A rock time-dependent damage evaluation method and system under long-term combined load based on time delay energy

Abstract

The application discloses a kind of long-term combined load under rock time-dependent damage evaluation method and system based on time lag energy, it is related to rock mechanics, underground engineering long-term stability evaluation and mine disaster early warning technical field.The method obtains the stress, strain and time data of rock under the combined action of constant load and cyclic disturbance load, identifies instantaneous strain, time-dependent cumulative strain and hysteresis elastic recovery strain;Accordingly, input energy density is decomposed into transient energy density and time lag energy density, and further decomposed into corresponding elastic energy density and dissipation energy density;Based on strength damage coefficient, time lag elastic energy density distribution coefficient and time lag damage activity, a joint evaluation index is constructed, and the damage stage of rock is determined according to the change trend of each index.The application can reflect the cumulative damage, energy storage attenuation and time lag dissipation enhancement characteristics of rock under combined load, and provide quantitative basis for long-term stability evaluation of deep rock mass.

Description

Technical Field

[0001] This invention relates to the fields of rock mechanics, long-term stability evaluation of underground engineering and early warning of mine disasters, and in particular to a method and system for evaluating the time-dependent damage of rocks under long-term combined loads based on time-delay energy. Background Technology

[0002] In deep mining, underground caverns, tunnel surrounding rock, slope rock masses, and underground energy storage projects, rock masses are subjected to complex stress environments for extended periods. On one hand, the rock mass bears approximately constant loads such as in-situ stress, overburden pressure, or tectonic stress; on the other hand, it is affected by periodic disturbance loads such as mining disturbances, mechanical vibrations, and periodic roof fractures. Therefore, engineering rock masses often exhibit a combined load state under the combined or alternating action of long-term constant loads and cyclic disturbance loads.

[0003] Existing methods for evaluating rock energy damage typically rely on input energy, elastic energy, and dissipated energy during loading to determine damage, reflecting the energy storage and dissipation characteristics of rocks under instantaneous loading conditions. However, under long-term combined loading, rock deformation is not solely caused by instantaneous loading; it also includes time-dependent deformation accumulated over time during load maintenance or cyclic disturbance, as well as viscoelastic recovery that occurs after unloading. If conventional energy methods are still used for direct damage evaluation, it is easy to mix instantaneous deformation energy with time-dependent deformation energy, making it difficult to distinguish between recoverable time-dependent energy storage and unrecoverable time-dependent dissipation, and also difficult to determine whether the rock has transitioned from a stable energy storage state to a time-dependent damage activation state.

[0004] To address the aforementioned issues, this paper proposes a method and system for evaluating the aging damage of rocks under long-term combined loads based on time-delay energy. This method incorporates strain aging accumulation and post-unloading elastic recovery into the energy calculation process, thereby compensating for the shortcomings of conventional energy damage evaluation that neglect the effects of aging. Summary of the Invention

[0005] In view of this, the present invention provides a method and system for evaluating the time-dependent damage of rocks under long-term combined loads based on time-delay energy. It is applicable to the energy evolution analysis, time-dependent damage identification and long-term stability evaluation of rocks under long-term constant loads, cyclic disturbance loads and their alternating combined loads. By decomposing time-delay energy and jointly evaluating multiple indicators, it solves the technical problems of conventional energy methods in distinguishing between transient damage and time-dependent damage and in identifying the damage activation transformation process.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy includes the following steps: S1: Data acquisition steps: Collect stress, strain, and time data of the rock to be evaluated under long-term combined load; S2: Strain identification step: Identify the instantaneous strain, time-accumulated strain, and viscoelastic recovery strain of the rock from the stress, strain, and time data collected in S1; S3: Energy decomposition calculation steps: Based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain, the input energy density of the rock during the loading process is decomposed into total transient energy density and total time-delay energy density; The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. S4: Calculation steps of the index: Calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density; S5: Damage evaluation steps: Integrate the strength damage coefficient, time-delay energy distribution index, and the changing trend of time-delay damage activity to comprehensively determine the age-related damage stage of the rock.

[0007] Optionally, the stress path of the long-term combined load in S1 includes a load-holding stage after loading to a preset stress level, an unloading and recovery stage, a cyclic disturbance stage, and a second unloading and recovery stage after cyclic disturbance, which is used to induce and record the time-dependent deformation and viscoelastic recovery process of the rock under long-term combined load. Long-term combined loads are constant loads, cyclic disturbance loads, or an alternating combination of the two.

[0008] The above methods can optionally include: instantaneous strain in S2: strain caused by stress change at the moment of loading or unloading; time-accumulated strain: strain accumulated over time or cycle during the constant load holding stage or the continuous cyclic disturbance stage; and viscoelastic recovery strain: reversible time-effect strain of rock recovering over time after unloading.

[0009] Optionally, in the above method, the input energy density during the rock loading process in S3 is the total input energy density of the rock. Decomposed into total transient energy density and total time delay energy density ,satisfy: ; Among them, the total transient energy density The total time-delay energy density corresponds to the energy input during the instantaneous loading process. This corresponds to the energy input generated by the accumulated strain over time under long-term load. Total transient energy density Further decomposed into transient elastic energy density and transient dissipation energy density ,satisfy:

[0010] Total time-delay energy density Further decomposed into time-delay elastic energy density and time-delay dissipation energy density ,satisfy:

[0011] In the formula, For transient elastic energy density, For transient dissipation energy density, The time-delayed elastic energy density, It represents the time-delayed dissipation energy density.

[0012] The above method, optionally, the total transient energy density and transient elastic energy density Calculate according to the following formulas: ; ; in, , and These are the first, second, and third principal stresses, respectively. , and These represent the instantaneous strain generated in the corresponding principal stress direction; , and These represent the instantaneous elastic strain generated in the corresponding principal stress direction; and the transient dissipated energy density. pass calculate; Total time delay energy density at time step and time-delay elastic energy density Calculate according to the following formulas: ; ; in, , and These are the corresponding principal stress directions at time [time]. The resulting cumulative strain over time, , and These are the corresponding principal stress directions at time [time]. The corresponding time-dependent elastic strain is determined by the hysteresis elastic recovery strain after unloading; the time-delayed dissipation energy density. pass calculate.

[0013] Optionally, in the above method, the time-delay energy allocation index in S4 includes the time-delay elastic energy allocation coefficient. and time-delay dissipation energy distribution coefficient ,in: ; ; in, and The first m Time-delayed elastic energy density and time-delayed dissipated energy density during alternating loading processes; Time-delay damage activity Calculate using the following formula: ; in, For the first m Time-delayed energy density during alternating loading processes The corresponding transient dissipation energy density; time-delay damage activity. It is proportional to the contribution of time-related damage to current dissipation damage.

[0014] The above method, optionally, uses the strength damage index in S5. Calculate using the following formula: ; in, and The first m Transient energy dissipation and time-delayed energy dissipation during alternating loading processes This refers to the cumulative dissipated energy during rock fracturing.

[0015] The above method may include, optionally, the S6 damage stage determination rule: (1) rise, Reduce: During the compaction adjustment stage, the rock mainly focuses on recoverable time-dependent energy storage and structural pore compaction; (2) High level stability Low value and stable: The rock mass is in a stable damage stage and its load-bearing structure is stable. (3) Slight decline and Slight increase: Damage development stage, micro-damage continues to accumulate; (4) Significant decline and Synchronous increase: During the damage activation phase, time-dependent irreversible dissipation is enhanced; (5) Continued decline and A sustained and significant increase: the stage of accelerated deterioration, with rock mass fissures connecting and nearing instability.

[0016] A rock aging damage evaluation system based on time-delay energy under long-term combined load, used to implement the rock aging damage evaluation method based on time-delay energy under long-term combined load as described above, comprising a data acquisition module, a strain identification module, an energy decomposition calculation module, an index calculation module, and a damage evaluation module connected in sequence. The data acquisition module is used to collect stress, strain, and time data of the rock to be evaluated under long-term combined loads. The strain identification module is used to identify the instantaneous strain, aging cumulative strain, and viscoelastic recovery strain of the rock from the collected stress, strain, and time data. The energy decomposition calculation module is used to decompose the input energy density of rock during loading into total transient energy density and total time-delay energy density based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain. The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. The index calculation module is used to calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and to calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density. The damage evaluation module is used to integrate the changing trends of strength damage coefficient, time-delay energy distribution index, and time-delay damage activity to comprehensively determine the stage of rock aging damage.

[0017] As can be seen from the above technical solution, compared with the prior art, the present invention provides a method and system for evaluating the time-dependent damage of rocks under long-term combined loads based on time-delay energy, which has the following beneficial effects: (1) Decomposing the energy of rocks under long-term combined loads into transient energy and time-delay energy can solve the problem of neglecting the time effect in traditional energy damage assessment; (2) By using the hysteretic elastic recovery strain after unloading to calculate the time-delayed elastic energy, the recoverable time-delayed energy storage capacity of rocks under long-term load can be identified. (3) By evaluating the contribution of irreversible time-delayed deformation to damage development through time-delayed energy dissipation and time-delayed damage activity, the process of rock transformation from stable energy storage to damage activation can be identified. (4) Combine the strength damage coefficient, time-delay elastic energy distribution coefficient, time-delay dissipation energy distribution coefficient and time-delay damage activity to avoid the one-sidedness of evaluation by a single index; (5) Applicable to the evaluation of time-dependent damage of rocks under long-term combined load environments such as coal mines, metal mines, underground caverns, tunnel surrounding rock and slope rock masses. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a flowchart of a method for evaluating the aging damage of rocks under long-term combined loads based on time-delay energy, as disclosed in this invention. Figure 2 This is a structural block diagram of a rock aging damage evaluation system based on long-term combined loads using time-delay energy, as disclosed in this invention. Figure 3 This is a schematic diagram of a long-term combined load stress path disclosed in this invention; Figure 4 This is a schematic diagram of the decomposition of transient energy and time-delay energy of rock disclosed in this invention; Figure 5 This is a flowchart of the rock aging damage evaluation based on time-delay energy disclosed in this invention. Detailed Implementation

[0020] 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.

[0021] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0022] See Figure 1 and Figure 5 As shown, this invention discloses a method for evaluating the time-dependent damage of rocks under long-term combined loading based on time-delay energy, comprising the following steps: S1: Data acquisition steps: Collect stress, strain, and time data of the rock to be evaluated under long-term combined load; S2: Strain identification step: Identify the instantaneous strain, time-accumulated strain, and viscoelastic recovery strain of the rock from the stress, strain, and time data collected in S1; S3: Energy decomposition calculation steps: Based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain, the input energy density of the rock during the loading process is decomposed into total transient energy density and total time-delay energy density; The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. S4: Calculation steps of the index: Calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density; S5: Damage evaluation steps: Integrate the strength damage coefficient, time-delay energy distribution index, and the changing trend of time-delay damage activity to comprehensively determine the age-related damage stage of the rock.

[0023] Furthermore, the stress path of the long-term combined load in S1 includes a load-holding stage after loading to the preset stress level, an unloading and recovery stage, a cyclic disturbance stage, and a second unloading and recovery stage after cyclic disturbance, used to induce and record the aging deformation and viscoelastic recovery process of the rock under long-term combined load; for details, see [link to documentation]. Figure 3 The diagram shown is a schematic diagram of a long-term combined load stress path.

[0024] Long-term combined loads are constant loads, cyclic disturbance loads, or an alternating combination of the two.

[0025] Furthermore, in S2, instantaneous strain is the strain caused by stress changes at the moment of loading or unloading; time-accumulated strain is the strain accumulated over time or cyclic process during the constant load holding stage or the continuous cyclic disturbance stage; and viscoelastic recovery strain is the reversible time-effect strain of the rock after unloading.

[0026] Furthermore, the input energy density during the rock loading process in S3 is the total input energy density of the rock. The total input energy density of the rock... Decomposed into total transient energy density and total time delay energy density ,satisfy: ; Among them, the total transient energy density The total time-delay energy density corresponds to the energy input during the instantaneous loading process. This corresponds to the energy input generated by the accumulated strain over time under long-term load. Total transient energy density Further decomposed into transient elastic energy density and transient dissipation energy density ,satisfy:

[0027] Total time-delay energy density Further decomposed into time-delay elastic energy density and time-delay dissipation energy density ,satisfy:

[0028] In the formula, For transient elastic energy density, For transient dissipation energy density, The time-delayed elastic energy density, This refers to the time-delayed dissipative energy density. Time-delayed elastic energy reflects the energy storage capacity corresponding to recoverable age-related deformation under long-term loading; time-delayed dissipative energy reflects dissipation behaviors such as irreversible viscoplastic deformation, crack propagation, particle slip, and structural degradation under long-term loading. For details, see [link to relevant documentation]. Figure 4 The diagram shown is a schematic diagram of the decomposition of transient energy and time-delay energy of rock disclosed in this invention.

[0029] Furthermore, the total transient energy density and transient elastic energy density Calculate according to the following formulas: ; ; in, , and These are the first, second, and third principal stresses, respectively. , and These represent the instantaneous strain generated in the corresponding principal stress direction; , and These represent the instantaneous elastic strain generated in the corresponding principal stress direction; and the transient dissipated energy density. pass calculate; Total time delay energy density at time step and time-delay elastic energy density Calculate according to the following formulas: ; ; in, , and These are the corresponding principal stress directions at time [time]. The resulting cumulative strain over time, , and These are the corresponding principal stress directions at time [time]. The corresponding time-dependent elastic strain is determined by the hysteresis elastic recovery strain after unloading; the time-delayed dissipation energy density. pass calculate.

[0030] When the long-term combined load includes cyclic disturbance load, the number of cycles in the cyclic disturbance load process is equivalent to the total cycle time, the cumulative strain generated during the cycle is taken as the time-dependent cumulative strain, and the strain recovery corresponding to the initial stage of cyclic loading and the end stage of cyclic unloading is taken as the instantaneous strain recovery. The transient energy density and time-delay energy density of the cyclic disturbance stage are calculated according to the above formula.

[0031] To avoid the problem that a single dissipation energy index cannot distinguish between instantaneous damage and time-dependent damage, this invention constructs the following evaluation index: time-delay elastic energy distribution coefficient. Time-delay dissipation energy distribution coefficient Time-delay damage activity Strength damage index .

[0032] Furthermore, the time-delay energy allocation index in S4 includes the time-delay elastic energy allocation coefficient. and time-delay dissipation energy distribution coefficient ,in: ; ; in, and The first m Time-delayed elastic energy density and time-delayed dissipated energy density during alternating loading processes; Time-delay damage activity Calculate using the following formula: ; in, For the first m Time-delayed energy density during alternating loading processes The corresponding transient dissipation energy density; time-delay damage activity. It is proportional to the contribution of time-related damage to current dissipation damage.

[0033] Furthermore, the strength damage index in S5 Calculate using the following formula: ; in, and The first m Transient energy dissipation and time-delayed energy dissipation during alternating loading processes The cumulative dissipated energy during rock fracturing; when When it is difficult to obtain directly, the cumulative dissipated energy after the last combined load is used as the benchmark to calculate the relative damage index, and the relative damage index is calibrated according to the change in compressive strength before and after loading.

[0034] Furthermore, S6 according to , , and The numerical values ​​and trends of these values ​​are used to determine the age-related damage state of the rock. The specific rules for determining the damage stage are as follows: (1) rise, Reduce: During the compaction adjustment stage, the rock mainly focuses on recoverable time-dependent energy storage and structural pore compaction; (2) High level stability Low value and stable: The rock mass is in a stable damage stage and its load-bearing structure is stable. (3) Slight decline and Slight increase: Damage development stage, micro-damage continues to accumulate; (4) Significant decline and Synchronous increase: During the damage activation phase, time-dependent irreversible dissipation is enhanced; (5) Continued decline and A sustained and significant increase: the stage of accelerated deterioration, with rock mass fissures connecting and nearing instability.

[0035] Furthermore, in S6, when When Am increases and Am decreases, it indicates that the rock primarily stores energy through pore compaction, contact surface adjustment, and recoverable time-dependent energy storage; when Stable at a high level and When the temperature is low, it indicates that the internal structure of the rock tends to be relatively stable; when... Started to fall and , When the value increases, it indicates that the irreversible time-dependent dissipation induced by long-term combined loads is enhanced, and the rock enters the damage activation stage; when Continued decline and When the value continues to rise, it indicates that the rock's energy storage capacity is declining over time, microcracks are expanding and viscoplastic deformation is intensifying, and the rock is entering a stage of accelerated deterioration.

[0036] and Figure 1 and Figure 5 Corresponding to the method shown, this invention also discloses a rock aging damage evaluation system based on time-delay energy under long-term combined loading, used to achieve... Figure 1 and Figure 5 The method shown is illustrated in the structural diagram. Figure 2 As shown, it includes a data acquisition module, a strain identification module, an energy decomposition calculation module, an index calculation module, and a damage assessment module connected in sequence. The data acquisition module is used to collect stress, strain, and time data of the rock to be evaluated under long-term combined loads. The strain identification module is used to identify the instantaneous strain, aging cumulative strain, and viscoelastic recovery strain of the rock from the collected stress, strain, and time data. The energy decomposition calculation module is used to decompose the input energy density of rock during loading into total transient energy density and total time-delay energy density based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain. The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. The index calculation module is used to calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and to calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density. The damage evaluation module is used to integrate the changing trends of strength damage coefficient, time-delay energy distribution index, and time-delay damage activity to comprehensively determine the stage of rock aging damage.

[0037] In one specific embodiment, the rock to be evaluated is first subjected to basic mechanical tests to obtain its initial compressive strength, dilatational stress, elastic modulus, and Poisson's ratio. Then, a long-term combined load test path is designed: the rock is loaded to a preset stress level and held under load, with the accumulated strain recorded during the holding period; after unloading to zero, the viscoelastic recovery strain is recorded; then, the rock is reloaded to the preset stress level and cyclic perturbation loads are applied, with the accumulated strain recorded during the cycle; after the cycle ends, the rock is unloaded again and the recovery deformation is recorded. This process can be repeated several times as needed for engineering projects.

[0038] After data acquisition, the stress-strain-time data for each stage are processed in segments. The strain at the moment of loading or unloading is used to calculate the transient energy, the cumulative strain during the load holding or cyclic disturbance period is used to calculate the total time-delay energy, and the viscoelastic recovery strain after unloading is used to calculate the time-delay elastic energy. The difference between the total time-delay energy and the time-delay elastic energy is the time-delay dissipation energy.

[0039] Then, calculate the values ​​for each stage separately. , , and When discovered At a high level and When the value is low, it indicates that the rock mainly stores recoverable time-dependent energy and is in a relatively stable state; when Decline and and When the value increases, it indicates that the irreversible aging dissipation under long-term combined loads is enhanced, and the microcracks inside the rock are expanded, the contact surface slips and viscoplastic deformations are reactivated; when the above trends continue to strengthen, the output evaluation results indicate that the rock has entered the damage activation or accelerated deterioration stage.

[0040] Therefore, this invention can establish a rock aging damage evaluation method with time-delay energy decomposition and time-delay damage index as the core, addressing the problem that conventional energy methods do not consider the effect of aging under long-term combined load stress paths.

[0041] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy, characterized in that, Includes the following steps: S1: Data acquisition steps: Collect stress, strain, and time data of the rock to be evaluated under long-term combined load; S2: Strain identification step: Identify the instantaneous strain, time-accumulated strain, and viscoelastic recovery strain of the rock from the stress, strain, and time data collected in S1; S3: Energy decomposition calculation steps: Based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain, the input energy density of the rock during the loading process is decomposed into total transient energy density and total time-delay energy density; The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. S4: Calculation steps of the index: Calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density; S5: Damage evaluation steps: Integrate the strength damage coefficient, time-delay energy distribution index, and the changing trend of time-delay damage activity to comprehensively determine the age-related damage stage of the rock.

2. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 1, characterized in that, The stress path of the long-term combined load in S1 includes the load holding stage after loading to the preset stress level, the unloading and recovery stage, the cyclic disturbance stage, and the unloading and recovery stage after the cyclic disturbance, which are used to induce and record the time deformation and viscoelastic recovery process of the rock under the long-term combined load. Long-term combined loads are constant loads, cyclic disturbance loads, or an alternating combination of the two.

3. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 2, characterized in that, Instantaneous strain in S2: strain caused by stress change at the moment of loading or unloading; time-accumulated strain: strain accumulated over time or cycle during the constant load holding stage or the continuous cyclic disturbance stage; viscoelastic recovery strain: reversible time-dependent strain of rock after unloading.

4. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy as described in claim 1, characterized in that, The input energy density of the rock during the loading process in S3 is the total input energy density of the rock. Decomposed into total transient energy density and total time delay energy density ,satisfy: ； Among them, the total transient energy density The total time-delay energy density corresponds to the energy input during the instantaneous loading process. This corresponds to the energy input generated by the accumulated strain over time under long-term load. Total transient energy density Further decomposed into transient elastic energy density and transient dissipation energy density ,satisfy: Total time-delay energy density Further decomposed into time-delay elastic energy density and time-delay dissipation energy density ,satisfy: In the formula, For transient elastic energy density, For transient dissipation energy density, The time-delayed elastic energy density, It represents the time-delayed dissipation energy density.

5. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 4, characterized in that, Total transient energy density and transient elastic energy density Calculate according to the following formulas: ； ； in, , and These are the first, second, and third principal stresses, respectively. , and These represent the instantaneous strain generated in the corresponding principal stress direction; , and These represent the instantaneous elastic strain generated in the corresponding principal stress direction; and the transient dissipated energy density. pass calculate; Total time delay energy density at time step and time-delay elastic energy density Calculate according to the following formulas: ； ； in, , and These are the corresponding principal stress directions at time [time]. The resulting cumulative strain over time, , and These are the corresponding principal stress directions at time [time]. The corresponding time-dependent elastic strain is determined by the hysteresis elastic recovery strain after unloading; the time-delayed dissipation energy density. pass calculate.

6. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 1, characterized in that, The time-delay energy allocation index in S4 includes the time-delay elastic energy allocation coefficient. and time-delay dissipation energy distribution coefficient ,in: ； ； in, and The first m Time-delayed elastic energy density and time-delayed dissipated energy density during alternating loading processes; Time-delay damage activity Calculate using the following formula: ； in, For the first m Time-delayed energy density during alternating loading processes The corresponding transient dissipation energy density; time-delay damage activity. It is proportional to the contribution of time-related damage to current dissipation damage.

7. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 1, characterized in that, S5 Medium Intensity Damage Index Calculate using the following formula: ； in, and The first m Transient energy dissipation and time-delayed energy dissipation during alternating loading processes This refers to the cumulative dissipated energy during rock fracturing.

8. The method for evaluating the time-dependent damage of rock under long-term combined loading based on time-delay energy according to claim 1, characterized in that, S6 Damage Stage Determination Rules: (1) rise, Reduce: During the compaction adjustment stage, the rock mainly focuses on recoverable time-dependent energy storage and structural pore compaction; (2) High level stability Low value and stable: The rock mass is in a stable damage stage and its load-bearing structure is stable. (3) Slight decline and Slight increase: Damage development stage, micro-damage continues to accumulate; (4) Significant decline and Synchronous increase: During the damage activation phase, time-dependent irreversible dissipation is enhanced; (5) Continued decline and A sustained and significant increase: the stage of accelerated deterioration, with rock mass fissures connecting and nearing instability.

9. A rock aging damage evaluation system based on time-delay energy under long-term combined loading, characterized in that, The method for evaluating the time-delayed damage of rocks under long-term combined load based on time-delay energy, as described in any one of claims 1-8, comprises a data acquisition module, a strain identification module, an energy decomposition calculation module, an index calculation module, and a damage evaluation module connected in sequence. The data acquisition module is used to collect stress, strain, and time data of the rock to be evaluated under long-term combined loads. The strain identification module is used to identify the instantaneous strain, aging cumulative strain, and viscoelastic recovery strain of the rock from the collected stress, strain, and time data. The energy decomposition calculation module is used to decompose the input energy density of rock during loading into total transient energy density and total time-delay energy density based on instantaneous strain, time-accumulated strain, and viscoelastic recovery strain. The total transient energy density is decomposed into transient elastic energy density and transient dissipated energy density, and the time-delay energy density is decomposed into time-delay elastic energy density and time-delay dissipated energy density. The index calculation module is used to calculate the time-delay energy distribution index based on the time-delay elastic energy density and the time-delay dissipated energy density, and to calculate the time-delay damage activity based on the time-delay dissipated energy density and the transient dissipated energy density. The damage evaluation module is used to integrate the changing trends of strength damage coefficient, time-delay energy distribution index, and time-delay damage activity to comprehensively determine the stage of rock aging damage.

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