Construction method of magnesium slag-based filling body damage constitutive model based on energy dissipation

Abstract

The application provides a kind of magnesium slag based filling body damage constitutive model construction method based on energy dissipation, and relates to filling body damage analysis technical field.The method first makes magnesium slag based filling body test piece under different magnesium slag powder grinding time conditions, and obtains the stress-strain curve of each test piece by test, analyzes the energy evolution curve of each test piece;Then the damage dissipation energy is introduced into the energy balance equation of filling body, and the damage variable related to damage dissipation energy is obtained;Then compare the damage constitutive model, construct the energy modified damage constitutive model of magnesium slag based filling body considering the compaction stage and residual strength;Finally, verify the effectiveness of the model.The energy modified damage constitutive model constructed by the application is reasonable and effective, which can well describe the damage evolution process of magnesium slag based filling body under uniaxial compression, realize quick and accurate magnesium slag based filling body damage analysis, and provide scientific reference for the safety of mine filling mining engineering.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of filling body damage analysis, in particular to a method for constructing a magnesium-slag-based filling body damage constitutive model based on energy dissipation. BACKGROUND

[0002] Under the continuous action of external load, micro-cracks will gradually emerge and damage will occur inside the filling body. These damages will continue to develop and accumulate with the continuous application of load, eventually leading to the failure of the filling body. Although a lot of research has been conducted on the damage characteristics and constitutive relationship of the filling body, most of the research focuses on the testing and analysis of macro-mechanical properties, and the energy dissipation mechanism in the damage process is not thoroughly explored. Traditional damage constitutive model construction is mostly based on statistical methods of stress-strain relationship, which often ignores the key characteristic of energy dissipation of the filling body in the process of force. In fact, when the filling body is subjected to external force, not only elastic and plastic deformation will occur, but also energy transformation and dissipation. These energy dissipation processes are closely related to the damage evolution of the filling body, so it is of great practical significance to study the damage characteristics and constitutive model of the filling body from the perspective of energy dissipation.

[0003] Currently, there is a lack of research on the damage characteristics and constitutive model of magnesium-slag-based filling body based on energy dissipation. At the same time, as a material with relatively weak strength, the mechanical properties and damage evolution of the filling body are significantly different from those of rock, concrete and other materials. In addition, the damage constitutive model of the tailings cemented filling body and other materials is a statistical damage constitutive model constructed by combining statistical strength theory and continuity damage theory. Since the compaction stage and residual strength in the stress-strain curve are ignored, this model cannot accurately describe the mechanical behavior of magnesium-slag-based filling body in the failure process, thereby affecting the accuracy of the deformation and failure prediction and evaluation of magnesium-slag-based filling body, and posing a potential threat to the safety of mine construction. SUMMARY

[0004] In order to solve the above technical problems existing in the prior art, the present application provides a method for constructing a magnesium-slag-based filling body damage constitutive model based on energy dissipation, which considers the energy correction damage constitutive model of the compaction stage and residual strength, is reasonable and effective, can well describe the damage evolution process of magnesium-slag-based filling body under uniaxial compression, and realizes fast and accurate magnesium-slag-based filling body damage analysis, providing a scientific reference for the safety of mine filling and mining engineering. The technical solution is as follows:

[0005] A method for constructing a magnesium-slag-based filling body damage constitutive model based on energy dissipation, the method comprising:

[0006] S1, magnesium slag-based filling body specimens under different magnesium slag powder grinding time conditions are prepared, uniaxial compression tests are respectively performed on the specimens to obtain stress-strain curves of each specimen, and energy evolution curves of each specimen are analyzed;

[0007] S2, damage dissipation energy is defined, damage dissipation energy is introduced into an energy balance equation of the filling body, and a damage variable related to the damage dissipation energy is obtained;

[0008] S3, a magnesium slag-based filling body energy modified damage constitutive model considering the compaction stage and residual strength is constructed by comparing the damage constitutive models based on the Weibull distribution and the energy method;

[0009] S4, the damage parameter calculation method in step S3 is combined to obtain the filling body damage parameter value result, the result is substituted into the damage constitutive model in step S3 to obtain a related model curve, and then the model curve is compared with the test result curve in step S1 to verify the effectiveness of the model.

[0010] The process of material damage is regarded as a process of structural phase to damage phase conversion, the damage dissipation energy in step S2 is the work done by the external force due to the conversion of the structural phase in the material to the damage phase, and the damage dissipation energy of the structural phase when the damage occurs is:

[0011]

[0012] wherein, A n is the area of the structural phase;

[0013] is the stress increment of the structural phase when the damage phase expands A d ;

[0014] is the stress increment of the structural phase when the damage phase expands A d ;

[0015] is the energy damage dissipation per unit area of expansion;

[0016] is the damage dissipation energy of the structural phase when the damage phase expands A d ;

[0017] σ n and ε n are the stress and strain of the structural phase, respectively.

[0018] The energy dissipation is closely related to the damage of the structural phase. When the area of the damage phase expands dA d , the energy dissipated by the system is .

[0019] The damage dissipation energy is incorporated into the energy balance equation of the filling body. The process for obtaining the damage variables related to the damage dissipation energy in step S2 is as follows:

[0020] The energy balance equation for the structural phase is established by dissipating the energy through the generation of a damaged phase from a structural phase of a certain area:

[0021]

[0022] According to classical continuum damage mechanics, its damage variable D e Defined as:

[0023]

[0024] Therefore, the damage variable can be represented as:

[0025]

[0026] By transforming both sides of the above equation, integrating, and then taking the exponent, we can obtain the expression for the damage variable:

[0027]

[0028] in: D e For damage variables; To extend the energy damage dissipation per unit area; dA d To expand the area of ​​the damaged phase; A n The area of ​​the structural phase; A extended the damaged phase d The strain increment generated by the structural phase at that time; σ n denoted as σ0, where σ0 is the stress of the structural phase; A is the area of ​​the representative volume element of the filling body.

[0029] Based on the strain equivalence theory, the damage constitutive model of a material can be expressed as:

[0030]

[0031] Where D represents the material damage variable;

[0032] The stress-strain relationship of a material's structural phase can be characterized by a simplified linear function:

[0033]

[0034] The damage evolution and constitutive model of the filling material in step S3 during uniaxial compression failure based on the energy method are as follows:

[0035]

[0036]

[0037] in, Stress during the material damage process; S is the strain during the material damage process; E is the elastic modulus of the material. D e For damage variables; To expand the energy loss dissipation per unit area.

[0038] The process of constructing the energy-corrected damage constitutive model for magnesium slag-based infill in step S3 is as follows:

[0039] (1) Before the yield stress point

[0040] To accurately simulate the loading process of the filling specimen before the yield stress point, a compaction coefficient is proposed. The compaction coefficient increases logarithmically with increasing strain; therefore, the expression for the compaction coefficient is:

[0041]

[0042] Where: n is a constant obtained by fitting experimental data. It is the strain corresponding to the yield stress. Strain during the material damage process;

[0043] Introducing the compaction coefficient into the damage constitutive model, we obtain the damage constitutive model of the filling material considering the compaction stage as follows:

[0044]

[0045] in, Let Ω1 be the stress during the material damage process, E be the elastic modulus of the material, and Ω1 be the energy dissipation per unit area before the yield stress point.

[0046] The boundary conditions can be determined from the stress-strain curves of the compaction and elastic stages of the filled specimen:

[0047]

[0048] in: The yield stress of the filling specimen;

[0049] By combining the boundary conditions of the filling body and the damage constitutive model, and simplifying, we can obtain:

[0050]

[0051] The parameter Ω1 is obtained as follows:

[0052]

[0053] (2) After the yield stress point

[0054] The energy damage description after the yield stress point is combined with the energy damage model. At the same time, the energy damage constitutive model of the infill body is modified by considering the correction factor γ after the residual strength is introduced into the peak. Therefore, the energy damage constitutive model of the infill body after the yield stress point is expressed by the following equation:

[0055]

[0056] in, D e Ω2 is the damage variable, and Ω2 is the energy dissipation per unit area after the yield stress point.

[0057] The boundary conditions can be determined from the stress-strain curve of the filled specimen:

[0058]

[0059] in: This represents the peak stress of the filling sample. The strain is the strain corresponding to the peak stress of the filling specimen.

[0060] Combining the boundary condition equations of the filling body and the damage constitutive model, we can obtain:

[0061]

[0062] The parameter Ω2 is obtained as follows:

[0063] .

[0064] In the final step S4, the damage parameters of the filling body are obtained according to the damage parameter calculation method. The above parameters are substituted into the damage constitutive model in step S3 to obtain the energy-corrected damage constitutive curve of the magnesium slag-based filling body. Then, it is compared with the experimental result curve in step S1 to verify the effectiveness of the model.

[0065] The damage parameters in step S4 include the energy damage dissipation Ω1 of the unit area before the yield stress point and the energy damage dissipation Ω2 of the unit area after the yield stress point.

[0066] The model validity verification process is as follows:

[0067] The effectiveness of the damage constitutive model is comprehensively judged by considering the quantitative parameters of the model curve fit (coefficient of determination, root mean square error) and the overall trend of the curve. If the calculated model curve shows a high degree of consistency with the experimental curve, it indicates that the damage constitutive model can accurately describe the mechanical behavior of the filling material, and the model is effective. Observing the degree of fit between the two curves, the larger the coefficient of determination and the smaller the root mean square error, the better the model fit and the higher the prediction accuracy.

[0068] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0069] The above-mentioned scheme, based on energy dissipation theory, overcomes the limitations of traditional model construction approaches. Traditional models often struggle to comprehensively and accurately characterize the complex mechanical behavior of infill bodies, while the energy-corrected damage constitutive model for magnesium slag-based infill bodies, which considers the compaction stage and residual strength, effectively solves this problem. This model uncovers the energy change patterns of magnesium slag-based infill bodies during the stress process, incorporating the crucial stress process of the compaction stage, and fully considering the residual strength retained after material failure. This allows the model to more realistically reflect the mechanical behavior of magnesium slag-based infill bodies under uniaxial compression failure.

[0070] With the help of this precise model, technicians can predict the mechanical characteristics of the backfill material under different working conditions in advance. This not only provides a solid and scientific reference for safe mining, helping to formulate reasonable mining plans and safety protection measures in advance and reduce safety risks during the mining process, but also provides strong support for the optimized design of mine engineering, improving mining efficiency and economic benefits.

[0071] Furthermore, by applying solid magnesium slag to the backfill material, this invention achieves effective disposal of industrial waste, reduces the pollution of the environment and the occupation of land resources caused by magnesium slag, and makes a positive contribution to the protection of the ecological environment, truly achieving a win-win situation for both economic and environmental benefits. Attached Figure Description

[0072] 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.

[0073] Figure 1 This is a flowchart of a method for constructing a damage constitutive model of magnesium slag-based infill body based on energy dissipation, provided by an embodiment of the present invention.

[0074] Figure 2These are the energy evolution curves of magnesium slag-based backfill bodies under different curing ages and magnesium slag grinding times in the embodiments of the present invention. Among them, (a-1) is grinding for 0 min and curing for 3 days, (a-2) is grinding for 0 min and curing for 7 days, (a-3) is grinding for 0 min and curing for 28 days, (b-1) is grinding for 40 min and curing for 3 days, (b-2) is grinding for 40 min and curing for 7 days, (b-3) is grinding for 40 min and curing for 28 days, (c-1) is grinding for 60 min and curing for 3 days, (c-2) is grinding for 60 min and curing for 7 days, (c-3) is grinding for 60 min and curing for 28 days, (d-1) is grinding for 80 min and curing for 3 days, (d-2) is grinding for 80 min and curing for 7 days, and (d-3) is grinding for 80 min and curing for 28 days.

[0075] Figure 3 These are the damage constitutive model curves of magnesium slag-based filling bodies under different curing ages and magnesium slag grinding times in the embodiments of the present invention. Among them, (a-1) is grinding for 0 min and curing for 3 days, (a-2) is grinding for 0 min and curing for 7 days, (a-3) is grinding for 0 min and curing for 28 days, (b-1) is grinding for 40 min and curing for 3 days, (b-2) is grinding for 40 min and curing for 7 days, (b-3) is grinding for 40 min and curing for 28 days, (c-1) is grinding for 60 min and curing for 3 days, (c-2) is grinding for 60 min and curing for 7 days, (c-3) is grinding for 60 min and curing for 28 days, (d-1) is grinding for 80 min and curing for 3 days, (d-2) is grinding for 80 min and curing for 7 days, and (d-3) is grinding for 80 min and curing for 28 days. Detailed Implementation

[0076] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0077] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0078] In this embodiment of the invention, sometimes a subscript such as W1 may be written in a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0079] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0080] This invention provides a method for constructing a damage constitutive model of magnesium slag-based infill bodies based on energy dissipation. For example... Figure 1 The flowchart shown illustrates a method for constructing a damage constitutive model for magnesium slag-based infill bodies based on energy dissipation. This method may include the following steps:

[0081] S1. Prepare magnesium slag-based filling specimens under different magnesium slag grinding time conditions, conduct uniaxial compression tests on the specimens to obtain stress-strain curves of each specimen, and analyze the energy evolution curves of each specimen.

[0082] S2. Define damage dissipation energy and introduce it into the energy balance equation of the filling body to obtain the damage variable related to damage dissipation energy.

[0083] S3. By comparing the damage constitutive models based on Weibull distribution and energy method, an energy-corrected damage constitutive model for magnesium slag-based infill bodies that considers the compaction stage and residual strength is constructed.

[0084] S4. Combine the damage parameter calculation method in step S3 to obtain the damage parameter values ​​of the filling body, substitute the above parameters into the damage constitutive model in step S3 to obtain the relevant model curves, and then compare them with the experimental result curves in step S1 to verify the effectiveness of the model.

[0085] The following description, in conjunction with specific embodiments, illustrates this point.

[0086] In practical applications, follow these steps:

[0087] Step 1: Prepare magnesium slag-based filling specimens under different magnesium slag grinding time conditions. Conduct uniaxial compression tests on the specimens to obtain stress-strain curves for each specimen, and analyze the energy evolution curves of each specimen.

[0088] Based on commonly used backfilling ratio parameters in mines, the backfill concentration was 72%, the ash-sand ratio was 1:4, and the cementing material was slag powder containing 30% magnesia slag. Magnesia slag with different grinding times was used as a variable, with grinding times of 0, 40, 60, and 80 min. Backfill samples were prepared as cylinders with a diameter of 50 mm and a height of 100 mm. During loading, displacement control was used to apply pressure to the samples at a constant loading rate (0.3 mm / min) until the specimens failed. Three specimens were tested under each condition, and the average value was taken.

[0089] Energy evolution curves of magnesium slag-based backfill bodies under different curing ages and magnesium slag grinding times, such as Figure 2 As shown. By Figure 2It can be seen that the uniaxial compression failure process of magnesium slag-based infill bodies under different conditions can be divided into four stages: compaction stage, elastic stage, yielding stage, and post-peak stage. The energy evolution of the deformation failure process of magnesium slag-based infill bodies under different conditions all show similar patterns. Extending the curing age can effectively hinder the initiation and propagation of cracks, inhibit the diffusion of energy inside the sample, thereby increasing the energy storage limit of the infill body, exhibiting higher linear elastic deformation capacity, and thus improving its load-bearing capacity.

[0090] Step 2: Define the damage dissipation energy and introduce it into the energy balance equation of the filling material to obtain the damage variable related to the damage dissipation energy.

[0091] The process of material damage is viewed as a transformation from structural phase to damage phase. The extra work done by external forces due to the transformation of structural phase to damage phase is defined as damage dissipation energy.

[0092] Consider a representative volume element of a filling body with area A. When the area of ​​the structural phase is A... n If the damage phase extends to A d At that time, the strain increment generated by the structural phase is The stress increment is The energy loss dissipation per unit area is Then, the damage dissipation energy of the structural phase when damage occurs is:

[0093]

[0094] Energy dissipation is closely related to damage to the structural phase. When the area of ​​the damaged phase expands by dA... d At that time, the energy dissipated by the system is .

[0095] By incorporating damage dissipation energy into the energy balance equation of the infill, damage variables related to damage dissipation energy are obtained, including:

[0096] The energy balance equation for the structural phase is established by dissipating the energy through the generation of a damaged phase from a structural phase of a certain area:

[0097]

[0098] According to classical continuum damage mechanics, its damage variable D e Defined as:

[0099]

[0100] Therefore, the damage variable can be represented as:

[0101]

[0102] By transforming both sides of the above equation, integrating, and then taking the exponent, we can obtain the expression for the damage variable:

[0103]

[0104] Step 3: Compare the damage constitutive models based on Weibull distribution and energy method, and construct an energy-corrected damage constitutive model for magnesium slag-based infill bodies that considers the compaction stage and residual strength.

[0105] Based on the strain equivalence theory, the damage constitutive model of a material can be expressed as:

[0106]

[0107] Where: E represents the elastic modulus of the material; D represents the material damage variable; and Represents stress and strain during the material damage process;

[0108] 3.1 Damage Constitutive Model Based on Weibull Distribution

[0109] Under load, damage occurs inside the filling material due to the deformation and failure of the micro-elements. This damage deformation is assumed to follow a Weibull distribution with the following probability density function:

[0110]

[0111] in: m , F 0 represents the shape and scale parameters of the Weibull distribution.

[0112] The damage evolution model based on the Weibull distribution during uniaxial compression failure of the filling material is as follows:

[0113]

[0114] Then, the damage constitutive model based on the Weibull distribution of the filling material during uniaxial compression failure can be derived as follows:

[0115]

[0116] The boundary conditions can be determined from the stress-strain curve of the filled specimen:

[0117]

[0118] in: This represents the peak stress of the filling sample. This represents the strain corresponding to the peak stress of the filling specimen.

[0119] However, after the test loading was completed, the stress-strain curve of the filled specimen showed that it still possessed a certain post-peak load-bearing capacity after damage and failure. The damage constitutive model obtained from the above equation cannot accurately simulate the failure process of the filled specimen after the stress peak, and the model curve does not agree well with the experimental curve. Therefore, based on the above equation, a damage correction coefficient is introduced... By modifying the constitutive model of the filling material damage, we can obtain:

[0120]

[0121] in: This is the damage correction factor, and .

[0122] Similarly, based on the probability density function of the Weibull distribution, the damage evolution model during the uniaxial compression failure of the filling material is the same as the above equation, and the modified damage constitutive model based on the Weibull distribution can be obtained as follows:

[0123]

[0124] Wherein: parameters m′ and F0′ are the same as the aforementioned parameters m and F0.

[0125] Combining the boundary conditions of the filling body and the modified damage constitutive model based on the Weibull distribution, we can obtain:

[0126]

[0127] To facilitate calculations, the constant can be set... And thus The parameters m′ and F0′ can be derived as follows:

[0128]

[0129] Based on the stress-strain curves of magnesium slag-based backfill bodies under different curing ages and magnesium slag grinding times, and combined with the above formula, the Weibull distribution damage parameters m′ and F0′ of the backfill body can be accurately obtained.

[0130] 3.2 Damage Constitutive Model Based on Energy Method

[0131] The stress-strain relationship of a material's structural phase can be characterized by a simplified linear function:

[0132]

[0133] The damage evolution and constitutive model of the filling material during uniaxial compression failure based on the energy method are as follows:

[0134]

[0135]

[0136] By combining the boundary conditions of the filling body and the damage constitutive model, the parameter Ω is integrally obtained as:

[0137]

[0138] 3.3 Construct an energy-corrected damage constitutive model for magnesium slag-based infill bodies that considers the compaction stage and residual strength, including:

[0139] 1) Before the yield stress point

[0140] To accurately simulate the loading process of the filling specimen before the yield point, a compaction coefficient is proposed. Its value increases logarithmically with increasing strain. Therefore, the expression for the compaction coefficient is:

[0141]

[0142] Where: n is a constant obtained by fitting experimental data. It is the strain corresponding to the yield stress.

[0143] Introducing this compaction coefficient, we obtain the following constitutive model for filler damage considering the compaction stage:

[0144]

[0145] Where: Ω1 represents the energy damage dissipation per unit area before the yield stress point;

[0146] The boundary conditions can be determined from the stress-strain curves of the compaction and elastic stages of the filled specimen:

[0147]

[0148] in: This represents the yield stress of the filling specimen.

[0149] By combining the boundary conditions of the filling body and the damage constitutive model, and simplifying, we can obtain:

[0150]

[0151] The parameter Ω1 is obtained as follows:

[0152]

[0153] (2) After the yield stress point

[0154] The energy damage description after the yield stress point is combined with the energy damage model. At the same time, the energy damage constitutive model of the infill body is modified by considering the correction factor γ after the residual strength is introduced into the peak. Therefore, the energy damage constitutive model of the infill body after the yield stress point is expressed by the following equation:

[0155]

[0156] in, D e Ω2 is the damage variable, and Ω2 is the energy dissipation per unit area after the yield stress point.

[0157] The boundary conditions can be determined from the stress-strain curve of the filled specimen:

[0158]

[0159] in: This represents the peak stress of the filling sample. The strain is the strain corresponding to the peak stress of the filling specimen.

[0160] Combining the boundary condition equations of the filling body and the damage constitutive model, we can obtain:

[0161]

[0162] The parameter Ω2 is obtained as follows:

[0163] .

[0164] Step 4: Combine the damage parameter calculation method to obtain the damage parameter values ​​of the filling body, substitute the above parameters into the damage constitutive model to obtain the relevant model curves, and then compare them with the experimental results to verify the effectiveness of the model.

[0165] The effectiveness of the damage constitutive model is comprehensively judged by considering the quantitative parameters of the model curve fit (coefficient of determination, root mean square error) and the overall trend of the curve. If the calculated model curve shows a high degree of consistency with the experimental curve, it indicates that the damage constitutive model can accurately describe the mechanical behavior of the filling material, and the model is effective. Observing the degree of fit between the two curves, the larger the coefficient of determination and the smaller the root mean square error, the better the model fit and the higher the prediction accuracy.

[0166] Calculate the coefficient of determination (R²) between the model curve and the experimental curve. 2 The calculation formula is as follows:

[0167]

[0168] Where N is the number of data points. Let the stress value of the model curve be the value at the i-th data point. Let i be the stress value of the experimental curve at the i-th data point. R represents the average stress value of the test curve. 2 The value of is between 0 and 1. The closer it is to 1, the higher the degree of agreement between the model curve and the experimental curve, and the better the model fits the experimental data.

[0169] The root mean square error (RMSE) between the model curve and the experimental curve is calculated using the following formula:

[0170]

[0171] The smaller the RMSE, the smaller the deviation between the model curve and the experimental curve, and the higher the prediction accuracy of the model.

[0172] Table 1. Mechanical parameters of magnesium slag-based backfill under different curing ages and magnesium slag grinding times.

[0173]

[0174] Table 2. Damage model parameters of magnesium slag-based infill bodies under different curing ages and magnesium slag grinding times.

[0175]

[0176] Table 3. Quantitative parameters for the degree of agreement between model curves and experimental curves.

[0177]

[0178] The comparative analysis in Table 3 reveals that the average values ​​of the coefficient of determination and root mean square error (RMSE) of the Weibull distribution model curve under different conditions are 0.73596 and 0.74329, respectively; the average values ​​of the coefficient of determination and RMSE of the energy method model curve under different conditions are 0.59115 and 0.85921, respectively; and the average values ​​of the coefficient of determination and RMSE of the energy correction model curve under different conditions are 0.94048 and 0.47359, respectively. Furthermore, the coefficient of determination of the energy correction model curve is consistently above 0.81639. These results indicate that the energy correction damage constitutive model fits the experimental data better and has higher predictive accuracy. On the other hand, from... Figure 3Comparative analysis revealed that the model curves based on the Weibull distribution for most infill specimens showed low agreement with the experimental curves before peak stress. This was primarily because the experimental curves for most infill specimens exhibited an upward concave shape during the initial compaction stage, and the established damage constitutive model neglected the influence of the initial compaction stage on the model curves. Furthermore, while the introduced damage correction coefficients showed significant improvement in the post-peak failure stage of the infill, they did not produce noticeable improvement during the initial compaction and elastic deformation stages. Simultaneously, the damage constitutive results based on the energy method also differed significantly from reality. This indicates that solely focusing on energy may not comprehensively and accurately describe the damage evolution of the infill during compression. In contrast, the energy-corrected damage constitutive model for infill, considering the compaction stage and residual strength, showed high consistency with the experimental curves. This model not only considered the characteristics of the infill during the initial compaction stage but also fully incorporated factors such as energy dissipation and residual strength during compression. Therefore, this corrected model can more accurately reflect the actual deformation and failure process of magnesium slag-based infill under different conditions.

[0179] In summary, the energy-corrected damage constitutive model for infill materials that considers the compaction stage and residual strength not only possesses high accuracy but also more realistically reflects the damage evolution process of the infill material. Compared with traditional statistically based damage constitutive models, this model considers the intrinsic mechanisms of infill damage and the macroscopic damage development laws more deeply, thus possessing clearer physical significance.

[0180] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for constructing a magnesium slag-based filling body damage constitutive model based on energy dissipation, characterized by, The method comprises: S1, making magnesium slag-based filling body test pieces under different magnesium slag powder grinding time conditions, respectively performing uniaxial compression test on the test pieces to obtain stress-strain curves of each test piece, and analyzing energy evolution curves of each test piece; S2, defining damage dissipation energy, introducing the damage dissipation energy into an energy balance equation of the filling body, and obtaining a damage variable related to the damage dissipation energy; S3, comparing a damage constitutive model based on Weibull distribution and an energy method, and constructing a magnesium slag-based filling body energy modified damage constitutive model considering a compaction stage and residual strength; S4, obtaining filling body damage parameter value results by combining a damage parameter calculation method in step S3, substituting the results into the damage constitutive model in step S3 to obtain a model curve, and then comparing the model curve with test result curves in step S1 to verify the effectiveness of the model; The magnesium slag-based filling body energy modified damage constitutive model in step S3 is constructed as follows: (1) Before the yield stress point In order to simulate the loading process of the specimen before the yield stress point accurately, the compression coefficient is proposed, which increases logarithmically with the increase of strain. Therefore, the expression of the compression coefficient is ； wherein: n is a constant obtained by fitting experimental data, is the strain corresponding to the yield stress, is the strain during the material damage process; The compaction coefficient is introduced into the damage constitutive model to obtain a filling body damage constitutive model considering the compaction stage: ； wherein, is the stress in the material damage process, E is the elastic modulus of the material; Ω1 is the energy damage dissipation of the extension unit area before the yield stress point; The boundary conditions can be obtained from stress-strain curves of the filling body sample in the compaction and elastic stages: ； wherein: σy is the yield stress of the filler sample; By combining the filling body boundary conditions and the damage constitutive model, the following equation can be obtained: ； The parameter Ω1 is solved as: ； (2) After the yield stress point The energy damage model is combined with the description of energy damage after the yield stress point, and the post-peak correction coefficient γ is introduced to consider the residual strength to modify the energy damage constitutive model of the filling body, Therefore, the energy damage constitutive model of the filling body after the yield stress point is represented by the following formula: ； where D e is the damage variable, Ω2is the energy dissipation per unit area after the yield stress point; The boundary conditions can be obtained from stress-strain curves of the filling body sample: ； wherein: is the peak stress of the filling body specimen; is the strain corresponding to the peak stress of the filling body specimen. By combining the filling body boundary condition equation and the damage constitutive model, the following equation can be obtained: ； The parameter Ω2 is solved as: 。 2. The method according to claim 1, wherein, The damage dissipation energy in step S2 is the work done by the external force due to the conversion of the structural phase into the damage phase in the material, and the damage dissipation energy of the structural phase when damage occurs is: ； wherein A n is the area of the structure phase; A for damage phase expansion d The strain increment produced by the structural phase; to extend the energy damage dissipation per unit area; dΩ is the damage phase expands A d when the damage of the structure phase dissipates energy; σ n and ε n are the stress and strain of the structural phase, respectively.

3. The method according to claim 1, wherein, The damage variable is obtained as follows: The energy balance equation of the structural phase is established by dissipating the structural phase of a certain area to generate a damage phase: ； According to classical continuum damage mechanics, its damage variable D e is defined as: ； Therefore, the damage variable can be expressed as: ； After integrating the deformation at both ends of the above equation and then taking the exponential of it, the expression of the damage variable can be obtained: ； where: D e is the damage variable; is the energy dissipation per unit area of damage extension; dA d is the area of damage phase extension; A n is the area of the structure phase; is the damage phase extension A d is the increment of strain generated by the structure phase; σ n is the stress of the structure phase; A is the representative volume element area of the filler.

4. The method according to claim 1, wherein, The damage constitutive model based on the energy method in step S3 is: ； wherein, is the stress in the material during damage; is the strain in the material during damage; E is the elastic modulus of the material; D e is the damage variable; is the energy dissipation per unit area of extension.

5. The method according to claim 1, wherein, The damage parameters in step S4 include the energy damage dissipation Ω1 of the expansion unit area before the yield stress point and the energy damage dissipation Ω2 of the expansion unit area after the yield stress point.

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