Method for constructing true triaxial shear dynamic model of anchor-rock combination under water chemical corrosion

Abstract

The present application relates to a kind of water chemical corrosion under anchor-rock combination true triaxial shear dynamic model construction method, the method is by grouping corrosion pretreatment to anchor rod and constructs corrosion parameter database, quantifies the mass loss law of anchor rod under different corrosion conditions;Subsequently, the mechanical response data of blank group and corrosion group sample are synchronously obtained by true triaxial disturbance shear test;Based on corrosion parameter, establish anchor rod damage variable function, accurately characterize corrosion damage evolution mechanism;The mechanical parameters of corrosion group sample are corrected using damage function, generate the predicted value of strength after corrosion;Combined with correction parameter, the fractional order constitutive model of elastic-viscoplastic coupling is constructed;Finally, realize dynamic verification by comparing model prediction and test curve.The method systematically solves the engineering problem of theoretical characterization modeling of anchor rock mass corrosion-true triaxial stress-dynamic disturbance coupling characteristics, and provides reliable theoretical tool for rock mass engineering support safety evaluation.

Description

Technical Field

[0001] This invention relates to the field of rock mechanical properties and engineering research technology, specifically to a method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion. Background Technology

[0002] In the field of rock mass engineering support, the anchor-rock assembly formed by anchor bolts and surrounding rock is the core structure ensuring the long-term stability of roadways. Due to the prevalence of acidic or alkaline groundwater in underground environments, anchor bolts are constantly exposed to hydrochemical corrosion, causing their mechanical properties to gradually deteriorate with corrosion. To accurately predict the safety status of support systems under corrosive conditions, it is necessary to establish dynamic models that can quantify the impact of hydrochemical corrosion on the mechanical behavior of the anchor-rock assembly. Such models must comprehensively consider the coupling effects of corrosion damage evolution, true triaxial stress state, and dynamic disturbance loads, thereby providing a reliable theoretical basis for rock mass engineering support design.

[0003] However, existing anchor-rock composite mechanical models have significant shortcomings: First, most models do not systematically consider the damage mechanism of water chemical corrosion on anchor materials, making it difficult to quantify the attenuation law of anchor strength under different corrosion conditions such as acidity / alkalinity and corrosion duration; second, when simulating dynamic shear response under true triaxial stress, existing methods lack an accurate description of the coupling relationship between corrosion damage and system strength attenuation, resulting in a large deviation between model predictions and actual engineering; in addition, in the existing model construction process, the calibration of corrosion damage parameters and the dynamic verification are disconnected, reducing the engineering applicability of the model. Summary of the Invention

[0004] Based on this, the purpose of this invention is to provide a method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion that can accurately quantify corrosion damage, construct a true triaxial dynamic shear response model, and verify the model through systematic experiments.

[0005] The objective of this invention is achieved through the following solution:

[0006] In a first aspect, the present invention provides a method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion, comprising the following steps:

[0007] S1: The anchor bolt samples were grouped and immersed in constant temperature solutions with different pH values ​​for different corrosion times. The mass of all anchor bolt samples before and after corrosion was measured, and a corrosion parameter database containing pH value, corrosion time and mass loss was generated.

[0008] S2: The pretreated anchor rods and rock samples are assembled into anchor-rock composite samples. At the same time, the blank control samples assembled with anchor rods that have not undergone corrosion pretreatment are assembled in the same way. Preset normal stress and lateral stress are applied to all samples, shear stress is applied in a multi-level incremental path and cyclic disturbance is applied simultaneously. Stress-strain data are recorded to generate a mechanical test database containing the crack initiation stress, failure stress and stress-strain curves of all samples.

[0009] S3: Process the corrosion parameter database, and establish a predetermined functional relationship between anchor bolt damage variables and pH value and corrosion time based on the mass loss rate, combined with pH value and corrosion time through data fitting, and generate a deterministic function for calculating anchor bolt damage variables under arbitrary corrosion conditions.

[0010] S4: Based on the deterministic function, the crack initiation stress and failure stress of the mechanical test dataset are proportionally attenuated and corrected. The initial stress value is corrected according to the linear attenuation relationship to generate the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion.

[0011] S5: Based on the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion, a yield function is constructed, an elastic-viscoplastic coupled differential equation system is established, and a fractional-order damage shear constitutive model is generated.

[0012] S6: Input the full-stage stress-strain curves of corrosion group specimens from the mechanical test database into the fractional-order damage shear constitutive model, use a global optimization algorithm to fit the parameters and compare them with the test curves to generate a verified true triaxial shear dynamic model.

[0013] In one embodiment, S1 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0014] S11: The anchor bolt samples were grouped into a blank group and a corrosion group. The corrosion group was immersed in solutions with different pH values ​​and kept at a constant temperature for different durations to generate a set of grouped anchor bolt samples.

[0015] S12: Quantify the mass loss of the grouped anchor bolt sample sets, measure the mass of each group of anchor bolts before and after corrosion, and calculate the percentage of mass loss of each group of anchor bolts.

[0016] S13: The percentage of mass loss is structured and associated with the pH value, corrosion time and percentage of mass loss of each group of anchor bolts in the grouped anchor bolt sample set to generate a corrosion parameter database.

[0017] In one embodiment, S2 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0018] S21: The pre-treated anchor bolts are assembled. The blank group anchor bolts are assembled with rocks to form a control group sample, and the corroded group anchor bolts are assembled with rocks of the same batch to form a corrosion group sample, thus generating an anchor-rock composite sample set.

[0019] S22: The anchor-rock composite sample set is subjected to stress field loading treatment, and a fixed confining pressure in the orthogonal direction is applied to stabilize the normal and lateral stresses to the preset values;

[0020] S23: The anchor-rock composite specimen under stress field is subjected to shear disturbance loading. The shear load is increased stepwise along an increasing path, and the cyclic fluctuation stress is superimposed simultaneously to generate dynamic shear response data containing stress-strain relationship.

[0021] S24: Perform feature extraction processing on dynamic shear response data, identify the stress-strain curve feature points of all specimens, and generate a mechanical test database containing the initial value of crack initiation stress, the initial value of failure stress, and the stress-strain curves of the entire stage.

[0022] In one embodiment, S3 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0023] S31: Construct input vectors for the corrosion parameter database, extract the pH value, corrosion time and mass loss percentage of each anchor bolt sample, and form a data matrix containing the correlation between environmental parameters and corrosion damage;

[0024] S32: Fit the data matrix with a nonlinear function, and use an exponential-time coupled equation to iteratively optimize the parameters of material corrosion constant, pH decay coefficient and time nonlinear factor to generate the initial damage variable function.

[0025] S33: Perform physical verification of the initial damage variable function, calculate the deviation between the mass loss rate predicted by the function and the measured mass loss rate under different corrosion conditions, and generate a deterministic function for calculating the anchor bolt damage variable under arbitrary corrosion conditions.

[0026] In one embodiment, the expression for the initial damage variable function of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention is as follows:

[0027]

[0028] Where D2 is the initial damage variable function, i.e., the anchor bolt damage variable, and ω is the corrosion constant of the material properties. ξ is the sensitivity factor of pH to corrosion rate, ξ is the nonlinear influencing factor of corrosion, pH is the acidity or alkalinity of the solution, and t is the corrosion time of the anchor bolt sample.

[0029] In one embodiment, S4 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0030] S41: Extract blank data from the mechanical test database, separate the initial values ​​of crack initiation stress and failure stress of the control group specimens, and generate a reference stress dataset;

[0031] S42: Based on the deterministic function, damage value mapping is performed on the corrosion group samples in the corrosion parameter database. The damage variable values ​​corresponding to the corrosion group samples are calculated according to the actual corrosion conditions, and the sample damage variable values ​​are generated.

[0032] S43: Based on the sample damage variable value, the reference stress dataset is proportionally attenuated, and the stress value after corrosion is calculated according to the preset attenuation relationship to generate the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion.

[0033] In one embodiment, S5 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0034] S51: The yield function is constructed for the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion. Based on the predicted value of the crack initiation stress after corrosion, the critical threshold of viscoplastic flow is defined to generate the yield function characterizing the yield condition of the material.

[0035] S52: The constitutive equation is derived for the yield function. Based on the linear relationship between stress and strain in the elastic deformation stage and the relationship between strain rate and yield function in the viscoplastic flow stage, a set of differential equations describing the material deformation process is established.

[0036] S53: Couple the differential equation system and combine the rock constitutive relation with the anchor bolt constitutive relation in parallel to generate a fractional-order damage shear constitutive model that characterizes the dynamic shear response of the anchor-rock composite.

[0037] In one embodiment, the expression for the yield function of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under water chemical corrosion provided by the present invention is as follows:

[0038]

[0039] Where F is the yield function, τ t σ is the shear stress experienced by the anchor-rock composite. n For normal stress, c is the internal friction angle of the corroded rock-anchor system. * σ represents the cohesion of the rock-anchor system after corrosion, K is the characteristic length parameter related to rock damage, and σ is the anchor bolt.p d represents the tensile strength of the rock. * The damage threshold of the rock. This represents the actual shear stress of the anchor bolt after corrosion.

[0040] In one embodiment, the model expression of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention is as follows:

[0041]

[0042] Where γ(t) is the model expression for the fractional-order damage-shear constitutive model, and τ t Let G be the shear stress on the anchor-rock composite, G be the elastic shear modulus of the rock when it is undamaged, F1 be the mechanical function related to the stable damage stage, F2 be the mechanical function related to the accelerated damage stage, D0 be the initial damage variable of the rock mass under hydrochemical conditions, D1 be the damage variable of the rock mass under shear stress loading, t be the shear stress loading time, α be the order of the fractional derivative, Γ(·) be the gamma function, η1 be the viscoelastic property coefficient, β be the order of the fractional derivative, η2 be the viscoelastic-plastic property coefficient, λ be the damage attenuation coefficient, and t1 be the initial time parameter.

[0043] In one embodiment, S6 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0044] S61: Extract characteristic segments from the full-stage stress-strain curves of corrosion samples in the mechanical test database, separate the characteristic data points of the elastic segment, yield segment, and failure segment, and generate a model calibration dataset.

[0045] S62: Perform parameter inversion processing on the model calibration dataset and the fractional-order damage shear constitutive model: use a global optimization algorithm to fit the material parameters of the fractional-order damage shear constitutive model, optimize the parameters by minimizing the deviation between the model prediction curve and the experimental curve, and generate the optimized fractional-order damage shear constitutive model;

[0046] S63: Dynamic response verification of the optimized fractional-order damage shear constitutive model: Based on experimental data under cyclic perturbation loading conditions, verify the consistency between the model's predicted strain rate and the actual strain rate, and generate a verified true triaxial shear dynamic model.

[0047] In summary, the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided in this application can effectively solve the problem of co-predicting anchor corrosion damage and dynamic mechanical response in rock mass engineering support by systematically integrating corrosion damage quantification, true triaxial dynamic testing and coupled modeling process. This method, based on the construction of a corrosion parameter database, can accurately quantify the mass loss law of anchor bolts under different pH values ​​and time periods, providing data support for the corrosion damage evolution mechanism. By simultaneously acquiring the full-stage mechanical response of blank and corroded samples through true triaxial perturbation shear tests, it can achieve a synergistic characterization of the corrosion environment and multiaxial stress state. The anchor bolt damage variable function established using data fitting can accurately describe the nonlinear attenuation law of anchor bolt strength under any corrosion condition. Based on this function, the mechanical parameters are proportionally attenuated to achieve dynamic prediction of the actual shear strength of the anchor bolt and the system's crack initiation stress after corrosion. The elastic-viscoplastic coupled constitutive model constructed with the corrected parameters can fully characterize the nonlinear deformation behavior and rate-related characteristics of the anchor-rock assembly under cyclic perturbation. Finally, by comparing the model predictions with the experimental curves through a global optimization algorithm, closed-loop verification of the dynamic shear response and improvement of model reliability can be achieved. This method overcomes the limitations of traditional models that do not systematically integrate corrosion damage mechanisms and true triaxial dynamic response. It can provide a theoretically complete and engineering-applicable dynamic prediction tool for the safety assessment of rock mass engineering support systems in highly corrosive strata, and significantly improve the accuracy and applicability of long-term stability analysis of rock mass process structures.

[0048] To better understand and implement this invention, the following detailed description is provided in conjunction with the accompanying drawings. Attached Figure Description

[0049] Figure 1 A flowchart illustrating a method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion, provided in an embodiment of this application;

[0050] Figure 2 A flowchart illustrating the deterministic function for generating anchor bolt damage variables provided in an embodiment of this application;

[0051] Figure 3a A graph showing the mass loss trend of the anchor bolt after corrosion time as a function of pH in the hydrochemical environment of corrosion, provided in an embodiment of this application.

[0052] Figure 3b A graph showing the trend of mass loss of the anchor bolt after corrosion time as provided in the embodiments of this application;

[0053] Figure 4 A schematic diagram illustrating the process of constructing a fractional-order damage-shear constitutive model provided in an embodiment of this application;

[0054] Figure 5A schematic diagram of the model principle of the fractional-order damage deterioration shear mechanics model of the anchor bolt-rock system provided in the embodiments of this application;

[0055] Figure 6a A comparison of theoretical and experimental curves for anchoring limestone with pH=3.5 and no anchor corrosion, provided in the embodiments of this application;

[0056] Figure 6b A comparison of theoretical and experimental curves for anchoring limestone at pH = 5.5 and with no anchor corrosion, provided in the embodiments of this application;

[0057] Figure 6c A comparison diagram of the theoretical and experimental curves of the anchor bolt soaking at pH=3 provided in the embodiments of this application;

[0058] Figure 6d A comparison diagram of the theoretical and experimental curves of the anchor bolt under pH=9 immersion conditions provided in this application embodiment;

[0059] Figure 6e A comparison diagram of theoretical and experimental curves of anchor bolts immersed for 15 days is provided for embodiments of this application.

[0060] Figure 6f A comparison chart of theoretical and experimental curves of the anchor bolt under 75-day immersion conditions provided in this application embodiment. Detailed Implementation

[0061] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0062] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0063] In one embodiment, such as Figure 1 As shown, a method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion is provided. This embodiment illustrates the application of this method to a terminal. It is understood that this method can also be applied to a server, and to a system including both a terminal and a server, and implemented through interaction between the terminal and the server. In this embodiment, the method includes the following steps:

[0064] S1: The anchor bolt samples were grouped and immersed in constant temperature solutions with different pH values ​​for different corrosion times. The mass of all anchor bolt samples before and after corrosion was measured, and a corrosion parameter database containing pH value, corrosion time and mass loss was generated.

[0065] Specifically, this embodiment uses HRB400 threaded steel to process anchor rod samples with a diameter of 11.7 mm and a length of 95 mm, with 3 parallel samples in each group. The system pre-treats the anchor rod samples by first polishing the surface oxide scale with 400#, 800#, and 1200# sandpaper in sequence until the metallic luster is exposed, then wiping the surface with anhydrous ethanol to remove surface oil stains, and then placing the samples in a vacuum drying oven at 60±2℃ for 24 hours to dry, and then cooling to room temperature for use. In this embodiment, four isothermal solutions with pH=3, 5, 7, and 9 are prepared. The pH=3 solution is obtained by adjusting deionized water with 0.1 mol / L hydrochloric acid, the pH=5 solution is prepared using an acetate-sodium acetate buffer system, the pH=7 solution is prepared directly using ultrapure water with a resistivity of 18.2 MΩ·cm, and the pH=9 solution is prepared using a borax-sodium hydroxide buffer system. Each solution is poured into a 500 mL polytetrafluoroethylene container, and then the container is placed in a isothermal water bath set at 59℃.

[0066] For example, the system divides the anchor bolt samples into two groups. The first group is further divided into four subgroups based on pH value, each immersed in one of four different constant-temperature solutions for a uniform immersion time of 30 days. The second group is immersed in a constant-temperature solution with pH=3 for immersion times of 0, 15, 30, 45, 60, and 75 days, respectively. The system uses an electronic analytical balance with an accuracy of 0.1 mg to weigh the initial mass of each sample before and after corrosion, calculates the mass loss and mass loss rate, and records the sample number, anchor bolt material, initial dimensions, solution pH value, constant-temperature temperature, immersion time, and mass data to construct a corrosion parameter database.

[0067] S2: The pretreated anchor rods and rock samples are assembled into an anchor-rock composite sample. At the same time, the blank control sample assembled with anchor rods that have not undergone corrosion pretreatment is assembled in the same way. Preset normal stress and lateral stress are applied to all samples, and shear stress is applied in a multi-level incremental path while cyclic disturbance is applied simultaneously. Stress-strain data are recorded to generate a mechanical test database containing the crack initiation stress, failure stress and stress-strain curves of all samples at all stages.

[0068] Specifically, this embodiment uses limestone from a deep mining area, which is processed into cuboid rock samples of 50mm×50mm×100mm according to GB / T 50266-2013. The samples are tested using an ultrasonic flaw detector to ensure that there are no obvious visible cracks and the wave velocity difference is ≤5%, while ensuring that the flatness error of the sample end face is ≤0.05mm. The system drills a blind hole with a diameter of 12mm and a depth of 95mm at the axis of the rock sample, with a drilling verticality error of ≤0.5°. Then, a treated anchor rod or an uncorroded anchor rod (blank control) is inserted to ensure that the anchor rod is coaxial with the drill hole and that the end face is flush with the end face of the rock sample. The system places the assembled anchor-rock composite sample in a standard curing chamber at 25±2℃ and relative humidity of 60±5% for 24 hours.

[0069] Preferably, the system applies a normal stress σ to all specimens. n =10MPa, lateral stress σ p =15MPa, loading rate of 0.5MPa / s, each stress level stabilizes for 5 minutes before proceeding to the next stage; the system operates at 0.4τ p →0.7τ p →0.8τ p →0.9τ p →τ p →The failure path involves applying shear stress at a rate of 0.005 mm / s. After each shear stress level stabilizes for 10 minutes, a cyclic perturbation with an amplitude of 0.8 MPa and a frequency of 2 Hz is applied via the system's cyclic perturbation module for 3600 seconds. The system uses a supporting dynamic data acquisition system to collect real-time data on normal stress, lateral stress, shear stress, and shear strain, recording the specimen's initiation stress τ. ci , destructive stress τ p A mechanical test database was constructed, which includes the specimen number of the composite, the corrosion conditions of the anchor bolt, the loading parameters, the characteristic stress, and the stress-strain data of the whole stage.

[0070] S3: Process the corrosion parameter database, and establish a predetermined functional relationship between anchor bolt damage variables and pH value and corrosion time based on the mass loss rate, combined with pH value and corrosion time through data fitting, thereby generating a deterministic function for calculating anchor bolt damage variables under arbitrary corrosion conditions.

[0071] Specifically, the system extracts the mass loss rate of each group of samples from the constructed corrosion parameter database, calculates the mass loss rate of three parallel samples in each group, and obtains the average mass loss rate of each group. The system processes the average mass loss rate data of each group, first calculating the standard deviation of each group's data, and then calculating the Grubbs statistic based on the standard deviation. The system compares the calculated Grubbs statistic with the critical value corresponding to the significance level α = 0.05. If the statistic is greater than the critical value, the corresponding outlier data is removed, and the average mass loss rate of the group is recalculated. The system defines the anchor bolt damage variable, first selecting the maximum average mass loss rate from all test groups, and using this maximum average mass loss rate as a benchmark, calculates the damage variable corresponding to the average mass loss rate of each group, ensuring that the damage variable is between 0 and 1.

[0072] For example, based on the principles of corrosion electrochemistry, the system assumes a correlation between damage variables and pH value and corrosion time, and selects a multivariate nonlinear regression method to construct a functional relationship. The system selects some experimental data to verify the initially constructed function, compares the consistency between the function calculation results and the experimental data, and adjusts the function form until it meets the accuracy requirements. The system determines the applicable conditions for the function as HRB400 anchor bolts, pH = 3-9, corrosion time 0-75 days, and temperature 59℃, and outputs the function expression and related parameters, forming a deterministic function that can calculate anchor bolt damage variables under arbitrary corrosion conditions.

[0073] S4: Based on the deterministic function, the crack initiation stress and failure stress of the mechanical test dataset are proportionally attenuated and corrected. The initial stress value is corrected according to the linear attenuation relationship to generate the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion.

[0074] Specifically, the system selects blank control sample data of anchor bolts immersed for 0 days from the mechanical test database, extracts the failure stress of three parallel blank control samples, calculates the average of the three failure stresses, and uses this average as the initial shear stress of the anchor bolt. The system also extracts the crack initiation stress of the three parallel blank control samples, calculates the average of the three crack initiation stresses, and uses this average as the system's initial crack initiation stress. Based on the linear decay relationship between damage and strength, the system first obtains the target corrosion conditions and calculates the anchor bolt damage variables under these corrosion conditions using a deterministic function.

[0075] For example, the system substitutes the calculated damage variables into a preset correction relationship to calculate the actual shear stress and system initiation stress of the anchor bolt after corrosion. Taking an anchor bolt soaked for 30 days at pH=3 as an example, the system first calculates the damage variables under this condition, and then substitutes them into the correction relationship to obtain the corresponding actual shear stress and system initiation stress. The system calculates the error between the correction value and the experimental value based on the experimental values ​​under the same corrosion conditions. If the error is greater than 15%, the system re-examines the calculation process of the damage variables and the correction relationship until the error is less than 15%. The system organizes the pH value, corrosion time, damage variables, initial shear stress, actual shear stress, initial initiation stress, and post-corrosion initiation stress under different corrosion conditions, sorts them in ascending order of corrosion time, and forms a correction parameter table.

[0076] S5: Based on the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion, a yield function is constructed, an elastic-viscoplastic coupled differential equation system is established, and a fractional-order damage shear constitutive model is generated.

[0077] Specifically, the system constructs a yield function based on the actual shear stress of the anchor bolt after corrosion and the initiation stress of the system after corrosion. Uniaxial compression tests are conducted on the limestone, and the internal friction coefficient of the limestone is calculated based on the test data. The initial shear stress of the anchor bolt is used as the yield shear stress of the anchor bolt and substituted into the shear yield function. The system determines the stage of the composite structure based on the calculated shear yield function. When the yield function value is less than 0, the composite structure is determined to be in the elastic stage; when the yield function value is greater than or equal to 0, the composite structure is determined to be in the viscoplastic yield stage. In the elastic stage, the system uses Hooke's law to construct a constitutive relation, extracts the first 10% of data points in the elastic segment of the stress-strain curve, obtains the shear modulus of the blank control sample through linear fitting, and calculates the elastic shear strain by combining the anchor bolt damage variable.

[0078] For example, the system can use fractional-order Caputo derivatives to describe viscoplastic deformation in the viscoplastic stage. By analyzing the characteristics of experimental curves of viscoplastic deformation under different corrosion conditions, the order range of the fractional-order derivatives is determined, and the correlation between viscoplastic deformation and time and yield function is constructed. When calculating the total shear strain, the system first calculates the elastic shear strain based on the constitutive relations of the elastic stage, and then calculates the viscoplastic shear strain based on the constitutive relations of the viscoplastic stage. The elastic shear strain and the viscoplastic shear strain are added together to obtain the total shear strain. The system integrates the constitutive relations of the elastic stage and the viscoplastic stage to form a fractional-order damage shear constitutive model.

[0079] S6: Input the full-stage stress-strain curves of corrosion group specimens from the mechanical test database into the fractional-order damage shear constitutive model, use a global optimization algorithm to fit the parameters and compare them with the test curves to generate a verified true triaxial shear dynamic model.

[0080] Specifically, the system filters stress-strain curves from a mechanical test database, discarding data with abnormal fluctuations, and selects six sets of curves under typical corrosion conditions as fitting data. Each set contains more than 1000 data points, and the data is imported into the parameter fitting tool in Excel format. Based on the conventional parameter ranges of rock mechanics tests, the system sets the initial range of model parameters and uses a combined algorithm of "quasi-Newton's method (BFGS) + general global optimization method" for parameter fitting. The system sets the iteration termination condition to a root mean square error change of less than 10. -5 With the goal of minimizing the root mean square error between the experimental curve and the model calculation curve, and taking the sample data of pH=3 and soaked for 30 days as an example, after completing the parameter fitting, the fitted parameters are recorded, and the corresponding root mean square error and goodness of fit are calculated and recorded.

[0081] For example, the system selects two sets of data from the database that were not used for fitting, inputs the data into the constructed fractional-order damage-shear constitutive model, and calculates the model curve. The system compares the model curve with the corresponding experimental curve, calculates the root mean square error between the two, and if the error is greater than 0.05, the initial range of parameters is readjusted and the model is fitted again until the error is less than 0.05, thus verifying the model's generalization ability. The system then organizes the verified model, including the model expression, parameters and confidence intervals under different corrosion conditions, a comparison of typical fitting curves, and the applicable range, forming the final true triaxial shear dynamic model.

[0082] In summary, the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided in this application can effectively solve the problem of co-predicting anchor corrosion damage and dynamic mechanical response in rock mass engineering support by systematically integrating corrosion damage quantification, true triaxial dynamic testing and coupled modeling process. This method, based on the construction of a corrosion parameter database, can accurately quantify the mass loss law of anchor bolts under different pH values ​​and time periods, providing data support for the corrosion damage evolution mechanism. By simultaneously acquiring the full-stage mechanical response of blank and corroded samples through true triaxial perturbation shear tests, it can achieve a synergistic characterization of the corrosion environment and multiaxial stress state. The anchor bolt damage variable function established using data fitting can accurately describe the nonlinear attenuation law of anchor bolt strength under any corrosion condition. Based on this function, the mechanical parameters are proportionally attenuated to achieve dynamic prediction of the actual shear strength of the anchor bolt and the system's crack initiation stress after corrosion. The elastic-viscoplastic coupled constitutive model constructed with the corrected parameters can fully characterize the nonlinear deformation behavior and rate-related characteristics of the anchor-rock assembly under cyclic perturbation. Finally, by comparing the model predictions with the experimental curves through a global optimization algorithm, closed-loop verification of the dynamic shear response and improvement of model reliability can be achieved. This method overcomes the limitations of traditional models that do not systematically integrate corrosion damage mechanisms and true triaxial dynamic response. It can provide a theoretically complete and engineering-applicable dynamic prediction tool for the safety assessment of rock mass engineering support systems in highly corrosive strata, significantly improving the accuracy and applicability of long-term stability analysis of mine structures.

[0083] In one embodiment, S1 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0084] S11: The anchor bolt samples are grouped into a blank group and a corrosion group. The corrosion group is immersed in solutions with different pH values ​​and kept at a constant temperature for different durations to generate a set of grouped anchor bolt samples.

[0085] Specifically, the system selected anchor rod samples with a diameter of 11.7 mm and a length of 95 mm processed from HRB400 threaded steel. All samples were pretreated: the sample surface was polished with 400# sandpaper for 5 minutes to remove the surface oxide scale, then 800# sandpaper was used to polish for another 3 minutes to refine the surface, and then 1200# sandpaper was used to polish for another 2 minutes until the surface showed a metallic luster. The degreased cotton was moistened with anhydrous ethanol and used to wipe the oil stains on the sample surface. After wiping, the sample was placed in a vacuum drying oven, the temperature was set to 60±2℃, the oven door was closed and the vacuum system was started to maintain the drying state for 24 hours. After drying, the oven door was opened and the sample was placed in a room temperature environment until the sample temperature was consistent with the room temperature.

[0086] For example, the system divides the pretreated samples into a blank group and a corrosion group. The blank group samples are set to soak for 0 days, and each group has 3 parallel samples. The corrosion group is divided into 4 subgroups according to the solution pH value, corresponding to solutions with pH = 3, 5, 7, and 9, respectively. Each pH subgroup is further divided into 5 subgroups according to the soaking time, with soaking times set to 15 days, 30 days, 45 days, 60 days, and 75 days, respectively. Each time subgroup also has 3 parallel samples. The system prepares four pH solutions: deionized water is measured and partially adjusted to pH = 3 with 0.1 mol / L hydrochloric acid, and calibrated with a pH meter; a pH = 5 buffer solution is prepared by mixing acetic acid and sodium acetate in a certain proportion, and calibrated with a pH meter; ultrapure water with a resistivity of 18.2 MΩ·cm is directly used as a pH = 7 solution; and a pH = 9 buffer solution is prepared by mixing borax and sodium hydroxide in a certain proportion, and calibrated with a pH meter. The system poured the four solutions into 500mL polytetrafluoroethylene containers, placed them in a constant temperature water bath, set the temperature to 59℃, and waited for the temperature to stabilize for 1 hour. Then, the samples of each group in the corrosion group were placed in the solution with the corresponding pH value. The blank group samples were placed in a dry container in the same constant temperature environment. The inner wall of the dry container was wiped with anhydrous ethanol in advance and left to stand for the preset soaking time to form a set of grouped anchor bolt samples.

[0087] S12: Quantify the mass loss of the grouped anchor bolt sample sets, measure the mass of each group of anchor bolts before and after corrosion, and calculate the percentage of mass loss of each group of anchor bolts.

[0088] Specifically, the system retrieves all samples from the grouped anchor bolt sample set according to the preset soaking time. The corrosion group samples are treated first: the sample surface is rinsed with deionized water 3 times, each rinse lasting 10 seconds to remove residual solution, and then the sample surface is wiped with degreased cotton soaked in anhydrous ethanol to dehydrate it. After wiping, the sample is placed in a vacuum drying oven, the temperature is set to 60±2℃, the vacuum system is started to -0.09MPa, and the drying state is maintained for 24 hours. The vacuum degree is recorded every 6 hours during the drying process. After the drying is completed, the sample is taken out and cooled to room temperature. The blank group samples are directly treated according to the same drying process.

[0089] Preferably, the system can use an electronic analytical balance with an accuracy of 0.1 mg. Before measurement, the balance calibration program is started, first calibrating the zero point, and then calibrating sequentially with 10g and 20g standard weights to ensure the error is less than 0.01 mg. The system then weighs each anchor bolt sample in the grouped anchor bolt sample set in ascending order of sample number, recording the pre-corrosion and post-corrosion mass of each sample: the pre-corrosion mass is the mass of the sample after pretreatment and before immersion, and the post-corrosion mass is the mass of the sample after immersion and drying. The initial and post-corrosion masses of each sample are recorded separately. Before each weighing, the sample surface is wiped with clean filter paper. The system calculates the average value of the initial and post-corrosion masses of each group of three parallel samples, and calculates the percentage of mass loss for each group of anchor bolts using the formula: "Percentage of mass loss = (average initial mass - average post-corrosion mass) / average initial mass × 100%". After the calculation is completed, another data processing flow is started to repeat the calculation to ensure consistency. Finally, the calculation result is retained to two decimal places.

[0090] S13: The percentage of mass loss is structured and associated with the pH value, corrosion time and percentage of mass loss of each group of anchor bolts in the grouped anchor bolt sample set to generate a corrosion parameter database.

[0091] Specifically, the system organizes the grouping information of the anchor bolt sample set: samples in the corrosion group are categorized according to pH value from low to high and corrosion time from short to long; samples at the same pH value are arranged sequentially according to immersion times of 15 days, 30 days, 45 days, 60 days, and 75 days; blank samples are categorized separately. The system clearly defines the grouping type, pH subgroup (corrosion group only), and immersion time for each sample group, and records the processing batch for each sample group. The system establishes a data association table with fields including sample number, processing batch, grouping type, pH value (blank group marked "none"), corrosion time, average initial mass, average post-corrosion mass, and percentage of mass loss. The corresponding data for each sample group are filled into the table, forming structured data entries. The system uses data comparison software to verify the correspondence between pH value, corrosion time, and mass data in each structured data entry. Entries with a mass data deviation exceeding 5% from the group average are marked "abnormal and awaiting verification," and the original weighing record of that sample is retrieved for re-verification.

[0092] Furthermore, the system integrates the verified structured data entries and constructs a corrosion parameter database in Excel format: it stores the data in sheets according to group type, with blank groups and corrosion groups each occupying one sheet. Each sheet has a data filtering function. The database fields retain the sample number, processing batch, group type, pH value, corrosion time (days), average initial mass (g), average post-corrosion mass (g), mass loss percentage (%), and data status (normal / abnormal pending verification). The database is then generated and saved.

[0093] In one embodiment, S2 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0094] S21: Assemble the pretreated anchor bolts, assemble the blank group anchor bolts with rocks to form a control group sample, and assemble the corroded group anchor bolts with rocks from the same batch to form a corrosion group sample, thus generating an anchor-rock composite sample set.

[0095] Specifically, the system first confirms the condition of the pre-treated anchor bolts. The blank group anchor bolts are pre-treated anchor bolts that have not been immersed in corrosion. Their surfaces are sanded until they reveal a metallic luster, degreased with anhydrous ethanol, and vacuum dried. The corroded group anchor bolts are anchor bolts corresponding to the group in the corrosion parameter database, with no residual corrosion solution or loose corrosion products on their surfaces. The system uses 50mm×50mm×100mm rock samples processed from the same batch of limestone. The end faces of the rock samples are ground, with a flatness error ≤0.05mm. They are tested with an ultrasonic flaw detector, with a wave velocity difference ≤5% and no internal cracks.

[0096] Preferably, the system fixes the drilling equipment at the axial position of the rock sample and drills blind holes with a diameter of 12 mm and a depth of 95 mm. During the drilling process, a verticality detector is used for real-time calibration to ensure that the verticality error is ≤0.5°. The system can be equipped with E-44 type epoxy resin adhesive. After weighing the resin and curing agent at a mass ratio of 10:3, it is placed in a container and stirred for 5 minutes until uniformly mixed. The adhesive is then injected into the blind holes of the rock sample to ensure a 100% filling rate. The system inserts blank group anchors into some blind holes of the rock sample and corrosion group anchors into the blind holes of the remaining rock sample samples of the same batch. The anchor positions are adjusted so that the end faces are flush with the end faces of the rock sample, with a coaxiality error ≤0.2 mm. The system places the assembled sample in a standard curing chamber, sets the temperature to 25±2℃, and maintains a relative humidity of 60±5% through a humidity control system. Curing is carried out for 24 hours until the adhesive is completely cured. All cured samples are integrated, and the corresponding anchor numbers and grouping information are labeled to generate an anchor-rock composite sample set.

[0097] S22: The anchor-rock composite sample set is subjected to stress field loading treatment, and a fixed confining pressure in the orthogonal direction is applied to stabilize the normal and lateral stresses to the preset values.

[0098] Specifically, the system places each specimen of the anchor-rock composite sample set into the specimen chamber of the true triaxial shear test system. The specimen is secured using a clamping device, ensuring the specimen center is aligned with the axis of the loading mechanism, and that the clamping force is uniform without localized compression. The system sets orthogonal confining pressure parameters: a preset value of 10 MPa for the normal confining pressure and 15 MPa for the lateral confining pressure, with the confining pressure directions perpendicular to the shear plane and shear direction, respectively. The system activates the normal confining pressure loading unit, setting the loading rate to 0.5 MPa / s. Normal pressure data is collected in real-time using a pressure sensor. When the pressure reaches 90% of the preset value, the loading rate is adjusted to 0.1 MPa / s until the pressure reaches 10 MPa. The system maintains the normal confining pressure stable for 5 minutes, monitoring pressure fluctuations. If the fluctuation exceeds 0.1 MPa, the loading unit is fine-tuned until the fluctuation is ≤0.1 MPa. The system initiates the lateral confining pressure loading unit according to the same procedure, with the loading rate initially at 0.5 MPa / s and then at 0.1 MPa / s, reaching 15 MPa and stabilizing for 5 minutes. Pressure fluctuations are monitored and adjusted accordingly. When the fluctuation amplitude of both normal and lateral stresses is ≤0.1 MPa for 3 consecutive minutes, the system determines that the stress field has reached a stable state, stops the confining pressure loading, and maintains the current stress state in preparation for subsequent shear loading.

[0099] S23: The anchor-rock composite specimen under stress field is subjected to shear disturbance loading. The shear load is increased stepwise along an increasing path, and cyclic fluctuation stress is superimposed simultaneously to generate dynamic shear response data containing stress-strain relationship.

[0100] Specifically, after the stress field stabilizes, the system activates the shear loading module, sets the shear load increment path, and uses the failure stress τ measured in the pre-test of the blank group specimens. p Based on this, the paths are successively 0.4τ p →0.7τ p →0.8τ p →0.9τ p →τ p → Failure. The system applies shear load at a loading rate of 0.005 mm / s. After each preset load level, the loading rate is stopped and the load is maintained for 10 minutes, during which shear stress and strain data are monitored in real time. During the stabilization phase of each load level, a cyclic disturbance module is activated, superimposing cyclic fluctuating stress. The fluctuating stress amplitude is set to 0.8 MPa, the frequency to 2 Hz, and the disturbance duration to 3600 s. Shear stress, shear strain, and time data are continuously collected during the disturbance process at a sampling frequency of 100 Hz. The data is stored in CSV format to a specified path.

[0101] Furthermore, the system monitors changes in shear stress during loading. If the shear stress suddenly drops by more than 15% under a certain load level, it is determined that the specimen has failed, and the shear loading and disturbance of the specimen are immediately stopped. If no failure occurs, the loading continues along the incremental path to the next load level until the specimen fails. After loading all specimens, all data are integrated to generate dynamic shear response data.

[0102] S24: Perform feature extraction processing on dynamic shear response data, identify the stress-strain curve feature points of all specimens, and generate a mechanical test database containing the initial value of crack initiation stress, the initial value of failure stress, and the stress-strain curves of the entire stage.

[0103] Specifically, the system imports the dynamic shear response data of all samples and extracts stress-strain curve data by sample number through a data reading program. Each curve contains continuous data points in three dimensions: time, shear stress, and shear strain. The system identifies feature points for each stress-strain curve. The initial crack initiation stress is determined by calculating the rate of change of the curve slope. When the curve slope decreases by more than 10% compared to the average slope of the previous five consecutive data points, the shear stress at the corresponding data point is recorded as the initial crack initiation stress. The initial failure stress is the shear stress value corresponding to the data point before the first decreasing trend appears after the shear stress in the curve reaches its maximum value.

[0104] For example, the system extracts the initial value of the crack initiation stress, the initial value of the failure stress, and the stress-strain curve data of each specimen from the start of loading to specimen failure. The system verifies the validity of the data, removing outlier data points with instantaneous stress jumps exceeding 20%, and supplementing missing data with linear interpolation of adjacent data points. The system categorizes and organizes the valid data according to specimen number, group type (control group / corrosion group), pH value of the corresponding anchor rod, and corrosion time, constructing a mechanical test database. The database fields include specimen number, group type, anchor rod pH value, anchor rod corrosion time, initial value of the crack initiation stress (MPa), initial value of the failure stress (MPa), and the data storage path for the stress-strain curve throughout the entire process, thus completing the database generation.

[0105] In one embodiment, such as Figure 2 The method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps in S3:

[0106] S31: Construct input vectors for the corrosion parameter database, extract the pH value, corrosion time, and percentage of mass loss for each group of anchor bolt samples, and form a data matrix containing the correlation between environmental parameters and corrosion damage.

[0107] Specifically, the system extracts the core parameters of all grouped anchor bolt samples from the constructed corrosion parameter database: solution pH value (denoted as pH, dimensionless, covering test settings of 3.0, 5.0, 7.0, and 9.0, corresponding to acidic to alkaline environments), corrosion time (denoted as t, in days, including 0d, 15d, 30d, 45d, 60d, and 75d, covering short-term to long-term corrosion cycles), and percentage of mass loss. The system constructs a data matrix according to the rule of "single sample group as rows, parameters as columns," with a matrix dimension of n×3 (n being the total number of groups, including blank groups and all corrosion groups). Preferably, the system preprocesses the data matrix, using the Grubbs test to identify and remove outlier data points. For missing "pH-t" combinations, three parallel anchor bolt samples are re-prepared, and the corrosion and mass measurement procedures of S11-S13 are repeated to supplement the data. The preprocessed data matrix directly establishes the mapping relationship between environmental parameters and corrosion damage indicators, forming a standardized input vector for subsequent function fitting.

[0108] S32: The data matrix is ​​fitted with a nonlinear function, and the material corrosion constant, pH decay coefficient and time nonlinear factor parameters are iteratively optimized using an exponential-time coupled equation to generate the initial damage variable function.

[0109] Specifically, using pH value and corrosion time t in the data matrix as independent variables, and the degree of corrosion damage reflected by the percentage of mass loss as the dependent variable, a pre-defined exponential-time coupled equation is used to perform nonlinear function fitting. The fitting equation is:

[0110]

[0111] Where D2 is the initial damage variable function, i.e., the anchor bolt damage variable, and ω is the corrosion constant of the material properties. pH is a sensitive factor for the corrosion rate. A higher pH value indicates a more significant impact of pH on the corrosion rate. ξ is a non-linear influencing factor for corrosion; when ξ = 1, corrosion increases linearly with time; when ξ < 1, the corrosion rate decreases with time (protected by corrosion products); when ξ > 1, the corrosion rate increases with time. pH represents the acidity or alkalinity of the solution, and t represents the corrosion time of the anchor bolt sample. The system sets the initial fitting parameters based on the experimental results: ω = 0.0012d. -1.25 , ξ = 1.25, with the sum of squared residuals Minimize the objective function through iterative optimization to generate an initial damage variable function, where D 2,calc,i For the calculated value, D 2,exp,i These are experimental values ​​derived from the percentage of quantity loss, up to and including residuals ≤5%.

[0112] S33: Perform physical verification of the initial damage variable function, calculate the deviation between the mass loss rate predicted by the function and the measured mass loss rate under different corrosion conditions, and generate a deterministic function for calculating the anchor bolt damage variable under arbitrary corrosion conditions.

[0113] Specifically, based on the correlation of damage mechanics, the system establishes a corresponding formula between anchor bolt damage variables and mass loss rate:

[0114]

[0115] Where, ω loss Let ω be the initial mass of the anchor bolt. fail The mass loss trend of the anchor bolt after corrosion time t varies with the pH of the water chemistry environment and different time periods, such as... Figure 3a , Figure 3b As shown, under the same corrosion time, the mass of the anchor bolt after corrosion exhibits a significant non-linear decrease with decreasing pH of the aqueous chemical environment; the lower the pH, the greater the mass loss of the anchor bolt. At the same pH, the mass of the anchor bolt after corrosion decreases with increasing corrosion days, and further decreases with increasing corrosion days. This indicates that in an acidic environment, the anchor bolt corrosion rate increases rapidly with increasing corrosion days.

[0116] For example, the system selects 5 groups of "pH-t" combination samples that were not involved in the fitting, such as pH=4.0, t=22d; pH=8.0, t=52d, and calculates the relative deviation:

[0117]

[0118] If all groups have δ≤5%, the initial function is deemed to meet the accuracy requirements and is determined as the deterministic function for calculating anchor bolt damage variables under arbitrary corrosion conditions; if there are groups with δ>5%, return to S32 to adjust the initial parameters and refit until the deviation of all groups meets the requirements, and finally output the deterministic function.

[0119] In one embodiment, S4 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0120] S41: Extract blank data from the mechanical test database, separate the initial values ​​of crack initiation stress and failure stress of the control group specimens, and generate a reference stress dataset.

[0121] Specifically, the system filters sample data labeled "control group" from the constructed mechanical test database, and extracts the initial values ​​of crack initiation stress and failure stress for this type of sample. The system then processes the extracted τ... ci0 and τ p0The data were validated, and outliers were removed using the 3σ criterion. The τ values ​​for each of the three parallel control group samples were also verified. ci0 τ p0 The arithmetic mean was calculated separately to obtain the initial average crack initiation stress τ of the control group. ci0,avg With the initial value of the average failure stress τ ci0,avg The system will τ ci0,avg τ p0,avg and the corresponding confining pressure parameters (normal stress σ) n =10MPa, lateral stress σ p =15MPa) and the control group sample numbers are linked and integrated to generate a reference stress dataset. This dataset serves as a reference for subsequent correction of the stress values ​​of corrosion group samples, ensuring the standardization of the correction process.

[0122] S42: Based on deterministic functions, damage value mapping is performed on corrosion group samples in the corrosion parameter database. The damage variable values ​​corresponding to the corrosion group samples are calculated according to the actual corrosion conditions, and the sample damage variable values ​​are generated.

[0123] Specifically, the system calls the deterministic function of the anchor bolt damage variable determined experimentally: D² = 0.00347·e -0.6·pH ·t m The parameters in the formula are defined as follows: 0.00347 is the material corrosion constant of HRB400 anchor bolts; 0.6 is the pH sensitivity factor for the anchor bolt corrosion rate, reflecting the strength of the influence of pH changes on the degree of corrosion; pH is the acidity or alkalinity of the corrosive solution, with a value range of 3 to 9, corresponding to the experimental solution conditions; t m D1 represents the corrosion time of the anchor bolt, and D2 represents the anchor bolt damage variable, ranging from 0 to 1, where 0 indicates no corrosion damage and 1 indicates complete corrosion failure. The system extracts the pH value and t value of the corrosion group samples from the corrosion parameter database. m Substitute the sample numbers one by one into the deterministic function to calculate the damage variable value D corresponding to each corrosion group sample. 2,i (i is the sample number of the corrosion group). The system calculates D. 2,i Perform a value range check; if D exists... 2,i <0 or D 2,i For cases where the value is greater than 1, trace back the pH value and t of the corresponding sample. m Original records, recalculated until all D 2,i Located in the 0-1 range, ultimately integrating all D values. 2,i Generate a set of sample damage variable values ​​D set ={D 2,i |i=1,2,...,n}, where n is the number of corrosion sample groups.

[0124] S43: Based on the sample damage variable value, the reference stress dataset is proportionally attenuated, and the stress value after corrosion is calculated according to the preset attenuation relationship to generate the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion.

[0125] Specifically, the system uses a proportional attenuation relationship to correct the baseline stress data. The correction formulas include the formula for calculating the crack initiation stress of the system after corrosion and the formula for calculating the actual shear stress of the anchor bolt after corrosion.

[0126] τ ci =τ ci0,avg *(1-D 2,i )

[0127] τ p =τ p0,avg *(1-D 2,i )

[0128] Where, τ ci The initiation stress of the corrosion-induced cracking system refers to the shear stress at the inflection point of the stress-strain curve of the corrosion-anchor-rock composite, τ. p τ represents the actual shear stress of the anchor bolt after corrosion, indicating the maximum shear stress that the anchor bolt can withstand in the corrosion group of samples. ci0,avg τ is the average initial stress value of the i-th group in the reference stress dataset, where τ is the initial stress value of the crack initiation stress. p0,avg The average initial value of the failure stress in the i-th group of the reference stress dataset, 1-D 2,i The strength retention coefficient after damage varies with the anchor bolt damage variable D. 2,i The increase and decrease reflect the proportion of mechanical strength retained after anchor corrosion. The system divides the reference stress data set S according to the sample number. base With the set of sample damage variable values ​​D set Perform a one-to-one matching and substitute the values ​​into the correction formula to calculate τ for each corrosion group sample. ci and τ p .

[0129] For example, the system extracts the measured crack initiation stress τ of the corresponding corrosion group specimen from the mechanical test database. meas,ci and measured failure stress τ meas,p Calculate the error using the relative error formula:

[0130]

[0131] Where, τ calc To correct the calculated value of the formula, τ meas The value is the measured value, and δ is the relative error; if δ > 15%, then D should be rechecked. 2,i The calculation process and reference stress data τ ci0,avg τ p0,avgThe effectiveness is verified until δ≤15%, and finally all calculated τ values ​​are integrated. ci and τ p Generate a sample number, D 2,i τ ci τ p The stress dataset after corrosion of the field.

[0132] In one embodiment, such as Figure 4 As shown, S5 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0133] S51: The yield function is constructed by processing the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion. Based on the predicted value of the crack initiation stress after corrosion, the critical threshold of viscoplastic flow is defined to generate the yield function characterizing the yield condition of the material.

[0134] Specifically, the system extracts the actual shear stress of the generated corroded anchor bolt and the initiation stress of the corroded system. The initiation stress of the corroded system is defined as the critical threshold for viscoplastic flow, and a yield function characterizing the material's yield condition is constructed based on this threshold. The expression for the yield function is:

[0135]

[0136] Where F is the yield function, τ t σ is the shear stress experienced by the anchor-rock composite. n For normal stress, c is the internal friction angle of the corroded rock-anchor system. * σ represents the cohesion of the rock-anchor system after corrosion, K is the characteristic length parameter related to rock damage, and σ is the anchor bolt. p d represents the tensile strength of the rock. * The damage threshold of the rock. This represents the actual shear stress of the anchor bolt after corrosion. The system uses this function to determine the material state: when F is less than 0, the material is in the elastic stage; when F is greater than or equal to 0, the material enters the viscoplastic stage, thus clarifying the conditions for the material to transition from elastic to viscoplastic.

[0137] S52: The constitutive equation is derived for the yield function. Based on the linear relationship between stress and strain in the elastic deformation stage and the relationship between strain rate and yield function in the viscoplastic flow stage, a set of differential equations describing the material deformation process is established.

[0138] Specifically, the system derives the constitutive equation based on the mechanical properties of the material during the elastic deformation stage and the viscoplastic flow stage. In the elastic deformation stage, the stress-strain relationship is linear, expressed as:

[0139]

[0140] Where, γ e G represents elastic shear strain, which is dimensionless; * The shear modulus of the anchor-rock assembly after corrosion is given in GPa. The strain rate during the viscoplastic flow stage is related to the yield function, expressed as:

[0141]

[0142] in, For viscoplastic shear strain rate, A * Let be the viscosity coefficient and n be the flow coefficient, both dimensionless. The system integrates the relationship between the two stages, establishing a set of differential equations describing the material deformation process. This set includes the stress-strain equations for the elastic stage and the strain rate equations for the viscoplastic stage. The total shear strain of the material under different stress states can be calculated using this set of equations. The total shear strain is the sum of the elastic shear strain and the viscoplastic shear strain, thus comprehensively describing the mechanical behavior of the material from loading to deformation.

[0143] S53: Couple the differential equation system and combine the rock constitutive relation with the anchor bolt constitutive relation in parallel to generate a fractional-order damage shear constitutive model that characterizes the dynamic shear response of the anchor-rock composite.

[0144] Specifically, such as Figure 5 As shown, the system combines the constitutive relations of the rock and the anchor bolt in parallel for coupled modeling. The anchor bolt and rock deform together; the anchor bolt's ability to resist external forces and undergo elastic deformation is much stronger than that of the rock, and the Young's modulus of the rock is less than that of the anchor cable. Therefore, the anchor cable can be considered an elastic body in the component model. Under the corrosive effects of water chemistry, the anchor bolt suffers damage, leading to a decrease in its modulus. Regarding the constitutive relation of the anchor bolt, based on the corrosion characteristics of the anchor bolt under water chemistry, the system uses the following formula to construct the constitutive equation of the anchor bolt, relating the shear stress and shear strain:

[0145] τ e =κ(1-D2)γ e

[0146] Where, τ e γ represents the shear stress borne by the anchor bolt; κ represents the material properties of the anchor bolt; D2 represents the damage variable of the anchor bolt under hydrochemical conditions (dimensionless, value 0–1); e This represents the shear strain of the anchor bolt.

[0147] To satisfy the physical constraints of anchor-rock coordinated deformation, the system establishes deformation coordination conditions through the following formula to ensure that the strain responses of the rock and the anchor are synchronized:

[0148] γt=γ y =γ m

[0149] Where, γ t γ represents the total shear strain of the anchor-rock composite. y Let the shear strain of the rock be denoted as . Based on the principle of synergistic bearing capacity, the system establishes a stress superposition relationship, matching the correlation logic between stress and strain in the differential equation system:

[0150] τ t -τ ci =τ y +τ m -τ ci

[0151] Where, τ t The total shear stress τ borne by the anchor-rock composite; ci The stress at which the rock begins to crack corresponds to the stress threshold in the differential equations that marks the transition from the elastic to the viscoplastic stage; τ y Shear stress borne by the rock.

[0152] For the constitutive relation of rocks, the system combines fractional-order damage theory with the stage division of differential equations to construct a model in different states. When the yield function F < 0 in step S51, the material is in the elastic stage, and the elastic shear strain is calculated using the following formula:

[0153]

[0154] Where, γ e τ is the elastic shear strain (dimensionless); t denoted as , where is the shear stress on the anchor-rock composite; G is the elastic shear modulus of the rock when it is undamaged; D0 is the initial damage variable of the rock mass under hydrochemical conditions; v0 is the wave velocity of the rock mass under the reference conditions; a is the temperature influence coefficient; C is the ambient temperature; b is the pH influence coefficient; pH is the pH value of the hydrochemical environment; v ref The reference wave velocity for non-destructive rock mass.

[0155] When the material enters the stable damage stage, i.e., when the initiation stress yield function F3≥0 and the critical stress yield function F4<0, the system introduces fractional-order viscoelastic properties, calculates the viscoelastic shear strain using formulas, and supplements the strain details of the viscoplastic stage in the differential equation system:

[0156]

[0157]

[0158] Where, γ ve η is the viscoelastic shear strain (dimensionless), t is the shear stress loading time, α is the fractional derivative order; η1 is the viscoelastic characteristic coefficient, D1 is the rock mass damage variable under shear stress loading, and Γ(·) is the gamma function.

[0159] When the material enters the accelerated damage stage, i.e., F4≥0, the system calculates the viscoelastic-plastic shear strain using a formula, which matches the dynamic characteristics of the viscoelastic strain rate formula in the differential equation system:

[0160]

[0161] Where, γ vp τ is the viscoelastic-plastic shear strain (dimensionless); cd η is the critical stress of the rock; β is the fractional derivative order; η2 is the viscoelastic-plastic property coefficient; λ is the damage attenuation coefficient; t1 is the initial time parameter.

[0162] As can be seen from the above construction process, when the stress state reaches and exceeds the crack initiation stress yield condition, the rock begins to deteriorate and deform. The viscoelastic-plastic strain rate is calculated using the Perzyna overstress theory.

[0163]

[0164] Where F3 is the crack initiation stress yield function; F0 is the initial value of the yield function, which is 1.

[0165] When F3 < 0, the system calculates the total shear strain in the elastic stage:

[0166]

[0167] When the stress state reaches and exceeds the shear critical stress yield condition, the rock undergoes nonlinear viscoplastic deformation. The viscoplastic strain rate is calculated using Perzyna overstress theory, which is expressed as follows:

[0168]

[0169] Where F4 is the shear stress yield function. When F3≥0 and F4<0, the rock shear mechanics model under hydrochemical conditions at different temperatures and pH is characterized as follows:

[0170]

[0171] in, F1 represents the relevant mechanical function during the stable damage stage. During the accelerated damage stage, the system integrates elastic, viscoelastic, and viscoelastic-plastic responses, and the total shear strain is calculated using the following formula:

[0172]

[0173] in, F2 is the mechanical function related to the accelerated damage stage.

[0174] Finally, the system integrates the shear strain calculation logic of each stage to generate a fractional-order damage shear constitutive model of the anchor-rock assembly. This model can take corrosion conditions (pH, corrosion time) and stress parameters (shear stress, loading time) as input and output the corresponding shear stress-strain relationship. It fully connects the elastic-viscoplastic stage characteristics of the differential equation set mentioned above and reflects the mechanical response law of the assembly under dynamic shear load.

[0175] In one embodiment, S6 of the method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion provided by the present invention specifically includes the following steps:

[0176] S61: Extract characteristic segments from the full-stage stress-strain curves of corrosion group specimens in the mechanical test database, separate the characteristic data points of the elastic segment, yield segment, and failure segment, and generate a model calibration dataset.

[0177] Specifically, the system retrieves the full-stage stress-strain curves of the corrosion group specimens from the mechanical test database and performs characteristic segment extraction on each curve. The elastic segment extraction is based on the linear relationship between stress and strain, determining the extraction range by calculating the rate of change of the curve slope. Stress-strain data points with a slope change rate less than 1% are classified as elastic segments. The yield segment extraction uses a constructed yield function threshold as the standard; data points from the point where the shear stress reaches the critical value that makes F equal to 0 to before the stress peak are classified as yield segments. The failure segment extraction is based on the stress decrease process after the stress peak; data points from the stress peak point to 80% of the stress peak are classified as failure segments. The system removes abnormal data points deviating from the overall trend in each characteristic segment. Abnormal data point determination is achieved by calculating the deviation between the data point and the fitted curve of 10 adjacent data points; data points with a deviation greater than 5% are removed. The system integrates the valid data points of the elastic, yield, and failure segments of all corrosion group specimens, associates them with the corresponding corrosion condition parameters according to the specimen number, and generates a model calibration dataset. This dataset contains fields for shear stress, shear strain, and corrosion condition parameters.

[0178] S62: Perform parameter inversion processing on the model calibration dataset and the fractional-order damage shear constitutive model: Use a global optimization algorithm to fit the material parameters of the fractional-order damage shear constitutive model, optimize the parameters by minimizing the deviation between the model prediction curve and the experimental curve, and generate the optimized fractional-order damage shear constitutive model.

[0179] Specifically, the system correlates the model calibration dataset with the generated fractional-order damage-shear constitutive model and performs parameter inversion processing. Preferably, the parameter inversion can employ a global optimization algorithm. The material parameters to be fitted include the shear modulus of the corroded rock, the shear modulus of the corroded anchor bolt, the viscosity coefficient of the anchor bolt, and the flow coefficient. The parameter inversion aims to minimize the deviation between the model prediction curve and the experimental curve. The deviation is calculated using the root mean square error formula:

[0180]

[0181] Where N is the total number of data points, γ pred,i To predict shear strain in the model, γ test,i To obtain the shear strain in the experiment, the system iteratively adjusts the parameters to be fitted until the RMSE is less than 0.02, thus completing parameter optimization. The system integrates the optimized parameters with the original fractional-order damage shear constitutive model structure to generate an optimized fractional-order damage shear constitutive model. This model can output more accurate shear strain predictions based on the input corrosion conditions and stress parameters.

[0182] S63: Dynamic response verification of the optimized fractional-order damage shear constitutive model: Based on experimental data under cyclic perturbation loading conditions, verify the consistency between the model's predicted strain rate and the actual strain rate, and generate a verified true triaxial shear dynamic model.

[0183] Specifically, the system extracts experimental data under cyclic perturbation loading conditions from a mechanical test database. This data includes shear stress-strain rate curves corresponding to different perturbation frequencies and amplitudes, which are used to perform dynamic response verification of the optimized fractional-order damage shear constitutive model. During the verification process, the system substitutes the cyclic perturbation loading parameters into the optimized model and calculates the model's predicted strain rate. Simultaneously extract the actual strain rate measured in the experiment. The system uses a relative error formula to calculate the degree of agreement:

[0184]

[0185] If the δ value of all verification data points is less than 10%, the model's dynamic response is deemed to have a satisfactory fit. If there are data points with a δ value greater than 10%, the system returns to S62 to readjust the iteration range of parameter inversion until the δ value of all data points is less than 10%. The system integrates the verified optimized model with the cyclic perturbation loading condition parameters, clarifies the applicable perturbation frequency range of 0-10Hz and amplitude range of 0-5MPa, and generates a verified true triaxial shear dynamic model. This model can accurately describe the dynamic shear response of the corroded anchor-rock assembly under cyclic perturbation.

[0186] Furthermore, to ensure the applicability of the aforementioned true triaxial shear dynamic model, this embodiment employs the quasi-Newton method in 1stOpt software, using the Quasi-Newton (BFGS) + general global optimization method to calculate the mechanical model parameters of the anchor bolt-limestone system under different hydrochemical environments after corrosion in true triaxial shear tests. Based on the test results of the anchor bolt-limestone system under different hydrochemical environments after corrosion, the shear rock damage mechanics model is verified, and the model parameters are shown in Table 1. Figures 6a-6f A comparison of the theoretical curves and experimental curves in the model shows that the model can accurately reflect the three-stage evolution process of shear deformation of the anchor bolt-limestone system after corrosion in different hydrochemical environments.

[0187]

[0188]

[0189] Table 1 Fitting parameters of the true triaxial perturbation shear model for the anchor-limestone system under different hydrochemical environments and pH conditions.

[0190]

[0191]

[0192] Table 1. Fitting parameters of the true triaxial perturbation shear model for the anchor-limestone system under different hydrochemical environments (pH) (continued)

[0193]

[0194] Table 1. Fitting parameters of the true triaxial perturbation shear model for the anchor-limestone system under different hydrochemical environments (pH) (continued)

[0195] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0196] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0197] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0198] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for constructing a true triaxial shear dynamic model of an anchor-rock composite under hydrochemical corrosion, characterized in that, Includes the following steps: S1: The anchor bolt samples were grouped and immersed in constant temperature solutions with different pH values ​​for different corrosion times. The mass of all anchor bolt samples before and after corrosion was measured, and a corrosion parameter database containing pH value, corrosion time and mass loss was generated. S2: The pretreated anchor rods and rock samples are assembled into anchor-rock composite samples. At the same time, the blank control samples assembled with anchor rods that have not undergone corrosion pretreatment are assembled in the same way. Preset normal stress and lateral stress are applied to all samples, shear stress is applied in a multi-level incremental path and cyclic disturbance is applied simultaneously. Stress-strain data are recorded to generate a mechanical test database containing the crack initiation stress, failure stress and stress-strain curves of all samples. S3: Process the corrosion parameter database, and establish a predetermined functional relationship between the anchor bolt damage variable and the pH value and corrosion time based on the mass loss rate combined with the pH value and corrosion time through data fitting, and generate a deterministic function for calculating the anchor bolt damage variable under any corrosion conditions. S4: Based on the deterministic function, the crack initiation stress and failure stress of the mechanical test database are proportionally attenuated and corrected. The initial stress value is corrected according to the linear attenuation relationship to generate the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion. S5: Based on the actual shear stress of the anchor bolt after corrosion and the crack initiation stress of the system after corrosion, construct the yield function, establish a set of differential equations for elastic-viscoplastic coupling, and generate a fractional-order damage shear constitutive model; S6: Input the full-stage stress-strain curves of the corrosion group specimens in the mechanical test database into the fractional-order damage shear constitutive model, use the global optimization algorithm to fit the parameters and compare them with the test curves to generate a verified true triaxial shear dynamic model. The step of proportionally attenuating and correcting the crack initiation stress and failure stress of the mechanical test dataset based on the deterministic function, correcting the initial stress value according to a linear attenuation relationship, and generating the actual shear stress of the anchor bolt and the crack initiation stress of the system after corrosion includes: S41: Perform blank group data extraction processing on the mechanical test database, separate the initial value of crack initiation stress and the initial value of failure stress of the control group specimen, and generate a reference stress dataset; S42: Based on the deterministic function, damage value mapping is performed on the corrosion group samples in the corrosion parameter database, and the damage variable values ​​corresponding to the corrosion group samples are calculated according to the actual corrosion conditions to generate sample damage variable values. S43: Based on the sample damage variable value, the benchmark stress dataset is proportionally attenuated, and the post-corrosion stress value is calculated according to the preset attenuation relationship to generate the actual shear stress of the post-corrosion anchor and the post-corrosion system crack initiation stress. Specifically, based on the actual shear stress of the corroded anchor bolt and the crack initiation stress of the corroded system, a yield function is constructed, an elastic-viscoplastic coupled differential equation system is established, and a fractional-order damage shear constitutive model is generated, including: S51: The actual shear stress of the corroded anchor and the crack initiation stress of the corroded system are processed to construct a yield function. Based on the predicted value of the crack initiation stress after corrosion, a critical threshold for viscoplastic flow is defined to generate a yield function characterizing the yield condition of the material. S52: The constitutive equation is derived for the yield function. Based on the linear relationship between stress and strain in the elastic deformation stage and the relationship between strain rate and yield function in the viscoplastic flow stage, a set of differential equations describing the material deformation process is established. S53: Perform coupled modeling on the differential equation system, combine the rock constitutive relation and the anchor bolt constitutive relation in parallel, and generate a fractional-order damage shear constitutive model that characterizes the dynamic shear response of the anchor-rock composite.

2. The method according to claim 1, characterized in that, S1 includes: S11: The anchor bolt samples were grouped into a blank group and a corrosion group. The corrosion group was immersed in solutions with different pH values ​​and kept at a constant temperature for different durations to generate a set of grouped anchor bolt samples. S12: Quantify the mass loss of the grouped anchor bolt sample set, measure the mass of each group of anchor bolts before and after corrosion in the grouped anchor bolt sample set, and calculate the percentage of mass loss of each group of anchor bolts. S13: The percentage of mass loss is structured and associated with the pH value, corrosion time and percentage of mass loss of each group of anchors in the grouped anchor sample set to generate a corrosion parameter database.

3. The method according to claim 1, characterized in that, S2 includes: S21: The pre-treated anchor bolts are assembled. The blank group anchor bolts are assembled with rocks to form a control group sample, and the corroded group anchor bolts are assembled with rocks of the same batch to form a corrosion group sample, thus generating an anchor-rock composite sample set. S22: The anchor-rock composite sample set is subjected to stress field loading treatment, and orthogonal direction fixed confining pressure is applied to stabilize the normal and lateral stresses to preset values; S23: The anchor-rock composite specimen under stress field is subjected to shear disturbance loading. The shear load is increased stepwise along an increasing path, and the cyclic fluctuation stress is superimposed simultaneously to generate dynamic shear response data containing stress-strain relationship. S24: Perform feature extraction processing on the dynamic shear response data, identify the stress-strain curve feature points of all specimens, and generate a mechanical test database containing the initial value of crack initiation stress, the initial value of failure stress, and the stress-strain curves of the entire process.

4. The method according to claim 1, characterized in that, S3 includes: S31: Construct an input vector for the corrosion parameter database, extract the pH value, corrosion time and mass loss percentage of each anchor bolt sample, and form a data matrix containing the correlation between environmental parameters and corrosion damage; S32: Fit the data matrix with a nonlinear function, and use an exponential-time coupled equation to iteratively optimize the material corrosion constant, pH decay coefficient and time nonlinear factor parameters to generate an initial damage variable function; S33: Perform physical verification on the initial damage variable function, calculate the deviation between the mass loss rate predicted by the function and the measured mass loss rate under different corrosion conditions, and generate a deterministic function for calculating the anchor bolt damage variable under arbitrary corrosion conditions.

5. The method according to claim 4, characterized in that, The expression for the initial damage variable function is: ； in, This is a function of the initial damage variable, i.e., the anchor bolt damage variable. The corrosion constant is a material property. pH is a sensitive factor for the corrosion rate. For nonlinear influencing factors of corrosion, The pH of the solution. This represents the corrosion time of the anchor bolt sample.

6. The method according to claim 1, characterized in that, The expression for the yield function is: ； in, Let be the yield function. The shear stress experienced by the anchor-rock composite. For normal stress, The internal friction angle of the rock-anchor system after corrosion. To the cohesion of the rock-anchor system after corrosion, Characteristic length parameters related to rock damage, For the tensile strength of the rock, The damage threshold of the rock. This represents the actual shear stress of the anchor bolt after corrosion.

7. The method according to claim 1, characterized in that, The model expression for the fractional-order damage-shear constitutive model is as follows: ； ； ； in, (t) is the model expression for the fractional-order damage-shear constitutive model. Let G be the shear stress experienced by the anchor-rock assembly, and G be the elastic shear modulus of the rock when it is undamaged. For the mechanical functions related to the stable damage stage, To accelerate the mechanical functions related to the damage phase, For the initial damage variable of rock mass under hydrochemical conditions, Let t be the rock mass damage variable under shear stress loading, and t be the shear stress loading time. The order of the fractional derivative. For gamma function, The viscoelastic property coefficient, The order of the fractional derivative. The coefficient of viscoelasticity and plasticity. The damage attenuation coefficient is... For the initial time parameter, These are the material properties of the anchor bolt; The damage variable for anchor bolts under hydrochemical conditions.

8. The method according to any one of claims 1-7, characterized in that, S6 includes: S61: Perform characteristic segment extraction processing on the full-stage stress-strain curves of the corrosion group specimens in the mechanical test database, separate the characteristic data points of the elastic segment, yield segment, and failure segment, and generate a model calibration dataset; S62: Perform parameter inversion processing on the model calibration dataset and the fractional-order damage shear constitutive model: use a global optimization algorithm to fit the material parameters of the fractional-order damage shear constitutive model, and optimize the parameters by minimizing the deviation between the model prediction curve and the experimental curve to generate the optimized fractional-order damage shear constitutive model; S63: Perform dynamic response verification on the optimized fractional-order damage shear constitutive model: verify the consistency between the model's predicted strain rate and the actual strain rate based on experimental data under cyclic perturbation loading conditions, and generate a verified true triaxial shear dynamic model.

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