanical properties of red sandstone with fractures under different loading rates

In order to study the effects of crack inclination angle and loading rate on rock mechanical properties, creep characteristics, and failure characteristics. Taking homogeneous red sandstone with different fracture angles as the research object, uniaxial compression tests and uniaxial compression creep tests were conducted at different loading rates. The results showed that under the same fracture angle, the loading rate was positively correlated with the peak strength, elastic modulus, instantaneous strain, creep strain, and steady-state creep rate of the sample, while negatively correlated with the peak strain. At the same loading rate, the mechanical properties and creep properties of the sample were controlled by the crack inclination angle α. With the increase of α, the peak strength, peak strain, instantaneous strain, creep strain and steady-state creep rate decreased first and then increased, and the elastic modulus increased. On the basis of rock creep testing, it is also important to establish a creep model that conforms to the actual test situation for studying rock creep characteristics. However, many models currently used cannot accurately describe the three stages of rock creep, especially the accelerated creep stage. Therefore, based on Burgers elements, this paper introduces plastic damage bodies based on damage rates and software components based on fractional calculus, A new creep model was obtained and its rationality was verified through experimental results. The results showed that the fit between the model and experimental data was above 0.97, indicating that the model can better describe the three stages of rock creep, especially reflecting the non-linear characteristics of the accelerated creep stage.

Calibrating high-dimensional rock creep constitutive models for geological disaster prevention: An application of data assimilation methods

The study of rock creep phenomena is of paramount importance due to its potential to trigger geological disasters, such as landslides. To predict and prevent such disasters, creep constitutive models are widely employed to comprehend the time-dependent deformation of rocks. These models encompass various mechanical parameters that describe the intricate stress-strain behaviors. Nevertheless, significant challenges persist in achieving accurate and consistent parameter estimation and state prediction. In this study, we introduce three advanced data assimilation (DA) methods, including one Markov chain Monte Carlo method, DREAM(KZS), and two ensemble smoother methods, ESMDA and ILUES. This marks the first application of such methods for calibrating rock creep models in the scenario of geological disaster prevention. We conducted numerical simulations under both low- and high-dimensional conditions to assess the performance of these DA methods. For the single partition model, all three DA methods demonstrated promising results. In the high-dimensional case, DREAM(KZS) displayed inefficiency, while both ESMDA and ILUES proved to be still effective. ESMDA offered improved data matching but tended to underestimate parameter uncertainties, whereas ILUES excelled in addressing the issue of equifinality. In a real-world case focusing on characterizing creep deformation at the Mogu tilting deformation body near the Lianghekou Dam, China, we employed all three DA methods, and they collectively demonstrated satisfactory performance. Particularly noteworthy is the enhanced performance of the DREAM(KZS) method during the accelerated creep phase, even in the presence of limited data. The findings of this research bear significant importance in reducing uncertainties associated with model parameters in the realm of rock mechanics, thereby advancing our capabilities in predicting and preventing disasters.

A microscopic approach to brittle creep and time-dependent fracturing of rocks based on stress corrosion model

A brittle creep and time-dependent fracturing process model of rock is established by incorporating the stress corrosion model into discrete element method to analyze the creep behavior and microcrack evolution in brittle rocks at a micro-scale level. Experimental validation of the model is performed, followed by numerical simulations to investigate the creep properties and microcrack evolution in rocks under single-stage loading, multistage loading, and confining pressure, at various constant stress levels. The results demonstrate that as the stress level increases in single-stage creep simulations, the time-to-failure progressively decreases. The growth of microcracks during uniaxial creep occurs in three stages, with tensile microcracks being predominant and the spatial distribution of microcracks becoming more dispersed at higher stress levels. In multi-stage loading-unloading simulations, microcracks continue to form during the unloading stage, indicating cumulative damage resulting from increased axial stress. Additionally, the creep behaviour of rocks under confining pressure is not solely determined by the magnitude of the confining pressure, but is also influenced by the magnitude of the axial stress. The findings contribute to a better understanding of rock deformation and failure processes under different loading conditions, and they can be valuable for applications in rock mechanics and rock engineering.

Leveraging the ETAS model to forecast mining microseismicity

SUMMARY Mining operations result in changes of the subsurface stress field that can lead to the occurrence of microseismic events. The development of strategies for forecasting and avoidance of significant events is crucial for safe and efficient operations of mines. One such example, discussed here is the observed induced microseismicity in soft rock potash mines. It is primarily driven by the rock excavations but can also be triggered by preceding events or can result from the delayed effects of plastic creep of soft rocks. Therefore, it is important from seismic hazard assessment and risk mitigation points of view to understand the statistical aspects of microseismicity in potash or other types of mines. In this study, the temporal evolution of the induced microseismicity from a potash mine in Saskatchewan is analysed and modelled. Specifically, the epidemic type aftershock sequence model is used to approximate the occurrence rate of the induced mining microseismicity. The estimated parameters signify that the microseismicity displays swarm-type characteristics with limited inter-event triggering. Moreover, the Bayesian predictive framework is used to compute the probabilities of the occurrences of the largest expected events above a certain magnitude for prescribed forecasting time intervals during the evolution of the sequence. This approach for computing the probabilities allows one to incorporate fully the uncertainties of the model parameters. The Markov Chain Monte Carlo sampling of the posterior distribution are used to generate parameter chains to quantify their variability. Furthermore, several statistical tests are conducted to assess the credibility of the obtained retrospective forecasts compared to the observed microseismicity. The obtained results show that the developed approach can accurately forecast the number of events and intensity of the sequence. It also provides a framework for computing the probabilities for the largest expected events.

Analysis of APB in vertical wells with evaporite layers: A 1D axisymmetric multilayer thermomechanical model

Temperature increases and creep in saline rocks can cause annular pressure buildup (APB), presenting a significant challenge in oil well operations, particularly in deep and ultra-deep pre-salt fields. This paper proposes a one-dimensional axisymmetric multilayer thermomechanical model that accounts for the influence of evaporite layers and thermomechanical effects on APB. We developed a finite element model that integrates heat transfer and thermomechanical interactions, utilizing a double deformation mechanism as a constitutive model to represent the viscous behavior of the rock formation. Additionally, this model enables the iterative calculation of fluid properties based on temperature and pressure conditions. To validate the model, we conducted case studies using widely adopted commercial finite element software. Its consistent results provide a deeper understanding of the pressure increases caused by the influence of saline rock and thermal effects, offering valuable insights into the safe and efficient operation of oil wells using a model with reduced computational complexity.

Review of the creep constitutive models for rocks and the application of creep analysis in geomechanics

AbstractThe creep behavior of rocks has been broadly researched because of its extensive application in geomechanics. Since the time-dependent stability of underground constructions is a critical aspect of geotechnical engineering, a comprehensive understanding of the creep behavior of rocks plays a pivotal role in ensuring the safety of such structures. Various factors, including stress level, temperature, rock damage, water content, rock anisotropy, etc., can influence rocks’ creep characteristics. One of the main topics in the creep analysis of rocks is the constitutive models, which can be categorized into empirical, component, and mechanism-based models. In this research, the previously proposed creep models were reviewed, and their main characteristics were discussed. The effectiveness of the models in simulating the accelerated phase of rock creep was evaluated by comparing their performance with the creep test results of different types of rocks. The application of rock’s creep analysis in different engineering projects and adopting appropriate creep properties for rock mass were also examined. The primary limitation associated with empirical and classical component models lies in their challenges when it comes to modeling the tertiary phase of rock creep. The mechanism-based models have demonstrated success in effectively simulating the complete creep phases; nevertheless, additional validation is crucial to establish their broader applicability. However, further investigation is still required to develop creep models specific to rock mass. In this paper, we attempted to review and discuss the most recent studies in creep analysis of rocks that can be used by researchers conducting creep analysis in geomechanics.

Investigating the Creep Damage and Permeability Evolution Mechanism of Phyllite Considering Non-Darcy’s Flow

This study investigates the intricate interplay of hydraulic coupling, creep damage, and permeability evolution mechanisms in phyllite, focusing on their relevance to tunnel engineering design and long-term stability in soft rock formations. To achieve this, conventional triaxial tests were conducted on saturated phyllite specimens under creep-seepage acoustic emission conditions. The results were systematically analyzed to unveil the inherent characteristics of creep deformation, seepage rate evolution, and damage progression in phyllite when subjected to stress–seepage coupling. Furthermore, a permeability model for representative volume element (RVE) was developed based on meso-mechanics principles, considering the distinctive attributes of low-permeability non-Darcy’s flow in rock. Consequently, a novel relationship between effective damage and permeability was established. We determined that seepage pressure induces three key effects on the creep damage mechanism of phyllite samples: (1) It adds to the existing stress through the superposition of osmotic pressure and axial load, (2) it induces tensile expansion stress because of pore water pressure, and (3) it softens the fracture surfaces to some extent. More importantly, this study validates the relationship between effective damage and permeability through the fitting of creep and damage parameters, which were obtained from the test results, and it reveals a square relationship between subsequent damage and permeability under stress conditions. The findings of this study provide a robust theoretical foundation for comprehending the evolution of damage and permeability characteristics during the creep process of rock under seepage conditions. We obtained essential insights and quantitative analyses for comprehending the damage mechanisms in rock creep under hydraulic coupling, which has significant implications for tunnel engineering and long-term rock stability assessments in soft rock environments.

Brittle initiation of dissolution–precipitation creep in plagioclase-rich rocks: insights from the Bergen arcs, Norway

The initiation of ductile shear zones commonly occurs spatially associated with fluid-rock reactions along brittle precursors. In many cases the relative timing of fracturing, fluid infiltration, reaction, and recrystallisation is unclear, making it difficult to disentangle mechanisms of shear zone initiation from subsequent deformation and recrystallisation. Here we present the study of the transition from a dry plagioclase-diopside-garnet-scapolite host granulite-facies lithology to (1) a low strain amphibolite-facies rock, and (2) a transition from low strain to high strain amphibolite-facies lithologies. Hydration of the granulite-facies precursor at amphibolite-facies conditions produces an assemblage comprised dominantly of plagioclase-amphibole-zoisite-clinozoisite-kyanite-scapolite-quartz. Detailed study of plagioclase chemistry and microstructures across these two transitions using Electron Backscatter Diffraction (EBSD) and Wavelength Dispersive Spectrometry (WDS) allows us to assess the degree of coupling between deformation and fluid-rock reaction across the outcrop. Plagioclase behaves dominantly in a brittle manner at the hydration interface and so the initial weakening of the rock is attributed to grain size reduction caused by fracture damage and fluid infiltration at amphibolite-facies conditions. Extensive fracturing-induced grain size reduction locally increases permeability and allows for continuing plagioclase and secondary mineral growth during shear. Based on plagioclase microstructures, such as, an inherited but dispersed crystallographic preferred orientation (CPO), truncation of chemical zoning, and the dominance of fine (5–150 µm), slightly elongate, polygonal grains we conclude that deformation is dominantly facilitated by dissolution–precipitation creep assisted by grain boundary sliding in the shear zone.

Creep damage constitutive model of rock based on the mechanisms of crack-initiated damage and extended damage

Since the classical element model cannot describe the nonlinear characteristics of rock during the entire compressive creep process, nonlinear elements and creep damage are generally introduced in the model to resolve this issue. However, several previous studies have reckoned that creep damage in rock only occurs in the accelerated creep stage and is only described by the Weibull distribution. Nevertheless, the creep damage mechanism of rocks is still not clearly understood. In this study, a reasonable representation of the damage variables of solid materials is presented. Specifically, based on the Gurson damage model, the damage state functions reflecting the constant creep stage and accelerated creep stage of rock are established. Further, the one-dimensional and three-dimensional creep damage constitutive equations of rock are derived by modifying the Nishihara model. Finally, the creep-acoustic emission tests of phyllite under different confining pressures are conducted to examine the creep damage characteristics of phyllite. And the proposed constitutive model is verified by analyzing the results of creep tests performed on saturated phyllite. Overall, this study reveals the relationship between the creep characteristics of rocks and the corresponding damage evolution pattern, which bridges the gap between the traditional theory and the quantitative analysis of rock creep and its damage pattern.

A Common Diffusional Mechanism for Creep and Grain Growth in Polymineralic Rocks: Application to Lower Mantle Viscosity Estimates

AbstractIn a previous study (Okamoto & Hiraga, 2022, https://doi.org/10.1029/2022jb024638), we concluded that diffusion creep and grain growth in polymineralic rocks proceed by a common diffusional mechanism. Here, we built on that finding and estimated lower mantle grain size and viscosity during a single mantle convection cycle dominated by diffusion creep. We approximated the lower mantle as a two‐phase material consisting of bridgmanite + ferropericlase and post‐perovskite + ferropericlase, depending on depth. We used previously reported self‐diffusivities for bridgmanite and post‐perovskite. We predict a bridgmanite grain‐size of tens to hundreds of microns shortly after the phase transition at ∼660 km depth. This size remains relatively constant until the mantle material enters the post‐perovskite zone, which is marked by significant grain growth up to ∼9 mm just prior to upwelling. This size is sufficient to prevent further grain growth until the mantle material reaches the top of the lower mantle. These grain sizes combined with the diffusivities yield viscosities that vary laterally and with depth. At a lateral temperature difference of up to 800 K in the lower mantle, fine‐grained cold downwelling mantle is almost as viscous as, or more likely to be softer than coarse‐grained hot upwelling mantle. The lateral viscosity variations cannot be more than 2 orders of magnitude, and we estimated viscosities of 1018–1020 Pa · s in the upper lower mantle, 5 × 1020–5 × 1022 Pa · s in the lower bridgmanite zone, and 1017–1019 Pa · s in the post‐perovskite zone, which compare well with the values estimated in previous geophysical modeling studies.

The role of long-term preparatory factors in mass rock creep deforming slopes: insights from the Zagros Mts. belt (Iran)

The long-term evolution of slopes affected by Mass Rock Creep deformations is controlled by both time-invariant predisposing factors, such as the geo-structural inheritance, and time-dependent preparatory conditions, including regional uplift and landscape evolution rates. However, the relationship among Deep-seated Gravitational Slope Deformations, drainage network evolution, and tectonics remains poorly defined. Here, we focused on an undocumented Deep-seated Gravitational Slope Deformation affecting an area of about 8 km2 in the SE tip termination of the Siah Kuh anticline in the Lorestan arc (Zagros Mts., Iran), upstream to the Mountain Front Fault. To assess the evolution processes which involved the slope up to the present, we integrated quantitative geomorphic analysis, optically stimulated luminescence dating of geomorphic markers, and SAR interferometry techniques. In detail, we semi-automatically extracted the river terrace treads to which we associated an elevation above the thalweg based on the Relative Elevation Model allowing the order definition. The plano-altimetric distribution of the treads and the OSL ages of two levels of strath terraces sampled in the field have been correlated along the river longitudinal profile, allowing the estimation of an uplift rate of 2.8 ± 0.2 mm year−1 and 0.42 ± 0.03 mm year−1, respectively upstream and downstream of the Mountain Front Fault. SAR interferometry was used to spot present-day shallow ground displacements associated with the ongoing slope deformation, by processing 279 satellite Sentinel-1 (A and B) radar images of the ascending and descending orbit spanning from 06 October 2014 to 31 March 2019. Different landslide mechanisms were distinguished across the fold axis, rototranslative to lateral spreading interpreted as two different evolutionary stages of the same process transposed spatially through the fold axis. Indeed, the rototranslative mechanism represents an advanced stage of the strain evolution while the lateral spreading is an earlier one. Finally, we infer that the variability in the spatial distribution of the slope deformation styles and patterns in the Lorestan arc is strictly related to the coupled evolution of the drainage system and tectonics. Involved volumes (from 0.6 up to 44 km3), local relief (from 400 up to 2000 m), incision rates (from 0.8 to 2.8 ± 0.2 mm year−1), and persistence time (from 104 to 105 years) represent the most important preparatory conditions and are predisposed by a moderately dipping downslope (from 8 to 25°) sedimentary sequence characterised by units with significantly different rheological behaviour.

A double tunnels model test study on mechanical properties of surrounding rock during tunnels excavation and creep stages

The tunnel engineering has become increasingly common with the needs of urban development. However, excavation sequence has a significant effect on the stability of the tunnel perimeter rock, which can lead to more unpredictable perimeter rock hazards and more difficulty in maintaining perimeter rock stability. In this study, to investigate the effect of different excavation sequences on tunnel deformation and creep, biaxial compression experiments were conducted on muddy siltstone specimens by using the acoustic emission (AE) and digital image correlation (DIC) techniques. The results indicated that, as the distance from the tunnel portal increases, the amount of stress and strain change decreases, with the largest values of stress changes occurring in the tunnel vault and middle area of twin tunnels. The specimen undergoes two stages in the creep process: deceleration creep and steady-state creep. The steady-state creep rate of the measurement points depends on the degree of excavation disturbance impact it experiences. The AE events during excavation can be divided into two phases: the quiet period when the specimen is not excavated and the active period when the specimen is excavated, and the cumulative counting curve shows a “stepwise” increase with the number of excavations. There is a sudden drop in the b-value during excavation and a decrease in the b-value during the deceleration creep phase. The results of this study can reflect the creep patterns of the surrounding rock under different excavation sequences, which can help to choose a more suitable excavation plan in terms of rock creep stability.

Residual subsidence time series model in mountain area caused by underground mining based on GNSS online monitoring

The residual subsidence caused by underground mining in mountain area has a long subsidence duration time and great potential harm, which seriously threatens the safety of people's production and life in the mining area. Therefore, it is necessary to use appropriate monitoring methods and mathematical models to effectively monitor and predict the residual subsidence caused by underground mining. Compared with traditional level survey and InSAR (Interferometric Synthetic Aperture Radar) technology, GNSS (Global Navigation Satellite System) online monitoring technology has the advantages of long-term monitoring, high precision and more flexible monitoring methods. The empirical equation method of residual subsidence in mining subsidence is effectively combined with the rock creep equation, which can not only describe the residual subsidence process from the mechanism, but also predict the residual subsidence. Therefore, based on GNSS online monitoring technology, combined with the mining subsidence model of mountain area and adding the correlation coefficient of the compaction degree of caving broken rock and the Kelvin model of rock mechanics, this paper constructs the residual subsidence time series model of arbitrary point on the ground in mountain area. Through the example, the predicted results of the model in the inversion parameter phase and the dynamic prediction phase are compared with the measured data sequence. The results show that the model can carry out effective numerical calculation according to the GNSS monitoring data of any point on the ground, and the model prediction effect is good, which provides a new method for the prediction of residual subsidence in mountain mining.

Nonlinear Nishihara model of soft rock based on damage mechanics and its parameter identification

The traditional Nishihara model is difficult to describe the nonlinear primary and accelerated creep characteristics of soft rock. Based on this, an improved nonlinear Nishihara model is established by modifying the unsteady dashpot and a nonlinear damaged viscoplastic body in series. The one-dimensional and three-dimensional creep constitutive equations of soft rock are derived. Levenberg-Marquardt algorithm is used to identify model parameters of creep test data of Cretaceous soft rock and red sandstone. The results show that the correlation coefficient between the fitted results of the improved nonlinear Nishihara model and the creep test data is above 0.97. The sensitive parameters λ,η′1 and a of the model are all within a reasonable range. It shows that the model can accurately reflect the characteristics of the unsteady primary creep stage and the nonlinear damage accelerated creep stage of soft rock, which is better than the traditional Nishihara model. The research results can provide theoretical guidance for similar soft rock creep model research.

Experimental Study on the Accelerating Creep of Rock Under Dry and Wet Conditions Based on a New Test Method

Creep tests under constant stress are among the most important tests for investigating the time-dependent behavior of rock. In previous studies, creep tests were conducted under various loading and environmental conditions; however, it was very difficult to demonstrate accelerating creep at failure at stresses less than 50% of strength in conventional creep tests. In this study, a new test method is proposed that combines an alternating loading-rate test and a creep test in the post-failure region. The accelerating creep as well as the loading-rate dependence of strength were successfully obtained simultaneously from a single specimen. This test method was applied to three rock types under dry and wet conditions. The results of Sanjome andesite under both dry and wet conditions, Kimachi sandstone under dry conditions, and Tage tuff under dry conditions showed a similar relationship between creep strain, creep strain rate, and residual time (i.e., creep lifetime minus elapsed time), from high to low creep stress levels, and a close relationship between accelerating creep and the loading-rate dependence of strength. Further, the mechanism responsible for the time dependence was found not to change significantly from high to low stress levels. In contrast, different results were obtained when high and low creep stress levels were compared in Kimachi sandstone and Tage tuff under wet conditions. The larger increase in creep strain with increasing creep strain rate at lower creep stress levels was related to the shape of the stress–strain curve in the post-failure region.

Long-term safety evaluation of soft rock tunnel structure based on knowledge decision-making and data-driven models

Tunnel structure are often subjected to continuous deformation caused by the creep effect of soft rock, leading to posing significant long-term operational risks. This paper focuses on ensuring the safe operation of a typical soft rock tunnel in the complex and dangerous mountainous area of western China. On the basis of studying the structural mechanic characteristics of the tunnel under the influence of soft rock creep, the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) model based on Analytic Hierarchy Process (AHP) and Entropy Weight Method (EWM) to determine subjective and objective weights, and game theory (GT) to obtain comprehensive weights was established. Additionally, the differential evolution-grey wolf optimization (DE-GWO) improved extreme learning machine (ELM) model was also constructed. By comparing the safety evaluation results of the two models on typical monitoring sections of soft rock tunnel structure, it is demonstrated that the proposed knowledge-based decision-making and data-driven models effectively and accurately evaluated the long-term safety of typical monitoring sections. Ulteriorly, to address the issue of structure safety evaluation caused by the inability to comprehensively monitor the entire tunnel (missing monitoring data), the DE-GWO improved ELM model was further adopted, and the structure safety status of the entire tunnel was precisely deduced.

Modeling of the creep and nonlinear damage effects of rocks and its application in tunnels

Modeling of the creep and nonlinear damage effects of rocks and its application in tunnels

Effects of creep of the salt rock formation on the failure of cement sheath integrity

Salt rock has a good sealing ability for oil and gas, but the creep of salt rock may cause wellbore integrity failure, and even cause safety accidents and economic losses in serious cases. Based on the creep law of salt rock obtained from the creep experiment of salt rock, the finite element model of casing-cement sheath-formation combination in salt rock formation is established. The effect of formation creep on the integrity of cement sheath under different uniform in-situ stress conditions is studied. The results show that the creep of salt rock will cause the shear failure of the cement sheath; reducing the elastic modulus of the cement sheath and increasing the Poisson's ratio of cement sheath will reduce the risk of shear failure of the cement sheath.

New accelerated rock creep model considering nonstationary viscosity coefficient

Accelerated creep models are popular research topics in rock mechanics. By analyzing the variation in the viscosity coefficient in the accelerated creep stage and defining the viscoplastic internal variable, a general evolution law for the viscosity coefficient was revealed, and a widely applicable accelerated creep model was proposed. First, the creep test data of 24 rock types were collected and analyzed. Subsequently, the contrast between the strength decrease in the accelerated creep-subsequent failure stage and the post-peak strength decrease in the elastoplastic process was evaluated, and the viscoplastic internal variable in the accelerated creep stage was defined. Subsequently, the evolution function between the normalized viscosity coefficient and the viscoplastic internal variable was established. Based on the test data for different rocks, the predicted curves accurately captured the evolution of the normalized viscosity coefficient with the viscoplastic strain increment and confining pressure in the accelerated creep stage. A new accelerated creep model was constructed by modifying the linear viscoplastic part of the Nishihara model using an established evolution model of the viscosity coefficient. The model demonstrated agreement with the experimental data for different rocks and yielded results close to the monitored tunnel convergence data.