Method for constructing fatigue constitutive model of limestone under water-power coupling and application

Abstract

The application discloses a kind of water-limestone fatigue constitutive model construction methods under the action of coupling, first according to independently developed seepage-stress coupling test device, the uniaxial cyclic loading and unloading test of limestone sample under the action of different seepage water pressure is carried out, the evolution characteristics of irreversible deformation cumulative curve with the increase of cycle number and damage evolution mechanism are analyzed.Second, select Nishihara model as the basic model of simulating rock fatigue deformation, introduce the nonlinear function related to load cycle number, improve Nishihara model without increasing the number of original model elements, obtain the limestone fatigue constitutive model proposed in the application.Finally, by parameter identification to the model parameters, according to the nonlinear relationship between the relevant model parameters and seepage water pressure is inverted from test data, the rationality and applicability of the model are verified, it is proved that the model can better reflect the fatigue deformation characteristics under the action of seepage-stress coupling.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for constructing and applying a fatigue constitutive model of limestone under hydro-mechanical coupling. Background Technology

[0002] With the gradual implementation of the "deep development" strategy, underground transportation engineering has shown strong development momentum. As early as 1991, the "Tokyo Declaration," adopted at the International Conference on "Urban Underground Space Utilization" held in Tokyo, proposed that "the 21st century is the century of humankind's development and utilization of underground space." Therefore, research on the mechanical characteristics and long-term stability of rock masses under complex stress environments has gradually attracted the attention of many researchers. In particular, regarding rock mass excavation and deformation evolution, the long-term stability of rock masses during unloading is often affected by dynamic disturbances such as mechanical excavation and vibration loads. Its stability is closely related to the dynamic stress level and disturbance frequency (velocity). Under stress disturbance environments, the excavation loading and unloading effects often cause structural adjustments and redistribution of internal stresses in the rock mass. Furthermore, permeability is an important factor that cannot be ignored in rock engineering, and the water-rock coupling effect is key to inducing rock mass strength deterioration or instability failure. This places higher demands on the study of rock mechanical properties under cyclic disturbance loads.

[0003] While the generalized Kelvin and Burger models can effectively simulate the decaying and steady-state rheological stages of rocks, they are less suitable for simulating the accelerated rheological stages. The Nishihara model, due to its yield limit, can well describe the decaying and steady-state rheological stages of rocks under low fatigue stress and also reflects the properties of the accelerated rheological stage under high fatigue stress. However, the Nishihara model's use of linear elastic deformation to simulate the deformation characteristics of the accelerated fatigue stage is not applicable.

[0004] Based on this, Fan et al. introduced nonlinear acceleration initiation elements into the Nishihara model, thus improving it; Luo et al. connected nonlinear viscoplastic bodies in series with the Nishihara body, establishing a seven-element model; Tang et al. replaced the Kelvin and Bingham bodies in the Nishihara model with the Muraya body and a nonlinear Bingham body, establishing a seven-parameter fatigue model. It can be seen that although the improved Nishihara models overcome the shortcomings of the classic Nishihara model in accurately simulating the accelerated rheological properties of rocks, the introduction of multiple new elements makes the improved models less concise, mainly due to the excessive number of model parameters, thus hindering practical applications.

[0005] Based on existing research findings and experimental results from this study, this paper selects the Nishihara model as the basic model for simulating rock fatigue deformation. By introducing a nonlinear function related to the number of load cycles, the Nishihara model is improved without increasing the number of elements in the original model, so that it can better reflect the fatigue deformation characteristics under the action of permeation-stress coupling. Summary of the Invention

[0006] To address the aforementioned problems, this invention provides a method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling. This model uses the Nishihara model as the basic model and introduces a nonlinear function related to the number of load cycles. Without increasing the number of elements in the original model, the Nishihara model is improved so that it can better reflect the fatigue deformation characteristics under permeability-stress coupling, making it suitable for practical applications.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling, characterized by the following steps:

[0009] Step 1: Prepare limestone samples;

[0010] Step 2: Cyclic loading and unloading tests were conducted on limestone samples under different permeable water pressures using a water-mechanical coupling test to analyze the evolution characteristics of the irreversible deformation accumulation curve as the number of cycles increases.

[0011] Step 3: Based on the analysis results of Step 2, the Nishihara fatigue model is improved to construct a limestone fatigue constitutive model;

[0012] Step 4: Solve for the key parameters in the limestone fatigue constitutive model and verify the established limestone fatigue constitutive model.

[0013] Furthermore, the specific steps of step 2 include:

[0014] Step 21: Inject water of different intensities into the water injection holes of the limestone sample and conduct a conventional uniaxial compression test to obtain the stress-strain curve of the limestone sample.

[0015] Step 22: Based on the results of the uniaxial compression test, set the upper limit stress, lower limit stress, and average stress of the cyclic loading and unloading.

[0016] Step 23: Gradually apply axial stress at a loading rate of 1 MPa / s until the cyclic average stress is reached;

[0017] Step 24: Cyclicly load the load 300 times, with the load waveform of each cycle being a triangular wave and the amplitude of the cyclic load being 20MPa, to conduct a uniaxial cyclic loading and unloading test.

[0018] Step 25: If the specimen does not fail after 300 cycles, continue to apply axial stress at a loading rate of 1 MPa / s until the specimen fails.

[0019] Step 26: Perform steps 21-25 on different types of limestone samples to obtain the corresponding cumulative irreversible deformation curves of the limestone samples;

[0020] Step 27: Analyze the irreversible deformation accumulation curve obtained in Step 26. The evolution characteristics obtained are that the irreversible deformation accumulation curve and the rock rheological curve have the same trend. The rheological characteristics and fatigue deformation characteristics of the rock have the same origin.

[0021] Furthermore, step 3 includes the following specific steps:

[0022] Step 31: Make basic assumptions about the fatigue characteristics and plastic deformation of rocks;

[0023] Step 32: Based on the basic assumptions, replace the elements in the Nishihara model with fatigue elements to obtain the Nishihara fatigue model of the rock:

[0024]

[0025] In the formula: σ cri E represents the yield stress of the rock. h E k η1 and η2 are the creep mechanical parameters of the rock, where E h E k η is the stiffness coefficient of the rock, and η1 and η2 are the viscosity coefficients of the rock;

[0026] Step 33: Define a nonlinear function F(N) to describe the accelerated fatigue stage of the rock:

[0027]

[0028]

[0029] In the formula: α is the rock fatigue parameter; N is the number of cycles; N * This represents the number of cycles corresponding to the starting point when the rock enters the accelerated deformation stage.

[0030] Step 34: Substitute equations (4) and (5) into equation (3) to obtain the limestone fatigue constitutive model:

[0031]

[0032] Furthermore, the basic assumptions of step 31 include:

[0033] 1) Stress equivalence assumption

[0034] Assuming that rock fatigue deformation is creep deformation under the action of an equivalent stress function, the equivalent fatigue stress function under triangular wave cyclic loading is expressed as:

[0035]

[0036] In the formula: σ F σ is the equivalent fatigue stress under cyclic loading conditions; f is the cyclic frequency; Δσ is the cyclic amplitude; σ0 is the average cyclic stress; σ cri σ is the critical value for cycle failure; c Uniaxial compressive strength;

[0037] 2) The assumption of continuity in deformation

[0038] By treating the amount of plastic deformation in the model as continuous, the plastic deformation of the rock can be expressed as:

[0039]

[0040] In the formula: The plastic deformation generated in the i-th cycle; Let represent the initial and final plastic deformation amounts for cycle i.

[0041] Furthermore, step 4 includes the following specific steps:

[0042] Step 41: Obtain the parameter E based on the initial point value (0, ε(0)) in the irreversible deformation accumulation curve. h ;

[0043] Step 42: For (0, N) * The parameters E are obtained by fitting the cumulative irreversible deformation curve within the range. k The values ​​of η1 and η2;

[0044] Step 43: Based on the cumulative irreversible deformation curve of the accelerated fatigue deformation stage, the fatigue parameter α is obtained by fitting.

[0045] Furthermore, the dimensions of the limestone sample are H×D=100mm×50mm, the non-parallelism of the end face is less than 0.02mm, and a water injection hole is provided at the center of the end face of the sample.

[0046] An application of a limestone fatigue constitutive model is characterized by using the limestone fatigue constitutive model as described in claim 1 to simulate the fatigue deformation characteristics of rock under hydro-mechanical coupling.

[0047] The beneficial effects of this invention are:

[0048] First, in order to study the strain characteristics of limestone under the coupled action of permeable water pressure and cyclic loading, this invention designed a permeability-stress coupling test device. Using this device, uniaxial cyclic loading and unloading tests were conducted on limestone samples under different permeable water pressures. The evolution characteristics of the irreversible deformation accumulation curve with the increase of the number of cycles and the damage evolution mechanism were analyzed. It was verified that the rheological characteristics and fatigue deformation characteristics of the rock are of the same origin. Therefore, a fatigue constitutive model that can reflect the deformation characteristics of limestone can be constructed based on rheological theory.

[0049] Secondly, this invention selects the Nishihara model as the basic model for simulating rock fatigue deformation, introduces a nonlinear function related to the number of load cycles, and improves the Nishihara model without increasing the number of elements in the original model, so that it can better reflect the fatigue deformation characteristics under the action of permeation-stress coupling. Furthermore, since the number of elements in the original model is not increased, it is more suitable for practical applications. Attached Figure Description

[0050] Figure 1 The present invention relates to a water-mechanical coupling test device.

[0051] Figure 2 The limestone sample prepared for this invention.

[0052] Figure 3 The stress-strain curves are from conventional uniaxial compression tests under different infiltration water pressures.

[0053] Figure 4 The cumulative curves of irreversible deformation of limestone under different intensities of seepage water pressure are shown.

[0054] Figure 5 The Nishihara fatigue model for rocks.

[0055] Figure 6 (a)-(f) are fatigue deformation curves relating the cumulative value of irreversible deformation to the number of cycles. Detailed Implementation

[0056] To enable those skilled in the art to better understand the technical solutions of the present invention, the technical solutions of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0057] This invention constructs a fatigue constitutive model for limestone under hydro-mechanical coupling, and the construction method includes the following steps:

[0058] 1. Hydraulic-mechanical coupling test

[0059] To investigate the strain characteristics and fatigue constitutive model of limestone under the coupled action of seepage water pressure and cyclic loading, this invention first utilizes, for example... Figure 1The hydraulic-mechanical coupling test apparatus shown was used to conduct conventional uniaxial cyclic loading and unloading tests on limestone samples under different intensities of seepage water pressure. The test specifically included:

[0060] (1) Fabrication of hydro-mechanical coupling specimens

[0061] The experimental material for this invention was selected from limestone in the entrance area of ​​the Guiyang Xiamaixi Tunnel. Limestone specimens were drilled according to the "Code for Rock Testing in Hydropower and Water Conservancy Projects (DLT5368-2007)" and then cut and ground to produce standard specimens with a height-to-diameter ratio of 2:1 and dimensions of H×D=100mm×50mm, with an end-face non-parallelism of less than 0.02mm. Strict control was maintained over the specimen processing accuracy during the manufacturing process. Density and P-wave velocity were tested on the rock specimens before the experiment, and specimens with obvious cracks, damage, or abnormal P-wave velocities were discarded to reduce the dispersion of the experimental results.

[0062] Polarizing microscopy observation of slices of limestone samples from the same batch showed that the rock mineral grains were uniformly distributed, fine-grained, and mostly secondary pores, classifying it as a low-porosity rock. Mineral composition analysis indicated that the main mineral component of the samples was calcite (CaCO3), with a content of 93.30–99.05%, while quartz (SiO2) and other minerals accounted for 0.95%–6.70%. A total of 18 samples were tested, with three parallel tests conducted at each permeation water pressure. Before the test, all limestone samples were dried at 105℃ for 24 hours and then sealed and degassed for 24 hours to ensure the same moisture content and pore pressure. The initial drying mass was measured, and the moisture content and dry density of the samples were calculated based on the mass difference. The sample dimensions, dry density, and P-wave velocity were obtained from the test scheme in Table 1. Table 1 shows that the average dry density and P-wave velocity of the limestone samples were 2.67 g / mm². 3 6.12 km / s.

[0063] Because the experiment required injecting different intensities of seepage water pressure into the limestone, a water injection hole was set at the center of the top end face of the limestone sample. The hole was 10 mm deep and 1.50 mm in diameter. Figure 2 As shown. To prevent high-pressure seepage water from escaping from the surface and end faces of the limestone sample, 4-6 layers of a water-stopping agent (mainly methylsiloxane, which acts as an adhesive between the sample and the metal) were continuously sprayed onto the surface at 5-8 minute intervals. After being left to air dry for 24 hours, an effective water-stopping boundary of 3-6 mm was formed. Experiments showed that the effect of the water-stopping layer on the compression deformation of the limestone was negligible.

[0064] (2) Conduct a hydro-hydraulic coupling test

[0065] To investigate the influence of seepage water pressure on the fatigue deformation characteristics of limestone, the water-mechanical coupling test (i.e., fatigue test) of this invention considered six seepage water pressures: 0, 2, 4, 6, 8, and 10 MPa. Specific test schemes are shown in Table 1. To provide a reference for rationally setting the mechanical parameters of cyclic loading and unloading, conventional uniaxial compression tests (loading rate of 1 MPa / s) were conducted on limestone samples under different seepage water pressure conditions to obtain the strength characteristics of the limestone and obtain its stress-strain curves, as shown below. Figure 3 As shown.

[0066] Table 1 Test Scheme

[0067]

[0068] Depend on Figure 3 It can be seen that the stress-strain curves under different permeation water pressures have similar shapes, all gradually rising to the peak stress and then rapidly falling, exhibiting brittle fracture characteristics. As the permeation water pressure borne by the limestone samples gradually increases, the increase in the number and size of internal dissolution pores will lead to a lengthening of the compaction stage and a corresponding shortening of the elastic stage of the stress-strain curve. The stress-strain curves after the peak show certain differences in their drop-off; the curves after the peak from 0 MPa to 4 MPa drop rapidly, while the curves after the peak from 6 MPa to 10 MPa show obvious oscillations before falling.

[0069] The uniaxial compressive strengths at 0, 2, 4, 6, 8, and 10 MPa were 102.25 MPa, 88.56 MPa, 74.15 MPa, 61.86 MPa, 57.48 MPa, and 55.21 MPa, respectively, with degradation coefficients of 13.39%, 27.48%, 39.50%, 43.78%, and 46.00%, respectively.

[0070] based on Figure 3 The peak intensity of the stress-strain curve is shown. Combined with Table 1, the upper and lower limits of the cyclic loading and unloading stress are set, with the average cyclic stress ranging from 20 to 55 MPa. A controlled stress loading method is used in the experiment, with a cyclic loading and unloading frequency of 1 Hz. First, the axial stress is gradually increased to the average cyclic stress (the average of the upper and lower limits of the cyclic stress) at a loading rate of 1 MPa / s. Then, a uniaxial cyclic loading and unloading test is conducted to obtain the fatigue characteristics of the limestone. In this cyclic loading and unloading test, the loading waveform of the cyclic load is a triangular wave, the cyclic load amplitude (i.e., the difference between the upper and lower limits of the cyclic stress) is 20 MPa, and the number of load cycles is set to 300. The cumulative irreversible deformation curve obtained after 300 cycles is shown in the attached figure. Figure 4As shown. If the specimen does not fail after 300 loading cycles, axial stress is continued to be applied at a loading rate of 1 MPa / s until the specimen fails. According to the above test plan, cyclic loading and unloading tests under different permeable water pressures were carried out on 18 limestone specimens XMX-1 to XMX-18. The fatigue characteristics of the limestone were studied based on the test results.

[0071] 2. Construction Method of Limestone Fatigue Constitutive Model under Hydro-Mechanical Coupling

[0072] Based on the above fatigue mechanics tests, combined with Figure 4 It can be seen that the cumulative irreversible deformation curves of limestone under different seepage water pressures exhibit a typical three-stage growth, representing the initial fatigue deformation stage, steady-state fatigue deformation stage, and accelerated fatigue deformation stage under water-mechanical coupling, which is consistent with the trend of rock rheological curves. Therefore, theoretically, the rheological characteristics and fatigue deformation characteristics of rocks have a common origin. Thus, a fatigue constitutive model reflecting the deformation characteristics of limestone can be constructed based on rheological theory.

[0073] This invention considers the influence of hydro-mechanical coupling and constructs a fatigue constitutive model for limestone. The construction method includes:

[0074] (1) Selection of fatigue model

[0075] As the above analysis shows, existing improved models based on the Nishihara model can overcome the shortcomings of classical models in simulating the accelerated rheological properties of rocks, but they suffer from too many parameters and are not convenient for practical applications. Therefore, this invention selects the Nishihara model as the basic model for simulating rock fatigue deformation, introduces a nonlinear function related to the number of load cycles, and improves the Nishihara model without increasing the number of components in the original model. This improves the model, better reflecting the fatigue deformation characteristics under water-mechanical coupling, and is also convenient for practical applications.

[0076] (2) Basic Assumptions

[0077] In order to quantitatively analyze the fatigue deformation characteristics of rocks using creep theory, the following assumptions are made:

[0078] ① Stress equivalence assumption

[0079] Rock fatigue deformation is assumed to be creep deformation under the action of an equivalent stress function. Based on rock cyclic loading tests, the equivalent fatigue stress function under triangular wave cyclic loading is expressed as:

[0080]

[0081] In the formula: σ Fσ is the equivalent fatigue stress under cyclic loading conditions; f is the cyclic frequency; Δσ is the cyclic amplitude; σ0 is the average cyclic stress; σ cri σ is the critical value for cycle failure; c Uniaxial compressive strength;

[0082] ② The assumption of continuity in deformation

[0083] During cyclic loading and unloading, the rock plastic deformation and damage corresponding to the stress peak in each cycle are not actually continuous; however, considering that the rock plastic deformation increases with the increase of the number of cycles, the plastic deformation in the model is considered continuous, and its expression is as follows:

[0084]

[0085] In the formula: The plastic deformation generated in the i-th cycle; Let represent the initial and final plastic deformation amounts for cycle i.

[0086] ③Establish a fatigue deformation model

[0087] When using the Nishihara model as the basic model for analyzing the fatigue characteristics of rocks under cyclic loading and unloading, the elements in the Nishihara model are replaced with fatigue elements, thereby endowing the Nishihara model with fatigue characteristics to simulate the fatigue characteristics of rocks, as shown in the attached figure. Figure 5 The Nishihara fatigue model of the rock shown includes generalized Kelvin bodies and viscoplastic bodies.

[0088] The state equation of the Nishihara fatigue model is:

[0089]

[0090] In the formula: σ cri E represents the yield stress of the rock. h E k η1 and η2 are the creep mechanical parameters of the rock, where E h E k η is the stiffness coefficient of the rock, and η1 and η2 are the viscosity coefficients of the rock.

[0091] To overcome the shortcomings of the traditional Nishihara fatigue model in that it cannot well fit the accelerated fatigue stage of rocks, this invention defines a nonlinear function F(N) to describe the accelerated fatigue stage of rocks.

[0092] The expression for the nonlinear function is:

[0093]

[0094]

[0095] In the formula: α is the rock fatigue parameter; N is the number of cycles; N * This represents the number of cycles corresponding to the starting point of the rock entering the accelerated deformation stage.

[0096] Substituting equations (4) and (5) into the state equation (3) of the Nishihara fatigue model, we obtain the expression for the fatigue deformation model (i.e., the fatigue constitutive model):

[0097]

[0098] As can be seen from equation (6), fatigue strain is a nonlinear function of the number of cycles, which can well reflect the fatigue deformation characteristics of rocks.

[0099] The key parameters in the fatigue constitutive model constructed as shown in equation (6) are solved as follows:

[0100] (1) When N = 0, we can obtain The value of ε(0) is the y-intercept of the cycle number-strain curve, which can be obtained from the basic theory of elasticity. h ;

[0101] (2) When N≤N * When the rock has not yet entered the accelerated deformation stage, the value of the F(N) function is 1, and the equation degenerates into the traditional Nishihara model equation, which can reflect the deformation characteristics of the rock in the initial fatigue stage and the steady-state fatigue stage. When N is small, It is a relatively small value, and the magnitude of ε(N) is determined by... Decision, among which The convergence rate is determined by the value of η1, which converges to 1. Value determination The magnitude of the value corresponds to the initial deformation stage of the fatigue curve, where the trend of the ε(N) function changes accordingly.

[0102] (3) It can be seen that η1 controls the slope of the curve in the initial fatigue stage, E k Control the maximum value of the curve in the initial fatigue stage. The initial fatigue stage of the control curve. As N increases, the value of ε(N) gradually approaches... At this point, ε(N) is a linear function equation, and the trend of its function curve corresponds to the steady-state fatigue stage of the fatigue curve, where the value of η2 controls the slope of the function. Correspondingly, in the Nishihara model, η2 controls the slope of the steady-state fatigue stage of the fatigue curve; It controls the steady-state fatigue stage of the fatigue curve.

[0103] 3. Validation of the fatigue constitutive model

[0104] To verify the rationality of the constructed fatigue deformation model and its adaptability to the above-mentioned hydro-mechanical coupling test results, the 1stOpt software was used to fit the cumulative irreversible deformation curves during the fatigue failure process of limestone under different seepage water pressures, and fatigue model parameters applicable to the fatigue failure of limestone under different seepage water pressures were obtained. The steps for determining the values ​​of the relevant parameters in equation (6) are as follows:

[0105] ① First, from the appendix Figure 4 The parameter E is obtained by considering the initial point (0, ε(0)). h ;

[0106] ②According to N * The physical meaning of (0, N) * The parameters E are obtained by fitting the cumulative irreversible deformation curve within the range. k The values ​​of η1 and η2;

[0107] ③ Based on the cumulative irreversible deformation curve of the accelerated fatigue deformation stage, the fatigue parameter α is obtained by fitting. The fatigue deformation curve between the cumulative irreversible deformation value and the number of cycles obtained based on equation (6) is shown below. Figure 6 As shown in Table 2, the fitting parameters of the fatigue deformation model are shown in Table 2.

[0108] Table 2 Fitting parameters of the fatigue deformation model

[0109]

[0110] As shown in Table 2, the correlation coefficients between the cumulative irreversible deformation value obtained using Equation (6) and the number of cycles in the fatigue deformation curve range from 0.996 to 0.973, indicating that the fitted model parameters exhibit good convergence. The increase in seepage water pressure has varying degrees of influence on the model parameters in the rock fatigue deformation model. With the increase of seepage water pressure, the model parameter E... k η1 and α show a gradually decreasing trend. Meanwhile, the model parameter E... h η2 exhibits varying degrees of dispersion as the seepage water pressure increases, where parameter E h Anomalies were observed at 2 MPa and 4 MPa, while the variation trend of parameter η2 was irregular. The data in Table 2 show that, compared to the state without permeable pressure, parameter E at 10 MPa permeable pressure... h Reduced by 86.50%, parameter E k The parameter η1 decreased by 97.5%, the parameter η2 decreased by 78.06%, and the parameter α decreased by 78.05%.

[0111] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling, characterized in that, Includes the following steps: Step 1: Prepare limestone samples; Step 2: Cyclic loading and unloading tests were conducted on limestone samples under different permeable water pressures using a water-mechanical coupling test to analyze the evolution characteristics of the irreversible deformation accumulation curve as the number of cycles increases. Step 3: Based on the analysis results of Step 2, the Nishihara fatigue model is improved to construct a limestone fatigue constitutive model; Step 4: Solve for the key parameters in the limestone fatigue constitutive model and verify the established limestone fatigue constitutive model.

2. The method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling as described in claim 1, characterized in that, Step 2 includes the following specific steps: Step 21: Inject water of different intensities into the water injection holes of the limestone sample and conduct a conventional uniaxial compression test to obtain the stress-strain curve of the limestone sample. Step 22: Based on the results of the uniaxial compression test, set the upper limit stress, lower limit stress, and average stress of the cyclic loading and unloading. Step 23: Gradually apply axial stress at a loading rate of 1 MPa / s until the cyclic average stress is reached; Step 24: Cyclicly load the load 300 times, with the load waveform of each cycle being a triangular wave and the amplitude of the cyclic load being 20MPa, to conduct a uniaxial cyclic loading and unloading test. Step 25: If the specimen does not fail after 300 cycles, continue to apply axial stress at a loading rate of 1 MPa / s until the specimen fails. Step 26: Perform steps 21-25 on different types of limestone samples to obtain the corresponding cumulative irreversible deformation curves of the limestone samples; Step 27: Analyze the irreversible deformation accumulation curve obtained in Step 26. The evolution characteristics obtained are that the irreversible deformation accumulation curve and the rock rheological curve have the same trend. The rheological characteristics and fatigue deformation characteristics of the rock have the same origin.

3. The method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling as described in claim 2, characterized in that, Step 3 includes the following specific steps: Step 31: Make basic assumptions about the fatigue characteristics and plastic deformation of rocks; Step 32: Based on the basic assumptions, replace the elements in the Nishihara model with fatigue elements to obtain the Nishihara fatigue model of the rock: Where: σ cri E represents the yield stress of the rock. h E k η is the stiffness coefficient of the rock, and η1 and η2 are the viscosity coefficients of the rock; Step 33: Define a nonlinear function F(N) to describe the accelerated fatigue stage of the rock: In the formula: α is the rock fatigue parameter; N is the number of cycles; N * This represents the number of cycles corresponding to the starting point when the rock enters the accelerated deformation stage. Step 34: Substitute equations (4) and (5) into equation (3) to obtain the limestone fatigue constitutive model:

4. The method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling as described in claim 3, characterized in that, The basic assumptions of step 31 include: 1) Stress equivalence assumption Assuming that rock fatigue deformation is creep deformation under the action of an equivalent stress function, the equivalent fatigue stress function under triangular wave cyclic loading is expressed as: Where: σ F σ is the equivalent fatigue stress under cyclic loading conditions; f is the cyclic frequency; Δσ is the cyclic amplitude; σ0 is the average cyclic stress; σ cri σ is the critical value for cycle failure; c Uniaxial compressive strength; 2) The assumption of continuity in deformation By treating the amount of plastic deformation in the model as continuous, the plastic deformation of the rock can be expressed as: In the formula: The plastic deformation generated in the i-th cycle; Let be the initial and final plastic deformation amounts for cycle i.

5. The method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling as described in claim 4, characterized in that, Step 4 includes the following specific steps: Step 41: Obtain the parameter E based on the initial point value (0, ε(0)) in the irreversible deformation accumulation curve. h ; Step 42: For (0, N) * The parameters E are obtained by fitting the cumulative irreversible deformation curve within the range. k The values ​​of η1 and η2; Step 43: Based on the cumulative irreversible deformation curve of the accelerated fatigue deformation stage, the fatigue parameter α is obtained by fitting.

6. The method for constructing a fatigue constitutive model of limestone under hydro-mechanical coupling as described in claim 1, characterized in that, The limestone sample has dimensions of H×D=100mm×50mm, the non-parallelism of the end face is less than 0.02mm, and a water injection hole is provided at the center of the end face of the sample.

7. An application of a fatigue constitutive model for limestone, characterized in that, The fatigue deformation characteristics of rock under hydro-mechanical coupling were simulated using the limestone fatigue constitutive model as described in claim 1.

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