Rock Elastic Modulus Research Articles

Determination of elastic modulus and anisotropy for rocks using digital drilling method

The main purpose of this study is to provide a digital drilling-based method for determining rock elastic modulus and evaluating the anisotropy. By considering a concept of crushed zone, the drilling response was characterized as the function of specific energy and drilling strength. On this basis, an equivalent elastic modulus was proposed to evaluate the rock elastic modulus. Moreover, an anisotropy index was proposed according to the difference in specific energy under different borehole directions. Digital drilling experiments were conducted for three lithologies at drilling directions namely 0, 60, and 120° (Based on vertical orientation), revealing the anisotropic effect exhibited in the rock. To validate the measurement of rock elastic modulus and its anisotropy, the compressive tests under same conditions were carried out. The results suggested that the proposed indicator provided an accurate evaluation for the rock's elastic modulus, with an error margin of less than 10%. Drilling-based anisotropy is identified in the drilling response, especially the critical state between cutting and friction. The statical indicator CoV (coefficient of variation) was utilized to characterize the anisotropy along the borehole. This research's innovation lies in providing an approach to evaluating rock anisotropy and determining its elastic modulus by considering the drilling response.

Measurement of the Static Nonlinear Third‐Order Elastic Moduli of Rocks: Problems and Applicability

AbstractThe third‐order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants (λ, μ), three nonlinear elastic moduli (A, B, C) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz‐rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path‐independence and small‐strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long‐standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long‐term safe storage of CO2 and generating process of geohazards.

Elastic modulus prediction for high-temperature treated rock using multi-step hybrid ensemble model combined with coronavirus herd immunity optimizer

Elastic modulus is a crucial mechanical parameter that measures the stiffness property of rock materials. In underground rock engineering, such as deep energy development and geological disposal of high-level nuclear waste, accurately determining the elastic modulus of engineering rock masses in high-temperature environments plays a vital role in understanding the instability-triggering conditions of hard and brittle rock masses in deep underground engineering and maintaining the safety and stability of deep underground engineering. Traditionally, conducting indoor experimental tests is time-consuming, labor-intensive, and costly. Therefore, developing a convenient and accurate rock elastic modulus prediction model based on machine learning technology holds significant importance. To this end, this study proposed a multi-step hybrid ensemble model (MHEM) for predicting high-temperature treated rock elastic modulus. The input parameters of the model include diameter, height, density, temperature, confining pressure, crack damage stress, and strength, while the output parameter is the elastic modulus. Subsequently, a coronavirus herd immunity optimizer (CHIO) intelligent optimization algorithm was employed to optimize the MHEM, and the CHIO-MHEM was established. Then, the performance of the developed models was compared and evaluated with eight other different prediction models. Finally, SHAP method and tree model feature analysis were used to quantify the feature importance of the prediction model. The research results indicate that, compared with other prediction models, the CHIO-MHEM exhibits superior performance, achieving accurate prediction of the elastic modulus of rocks treated at different high temperatures. Additionally, among all input parameters, rock density and temperature have the most significant influence on the rock elastic modulus.

Investigation on the effect of the relative position between fracture and injection-production well on thermal extraction performance

The development of hot dry rock (HDR) resources is mainly through hydraulic fracturing to build fracture in low permeability high-temperature rock to form working fluid flow channels. The control mechanism of thermal transfer and conversion process in fracture system is the key to influence thermal extraction effect. In this paper, a temperature-hydraulic-mechanical (THM) coupling model of fractured rock mass is established considering the temperature variation of rock elastic modulus and Poisson's ratio. The dynamic changes of fracture aperture and permeability are investigated. Taking fractured HDR reservoir as a case study, the depletion thermal extraction process of dual-well enhanced geothermal system (EGS) is simulated, the spatial-temporal evolution of multi-field are analyzed. The results show that the cold front of the horizontal and vertical single fracture model advance in an oval shape and a rectangle shape, respectively. Over 30 years, the horizontal fracture aperture typically changes by a factor ranging from 1.02 to 1.12, permeability typically changes by a factor ranging from 5 to 15. The vertical fracture aperture typically changes by a factor ranging from 1.02 to 1.14, permeability typically changes by a factor ranging from 10 to 25.

Experimental investigation of pore-filling substitution effect on frequency-dependent elastic moduli of Berea sandstone

SUMMARY Based on both forced oscillation and ultrasonic pulse transmission methods, we investigated solid pore infill influences on rock elastic moduli in a broad frequency range $[ {1 - 3000,\,\,{{10}^6}} ]$ Hz for different differential pressures. For a Berea sandstone sample, filled sequentially by solid (${22\,\,^{\rm{o}}}{\rm{C}}$), quasi-solid (${26\,\,^{\rm{o}}}{\rm{C}}$) and liquid (${34\,\,^{\rm{o}}}{\rm{C}}$) octadecane, a frequency-dependence was found for the Poisson's ratio, Young's modulus and bulk modulus, nevertheless, these elastic parameters were strongly suppressed by increasing pressures. Experimental measurements showed that shear wave velocity and modulus of solid-octadecane-filled samples are significantly larger than those of the dry and liquid-octadecane-filled ones, implying the potential stiffening effects related to solid infill in compliant pores. A three porosity structure model, which describes the solid stiffening effects related to equant, compliant and the intermediate pores with aspect ratios larger than those of compliant pores but much less than those of stiff pores, was used to compare against the experimentally measured elastic properties for octadecane pore infill, together with several other fluid/solid substitution theories. The agreement between experimental measurements and theoretical predictions is reasonably good for the sandstone tested, providing that the three porosity model can be applied for pressure- and frequency-dependent elastic moduli estimations for a viscoelastic pore-infill-saturated sandstone. Evaluating the combined squirt flow mechanism responsible for the observed moduli dispersion and attenuation is of great importance to reduce potential errors in seismic AVO inversion and 4-D seismic monitoring of gas-hydrate or bitumen-saturated reservoir, especially for reservoir rocks with complex microstructures and heterogeneous pore types.

The response mechanism and testing method of the rock elastic modulus while drilling

The elastic modulus is a basic parameter reflecting the deformation resistance and energy concentration characteristics of rock. The traditional testing method of the rock elastic modulus needs to core the surrounding rock and testing it in the laboratory, which has difficulty reflecting the rock mechanical properties under the engineering site environment, and uncontrolled broken surrounding rock is difficult to core for testing. Digital drilling technology provides a new idea for in situ testing of the rock’s elastic modulus. The key is to establish a quantitative relationship between the elastic modulus and drilling data. In this paper, the relationship between rock cutting energy density and drilling data is established, and a series of rock digital drilling tests are carried out. The response law of the drilling data and cutting energy density to the rock elastic modulus is clarified. The inversion model of the rock elastic modulus while drilling (DP-E model) is established. The verification test results indicate that the average difference rate of the test results based on the DP-E model is 7.06% compared with the compression test method, which verifies the effectiveness of the model. This study provides a theoretical basis for in situ testing of the rock elastic modulus.

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.

Seismic source of rock drill and its application in in-situ vibration monitoring of rock mass

This study suggests the use of a seismic source of a rock drill as a new excitation method for real-time monitoring of the vibration frequency of rock masses in tunnel engineering. In this study, a laboratory rock drill seismic source test system was developed. The rock mass excitation and vibration response under real in situ stress were simulated, and a natural frequency test of different lithologic materials under various in situ stresses was carried out based on the developed system. Empirical equations for estimating natural frequency were established using regression analysis. The test results show that (1) the laboratory rock drill seismic source test system exhibits good performance and can simulate the horizontal excitation process of the tunnel rock drill. Rock drill excitation may be used as the seismic source to continuously measure the in-situ vibration information of the rock mass. (2) The natural frequency of rock is positively correlated with rock elastic modulus and geostress and negatively correlated with rock density. This is not directly related to the seismic source.

Study on the size effect of rock elastic modulus considering the influence of joint roughness

The elastic modulus of rocks is a measure of the ability of rocks to resist elastic deformation. It is related to the size of rocks and can effectively measure the internal physical and mechanical strength of rocks. The development of joint fractures is the main reason for the size effect of rocks. Therefore, exploring the influence of joint roughness on the elastic modulus of rocks of different sizes is of great significance in mining rock mechanics. The article investigates the size effect of joint roughness on elastic modulus of rocks by establishing simulation schemes for 30 working conditions. By analyzing the stress-strain curves of rocks with different roughness and sizes, the deformation and failure patterns of rocks with different sizes were obtained. Research has found that the elastic modulus of rocks is in a power function relationship with joint roughness, while the elastic modulus of rocks is negatively exponentially related to rock size; The characteristic elastic modulus of rocks is in a power function relationship with joint roughness. The above relationships not only reveal the variation of rock elastic modulus with size, but also reveal the influence of joint roughness on elastic modulus, providing important basis for understanding the stability of mining rock engineering.

Stability Analysis of Soil and Rock Mixed Slope Based on Random Heterogeneous Structure

Due to the complexity in the heterogeneous internal structure and interactions between rocks and soil, the slide of soil–rock mixed slope is usually more complex than that of a homogeneous soil slope. This paper investigated the stability of soil–rock mixed slopes with finite element method (FEM) based on random heterogeneous structure. An image-aided approach was used to generate the 2-D and 3-D digital rocks to ensure the morphology of digital rocks was similar with the real rocks. The 2-D and 3-D soil–rock mixed slopes were then generated by placing the digital rocks into the soil matrix. The generated heterogeneous structures of soil–rock mixed slope were imported into ABAQUS for numerical analysis. The effect of rock content, spatial distributions, material properties, and rock–soil interface on the stability of soil–rock mixed slopes were analyzed. Results show that the stability factor of the soil–rock mixed slope increases with the increase of rock content. The rocks can play a certain degree of antislide effect in the slope. The uneven spatial distribution of rocks has effect on the overall stability of soil–rock mixed slope. This effect is more significant when the rock content is moderate. Rocks distributed in the middle layer of the slope may improve the overall antisliding performance of the slope. The stability factor decreases with the increase of rock density. While the effect of rock elastic modulus on stability of soil–rock mixed slope is relatively limited. The contact condition at the soil–rock interface has effect on the overall stability of soil–rock mixed slope. It is recommended to properly determine the interface properties for stability analysis of soil–rock mixed slope.

Preliminary design and evaluation method for the seismic isolation layer of a shield tunnel

Theoretical analyses and numerical simulations, proposed to increase the efficiency of tunnel seismic isolation measures, are too complex for solving practical problems. Herein, a simplified design method for a tunnel isolation layer is developed for preliminary calculations of the required physical parameters based on the surrounding rock conditions and seismic isolation performance. The internal force response of a shield tunnel in homogeneous ground before and after the installation of a seismic isolation layer is determined using the proposed method, considering the coupled effect of the isolation layer and surrounding rock by calculating the equivalent elastic modulus. The effectiveness of the derived method is verified using wave function expansion and finite element numerical simulation methods. The results obtained using the simplified design formulae are consistent with those obtained using the wave function expansion method. Furthermore, the effects of the seismic wave frequency, surrounding rock type, elastic modulus, and thickness of the seismic isolation layer on the seismic isolation effect are examined via parametric analysis. The proposed method could be applied to preliminary design and evaluation of seismic isolation layers for shield tunnels with different surrounding rock types.

Rock-physics modeling of deep clastic reservoirs considering the relationship between microscopic pore structure and permeability

Deep clastic reservoirs often exhibit low porosity and low permeability due to the influence of factors such as the sedimentary environment, the ground stress field, etc. The targeted seismic rock physics model can not only specify the microscopic main controlling factors that effect the macro-elastic response of rocks but also predict the shear wave velocity. Thereby, it guides reservoir prediction. Therefore, constructing a rock physics model that considers the pore-permeability relationship, pore structure, and consolidation compaction of reservoir rocks is especially crucial. However, there is the challenge of constructing direct rock-physics relationships between permeability parameters and elastic or physical property parameters. Consequently, the relationship between permeability and pore type is developed in this study using laboratory measurement data. Building upon this foundation, the calculated elastic modulus of the dry rock skeleton is further corrected by the consolidation compaction parameters and the optimization algorithm. Numerical analysis indicates that permeability parameters introduced in the modeling process can serve as guiding factors for different pore type proportions. Additionally, the compaction coefficient exerts a significant influence on the rock's elastic modulus. The applicability and effectiveness of the modeling are confirmed through the utilization of measured well data from the East China Sea.

Energy Accumulation Law of Different Forms of Coal–Rock Combinations

Coal–rock disasters are becoming more and more severe as the intensity of coal mining increases. Due to its destructive power and resulting extensive area damage, rock burst is among the most critical threats to coal mine safety. It results from the combined action of the coal and the rock when affected by the mining process. To this end, we used a combination of coal and rock to conduct our studies. Combining a uniaxial compression experiment with theoretical analysis, this work investigated how different lithologies and coal–rock height ratios affect the mechanical properties of this combination and the law governing energy accumulation. We determined the following: When the coal–rock height ratios are dissimilar, the peak strength and modulus of elasticity of the combination show a negative correlation with the coal thickness share, and the pre-peak energy accumulation and impact energy index of the combination is positively correlated with the coal thickness percentage. In combination with the same coal–rock height ratio, the peak strength, elastic modulus, pre-peak energy accumulation, and impact energy index all increase with increased rock strength and elastic modulus. The presence of a hard rock layer affects the accumulation of pre-peak energy. Based on the experimental analysis, a theoretical model was established, and the surrounding rock stress negatively correlates with the percentage of coal thickness; the energy stored in the surrounding rock is directly proportional to the coal in the zone. Therefore, we inferred that the stress distribution of the surrounding rock as coal thickness changes is abnormal; substantial energy accumulation can swiftly initiate dynamic disasters, such as rock bursts. This study has important reference significance for preventing and controlling rock bursts in areas where coal thickness changes.

Factors affecting casing equivalent stress in multi-cluster fracturing of horizontal shale gas wells: finite element study on Weirong Block, southern Sichuan Basin, China

Multi-cluster fracturing technology was often used in horizontal well reservoir reconstruction to achieve production increase, which also affected casing equivalent stress distribution. This paper focuses on multi-cluster fracturing and establishes a fracturing model in line with the reality. The three-dimensional finite element model of multi-cluster fracture-formation-cement sheath-casing was proposed, the influence of cluster spacing and fracturing cluster number on casing equivalent stress was studied. On this basis, a single segment 8-cluster three-dimensional finite element model was developed. The influence of rock elastic modulus, casing inner wall pressure, geostress change and elastic modulus of cement sheath on casing equivalent stress was simulated from two aspects of uniform and non-uniform extrusion of wellbore. Actual data was used and analyzed for the fracturing section of a well in Weirong Block, southern Sichuan Basin, China. The results showed that the casing equivalent stress decreased with the increase of fracture dip angle. The casing equivalent stress increased with the increase of cluster spacing; however, it decreased with the increase of rock elastic modulus. The casing equivalent stress increased with the increase of casing wall pressure. Also, the cracks extrude the casing evenly did not affect the change on casing equivalent stress. It was also found that, when casing was uniformly squeezed by multiple fractures, the difference of ground stress had little effect on casing equivalent stress, while non-uniform extrusion had greater effect on casing equivalent stress. Further, when there was no wellhead pumping pressure, the casing equivalent stress increased with the increase of the elastic modulus of the cement sheath, and decreased on the contrary. The elastic modulus of rock was lower than that of cement sheath, and the casing equivalent stress increased with the increase of the elastic modulus of cement sheath, and decreased on the contrary. The research results had certain guiding significance for the prevention and control of casing damage in fracturing section.

Effective elastic properties and S-wave anisotropy for rocks containing any oriented penny-shaped cracks in transversely isotropic background

Fractures have a significant influence on rock elastic properties. The existing elastic models for cracked medium mainly consider the crack dip angle. In this work, based on the previous transversely isotropic (TI) background and arbitrary dip crack model, a theoretical model is derived using the Bond transform matrix to quantify the effects of any oriented penny-shaped cracks on the elastic properties of rocks with a TI background. Based on this model, the effects of crack orientation on rock elastic properties are studied. Particularly, a special case with random crack orientation is investigated by using the spherical averaging of the crack compliance matrix with any orientations. Furthermore, the S-wave anisotropy for rocks containing multiple crack sets also is analyzed. The results indicate that the crack orientation has a great influence on rock elastic properties. Especially, the rock elastic properties indicate nonlinear changes with crack azimuth angles when cracks are inclined with respect to the TI background isotropic plane. The randomly oriented cracks decrease the overall rock elastic moduli but have little effect on rock anisotropy. For rocks containing multiple crack sets, parallel crack sets have great effects on the S-wave anisotropy, whereas the effects of orthogonal crack sets are negligible. Using this model, a complete workflow for the inversion of fracture properties using field data measured by acoustic logging is introduced. To explain the effect of crack azimuth angle, the crack density is inverted without considering crack orientation, only considering crack dip angle, and considering both crack dip and azimuth angles. The results indicate that the inversion results considering the crack dip and azimuth angles are in good agreement with the resistivity imaging results. This work provides the theoretical basis for fracture properties inversion for rocks with a TI background.

Application of Non-Destructive Test Results to Estimate Rock Mechanical Characteristics—A Case Study

Accurately determining rock elastic modulus (EM) and uniaxial compressive strength (UCS) using laboratory methods requires considerable time and cost. Hence, the development of models for estimating the mechanical properties of rock is a very attractive alternative. The current research was conducted to predict the UCS and EM of sandstone rocks using quartz%, feldspar%, fragments%, compressional wave velocity (PW), the Schmidt hardness number (SN), porosity, density, and water absorption via simple regression, multivariate regression (MVR), K-nearest neighbor (KNN), support vector regression (SVR) with a radial basis function, the adaptive neuro-fuzzy inference system (ANFIS) using the Gaussian membership (GM) function, and the back-propagation neural network (BPNN) based on various training algorithms. The samples were categorized as litharenite and feldspathic litharenite. By increasing the feldspar% and quartz% and decreasing the fragments%, the static properties increased. The results of the statistical analysis showed that the SN and porosity have the greatest effect on the UCS and EM, respectively. Among the Levenberg–Marquardt (LM), Bayesian regularization, and Scaled Conjugate Gradient training algorithms using the BPNN method, the LM achieved the best results in forecasting the UCS and EM. The ideal obtained BPNN, using a trial-and-error process, contains four neurons in a hidden layer with eight inputs. All five models attained acceptable accuracy (correlation coefficient greater than 70%) for estimating the static properties. By comparing the methods, the ANFIS showed higher precision than the other methods. The UCS and EM of the samples can be determined with very high accuracy (R2 > 99%).

Developing Two Hybrid Algorithms for Predicting the Elastic Modulus of Intact Rocks

In the primary and final designs of projects related to rock mechanics and engineering geology, one of the key parameters that needs to be taken into account is the intact rock elastic modulus (E). To measure this parameter in a laboratory setting, core samples with high-quality and costly tools are required, which also makes for a time-consuming process. The aim of this study is to assess the effectiveness of two meta-heuristic-driven approaches to predicting E. The models proposed in this paper, which are based on integrated expert systems, hybridize the adaptive neuro-fuzzy inference system (ANFIS) with two optimization algorithms, i.e., the differential evolution (DE) and the firefly algorithm (FA). The performance quality of both ANFIS-DE and ANFIS-FA models was then evaluated by comparing them with ANFIS and neural network (NN) models. The ANFIS-DE and ANFIS-FA models were formed on the basis of the data collected from the Azad and Bakhtiari dam sites in Iran. After applying several statistical criteria, such as root mean square error (RMSE), the ANFIS-FA model was found superior to the ANFIS-DE, ANFIS, and NN models in terms of predicting the E value. Additionally, the sensitivity analysis results showed that the P-wave velocity further influenced E compared with the other independent variables.

Impact of Creep Effect on Hydraulic Fracture Long-Term Conductivity in Deep Shale Reservoirs

Abstract The main factor contributing to the decline in effective fracture width and conductivity is proppant embedding into the fracture surface. In the deep shale's high-temperature, high-pressure, and high-stress environment, the rheological properties of rock cause proppant embedding to be deeper. Additionally, the effect of hydraulic fracture is difficult to maintain after fracturing, which causes a sharp decline in cumulative production. In this paper, the Hertz contact theory is used to establish a long-term fracture conductivity model that incorporates the two embedding behaviors of proppant elastic deformation and reservoir creep deformation. Through time integration, the variation of long-term fracture conductivity is obtained. The experimental data and the theoretical model agree well. The results show that long-term fracture conductivity gradually decreases as the proppant progresses from the elastic embedding stage to the creep embedding stage. The elastic modulus, viscoelastic coefficient, and particle size significantly impact on the fracture width. The rock's elastic modulus and viscoelastic coefficient have a negligible impact on the long-term fracture conductivity, which is positively correlated with sand concentration, proppant particle size, and elastic modulus. In this research, an accurate and effective analysis model is proposed to quantify the long-term fracture conductivity, reveal the hydraulic fracture closure mechanism of deep shale under high temperature and high stress, and provide technological solutions for long-term maintenance of high conductivity fracture channels, which is useful to increase deep shale production efficiency, lower the production decline rate, and extend the stable production cycle.

Digital Rock Mechanical Properties by Simulation of True Triaxial Test: Impact of Microscale Factors

Complex fractures and pore structures in the rock strongly influence the mechanical properties, and the process from compression to failure is complicated. Under the action of rock stress, pore structure deformation and fractures close or propagate, easily leading to deterioration in the rock mechanical properties until rock failure. Thus, the effects of microscale factors are critical in mechanical properties such as rock strength, elastic modulus, and stress–strain state under the triaxial stress state. It is difficult for physical and mechanical experiments to obtain the qualitative rules of regular structures, but numerical simulation can make up for this defect. In this work, the accuracy of the model was proven through a comparison with previous experimental results. The true triaxial numerical simulation experiments were conducted on representative rocks and natural pore structures. These simulated results revealed that the pore and throat parameters will change abruptly when the particle model volumetric strain is between 0.0108 and 0.0157. When the fracture angle is between 45° and 75°, the fracture has a great influence on the peak stress. The angle between the natural fracture and the fracturing direction should be less than 45° as much as possible. Clay affects the rock strength by influencing the force chains formed by the rock skeleton. Fracturing is easier when the structural clay content is higher than 25%. It is easier to fracture in a direction parallel to the laminated clay when the clay content is below 27%. This work indicates the effects of rock particles, fractures, and clay on the mechanical parameters, providing key fundamental data for further quantifying the fracturing patterns.

Peridynamic investigation on crack propagation mechanism of rock mass during excavation of tunnel group in cold regions

An extended ordinary state-based peridynamic model was developed to investigate the crack propagation of surrounding rock due to tunnel excavation. The frost heave effect on the crack surface was described by an equivalent pressure density. Two numerical examples were conducted to verify the effectiveness and robustness of the proposed model. Moreover, the influence of frost heave pressure, buried depth and rock elastic modulus on damage characteristics of the surrounding rock was investigated. The results demonstrate that massive microcrack damage will be formed at the invert when the tunnel is excavated in a deeply buried rock mass or soft rock stratum. HIGHLIGHTS A peridynamic model of rock mass under excavation and frost heave was constructed. Damage characteristics of surrounding rock could be simulated efficiently. Frost heave load was exerted on the crack surface by an equivalent pressure density. The effects of frost heave load, buried depth and rock elastic modulus were studied.