Cumulative damage analysis method and system for limestone under cyclic loading

Abstract

The present invention relates to the field of limestone damage analysis technology, and in particular to a method and system for analyzing the cumulative damage of limestone under cyclic loads, the method comprising the following steps: preparing a plurality of limestone samples; conducting a cyclic impact test on the limestone samples, and performing stress-strain analysis and energy dissipation law analysis according to the experimental results; constructing a cumulative damage constitutive model of the limestone samples based on the results of the stress-strain analysis and the energy dissipation law analysis; and using the cumulative damage constitutive model to analyze the cumulative damage of the limestone under cyclic loads. The cumulative damage constitutive model constructed by the present invention based on the cyclic impact test can better reflect the cumulative damage evolution of the limestone under cyclic loads, and can provide reliable guidance for the cyclic blasting construction of underground engineering.

Description

Technical Field

[0001] The invention relates to the technical field of limestone damage analysis, and in particular to a limestone cumulative damage analysis method and system under cyclic load. Background Art

[0002] The constitutive model can reflect the macroscopic mechanical properties of the material, so establishing a reasonable constitutive model has always been a key issue in the development of rock mechanics theory and practical engineering. By establishing a reasonable constitutive model, the deformation of the rock in the engineering environment and under the relevant loads can be predicted, and then the surrounding rock damage analysis can be performed to evaluate the stability of the surrounding rock, which will ultimately guide the safe construction of the project. At present, most of the research on constitutive models focuses on single impacts, and there are few studies on the cumulative damage constitutive model under cyclic loads. However, in mining and tunnel blasting projects, rocks are often subjected to cyclic loads. Therefore, studying the cumulative damage constitutive model of limestone under cyclic impact has important reference value for underground engineering. Summary of the invention

[0003] In view of the defects in the prior art, the present invention provides a method and system for analyzing the cumulative damage of limestone under cyclic loads.

[0004] In order to achieve the above-mentioned purpose, in the first aspect, the present invention provides a method for analyzing the cumulative damage of limestone under cyclic loads, the method comprising the following steps: preparing a plurality of limestone samples; conducting a cyclic impact test on the limestone samples, and performing stress-strain analysis and energy dissipation law analysis based on the experimental results; constructing a cumulative damage constitutive model of the limestone samples based on the results of the stress-strain analysis and the energy dissipation law analysis; and using the cumulative damage constitutive model to analyze the cumulative damage of the limestone under cyclic loads. The cumulative damage constitutive model constructed by the present invention based on the cyclic impact test can better reflect the cumulative damage evolution of limestone under cyclic loads, and can provide reliable guidance for cyclic blasting construction of underground engineering.

[0005] Optionally, the step of performing a cyclic impact test on the limestone sample and performing stress-strain analysis and energy dissipation law analysis according to the experimental results comprises the following steps:

[0006] Set multiple impact air pressures;

[0007] For each of the limestone samples, a cyclic impact test is performed on the sample using a fixed impact air pressure, and the incident wave, reflected wave and transmitted wave of the limestone sample are measured simultaneously;

[0008] Calculating the average stress, average strain, reflected energy, transmitted energy and absorbed energy of the limestone sample according to the measurement results of the incident wave, the reflected wave and the transmitted wave;

[0009] The average stress and the average strain are used to draw stress-strain curves under different impact gas pressures, as well as variation trend diagrams of the reflected energy, the transmitted energy, and the absorbed energy.

[0010] Optionally, the average stress and the average strain respectively satisfy the following relationship:

[0011]

[0012]

[0013] Where s is the mean stress, is the average strain, A is the cross-sectional area of ​​the limestone sample, is the cross-sectional area of ​​the rod, E is the elastic modulus of the limestone sample, is the strain amplitude of the incident wave, is the strain amplitude of the reflected wave, is the strain amplitude of the transmitted wave, c is the propagation speed of the stress wave in the limestone sample, is the length of the limestone sample, is the strain caused by the incident wave, is the strain caused by the reflected wave, is the strain caused by the transmitted wave, and t is the propagation time of the stress wave in the limestone sample.

[0014] Optionally, the reflected energy, the transmitted energy and the absorbed energy respectively satisfy the following relationships:

[0015]

[0016]

[0017]

[0018] in, is the reflected energy, is the cross-sectional area of ​​the rod, is the propagation speed of stress wave in the rod, is the initial elastic modulus of the limestone sample, t is the propagation time of the stress wave in the limestone sample, is the strain caused by the reflected wave, is the transmission energy, is the strain caused by the transmitted wave, is the absorbed energy, is the strain caused by the incident wave.

[0019] Optionally, constructing the cumulative damage constitutive model of the limestone sample based on the results of the stress-strain analysis and the energy dissipation law analysis comprises the following steps:

[0020] Determine damage variables according to energy data, and then obtain a state equation of the damage body, wherein the energy data includes the reflected energy, the transmitted energy, and the absorbed energy;

[0021] The limestone sample is regarded as a collection of a large number of micro-elements, and the strength of the micro-elements obeys Weibull distribution, and then the statistical damage variable is calculated;

[0022] Based on the statistical damage variables, a constitutive equation of a first damaged body is obtained according to the generalized Hooke's law, and then a constitutive equation of a second damaged body is obtained by combining the state equation of the damaged body;

[0023] The limestone sample is regarded as a combined mechanical model consisting of a generalized Kelvin body, a Bingham body and a damage body in parallel;

[0024] Constructing the cumulative damage constitutive model based on the constitutive equation of the generalized Kelvin body, the constitutive equation of the Bingham body and the constitutive equation of the damage body;

[0025] The cumulative damage constitutive model is verified based on the results of the stress-strain analysis.

[0026] Optionally, the damage variable and the damaged body state equation satisfy the following relationship respectively:

[0027]

[0028]

[0029] in, is the damage variable, n is the number of cyclic impacts, , and is the coefficient, is the elastic modulus of the limestone sample after n cycles of impact, is the initial elastic modulus of the limestone sample.

[0030] Optionally, the statistical damage variable satisfies the following relationship:

[0031]

[0032] in, is the statistical damage variable, F is the distribution variable of the strength of the microelement, and m are the parameters of the Weibull distribution.

[0033] Optionally, the damaged body constitutive equation includes the first damaged body constitutive equation and the second damaged body constitutive equation, and the damaged body constitutive equation satisfies the following relationship:

[0034]

[0035] in, is the stress of the damaged body, is the initial elastic modulus of the limestone sample, is the statistical damage variable, is the damage variable, For The corresponding strain of the damaged body is, is the proportional relationship between the transverse strain and the longitudinal strain of the limestone sample, is the stress perpendicular to the stress direction of the damaged body.

[0036] Optionally, the cumulative damage constitutive model satisfies the following relationship:

[0037]

[0038] in, is the stress of the limestone sample, is the stress of the damaged body, is the stress of the generalized Kelvin body, is the stress of the Bingham body, , and is the elastic modulus of each mechanical element related to the generalized Kelvin body in the combined mechanical model, is the strain of the generalized Kelvin body at time t, for The derivative of is the viscosity coefficient of the generalized Kelvin body, , is the strain of the Bingham body at time t, for The derivative of is the viscosity coefficient of the Bingham body, is the critical stress value, is the elastic modulus of the mechanical elements related to the Bingham body in the combined mechanical model.

[0039] In summary, this method first conducts cyclic impact tests on limestone samples, and performs stress-strain curve analysis and energy dissipation law analysis, which provides data support for the cumulative damage analysis of limestone under cyclic loads; secondly, this method obtains the damage variables and state equations of the damaged body of limestone under cyclic loads, and at the same time regards the limestone sample as a collection composed of a large number of micro-elements to calculate the statistical damage variables, and then combines the generalized Hooke's law to obtain the damage body constitutive equation, which provides a basis for constructing a cumulative damage constitutive model; finally, this method regards the limestone sample as a combined mechanical model composed of a generalized Kelvin body, a Bingham body and a damage body in parallel, and then constructs a cumulative damage constitutive model. This model more accurately reflects the evolution trend of the cumulative damage of limestone under cyclic loads, which can not only improve the theoretical research on the mechanical properties of rocks under different external environments, but also provide reliable guidance for the cyclic blasting construction of underground engineering.

[0040] In a second aspect, the present invention provides a system for analyzing the cumulative damage of limestone under cyclic loading, the system comprising: a data acquisition device, a data query device, a processor and a storage device, the storage device comprising a computer-readable storage medium, the computer-readable storage medium storing a computer program, the computer program comprising program instructions, the program instructions when executed by the processor, enabling the processor to implement the method for analyzing the cumulative damage of limestone under cyclic loading provided by the present invention. The system can stably execute the method provided by the present invention, can improve the efficiency of the analysis of the cumulative damage of limestone under cyclic loading, and can improve the practicality of the method provided by the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0042] Figure 1 It is a schematic flow chart of a method for analyzing cumulative damage of limestone under cyclic loading according to an embodiment of the present invention;

[0043] Figure 2 The stress-strain curve diagram of the limestone sample when the impact gas pressure is 0.15 MPa in the embodiment of the present invention;

[0044] Figure 3 The stress-strain curve diagram of the limestone sample when the impact gas pressure is 0.2 MPa in the embodiment of the present invention;

[0045] Figure 4The stress-strain curve diagram of the limestone sample when the impact gas pressure is 0.25 MPa in the embodiment of the present invention;

[0046] Figure 5 is a graph showing the changing trend of reflected energy under different impact pressures according to an embodiment of the present invention;

[0047] Figure 6 is a graph showing the variation trend of transmission energy under different impact gas pressures according to an embodiment of the present invention;

[0048] Figure 7 is a graph showing a change trend of the absorbed energy under different impact air pressures according to an embodiment of the present invention;

[0049] Figure 8 is a damage variable evolution diagram under different impact gas pressures of an embodiment of the present invention;

[0050] Fig. 9 It is the fitting result of the damage variable at 0.15MPa of the embodiment of the present invention;

[0051] Fig.10 It is the fitting result of the damage variable at 0.2MPa of the embodiment of the present invention;

[0052] Fig.11 The test curve and theoretical curve at 0.15 MPa of the embodiment of the present invention;

[0053] Fig.12 The test curve and theoretical curve at 0.2 MPa of the embodiment of the present invention;

[0054] Fig.13 The test curve and theoretical curve at 0.25 MPa of the embodiment of the present invention;

[0055] Fig.14 Schematic diagram of the framework of a limestone cumulative damage analysis system under cyclic loading according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The specific embodiments of the present invention will be described in detail below. It should be noted that the embodiments described herein are only for illustration and are not intended to limit the present invention. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present invention. However, it is obvious to those of ordinary skill in the art that these specific details do not need to be adopted to implement the present invention. In other examples, in order to avoid confusing the present invention, known circuits, software or methods are not specifically described.

[0057] Throughout the specification, references to "one embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in conjunction with the embodiment or example is included in at least one embodiment of the present invention. Therefore, the phrases "in one embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily all refer to the same embodiment or example. In addition, particular features, structures, or characteristics may be combined in one or more embodiments or examples in any suitable combination and / or subcombination. In addition, it should be understood by those of ordinary skill in the art that the figures provided herein are for illustrative purposes and that the figures are not necessarily drawn to scale.

[0058] It should be noted in advance that, in an optional embodiment, except for independent explanations, the same symbols or letters appearing in all formulas have the same meanings and values.

[0059] In an alternative embodiment, see Figure 1 The present invention provides a method for analyzing the cumulative damage of limestone under cyclic loading, the method comprising the following steps:

[0060] S1. Prepare multiple limestone samples.

[0061] Specifically, in this embodiment, all limestone samples are standard cylindrical rock samples and come from the same rock. When preparing the limestone samples, it is necessary to strictly ensure that the non-parallelism of the two end faces of the limestone samples and the non-perpendicularity between the end face and the side face are controlled within 0.02 mm.

[0062] More specifically, the limestone sample had a diameter of 75 mm and a height of 37.5 mm.

[0063] S2. Perform a cyclic impact test on the limestone sample, and perform stress-strain analysis and energy dissipation law analysis based on the experimental results.

[0064] Wherein, step S2 specifically includes the following steps:

[0065] S21. Setting multiple impact air pressures.

[0066] Specifically, in this embodiment, a confining pressure machine is installed on the basis of the SHPB test device, and the confining pressure value is set to 2MPa, and a cyclic impact test is performed on the limestone sample under different impact air pressure conditions. Before the test begins, vaseline is evenly applied on both sides of the limestone sample that need to contact the incident rod and the transmission rod, and then it is placed in the center of the confining pressure machine and firmly clamped by the incident rod and the transmission rod. Three impact air pressures are determined based on the results of the pre-impact test, which are 0.15MPa, 0.20MPa and 0.25MPa respectively.

[0067] S22. For each of the limestone samples, a cyclic impact test is performed on it using a fixed impact air pressure, and the incident wave, reflected wave and transmitted wave of the limestone sample are measured simultaneously.

[0068] Specifically, in this embodiment, a cyclic impact test is performed on the first limestone sample at 0.15 MPa until the sample is destroyed, a cyclic impact test is performed on the second limestone sample at 0.20 MPa until the sample is destroyed, and a cyclic impact test is performed on the third limestone sample at 0.25 MPa until the sample is destroyed. When performing the cyclic impact test, the incident wave, the reflected wave, and the transmitted wave are measured by the strain gauges attached to the incident rod and the transmission rod.

[0069] Furthermore, in order to ensure the accuracy of the data, three parallel tests were carried out for each shock air pressure, and the average values ​​of the incident wave, reflected wave, and transmitted wave collected in the three parallel tests were calculated under the same shock air pressure as the final data.

[0070] S23. Calculate the average stress, average strain, reflected energy, transmitted energy and absorbed energy of the limestone sample according to the measurement results of the incident wave, the reflected wave and the transmitted wave.

[0071] Specifically, in this embodiment, according to the one-dimensional stress wave assumption, the cross section of the rod will maintain its planar state when the stress wave propagates in the rod, and the stress wave waveform on each cross section of the rod is consistent, and these stress waves propagate in the axial direction of the rod in a one-dimensional form. Since the incident rod and the transmission rod always maintain an elastic state during the entire propagation process, the influence of the strain rate effect on the analysis can be ignored. In addition, when the diameter of the rod is small enough, the influence of the lateral inertia effect becomes negligible and can be ignored. Based on these conditions, the one-dimensional elastic stress wave theory can be used to conduct an in-depth analysis of the propagation process of the stress wave in the rod. At the same time, based on the assumption of stress uniformity, when the size of the sample is small enough in the stress propagation direction, the time required for the stress wave inside the sample to propagate back and forth between the two end faces will be very short compared to the loading time. This ensures that the sample can reach a state of stress equilibrium before failure. Therefore, in the analysis process, the stress wave effect inside the sample can be ignored, and the influence of the strain rate effect on the performance of the sample can be mainly focused on. In summary, assuming that the stress wave in the elastic rod does not diffuse, the average stress and average strain of the limestone sample satisfy the following relationship:

[0072]

[0073]

[0074] Where s is the mean stress, is the average strain, A is the cross-sectional area of ​​the limestone sample, is the cross-sectional area of ​​the rod, E is the elastic modulus of the limestone sample, is the strain amplitude of the incident wave, is the strain amplitude of the reflected wave, is the strain amplitude of the transmitted wave, c is the propagation speed of the stress wave in the limestone sample, is the length of the limestone sample, is the strain caused by the incident wave, is the strain caused by the reflected wave, is the strain caused by the transmitted wave, and t is the propagation time of the stress wave in the limestone sample.

[0075] Furthermore, the energy evolution law of rocks under load has always been a hot research object in rock mechanics and practical engineering. In the SHPB test, the energy carried by the stress wave can be mainly divided into: the energy carried by the incident wave, that is, the incident energy; the energy carried by the reflected wave, that is, the reflected energy; the energy carried by the transmitted wave, that is, the transmitted energy; the dissipated energy, that is, the dissipated energy. In the cyclic impact test, part of the energy carried by the stress wave is reflected back to the incident rod when it contacts the limestone sample, and part of it is absorbed when new cracks are generated, and the remaining energy continues to propagate through the limestone sample. Therefore, the process of limestone sample damage can be understood as the limestone sample absorbing the energy carried by the stress wave, causing the cracks inside the limestone sample to expand and penetrate, thereby causing the limestone sample to be damaged. Therefore, the reflected energy, the transmitted energy and the absorbed energy can all reflect the damage inside the limestone sample. The reflected energy, the transmitted energy and the absorbed energy satisfy the following relationships respectively:

[0076]

[0077]

[0078]

[0079] in, is the reflected energy, is the propagation speed of stress wave in the rod, is the initial elastic modulus of the limestone sample, t is the propagation time of the stress wave in the limestone sample, is the transmitted energy, To absorb energy.

[0080] S24. Using the average stress and the average strain, draw stress-strain curves under different impact gas pressures, as well as a variation trend diagram of the reflected energy, the transmitted energy, and the absorbed energy.

[0081] Specifically, in this embodiment, see Figure 2 , Figure 3 and Figure 4 , with the average stress as the vertical axis and the average strain as the horizontal axis, the stress-strain curves under different impact pressure conditions are plotted. From the morphological classification, the stress-strain curve can be divided into an open type and a rebound type. The rebound stress-strain curve mainly appears in the early stage of cyclic impact. The main characteristics are that the peak stress is large during the entire cyclic impact process, and the strain growth rate is small in the early stage of impact. The limestone sample has a strong deformation resistance at this time. After the first unloading stage, the strain decreases with the decrease of stress, and the phenomenon of post-peak rebound occurs, indicating that the sample still has elastic deformation, and the sample structure has not been damaged at this time. Figure 2 The stress-strain curves corresponding to the first to third impacts and Figure 3 The stress-strain curves corresponding to the first and second impacts in the test. The open type mainly appears in the middle and late stages of the cyclic impact. Its main characteristics are that the peak stress has dropped significantly compared with the first impact, the strain is the largest in the entire cyclic impact, the strain growth rate is accelerated at the initial stage of the impact, and the rebound phenomenon after the peak disappears. Analysis shows that with the accumulation of the number of impacts, the internal cracks of the sample gradually expand, resulting in a continuous decrease in its bearing capacity and a gradual weakening of its elastic deformation capacity. The sample is on the verge of destruction, such as Figure 2 The stress-strain curves corresponding to the fourth and fifth impacts are shown in Fig. Figure 3 The stress-strain curve corresponding to the fourth impact in Figure 4 Stress-strain curve corresponding to the first impact.

[0082] Furthermore, when the confining pressure is 2 MPa, the reflected energy, transmitted energy and absorbed energy of each cyclic impact test are calculated and recorded, and the reflected energy, transmitted energy and absorbed energy under different impact times and different impact pressures are obtained as shown in Table 1:

[0083] Table 1 Reflected energy, transmitted energy and absorbed energy at different impact pressures and impact times

[0084]

[0085] With the impact number as the horizontal axis and the energy as the vertical axis, the changing trend diagram of reflected energy, transmitted energy and absorbed energy under different impact pressures is drawn according to the data in Table 1, as shown in order. Figure 5 , Figure 6 and Figure 7 shown.

[0086] S3. Constructing a cumulative damage constitutive model of the limestone sample based on the results of the stress-strain analysis and the energy dissipation law analysis.

[0087] S31. Determine damage variables according to energy data, and then obtain a state equation of the damage body, wherein the energy data includes the reflected energy, the transmitted energy, and the absorbed energy.

[0088] Specifically, in this embodiment, in order to further reveal the cumulative damage law of the limestone sample under cyclic impact, the energy data in Table 1 are further processed to specifically satisfy the following formula:

[0089]

[0090] in, is the damage variable, is the absorbed energy of the limestone sample after n cycles of impact, is the dissipated energy of the limestone sample after n cycles of impact.

[0091] More specifically, when the confining pressure is 2MPa and the impact gas pressure is 0.15MPa and 0.20MPa respectively, the specific values ​​of the damage variables are shown in Table 2:

[0092] Table 2 Damage variables when the impact pressure is 0.15MPa and 0.20MPa

[0093]

[0094] With the impact number as the horizontal axis and the damage variable as the vertical axis, the damage variable evolution diagram under different impact pressures is drawn according to the data in Table 2. Figure 8 As shown. Figure 8 It can be seen that the evolution trend of the damage variables of the limestone sample shows a linear growth type, the cumulative damage development time is short and the process is fast, and the internal damage of the sample accumulates step by step under the action of the impact load, eventually leading to the destruction of the sample. In order to further explore the influence of the number of impacts on rock damage, it is very important to accurately describe the cumulative damage evolution process. Therefore, it is of great significance to select a mathematical equation that can accurately reflect this process. This embodiment uses a cubic polynomial function to respectively Figure 8 The damage variable scatter points under different shock pressures are fitted, and the damage variables satisfy the following relationship:

[0095]

[0096] in, , and is the coefficient. When the impact pressure is 0.15MPa, the fitting results are as follows Fig. 9 As shown, , and The values ​​are 0.012, 0.772 and 0.183 respectively. When the impact pressure is 0.2MPa, the fitting results are as follows Fig.10 As shown, , and The values ​​are 0.006, 1.225 and 0.24 respectively. Fig. 9 and Fig.10 It can be seen that the fitting results are very close to the test data. When the impact gas pressure is 0.15 MPa, the correlation coefficient between the fitting results and the test data is 0.99; when the impact gas pressure is 0.20 MPa, the correlation coefficient between the fitting results and the test data is 0.994, which shows that the fitting results are correct and can be used to calculate the limestone damage variables under medium and low confining pressures.

[0097] Furthermore, it is assumed that the damaged body in the limestone sample is isotropic, a linear elastic body before damage, and complies with the strain equivalence principle. Therefore, the initial state of the limestone sample is taken as the first damage state, and the state after cyclic impact n times is taken as the second damage state, then the damaged body satisfies the following relationship:

[0098]

[0099] in, is the initial stress of the limestone sample, is the stress of the limestone sample after the nth cycle impact, is the elastic modulus of the limestone sample after n cycles of impact. According to this relationship and the damage mechanics formula, the state equation of the damaged body of the limestone sample can be obtained. The state equation of the damaged body satisfies the following relationship:

[0100]

[0101] S32. The limestone sample is regarded as a collection of a large number of microelements, and the strength of the microelements obeys Weibull distribution, and then the statistical damage variable is calculated.

[0102] Specifically, in this embodiment, the natural limestone sample has a large number of randomly distributed defects. The limestone sample is regarded as a collection of a large number of micro-elements, and the strength of the micro-element obeys the Weibull distribution. The probability density function of the micro-element strength is It is expressed as:

[0103]

[0104] Among them, F is the distribution variable of the strength of the microelement; and m are parameters of the Weibull distribution, which are related to the mechanical properties of rocks.

[0105] As the number of impacts increases, the number of micro-elements that lose their bearing capacity gradually increases. Based on the assumption that the micro-element strength obeys the Weibull distribution, a statistical damage variable is introduced. , let the total number of micro-elements be N, and the number of micro-elements that lose their bearing capacity under load is , the statistical damage variable can be expressed by the following expression:

[0106]

[0107] Among them, the number of micro-element destructions within the interval [0, y] of micro-element strength is , y is the upper limit of the interval. According to all the relationship equations provided in step S32, it can be obtained that the statistical damage variable satisfies the following relationship:

[0108]

[0109] S33. Based on the statistical damage variables, the constitutive equation of the first damaged body is obtained according to the generalized Hooke's law, and then the constitutive equation of the second damaged body is obtained by combining the state equation of the damaged body.

[0110] Specifically, in this embodiment, the constitutive equation of the first damaged body satisfies the following relationship:

[0111]

[0112] in, is the stress of the damaged body, For The corresponding strain of the damaged body is, is the proportional relationship between the transverse strain and the longitudinal strain of the limestone sample, is the stress perpendicular to the stress direction of the damaged body.

[0113] However, the first damage body constitutive equation is only applicable to the stress calculation under a single impact load. In order to establish a damage constitutive model of rock under cyclic impact load, the number of cyclic impacts needs to be introduced into the damage body constitutive model. Therefore, the first damage body constitutive equation is rewritten according to the damage body state equation to obtain the second damage body constitutive equation. The second damage body constitutive equation satisfies the following relationship:

[0114]

[0115] Since the constitutive equation of the second damaged body introduces Therefore, the number of cyclic impacts is introduced into the constitutive equation of the second damage body, which is suitable for the stress calculation under cyclic impact loads.

[0116] According to the constitutive equation of the first damage body and the constitutive equation of the second damage body, the constitutive equation of the damage body can be written to satisfy the following relationship:

[0117]

[0118] S34. The limestone sample is regarded as a combined mechanical model consisting of a generalized Kelvin body, a Bingham body and a damage body in parallel.

[0119] Specifically, in this embodiment, since the limestone sample has both damage characteristics and viscoelastic plasticity, according to the component combination theory, the limestone sample is regarded as a combined mechanical model consisting of a generalized Kelvin body, a Bingham body and a damage body in parallel.

[0120] S35. Constructing the cumulative damage constitutive model based on the constitutive equation of the generalized Kelvin body, the constitutive equation of the Bingham body and the constitutive equation of the damage body.

[0121] Specifically, in this embodiment, for the generalized Kelvin body, its constitutive equation is:

[0122]

[0123] in, is the stress in the generalized Kelvin body, and is the elastic modulus of each mechanical element related to the generalized Kelvin body in the combined mechanical model, is the strain of the generalized Kelvin body at time t, for The derivative of is the viscosity coefficient of the generalized Kelvin body.

[0124] For the Bingham body, in order to make the formula less complicated and general, only the existence of the plastic body is considered, and its constitutive equation is as follows:

[0125]

[0126] in, is the stress of the Bingham body, is the strain of the Bingham body at time t, for The derivative of is the viscosity coefficient of the Bingham body, is the critical stress value, is the elastic modulus of the mechanical elements related to the Bingham body in the combined mechanical model. Determined by the starting point of the yield stage of the stress-strain curve.

[0127] According to the series-parallel rule, the cumulative damage constitutive model of the limestone sample can be written to satisfy the following relationship:

[0128]

[0129] in, is the stress of the limestone sample.

[0130] S36. Verifying the cumulative damage constitutive model according to the result of the stress-strain analysis.

[0131] Specifically, in this embodiment, for the limestone sample, the values ​​of the parameters in the cumulative damage constitutive model are shown in Table 3:

[0132] Table 3 Numerical values ​​of various parameters in the cumulative damage constitutive model

[0133] Impact air pressure / MPa <![CDATA[E 21 / GPa]]> <![CDATA[E 22 / GPa]]> <![CDATA[η2]]> <![CDATA[E 31 / GPa]]> <![CDATA[η3]]> m 0.15 12.53 7.984 0.207 3.865 0.453 1.52 0.2 14.56 7.215 0.231 6.759 0.276 1.8 0.25 15.718 9.457 0.306 13.765 0.221 2.28

[0134] Furthermore, the data in Table 3 are introduced into the cumulative damage constitutive model, and the stress-strain curves of the first impact under 0.15MPa, 0.20MPa and 0.25MPa impact pressures are used as experimental curves. The stress-strain curves obtained using the cumulative damage constitutive model are used as theoretical curves. The experimental curves are used to verify the theoretical curves. The results are as follows: Fig.11 , Fig.12 and Fig.13 shown.

[0135] Under the impact pressure of 0.15MPa, 0.20MPa and 0.25MPa, the correlation coefficients between the experimental curve and the theoretical curve are 0.98393, 0.98744 and 0.99565 respectively. From the perspective of the curve line shape, the theoretical curve obtained by the cumulative damage constitutive model is consistent with the experimental curve in the overall trend. Although there are slight differences in the specific values, the overall trend is consistent, indicating that the cumulative damage constitutive model can better express the failure process of the limestone specimen. The elastic stages of the two are basically the same, there is a certain error in the plastic stage, and the failure stage is highly overlapped. From an overall perspective, the theoretical curve of the cumulative damage constitutive model has a good fit to the experimental curve under different impact pressures, and can accurately reflect the mechanical properties of the limestone specimen under cyclic impact.

[0136] S4. Use the cumulative damage constitutive model to analyze the cumulative damage of limestone under cyclic loading.

[0137] Specifically, in this embodiment, step S36 has verified the accuracy of the cumulative damage constitutive model provided in this embodiment. Therefore, the cumulative damage constitutive model can be directly used to calculate the stress of limestone under cyclic loading, thereby reflecting the cumulative damage evolution of limestone under cyclic loading, and providing reliable guidance for the cyclic blasting construction of underground engineering.

[0138] It should be noted that, in some cases, the actions described in the specification can be performed in a different order and still achieve the desired results. In this embodiment, the order of steps given is only to make the embodiment appear clearer and easier to explain, rather than to limit it.

[0139] In an alternative embodiment, see Fig.14 The present invention also provides a limestone cumulative damage analysis system under cyclic load, the limestone cumulative damage analysis system under cyclic load comprises: a data acquisition device 1, a data query device 2, a processor 3 and a storage 4, the storage 4 comprises a computer-readable storage medium, the computer-readable storage medium stores a computer program, the computer program comprises program instructions, and when the program instructions are executed by the processor 3, the processor 3 implements the limestone cumulative damage analysis method under cyclic load provided by the present invention.

[0140] Specifically, in this embodiment, the data acquisition device 1 is used to collect data generated by the cyclic impact test, and the data query device 2 is used to query the data generated by the cyclic impact test and the results of analyzing the cumulative damage of limestone under cyclic load using the cumulative damage constitutive model.

[0141] The system can stably execute the method provided by the present invention, can improve the efficiency of the cumulative damage analysis of limestone under cyclic loads, and can improve the practicability of the method of the present invention.

[0142] In summary, this method firstly conducts cyclic impact tests on limestone samples, and analyzes stress-strain curves and energy dissipation laws, providing data support for the analysis of cumulative damage of limestone under cyclic loads; secondly, this method obtains the damage variables and state equations of the damage body of limestone under cyclic loads, and at the same time regards the limestone sample as a collection composed of a large number of micro-element bodies to calculate the statistical damage variables, and then obtains the damage body constitutive equation in combination with the generalized Hooke's law, which provides a basis for constructing a cumulative damage constitutive model; finally, this method regards the limestone sample as a combined mechanical model composed of a generalized Kelvin body, a Bingham body and a damage body in parallel, and then constructs a cumulative damage constitutive model, which more accurately reflects the evolution trend of the cumulative damage of limestone under cyclic loads, which can not only improve the theoretical research on the mechanical properties of rocks under different external environments, but also provide reliable guidance for the cyclic blasting construction of underground engineering. In addition, this system can stably execute the method provided by the present invention, improve the efficiency of the cumulative damage analysis of limestone under cyclic loads, and improve the practicality of the method of the present invention.

[0143] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. These modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be included in the scope of the claims and specification of the present invention.

Claims

1. The cumulative damage analysis method of limestone under cyclic loading is characterized by: The steps include: preparing multiple limestone samples; Performing a cyclic impact test on the limestone sample, and performing stress-strain analysis and energy dissipation law analysis based on the experimental results; Constructing a cumulative damage constitutive model of the limestone sample based on the results of the stress-strain analysis and the energy dissipation law analysis; The cumulative damage constitutive model is used to analyze the cumulative damage of limestone under cyclic loading; The cyclic impact test on the limestone sample and the stress-strain analysis and energy dissipation law analysis according to the experimental results include the following steps: Set multiple impact air pressures; For each of the limestone samples, a cyclic impact test is performed on the sample using a fixed impact air pressure, and the incident wave, reflected wave and transmitted wave of the limestone sample are measured simultaneously; Calculating the average stress, average strain, reflected energy, transmitted energy and absorbed energy of the limestone sample according to the measurement results of the incident wave, the reflected wave and the transmitted wave; Using the average stress and the average strain to draw stress-strain curves under different impact gas pressures, as well as a variation trend diagram of the reflected energy, the transmitted energy, and the absorbed energy; The average stress and the average strain respectively satisfy the following relationship: ， ， Where s is the mean stress, is the average strain, A is the cross-sectional area of ​​the limestone sample, is the cross-sectional area of ​​the rod, E is the elastic modulus of the limestone sample, is the strain amplitude of the incident wave, is the strain amplitude of the reflected wave, is the strain amplitude of the transmitted wave, c is the propagation speed of the stress wave in the limestone sample, is the length of the limestone sample, is the strain caused by the incident wave, is the strain caused by the reflected wave, is the strain caused by the transmission wave, and t is the propagation time of the stress wave in the limestone sample; The reflected energy, the transmitted energy and the absorbed energy respectively satisfy the following relationships: ， ， ， in, is the reflected energy, is the cross-sectional area of ​​the rod, is the propagation speed of stress wave in the rod, is the initial elastic modulus of the limestone sample, t is the propagation time of the stress wave in the limestone sample, is the strain caused by the reflected wave, is the transmission energy, is the strain caused by the transmitted wave, is the absorbed energy, is the strain caused by the incident wave; The cumulative damage constitutive model of the limestone sample based on the results of the stress-strain analysis and the energy dissipation law analysis comprises the following steps: Determine damage variables according to energy data, and then obtain a state equation of the damage body, wherein the energy data includes the reflected energy, the transmitted energy, and the absorbed energy; The limestone sample is regarded as a collection of a large number of micro-elements, and the strength of the micro-elements obeys Weibull distribution, and then the statistical damage variable is calculated; Based on the statistical damage variables, a constitutive equation of a first damaged body is obtained according to the generalized Hooke's law, and then a constitutive equation of a second damaged body is obtained by combining the state equation of the damaged body; The limestone sample is regarded as a combined mechanical model consisting of a generalized Kelvin body, a Bingham body and a damage body in parallel; Constructing the cumulative damage constitutive model based on the constitutive equation of the generalized Kelvin body, the constitutive equation of the Bingham body and the constitutive equation of the damage body; Verifying the cumulative damage constitutive model according to the result of the stress-strain analysis; The damage variable and the state equation of the damaged body respectively satisfy the following relationship: ， ， in, is the damage variable, n is the number of cyclic impacts, , and is the coefficient, is the elastic modulus of the limestone sample after n cycles of impact, is the initial elastic modulus of the limestone sample; The statistical damage variables satisfy the following relationship: ， in, is the statistical damage variable, F is the distribution variable of the strength of the microelement, and m are the parameters of the Weibull distribution; The damaged body constitutive equation includes the first damaged body constitutive equation and the second damaged body constitutive equation, and the damaged body constitutive equation satisfies the following relationship: ， in, is the stress of the damaged body, is the initial elastic modulus of the limestone sample, is the statistical damage variable, is the damage variable, For The corresponding strain of the damaged body is, is the proportional relationship between the transverse strain and the longitudinal strain of the limestone sample, is the stress perpendicular to the stress direction of the damaged body; The cumulative damage constitutive model satisfies the following relationship: ， in, is the stress of the limestone sample, is the stress of the damaged body, is the stress of the generalized Kelvin body, is the stress of the Bingham body, , and is the elastic modulus of each mechanical element related to the generalized Kelvin body in the combined mechanical model, is the strain of the generalized Kelvin body at time t, for The derivative of is the viscosity coefficient of the generalized Kelvin body, , is the strain of the Bingham body at time t, for The derivative of is the viscosity coefficient of the Bingham body, is the critical stress value, is the elastic modulus of the mechanical elements related to the Bingham body in the combined mechanical model.

2. A limestone cumulative damage analysis system under cyclic loading, the limestone cumulative damage analysis system under cyclic loading comprising: A data acquisition device, a data query device, a processor and a storage device, wherein the storage device comprises a computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, wherein the computer program comprises program instructions, and when the program instructions are executed by the processor, the processor implements the method for analyzing the cumulative damage of limestone under cyclic load as claimed in claim 1.

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