Rock damage strength identification and instability discrimination method based on energy rate response difference

Abstract

The application discloses a rock damage strength identification and instability discrimination method based on energy rate response difference, obtains rock elastic strain energy and dissipation strain energy through axial stress-strain curve data, calculates rock sample elastic energy rate and dissipation energy rate data through differential calculation of energy parameters on strain, and determines the damage strength value of the rock sample through the peak value of the energy rate response difference curve of the elastic energy rate and the dissipation energy rate difference, so that the instability state of the rock material can be judged. The method does not need to monitor additional data, is simple to operate, has a unique identification point, is good in objectivity, and is relatively accurate and reliable in identification result.

Description

Technical Field

[0001] This invention relates to the field of rock mechanics and engineering technology, specifically to a method for identifying rock damage strength and determining instability based on energy rate response difference. Background Technology

[0002] With the increasing depletion of shallow resources, rock engineering projects in mining, transportation, and hydropower are continuously extending into deeper areas. Excavation and unloading lead to stress redistribution in deep rock masses, which can easily induce engineering disasters such as rock bursts and collapses, seriously threatening the safety of construction personnel and equipment. As the basic carrier of rock mass engineering, accurately identifying its damage intensity (σ) is crucial. cd Establishing reliable methods for identifying instability precursors is of significant theoretical and engineering value for assessing the stability of engineering rock masses and preventing deep dynamic disasters. Currently, scholars both domestically and internationally have proposed various methods for determining rock damage intensity, which can be summarized into the following categories:

[0003] Strain analysis method: such as identifying the various stages of crack propagation by crack volumetric strain or axial strain difference curve.

[0004] Acoustic emission method: using abrupt changes in acoustic emission signals (such as ring count, energy, b-value) to characterize the aggravation of internal damage in rocks.

[0005] Energy evolution method: Based on the energy-driven nature of rock failure, it finds characteristic inflection points by analyzing the ratio of input energy, elastic energy and dissipated energy (such as energy ratio and energy storage limit).

[0006] Loading-unloading response ratio method: The stability of rock mass is evaluated by comparing the rate of change of rock mass response parameters (such as strain and wave velocity) during loading and unloading stages.

[0007] While each of the above methods has its advantages, some limitations remain in practical applications. For example, traditional energy evolution methods often use cumulative energy or its ratio as a criterion. However, the response of cumulative energy to microscopic damage exhibits a certain lag, and the ratio form generates multiple characteristic values, leading to errors in the identification results. More importantly, the relative energy index obtained by the energy ratio method cannot assess the absolute amount of energy released after instability, and cannot reflect the severity of rock damage. While the loading / unloading response ratio method introduces the concept of response, its implementation usually requires complex loading / unloading paths, limiting its application in conventional experiments or field monitoring.

[0008] Therefore, there is an urgent need to develop a method for identifying rock instability that is physically clear, easy to operate, and can sensitively detect early signs of rock instability. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a precise, reliable, unique, and easy-to-operate method for identifying rock damage intensity and instability based on energy rate response difference.

[0010] Therefore, the present invention provides a method for identifying rock damage intensity and determining instability based on energy rate response difference, comprising the following steps:

[0011] Step S1. Obtain the rock sample to be monitored and process it into a standard cylindrical rock specimen;

[0012] Step S2. Perform a uniaxial compression test on the specimen, record the axial stress and axial strain during the test, and obtain stress-strain data; Step S3. Calculate the input strain energy, elastic strain energy, and dissipated strain energy of the specimen based on the stress-strain data; Step S4. Calculate the elastic energy rate and dissipated energy rate of the specimen, and obtain standardized elastic energy rate and dissipated energy rate data through a data smoothing method. The elastic energy rate and dissipated energy rate are the derivatives of the elastic strain energy and dissipated strain energy at the corresponding strain values, respectively; Step S5. Calculate the energy rate response difference based on the standardized elastic energy rate data and dissipated energy rate data. The energy rate response difference is the difference between the elastic energy rate and the dissipated energy rate at the same strain point; Step S6. The stress corresponding to the maximum value of the energy rate response difference data is the rock damage strength, which can be used to determine the instability state of the rock material; before the energy rate response difference curve reaches its peak, the rock is in a stable damage development stage; after reaching the peak, the rock enters the instability and failure stage.

[0013] Specifically, in step S1, the rock sample to be monitored is obtained and processed into a standard cylindrical rock sample with a diameter of 50 mm, a height of 100 mm, and a height-to-diameter ratio of 2:1.

[0014] Specifically, step S3 includes the following process:

[0015] The input strain energy of a rock specimen is the area under the stress-strain curve. Under a certain stress-strain condition, the input strain energy of the rock specimen is expressed as:

[0016] (1);

[0017] In the formula: u i The input strain energy is σ, where σ is the stress data and ε is the strain data;

[0018] The elastic strain energy of the rock sample is expressed as:

[0019] (2);

[0020] In the formula: u e For elastic strain energy, εe The data represents elastic strain, where E is the elastic modulus.

[0021] The dissipated strain energy of the rock sample is expressed as:

[0022] (3);

[0023] In the formula: u d This is to dissipate strain energy.

[0024] Specifically, step S4 includes the following process:

[0025] The elastic energy rate and dissipated energy rate of a rock specimen are the derivatives of its elastic strain energy and dissipated strain energy at the corresponding strain values. Under a certain stress-strain condition, the elastic energy rate of the rock specimen is expressed as:

[0026] (4);

[0027] Where: G e Elastic energy level;

[0028] The energy dissipation rate of the rock sample is expressed as:

[0029] (5);

[0030] Where: G d The rate of energy dissipation;

[0031] Then, a data smoothing method was used to obtain standardized elastic energy rate and dissipation energy rate data.

[0032] Specifically, step S6 includes the following process:

[0033] The energy rate response difference curve and the stress-strain curve are placed in the same coordinate system, with the horizontal axis representing the strain value of the rock sample, one vertical axis representing the energy rate response difference value of the rock sample, and the other vertical axis representing the stress value of the rock sample.

[0034] The stress value corresponding to the peak point of the energy rate response difference curve is the damage strength value of the rock sample, and the corresponding strain is the critical strain value. Based on the different stages before and after the peak of the energy rate response difference curve, the stable damage development stage and the unstable failure stage of the rock are divided, thereby realizing the quantitative judgment of the rock instability state.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] This invention abandons the traditional method's reliance on accumulated energy and instead employs the differential energy rate with respect to deformation. This change makes the index more sensitive to the propagation of microcracks within the rock, enabling it to detect the critical point of material transition from stable damage to unstable failure earlier and more accurately.

[0037] The energy rate response difference index proposed in this invention is essentially the instantaneous difference between the rock's ability to store elastic energy and its ability to consume energy. The evolution curve of this index shows a single and significant peak before the rock becomes unstable, overcoming the defect of the traditional energy ratio method that may produce multiple feature points, realizing the unique identification of damage intensity, and effectively avoiding interference from human subjective factors.

[0038] The peak value (absolute value) of the energy rate response difference reflects the gap between the energy release potential and energy dissipation capacity of a rock at the critical moment of instability. This absolute difference can, to some extent, characterize the likelihood and intensity of subsequent severe damage to the rock (such as rockburst), making up for the inadequacy of traditional relative indicators (such as energy ratio) in assessing the degree of damage.

[0039] The method of this invention only requires conventional uniaxial compression test stress-strain data, without the need for complex loading and unloading paths or additional acoustic emission monitoring equipment. The calculation process is clear and easy to program for automated processing, and it has broad prospects for promotion in both laboratory research and field engineering applications. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0042] Figure 2 A schematic diagram illustrating the calculation principle of input strain energy, elastic strain energy, and dissipated strain energy for rock samples in this invention;

[0043] Figure 3 The stress-strain and energy evolution curves for the granite case of this invention are shown below.

[0044] Figure 4 The stress-strain and energy evolution curves for the sandstone case of this invention are shown below.

[0045] Figure 5 The energy rate evolution curve for the granite case of this invention is shown below;

[0046] Figure 6 This is the energy rate evolution curve of the sandstone case of this invention;

[0047] Figure 7 The energy rate response difference curve for the granite case of this invention;

[0048] Figure 8 This is the energy rate response difference curve for the sandstone case of this invention;

[0049] Figure 9 The acoustic emission verification curve for the granite example of this invention;

[0050] Figure 10 This is the acoustic emission verification curve for the sandstone case of this invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, a method for identifying rock damage intensity and determining instability based on energy rate response difference includes the following steps:

[0053] S1. Obtain the rock sample to be monitored and process it into a standard cylindrical rock specimen with a diameter of 50 mm, a height of 100 mm, and a height-to-diameter ratio of 2:1;

[0054] S2. Perform a uniaxial compression test on the standard rock specimen obtained in step S1 and record the axial stress and axial strain values ​​during the test to obtain the stress-strain data of the rock specimen.

[0055] S3. Calculate the input strain energy, elastic strain energy, and dissipated strain energy of the rock sample based on the stress-strain data obtained in step S2. This includes the following steps:

[0056] like Figure 2 As shown, the input strain energy of a rock sample is the area under the stress-strain curve. Under a certain stress-strain condition, the input strain energy of the rock sample is expressed as:

[0057] (1);

[0058] In the formula: u i The input strain energy is σ, where σ is the stress data and ε is the strain data;

[0059] The elastic strain energy of the rock sample is expressed as:

[0060] (2);

[0061] In the formula: u e For elastic strain energy, ε e The data represents elastic strain, where E is the elastic modulus.

[0062] The dissipated strain energy of the rock sample is expressed as:

[0063] (3)

[0064] In the formula: u d To dissipate strain energy;

[0065] S4. Based on the elastic strain energy data and dissipated strain energy data of the rock sample obtained in step S3, calculate the elastic energy rate and dissipated energy rate data of the rock sample, and obtain standardized energy rate data. This includes the following steps:

[0066] The elastic energy rate and dissipated energy rate of a rock specimen are the derivatives of its elastic strain energy and dissipated strain energy at the corresponding strain values. Under a certain stress-strain condition, the elastic energy rate of the rock specimen is expressed as:

[0067] (4);

[0068] Where: G e Elastic energy level;

[0069] The energy dissipation rate of the rock sample is expressed as:

[0070] (5);

[0071] Where: G d The rate of energy dissipation;

[0072] Since the elastic energy rate and dissipated energy rate obtained in step S4 above are quite volatile, a data smoothing method is used to obtain standardized elastic energy rate and dissipated energy rate data.

[0073] S5. Calculate the energy rate response difference (ERRD) by subtracting the standardized elastic energy rate and dissipated energy rate data obtained in S4. The energy rate response difference is the difference between the elastic energy rate and the dissipated energy rate at the same strain point.

[0074] (6);

[0075] S6. Analyze the energy rate response difference data obtained in S5. The stress corresponding to the maximum value of the energy rate response difference data is the rock damage strength, which can be used to determine the instability state of the rock material. Specifically, before the energy rate response difference curve reaches its peak, the rock is in a stable damage development stage; after reaching the peak, the rock enters the instability and failure stage. The specific steps include the following:

[0076] The energy rate response difference curve and the stress-strain curve are placed in the same coordinate system, with the horizontal axis representing the strain value of the rock sample, one vertical axis representing the energy rate response difference value of the rock sample, and the other vertical axis representing the stress value of the rock sample.

[0077] The stress-strain value corresponding to the peak of the energy rate response difference curve is the critical instability value of the rock sample, where stress is determined as the damage strength value of the rock sample; thus, the stable and unstable states of the rock sample can be determined based on different stages before and after the peak of the energy rate response difference curve.

[0078] The rock damage strength identification and instability judgment method based on the energy rate response difference index provided by this invention only requires a uniaxial compression test on the rock sample. The elastic strain energy and dissipated strain energy of the rock are obtained through the axial stress-strain curve data. The elastic energy rate and dissipated energy rate data of the rock sample are calculated by calculating the differential of the energy parameters on the strain. The damage strength value of the rock sample is determined by the difference between the elastic energy rate and the dissipated energy rate, i.e., the peak value of the energy rate response difference curve. Based on this, the instability state of the rock material can be judged.

[0079] The method of this invention does not require monitoring of additional data, has a clear calculation method, a unique identification point, and can be completed entirely by computer, avoiding the influence of human subjective factors. It can be widely applied to the study of rock mechanical properties in engineering fields such as mining, hydropower, and transportation.

[0080] The method of the present invention will be further described below with reference to two embodiments:

[0081] Taking the rock damage strength identification and instability discrimination method based on the energy rate response difference index for granite and sandstone samples as an example, the method of the present invention is described in detail.

[0082] S1. The granite and sandstone samples to be tested are processed into standard granite cylindrical specimens and sandstone cylindrical specimens, with a diameter of 50 mm, a height of 100 mm, and a height-to-diameter ratio of 2:1;

[0083] S2. The granite and sandstone specimens were subjected to uniaxial compression tests on a rock mechanics testing machine, with a load control mode of 2 kN / s. The axial strain and axial stress values ​​during the test were measured and recorded to obtain the stress-strain data of the granite and sandstone specimens.

[0084] S3. Based on the stress-strain data obtained in step S2, use... Figure 2 Using the energy calculation methods of formulas (1) to (3), the input strain energy, elastic strain energy, and dissipated strain energy data of granite and sandstone samples were calculated respectively, and stress-strain diagrams and energy evolution diagrams of granite and sandstone samples were plotted, as follows: Figure 3 , Figure 4 As shown;

[0085] S4. Based on the elastic strain energy data and dissipated strain energy data of the granite and sandstone samples obtained in step S3, the elastic energy rate and dissipated energy rate data of the granite and sandstone samples are calculated using the energy rate calculation methods of formulas (4) and (5), respectively. Since the integral data of elastic strain energy and dissipated strain energy with respect to strain are relatively volatile, a data smoothing method is used to obtain standardized elastic energy rate and dissipated energy rate curves, such as... Figure 5 , Figure 6 As shown;

[0086] S5. Based on the standardized elastic energy rate and dissipated energy rate data obtained in step S4, calculate the difference using the energy rate response difference calculation method in formula (6) for granite and sandstone samples respectively:

[0087] S6. Analyze the energy rate response difference data obtained in step S5. Place the energy rate response difference curves and stress-strain curves of the granite and sandstone samples on the same coordinate system. The horizontal axis represents the strain value of the rock sample, one vertical axis represents the energy rate response difference value of the rock sample, and the other vertical axis represents the stress value of the rock sample. Figure 7 , Figure 8 As shown.

[0088] Depend on Figure 7 , Figure 8 It can be seen that the peak value of the energy rate response difference curve for the granite sample corresponds to a stress of 96.17 MPa and a strain of 0.0062, which is the critical instability value for the granite sample. Before this value, the granite sample is in a stable state; after this value, the granite sample enters an unstable state. The 96.17 MPa value is determined as the damage strength of the granite sample. Similarly, the peak value of the energy rate response difference curve for the sandstone sample corresponds to a stress of 67.78 MPa and a strain of 0.0060, which is the critical instability value for the sandstone sample. Before this value, the sandstone sample is in a stable state; after this value, the sandstone sample enters an unstable state. The 67.78 MPa value is determined as the damage strength of the sandstone sample.

[0089] Reliability verification: The reliability of the method of the present invention is demonstrated by calculating the acoustic emission count during uniaxial compression based on the embodiments of granite and sandstone samples.

[0090] By arranging acoustic emission monitoring equipment on the specimen, acoustic emission information is recorded synchronously, and the microcrack activity inside the specimen is characterized by the cumulative ringing count of acoustic emission. For example... Figure 9 The acoustic emission verification curve of the pattern shown in Figure 10, combined with... Figure 9 As can be seen from Figure 10, the rock damage intensity identified by the method of the present invention corresponds to the moment of rapid increase in acoustic emission count. At this moment, a large acoustic emission count value is generated first, indicating that the microcrack activity inside the rock is active. The crack activity captured by acoustic emission verifies that the rock sample gradually transforms into an unstable state, thus verifying the reliability of the method of the present invention.

[0091] In summary, the rock damage strength identification and instability judgment method based on the energy rate response difference index provided by this invention only requires uniaxial compression testing of the rock sample. The strain energy of the rock is calculated using axial stress-strain curve data, thereby obtaining the energy rate. The damage strength of the rock sample is then identified using the energy rate response difference index, which can be used to determine the instability state of the rock material. The reliability of this method is verified by simultaneously detecting microcrack activity using acoustic emission equipment. This method has the advantages of clear principles, simple operation, unique identification points, and good objectivity, making it worthy of widespread application.

[0092] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying rock damage intensity and determining instability based on energy rate response difference, characterized in that, Includes the following steps: Step S1. Obtain the rock sample to be monitored and process it into a standard cylindrical rock specimen; Step S2. Perform a uniaxial compression test on the specimen, record the axial stress and axial strain during the test, and obtain stress-strain data; Step S3. Based on the stress-strain data, calculate the input strain energy, elastic strain energy, and dissipated strain energy of the specimen; Step S4. Calculate the elastic energy rate and dissipated energy rate of the sample, and obtain standardized elastic energy rate and dissipated energy rate data through a data smoothing method. The elastic energy rate and dissipated energy rate are the derivatives of elastic strain energy and dissipated strain energy at the corresponding strain values, respectively. Step S5. Calculate the energy rate response difference based on the standardized elastic energy rate data and dissipated energy rate data. The energy rate response difference is the difference between the elastic energy rate and the dissipated energy rate at the same strain point. Step S6. The stress corresponding to the maximum value of the energy rate response difference data is the rock damage strength, which is used to determine the instability state of the rock material. Before the energy rate response difference curve reaches its peak, the rock is in a stable damage development stage; after reaching the peak, the rock enters the instability and failure stage.

2. The method for identifying rock damage intensity and determining instability according to claim 1, characterized in that: In step S1, the rock sample to be monitored is obtained and processed into a standard cylindrical rock sample with a diameter of 50 mm, a height of 100 mm, and a height-to-diameter ratio of 2:

1.

3. The method for identifying rock damage intensity and determining instability according to claim 1, characterized in that, Step S3 specifically includes the following process: The input strain energy of a rock specimen is the area under the stress-strain curve. Under a certain stress-strain condition, the input strain energy of the rock specimen is expressed as: (1)； In the formula: u i The input strain energy is σ, where σ is the stress data and ε is the strain data; The elastic strain energy of the rock sample is expressed as: (2)； In the formula: u e For elastic strain energy, ε e The data represents elastic strain, where E is the elastic modulus. The dissipated strain energy of the rock sample is expressed as: (3)； In the formula: u d This is to dissipate strain energy.

4. The method for identifying rock damage intensity and determining instability according to claim 1, characterized in that, Step S4 specifically includes the following process: The elastic energy rate and dissipated energy rate of a rock specimen are the derivatives of its elastic strain energy and dissipated strain energy at the corresponding strain values. Under a certain stress-strain condition, the elastic energy rate of the rock specimen is expressed as: (4)； Where: G e It is the elastic energy level; The energy dissipation rate of the rock sample is expressed as: (5)； Where: G d The rate of energy dissipation; Then, a data smoothing method was used to obtain standardized elastic energy rate and dissipation energy rate data.

5. The method for identifying rock damage intensity and determining instability according to claim 1, characterized in that, Step S6 specifically includes the following process: The energy rate response difference curve and the stress-strain curve are placed in the same coordinate system, with the horizontal axis representing the strain value of the rock sample, one vertical axis representing the energy rate response difference value of the rock sample, and the other vertical axis representing the stress value of the rock sample. The stress value corresponding to the peak point of the energy rate response difference curve is the damage strength value of the rock sample, and the corresponding strain is the critical strain value. Based on the different stages before and after the peak of the energy rate response difference curve, the stable damage development stage and the unstable failure stage of the rock are divided, thereby realizing the quantitative judgment of the rock instability state.

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