A method, apparatus, equipment, medium, and product for constructing a creep model of coal pillars in residual mining areas.
By introducing water immersion damage variables into the creep model of coal pillars in residual mining areas, the evolution relationship of coal mechanical parameters with water content is established. This solves the problem that existing models are difficult to describe the creep behavior of coal pillars under water immersion conditions, and achieves more accurate prediction of long-term deformation and damage evolution, thereby improving the reliability of stability analysis and safe recovery of coal pillars in residual mining areas.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TAIYUAN UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-04-20
- Publication Date
- 2026-07-14
AI Technical Summary
Existing coal creep models are insufficient to accurately describe the creep behavior and damage evolution of coal pillars under immersion conditions. In particular, when coal pillars in residual mining areas are subjected to long-term water-mechanical coupling, existing models are unable to reflect their time-varying deformation characteristics and damage evolution, resulting in insufficient accuracy in coal pillar stability analysis and safety assessment.
By constructing a creep model for coal pillars in residual mining areas, introducing water immersion damage variables, establishing the evolution relationship of coal body mechanical parameters with water content, and combining water immersion damage variables of elastic, viscoelastic, and viscoplastic elements, the nonlinear viscoelastic-plastic creep model is corrected, forming a model that can realistically describe the long-term deformation characteristics and damage process of coal pillars in a water immersion environment.
It improves the accuracy and engineering applicability of predicting coal pillar creep behavior, and can more realistically reflect the long-term deformation characteristics and damage evolution of coal pillars in water immersion environments, thereby enhancing the reliability and engineering applicability of coal pillar safety assessment and resource recovery in residual mining areas.
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Abstract
Description
Technical Field
[0001] This application relates to the field of rock mechanics, and in particular to a method, apparatus, equipment, medium, and product for constructing a creep model of coal pillars in residual mining areas. Background Technology
[0002] With the increasing intensity and duration of coal mining, high-quality, easily accessible coal resources are gradually decreasing, and many mines are entering a stage of resource depletion or marginal mining. In the early stages of coal mining, limited by factors such as mining theory, technical equipment, and safety requirements, relatively conservative mining methods such as pillar mining and open-cut mining were widely adopted, leaving behind a large number of coal pillars in the goaf. These coal pillars are typically distributed in old or residual mining areas, forming so-called residual mining area coal pillars. They have low recovery rates and significant resource waste, but also possess characteristics such as shallow burial, stable occurrence, and high reuse value. In the current context of increasingly scarce coal resources and intensive resource development, the safe and efficient recovery of residual mining area coal pillars has become one of the important ways to improve coal resource recovery rates and extend the service life of mines. However, residual mining area coal pillars have long been in a complex geological and mechanical environment, and under the long-term stress of the overlying strata, their internal structure has undergone varying degrees of damage and deterioration. Meanwhile, the residual mining areas are often adjacent to goaf areas, old roadways or aquifers. During long-term service, the coal pillars are inevitably soaked or seeped by groundwater, which leads to an increase in the moisture content of the coal body and a significant change in its mechanical properties.
[0003] Existing research indicates that coal exhibits significant creep characteristics under long-term loading, with deformation continuously developing over time, potentially leading to coal pillar instability, roof collapse, and sudden dynamic disasters. The involvement of water further exacerbates the coal structure deterioration process. Water immersion causes softening of internal mineral particles, destruction of the cemented structure, and propagation of microcracks, significantly reducing the coal's strength parameters, elastic modulus, and viscous properties, thereby altering the long-term deformation and failure patterns of the coal pillar. Therefore, accurately describing the creep behavior of coal pillars under water immersion conditions is of significant engineering importance in the stability analysis and safety assessment of coal pillars in residual mining areas.
[0004] Currently, most existing coal creep models are based on ideal dry conditions or simple water-bearing conditions, typically employing classical viscoelastic-plastic models or empirical constitutive relations. They fail to adequately consider the impact of water on coal mechanical parameters, and particularly lack a systematic model that integrates the damage effects caused by water immersion with the evolution of creep parameters. In the unique environment of residual mining areas, which are subject to long-term water-mechanical coupling, existing models struggle to accurately reflect the time-varying deformation characteristics and damage evolution of coal pillars, thus limiting their practical application in engineering. Therefore, there is an urgent need to propose a creep model and its construction method that comprehensively considers the water immersion damage effect and reflects the evolution of coal pillar mechanical parameters in residual mining areas as water content changes. This would provide a reliable theoretical foundation and technical support for the long-term stability analysis and safe recovery of coal pillars in residual mining areas. Summary of the Invention
[0005] The purpose of this application is to provide a method, apparatus, equipment, medium, and product for constructing a creep model of coal pillars in residual mining areas, which can improve the accuracy and engineering applicability of predicting the long-term deformation and stability of coal pillars in residual mining areas under water immersion conditions.
[0006] To achieve the above objectives, this application provides the following solution: Firstly, this application provides a method for constructing a creep model of coal pillars in residual mining areas, including: To obtain the stress-strain-time relationship of coal under different immersion states under load; The initial nonlinear viscoelastic-plastic creep model was determined based on the stress-strain-time relationship. The water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements are determined based on the relationship between the creep parameters and the water content. The initial nonlinear viscoelastic-plastic creep model was corrected based on the water immersion damage variables of the elastic, viscoelastic, and viscoplastic elements to obtain the final coal pillar creep model.
[0007] In one embodiment, obtaining the stress-strain-time relationship of coal under load in different immersion states specifically includes: Taking the coal pillar in the residual mining area as the research object, the stress-strain-time relationship of the coal body under different water immersion states is obtained through creep test or existing experimental data.
[0008] In one embodiment, the initial nonlinear viscoelastic-plastic creep model is expressed as follows: ; in, σ For the total stress of the model, ε σ is the total strain of the model. ∞E1 represents the long-term strength of the coal body, E2 represents the instantaneous elastic modulus, η1, η2, and η3 represent the viscosity coefficients in the model elements corresponding to different creep stages, and t represents time.
[0009] In one embodiment, the expression for the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element is as follows: ; in, w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） The effect of moisture content changes on the viscosity coefficient of model elements at different creep stages.
[0010] In one embodiment, the expression for the final coal pillar creep model is: ; in, σ For the total stress of the model, ε ( t , w ) represents the equation for strain with respect to moisture content and time; n is the creep exponent; η1, η2, and η3 are the threshold stress; η1, η2, and η3 are the viscosity coefficients in the model elements corresponding to different creep stages. w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） The effect of moisture content changes on the viscosity coefficient of model elements at different creep stages.
[0011] In one embodiment, the method for constructing the creep model of the coal pillar in the residual mining area further includes: Deformation prediction is performed based on the final coal pillar creep model.
[0012] Secondly, this application provides a device for constructing a creep model of coal pillars in a residual mining area, comprising: The acquisition module is used to obtain the stress-strain-time relationship of coal under different immersion states under load. The initial nonlinear viscoelastic-plastic creep model determination module is used to determine the initial nonlinear viscoelastic-plastic creep model based on the stress-strain-time relationship. The water immersion damage variable determination module is used to determine the water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements based on the relationship between the creep parameters and the water content. The correction module is used to correct the initial nonlinear viscoelastic-plastic creep model based on the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element to obtain the final coal pillar creep model.
[0013] Thirdly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method for constructing a residual mining area coal pillar creep model.
[0014] Fourthly, this application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method for constructing the residual mining area coal pillar creep model.
[0015] Fifthly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the method for constructing the residual mining area coal pillar creep model.
[0016] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides a method, apparatus, equipment, medium, and product for constructing a creep model of coal pillars in residual mining areas. By determining the water immersion damage variables of elastic, viscoelastic, and viscoplastic elements based on the relationship between various creep parameters and water content, the initial nonlinear viscoelastic-plastic creep model is corrected based on these water immersion damage variables to obtain the final coal pillar creep model. Introducing water immersion damage variables incorporates the deterioration of coal structure, degradation of mechanical parameters, and damage accumulation caused by water immersion into the creep model. This effectively overcomes the shortcomings of existing creep models that are mostly based on dry conditions or ignore the influence of water, enabling the model to realistically describe the long-term deformation characteristics of coal pillars in residual mining areas under water immersion conditions. By uniformly correcting creep parameters such as elastic modulus, viscous modulus, and viscosity coefficient through water immersion damage variables, the uncertainty caused by using fixed parameters or empirical correction coefficients is avoided, improving the accuracy, reliability, and engineering applicability of coal pillar creep behavior prediction. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0018] Figure 1 This is a schematic diagram of a nonlinear viscoelastic-plastic creep model; Figure 2 This is a schematic diagram of the instantaneous elastic modulus E1 as a function of moisture content; Figure 3 This is a schematic diagram of the viscosity modulus E2 as a function of moisture content; Figure 4 This is a schematic diagram of the viscosity coefficient η1 as a function of water content; Figure 5 This is a schematic diagram of the viscosity coefficient η2 as a function of water content; Figure 6 This is a schematic diagram of the viscosity coefficient η3 as a function of moisture content; Figure 7 A schematic diagram of a nonlinear viscoelastic-plastic creep model for a coal pillar in a residual mining area, taking into account water immersion damage; Figure 8 A schematic diagram illustrating the method for constructing a creep model of coal pillars in residual mining areas; Figure 9 A schematic diagram of the functional modules of a device for constructing a creep model of a coal pillar in a residual mining area, provided in an embodiment of this application; Figure 10 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation
[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0020] The relevant technology constructs creep equations for the viscosity coefficient affected by water pressure and time, as well as nonlinear creep equations considering damage effects, based on operational instructions. Substituting the creep equations for the viscosity coefficient affected by water pressure and time into a pre-set Nishihara model generates a nonlinear creep model considering the influence of water pressure. Substituting the nonlinear creep equations considering damage effects into the nonlinear creep model considering water pressure generates a creep model of fractured rock under water-rock coupling. The constructed models yield unified functional expressions that describe the creep process of fractured rock considering water pressure, initial damage, damage correction coefficients, and damage evolution, and can be applied to the long-term stability analysis of relevant engineering projects. This technology mainly targets the creep process of general rock masses under water-rock coupling conditions. Essentially, it provides a model for rock mechanics engineering design. However, it does not conduct in-depth research on the damage evolution and creep behavior of coal bodies, especially coal pillars, under water immersion conditions. This results in significant differences from the water-bearing damage mechanism and time-varying parameter characteristics of coal pillars in residual mining areas. Furthermore, it does not consider the cumulative effects of water on the softening of the internal structure of the coal body and the propagation of microcracks on the evolution of creep parameters. Extending the model to the stability analysis of coal pillars will lead to significant deviations. The method does not systematically reveal how the water-bearing state changes over time and affects the division of creep stages and the critical failure conditions, which is not convenient for the safety evaluation of engineering projects in residual mining areas.
[0021] Other related technologies combine elastic elements, fractional-order viscoelastic-plastic elements, and damage fractional-order viscoplastic elements to form creep models, and introduce three-dimensional strength criteria and constitutive construction steps to achieve constitutive description of the creep initiation and acceleration stages of rocks. The method is applicable to long-term creep failure analysis of deep rock masses, and the model's effectiveness has been verified through true triaxial experiments. However, it focuses on extracting the creep constitutive laws of the entire rock mass under complex stress states, and does not model or describe the structural damage and parameter change mechanisms caused by water in coal bodies, especially coal pillars under water-bearing conditions. Although damage fractional-order viscoplastic elements are used to improve the model's fitting ability, there is a lack of systematic consideration of the material property degradation laws caused by water-bearing damage (such as the changes in strength, stiffness, and internal friction angle with water content). It mainly provides model construction methods, without clearly giving the dynamic evolution process of creep parameters under water-bearing conditions and the unified parameter determination steps related to water immersion damage, making it not entirely suitable for the water immersion-creep analysis needs of coal pillars in residual mining areas.
[0022] To address the technical shortcomings in existing long-term stability analysis of coal pillars in residual mining areas, this application takes the time-varying deformation characteristics of coal pillars in residual mining areas under long-term load-bearing and water immersion environments as the research object, and proposes a method for constructing a creep model of coal pillars in residual mining areas that considers the water immersion damage effect. The aim is to solve the problem that existing technologies cannot accurately describe the creep behavior and damage evolution law of coal pillars under water immersion conditions.
[0023] Specifically, existing coal creep models are mostly based on dry or simplified water-bearing conditions, typically using fixed mechanical parameters or empirical correction coefficients to describe the long-term deformation behavior of the coal body. These models fail to fully reflect the weakening and cumulative damage effects of water immersion on the internal structure, mechanical properties, and creep parameters of the coal body. In residual mining environments, coal pillars are subjected to the combined effects of overlying strata stress and groundwater immersion over long periods. Key parameters such as elastic modulus, viscous modulus, and viscosity coefficient continuously evolve with the degree of water immersion. Existing models struggle to accurately characterize the time-varying characteristics of these parameters, resulting in insufficient accuracy in predicting long-term coal pillar deformation and low reliability of safety assessment results.
[0024] In addition, although some existing creep models have introduced damage variables or nonlinear elements, they lack a model framework that can uniformly represent the water immersion damage mechanism and the creep parameter evolution process. A systematic modeling method that is applicable to coal pillars in residual mining areas and can reflect the coupling effect of water immersion damage and creep behavior has not yet been formed, making it difficult to meet the actual needs of long-term stability analysis and safe recovery design of coal pillars in residual mining areas.
[0025] Based on the above problems, the purpose of this application is to: establish the evolution relationship of coal body mechanical parameters with the degree of water immersion by introducing water immersion damage variables, organically couple the water immersion damage effect into the coal pillar creep constitutive model, and construct a residual mining area coal pillar creep model that can simultaneously reflect the instantaneous deformation, steady-state creep and accelerated creep characteristics of the coal pillar. The aim is to improve the accuracy and engineering applicability of predicting the long-term deformation and stability of residual mining area coal pillars under water immersion environment, and provide reliable theoretical basis and technical support for the safety assessment and reasonable recovery of residual mining area coal pillars.
[0026] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0027] In one exemplary embodiment, such as Figure 8 As shown, a method for constructing a creep model of coal pillars in a residual mining area is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In the embodiments of this application, the method includes the following steps.
[0028] Step 101: Obtain the stress-strain-time relationship of coal under different immersion states under load.
[0029] Step 102: Determine the initial nonlinear viscoelastic-plastic creep model based on the stress-strain-time relationship.
[0030] Step 103: Determine the water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements based on the relationship between the creep parameters and water content.
[0031] Step 104: Correct the initial nonlinear viscoelastic-plastic creep model based on the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element to obtain the final coal pillar creep model.
[0032] By introducing water immersion damage variables, the deterioration of coal structure, degradation of mechanical parameters, and accumulation of damage caused by water immersion are incorporated into the creep model. This effectively overcomes the shortcomings of existing creep models that are mostly based on dry conditions or ignore the influence of water. The model can realistically describe the long-term deformation characteristics of coal pillars in residual mining areas under water immersion conditions. By uniformly correcting creep parameters such as elastic modulus, viscous modulus, and viscosity coefficient through water immersion damage variables, the uncertainty caused by using fixed parameters or empirical correction coefficients is avoided, thus improving the accuracy, reliability, and engineering applicability of coal pillar creep behavior prediction.
[0033] In an exemplary embodiment, the stress-strain-time relationship of coal under load under different water immersion states is obtained, specifically including: taking the coal pillar in the residual mining area as the research object, and obtaining the stress-strain-time relationship of coal under load under different water immersion states through creep tests or existing experimental data.
[0034] In an exemplary embodiment, the method for constructing the residual mining area coal pillar creep model further includes: performing deformation prediction based on the final coal pillar creep model.
[0035] In another exemplary embodiment, this application systematically characterizes the time-varying deformation and damage evolution behavior of coal pillars in residual mining areas under the combined effects of long-term load and water immersion by combining the water immersion damage mechanism with the constitutive relation of coal body creep. This application also provides a specific process for constructing a creep model of coal pillars in residual mining areas in practical applications, including the following steps.
[0036] Step 1: Taking the coal pillar in the residual mining area as the research object, and considering the real engineering environment in which the coal pillar is located during long-term service, the long-term stress of the overlying strata and the water immersion effect caused by groundwater soaking or seepage are simultaneously included in the analysis framework.
[0037] Based on this, through creep tests or existing experimental data, the stress-strain-time relationship of coal under long-term loading under different immersion states was obtained, and the typical deformation characteristics of coal in the instantaneous deformation stage, steady-state creep stage, and accelerated creep stage were identified, thus obtaining the initial nonlinear viscoelastic-plastic creep model. Figure 1 The corresponding constitutive equation is Equation 5.
[0038] Specifically, a nonlinear viscoelastic-plastic creep model is constructed.
[0039] In the Burgers model ( Figure 1Based on the series connection of parts 1, 2, and 3, a nonlinear damage viscoplastic element is connected in series. Figure 1 Part 4 describes the deformation over time during the accelerated creep stage of the coal pillar in the residual mining area. The established nonlinear damage viscoelastic-plastic creep model is as follows: Figure 1 As shown in the model. E 1. E 2 represents the instantaneous elastic modulus and viscous modulus, respectively. η 1. η 2. η 3 represents the viscosity coefficient. σ ∞ Let be the long-term strength of the coal body. The corresponding creep equation is shown below.
[0040] When applied stress σ<σ ∞ At that time, the above model ( Figure 1 Part 4 (viscoplastic body) is ineffective; the model degenerates into the Burgers model, which consists of elastic elements ( Figure 1 Part 1), viscous elements ( Figure 1 Part 2) and viscoelastic elements ( Figure 1 The third part of the structure is composed of three parts, and its constitutive equation is: (1) in, This is the first derivative of stress with respect to time; This is the second derivative of stress with respect to time; The first derivative of strain with respect to time; The second derivative of strain with respect to time.
[0041] The creep equation corresponding to the Burgers model is: (2) When applied stress σ ≥ σ ∞ At this time, all parts of the above model are active, and the corresponding creep state equation is: (3) In the formula, σ 1. σ 2. σ 3 and σ 4 respectively correspond to Figure 1 Stress in parts 1, 2, 3, and 4 of the model; ε 1. ε 2. ε 3 and ε 4 corresponds to the strains of parts 1, 2, 3, and 4, respectively; σ and εThese represent the total stress and total strain of the model, respectively. for ε The first derivative of 1; for ε The first derivative of 2; for ε The first derivative of 3; for ε The first derivative of 4.
[0042] Applying the Laplace transformation to equation (3), we obtain the corresponding creep equation: (4) In summary, the creep equation for the coal pillar in the residual mining area under different conditions, i.e., the expression of the initial nonlinear viscoelastic-plastic creep model, is as follows: (5) t is time 。 The corresponding creep model is as follows Figure 1 .
[0043] Step 2: Based on the initial nonlinear viscoelastic-plastic creep model, by introducing the water immersion damage variable (Equation 7) into the constitutive model equation of each component (Equation 5), a residual mining area coal pillar creep constitutive model equation considering the water immersion damage effect is formed (Equation 8), so that the model can simultaneously reflect the instantaneous deformation, steady-state creep and accelerated creep process of the coal pillar under water immersion conditions.
[0044] Specifically, damage variables for coal bodies with different moisture contents are defined based on changes in the elastic modulus. The definition considers the damage to be essentially a deterioration of the material's inherent mechanical properties. In the creep model, the change in the elastic modulus E1, which characterizes instantaneous deformation, decreases with increasing moisture content. Therefore, the damage to the instantaneous elastic modulus caused by changes in moisture content can be defined as follows:
[0045] (6) In the formula, E 1(0) is the instantaneous elastic modulus when the moisture content is 0, in MPa; E 1( w () represents the instantaneous elastic modulus at different moisture contents, in MPa. This refers to the damage to creep parameters caused by moisture content.
[0046] According to the relationship between various creep parameters and moisture content (e.g.) Figures 2-6 The corresponding damage evolution equations are obtained by fitting the curve (i.e., the expressions for the water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements are as follows): (7) Where E1 is the instantaneous elastic modulus, E2 is the viscous modulus, and η1, η2, and η3 are the viscosity coefficients in the model elements corresponding to different creep stages. w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） The effect of moisture content changes on the viscosity coefficient of model elements at different creep stages. D 3（w）、 D 4（w）、 D 5（w） These correspond to η1, η2, and η3 respectively.
[0047] Substituting equation (7) into equation (5), and considering the correction of the initial model after water immersion damage, we obtain the creep equation considering the water-bearing damage effect, that is, the final coal pillar creep model equation is: (8) σ For the total stress of the model, ε ( t , w ) represents the equation for strain with respect to moisture content and time; n is the creep exponent; η1, η2, and η3 are the threshold stress; η1, η2, and η3 are the viscosity coefficients in the model elements corresponding to different creep stages. w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） This represents the damage to the viscosity coefficients of model elements corresponding to different creep stages caused by changes in moisture content. The corresponding creep model for moisture-related damage is as follows: Figure 7 As shown.
[0048] This application constructs a creep model that can realistically reflect the long-term deformation and damage evolution characteristics of coal pillars in residual mining areas under water immersion conditions. This model not only improves the accuracy of predicting the long-term stability of coal pillars, but also enhances the applicability of the model in safety assessment and resource recovery projects of coal pillars in residual mining areas. It has strong engineering practical value and promotion significance.
[0049] This application can more realistically and comprehensively reflect the mechanical behavior of coal pillars in residual mining areas under the combined action of long-term load and water immersion. It has significant beneficial effects in terms of theoretical perfection and engineering applicability, specifically reflected in the following aspects: (1) It can truly reflect the influence of water immersion on the creep behavior of coal pillars.
[0050] This application introduces water immersion damage variables into the constitutive relation of coal pillar creep. By incorporating these variables, the deterioration of coal structure, degradation of mechanical parameters, and damage accumulation caused by water immersion are included in the creep model. This effectively overcomes the shortcomings of existing creep models, which are mostly based on dry conditions or ignore the influence of water. The model can realistically describe the long-term deformation characteristics of coal pillars in residual mining areas under water immersion conditions. This application breaks through the limitations of traditional coal pillar creep models, which are mostly based on dry or simplified water-bearing conditions. By introducing water immersion damage variables, the deterioration of coal structure, strength, and stiffness caused by water immersion are uniformly attributed to quantifiable damage effects, realizing the transformation of water immersion effects from qualitative description to quantitative modeling.
[0051] (2) Achieve a unified characterization of the evolution of creep parameters with the degree of immersion.
[0052] This application establishes the evolution relationship of key creep parameters of coal body with the degree of water immersion. Focusing on key creep parameters such as elastic modulus, viscous modulus, and viscosity coefficient, it establishes their evolution relationship with the degree of water immersion. Furthermore, it uses damage variables to uniformly correct these parameters, avoiding the uncertainties caused by using fixed parameters or empirical correction coefficients, which fail to reflect real engineering conditions. This improves the accuracy and reliability of predicting coal pillar creep behavior.
[0053] (3) It can fully describe the mechanical response of the entire process of coal pillar creep.
[0054] The constructed creep model can simultaneously characterize the instantaneous deformation stage, steady-state creep stage, and accelerated creep stage of a coal pillar. It is suitable for analyzing the long-term deformation process of coal pillars under different stress levels and different immersion conditions, and is helpful for accurately identifying the critical state of coal pillars entering accelerated creep and instability failure.
[0055] (4) The model has a clear structure and the construction method is operable.
[0056] This application improves upon the classic viscoelastic-plastic creep model framework, resulting in a clear model structure and well-defined physical meaning. The proposed construction method is complete in steps and logically sound, facilitating the determination of model parameters through experimental data or engineering monitoring data, and possesses strong engineering feasibility.
[0057] (5) Improve the stability analysis and safety assessment of coal pillars in residual mining areas.
[0058] By more accurately predicting the long-term deformation and damage evolution process of coal pillars in residual mining areas under water immersion conditions, this application can provide a reliable theoretical basis for stability analysis, instability risk assessment, and safe recovery scheme design of coal pillars in residual mining areas. This will help reduce the risk of disasters such as roof collapse induced by coal pillar instability and improve the level of safe production in mines.
[0059] (6) It has good engineering promotion value.
[0060] The technical solution presented in this application is applicable to various types of coal pillars in residual mining areas and different water immersion conditions. It can provide a reference for the long-term deformation analysis of coal bodies similarly affected by water-mechanical coupling, and has good versatility and prospects for widespread application. The model construction and parameter determination methods in this application are closely combined with the actual working conditions of coal pillars in residual mining areas under long-term loading and easy water immersion. It is applicable to the stability analysis, long-term deformation prediction, and safety assessment of coal pillars in residual mining areas, and has clear engineering relevance.
[0061] (7) Construction of the coupling model of water immersion damage and viscoelastic-plastic creep Based on the classical viscoelastic-plastic creep model framework, this application embeds the water immersion damage variable into the constitutive parameters of each component of the model, enabling the model to simultaneously reflect the instantaneous deformation, steady-state creep, and accelerated creep of the coal pillar under water immersion conditions, thus forming a water immersion damage creep model with clear physical meaning.
[0062] Based on the same inventive concept, this application also provides a residual mining area coal pillar creep model construction device for implementing the above-mentioned residual mining area coal pillar creep model construction method. The solution provided by this device is similar to the solution described in the above-mentioned method. Therefore, the specific limitations of one or more residual mining area coal pillar creep model construction device embodiments provided below can be found in the limitations of the residual mining area coal pillar creep model construction method above, and will not be repeated here.
[0063] In one exemplary embodiment, such as Figure 9 As shown, a device for constructing a creep model of a coal pillar in a residual mining area is provided, comprising: The acquisition module is used to obtain the stress-strain-time relationship of coal under different immersion states under load.
[0064] The initial nonlinear viscoelastic-plastic creep model determination module is used to determine the initial nonlinear viscoelastic-plastic creep model based on the stress-strain-time relationship.
[0065] The water immersion damage variable determination module is used to determine the water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements based on the relationship between various creep parameters and water content.
[0066] The correction module is used to correct the initial nonlinear viscoelastic-plastic creep model based on the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element to obtain the final coal pillar creep model.
[0067] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 10 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores data for constructing a creep model of a coal pillar in a residual mining area. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communicating with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for constructing a creep model of a coal pillar in a residual mining area.
[0068] Those skilled in the art will understand that Figure 10 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer equipment to which the present application is applied. Specific computer equipment may include, for example, [the following is a list of possible additional structures]. Figure 10 The embodiments show more or fewer components, combinations of certain components, or different component arrangements. In one exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the above-described method embodiments.
[0069] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method embodiments.
[0070] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described method embodiments.
[0071] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.
[0072] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).
[0073] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.
[0074] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0075] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method for constructing a creep model of coal pillars in residual mining areas, characterized in that, include: To obtain the stress-strain-time relationship of coal under different immersion states under load; The initial nonlinear viscoelastic-plastic creep model was determined based on the stress-strain-time relationship. The water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements are determined based on the relationship between various creep parameters and water content. The initial nonlinear viscoelastic-plastic creep model was corrected based on the water immersion damage variables of the elastic, viscoelastic, and viscoplastic elements to obtain the final coal pillar creep model.
2. The method for constructing a creep model of a coal pillar in a residual mining area according to claim 1, characterized in that, To obtain the stress-strain-time relationship of coal under different immersion states and loading, specifically including: Taking the coal pillar in the residual mining area as the research object, the stress-strain-time relationship of the coal body under different water immersion states is obtained through creep test or existing experimental data.
3. The method for constructing a creep model of a coal pillar in a residual mining area according to claim 1, characterized in that, The initial expression for the nonlinear viscoelastic-plastic creep model is: ； in, σ For the total stress of the model, ε σ is the total strain of the model. ∞ E1 represents the long-term strength of the coal body, E2 represents the instantaneous elastic modulus, η1, η2, and η3 represent the viscosity coefficients in the model elements corresponding to different creep stages, and t represents time.
4. The method for constructing a creep model of a coal pillar in a residual mining area according to claim 1, characterized in that, The expressions for the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element are as follows: ； in, w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） The effect of moisture content changes on the viscosity coefficient of model elements at different creep stages.
5. The method for constructing a creep model of a coal pillar in a residual mining area according to claim 1, characterized in that, The expression for the final coal pillar creep model is as follows: ； in, σ For the total stress of the model, ε ( t , w ) represents the equation for strain with respect to moisture content and time; n is the creep exponent; η1, η2, and η3 are the threshold stress; η1, η2, and η3 are the viscosity coefficients in the model elements corresponding to different creep stages. w Moisture content, D 1（w） The damage to the elastic modulus caused by changes in moisture content; D 2（w） The effect of moisture content changes on the viscous modulus; D 3（w）、 D 4（w）、 D 5（w） The effect of moisture content changes on the viscosity coefficient of model elements at different creep stages.
6. The method for constructing a creep model of a coal pillar in a residual mining area according to claim 1, characterized in that, Also includes: Deformation prediction is performed based on the final coal pillar creep model.
7. A device for constructing a creep model of a coal pillar in a residual mining area, characterized in that, include: The acquisition module is used to obtain the stress-strain-time relationship of coal under different immersion states under load. The initial nonlinear viscoelastic-plastic creep model determination module is used to determine the initial nonlinear viscoelastic-plastic creep model based on the stress-strain-time relationship. The water immersion damage variable determination module is used to determine the water immersion damage variables of elastic elements, viscoelastic elements, and viscoplastic elements based on the relationship between various creep parameters and water content. The correction module is used to correct the initial nonlinear viscoelastic-plastic creep model based on the water immersion damage variables of the elastic element, viscoelastic element, and viscoplastic element to obtain the final coal pillar creep model.
8. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the method for constructing a creep model of a coal pillar in a residual mining area as described in any one of claims 1-6.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for constructing a creep model of a coal pillar in a residual mining area as described in any one of claims 1-6.
10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the method for constructing a creep model of a coal pillar in a residual mining area as described in any one of claims 1-6.