Constitutive Model and Parameter Calibration Method for Permafrost Considering Temperature and Time Effects

Abstract

A constitutive model and parameter calibration method for permafrost considering temperature and time effects are proposed, including: construction of the basic model framework; laboratory experiments and construction of core equations; construction of elastoplastic constitutive relations; construction of stress-strain relations considering temperature and time effects; and inversion calibration of model parameters. Through the progressive and synergistic implementation of the above steps, this method realizes a systematic R&D process from theoretical framework to experimental verification and then to parameter calibration, effectively solving the problem of modeling the complex mechanical behavior of permafrost under the coupled effects of temperature and time.

Description

Technical Field

[0001] This invention belongs to the technical field of geotechnical engineering, specifically relating to constitutive models and parameter calibration methods for permafrost that take into account temperature and time effects. Background Technology

[0002] my country is a country with a large permafrost population, with permafrost covering 22.3% of its land area. The stability of permafrost has a significant impact on the construction and operation of local roadbeds, bridges, tunnels, and other engineering projects. Permafrost engineering projects, such as high-speed railways in high-latitude cold regions and the Qinghai-Tibet Railway at high altitudes, are closely related to the properties and evolution of the permafrost involved. In recent years, with the influence of climate warming and humidification, the average temperature rise rate on the Qinghai-Tibet Plateau has reached 0.3~0.4℃ / 10a, and the temperature of permafrost has generally increased by 0.13±0.07℃ / 10a, while the thickness of the active layer has increased by 59.9±12.7cm / 10a. The trend of permafrost degradation has intensified, affecting the stability of permafrost engineering projects and leading to the deformation and development of roadbeds and other infrastructure, as well as an increase in thermal thawing disasters. Permafrost is a complex multiphase system composed of soil, ice, and unfrozen water, which is highly sensitive to changes in environmental temperature and its properties are easily variable, with significant time-varying effects during warming. Under the influence of climate change or human activities, once permafrost warms, it will go through a slow, complex, and long-term deformation stage of permafrost creep, a phase transformation deformation and strength loss stage of permafrost thawing, and a large deformation stage of compression consolidation under its own weight and additional stress after thawing. This will cause a decrease in its bearing capacity and an increase in deformation, which will have an adverse impact on railway engineering infrastructure.

[0003] Temperature rise leading to permafrost degradation and time-related deformation are the core causes of long-term service degradation in permafrost engineering projects. Existing empirical models considering time effects, such as the Norton-Bailey model and the Sine-Hyperbolic model, are simple in form, but their establishment does not start from the physical properties of permafrost and cannot directly describe volumetric deformation, resulting in limitations such as dependence on experimental laws and specific creep behavior. Component models, such as the Maxwell model and the Kelvin-Voigt model, are simple in form and have clearly defined physical meanings for their parameters, but they have many parameters that are difficult to determine and cannot well describe complex multi-directional loading conditions. Elastic-viscoplastic models, such as the Perzyna model, Lai Yuanming's frozen sand model, Yao Yangping's negative creep characteristic model, and the Kachanov-Rabotnov damage creep model, can describe complex path loading, but their forms are complex and difficult to generalize. Existing constitutive models for permafrost that consider temperature effects include damaged elastic constitutive models, constitutive models based on Sevostianov theory, and artificial permafrost constitutive models using cascaded correlation neural networks. However, quantitative models that consider the time-dependent evolution of performance parameters after permafrost degradation are still rare, and quantitative analysis of the time-varying mechanisms and multi-stage degradation patterns of high-temperature permafrost across the entire temperature range is lacking. There is an urgent need to construct constitutive models for permafrost that can simultaneously describe both temperature and time effects. Furthermore, due to differences in stress paths, initial confining pressures, and initial void ratios in soil and rock materials, various phenomena such as hardening or softening and particle breakage may occur, leading to extremely complex stress-strain relationships. Moreover, predictions of experimental data for the same material under different initial conditions must use the same set of parameters, with varying sensitivities and magnitudes among the parameters, resulting in a complex and diverse range of experimental variables. Therefore, when determining constitutive model parameters based on inversion from indoor experimental data, high demands are placed on the adaptability, accuracy, and stability of the algorithm. There is an urgent need to propose parameter calibration methods with global optimization capabilities and a unified input format. Existing technologies, such as application number CN202211192200.2, disclose a method for characterizing creep deformation of lenticular frozen soil and its application. This method is mainly based on creep test results of lenticular frozen soil with different structural types, constructing a creep data characterization formula compatible with structural damage, and verifying it through data fitting inversion. When constructing the model, an exponential function related to stress and time is used to characterize the hardening parameters of frozen soil, and a Weibull distribution function with time factor is used to characterize the creep damage parameters. Furthermore, a generalized Kelvin and Bingham model is used to characterize the elasticity, viscoelasticity, and viscoplasticity of lenticular frozen soil throughout the creep process.The main shortcomings of this technical solution are: ① Key parameters of the model, such as elastic modulus and long-term strength, are mainly determined based on the measured creep curve. The creep exponential function expression is essentially an empirical model, which has limitations such as being unable to directly describe volumetric deformation and having dependence on experimental laws and specific creep behaviors; ② The model considers the influence of time factors in the creep hardening parameters and damage parameters of frozen soil, but does not consider the influence of temperature changes on the function form and parameter values, and cannot simulate the differences in the deformation characteristics of frozen soil under different heating conditions.

[0004] Application number CN202411456572.0 discloses a simulation method for a discrete element contact model of non-decaying creep in frozen soil. This method mainly addresses the limitations of conventional discrete element method (DEM) simulation of frozen soil creep by establishing a Burgers first viscoelastic model for frozen soil. It further introduces a damage element and connects the first viscoelastic model and the damage element in series to establish a non-decaying creep discrete element contact model for frozen soil. This achieves good simulation of the three stages of creep in frozen soil: initial creep, steady creep, and non-decaying creep. The method and steps for simulation calculations using this model are also proposed in conjunction with the central difference method. The main shortcomings of this technical solution are: ① Its core model, the Burgers model, is mainly based on cascaded viscous and elastic elements such as the Maxwell model and the Kelvin model. Essentially, it still belongs to the category of element combination models and their improved versions. While its form is simple and the physical meaning of each parameter is clear, it cannot well describe complex multi-directional loading conditions; ② The model considers the time effect to a certain extent, i.e., the stiffness K of the damage element... D The value decreases over time, but it requires separate modeling for the periods when the permafrost is undamaged and the periods when it is damaged, and a unified model for all time periods has not been achieved; ③ The model does not consider the influence of different temperature ranges and does not incorporate temperature effects.

[0005] Application number CN202411531649.6 discloses a calculation method for the elastoplastic model of frozen and reinforced soil and rock in shield tunneling. This method mainly constructs an elastoplastic constitutive model of the soil layer under freezing conditions, which considers the hardening parameters of the soil layer under freezing conditions, and an elastoplastic constitutive model of the soil layer under thawing conditions, which considers the softening parameters of the soil layer under thawing conditions. Based on a sample library of soil and rock materials with water content and soil temperature as inputs and hardening and softening parameters as outputs, a support vector machine model is used for training to obtain the shear modulus and bulk modulus of the intelligent surrogate model, and then constructs a stress-strain constitutive expression that considers hardening and softening factors. The main shortcomings of this technical solution are: ① The method considers the temperature effects of freezing and thawing, but does not consider the influence of time on the parameters and deformation laws of frozen soil; ② The core hardening parameter H(w,t), softening parameter S(w,t), and related model output results of this model all rely on the data training of the intelligent agent model. Its sample library mainly comes from the elastic modulus measured by uniaxial tests of the corresponding specimens obtained through freezing and thawing tests. The size of the sample library and potential interference factors of the test have a significant impact on the reliability of the model.

[0006] Application number CN202410398656.7 discloses a method for inverting soil constitutive model parameters based on a coupled optimization approach. This method mainly addresses the problem of constitutive model parameter optimization and inversion in conventional experiments, providing a method for inverting soil constitutive model parameters based on a coupled optimization approach, improving the inversion calculation speed, stability, and accuracy. It considers two cases: known and unknown initial shear void ratio. A coupled optimization algorithm is formed based on a differential evolution algorithm and a state transition algorithm considering the range and sensitivity correction of soil and rock constitutive parameters, and convenient inversion calculations are achieved on the general Excel platform. The main shortcomings of this technical solution are: ① The Excel platform includes Duncan-Chang EB model, modified Cambridge model, Mohr-Coulomb model, and CSUH model, but does not include the unified hardening constitutive model of permafrost considering time and temperature effects; ② Because the unified hardening constitutive model of permafrost considering time and temperature effects has more time-related variables, its unified input format is no longer suitable for the unified hardening constitutive model of permafrost considering time and temperature effects. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a unified constitutive model and parameter calibration method for permafrost hardening that considers temperature and time effects. This model can characterize the properties of permafrost strength, pre-consolidation compressive stress, strain hardening, and softening under different temperatures, time factors, and stress paths. It is applicable to the field of permafrost performance analysis and evaluation considering environmental temperature changes and long-term deformation, and provides support for permafrost engineering construction in high-altitude and cold regions under warming conditions such as climate warming and humidification. The technical solution is as follows:

[0008] Step 1: Building the basic framework of the model

[0009] A general framework for a constitutive model of permafrost encompassing temperature and time effects was established, clarifying the model's core modules (temperature influence module and time influence module) and their interactions. By defining the influence mechanism of temperature on permafrost strength, preconsolidation pressure, and critical state, as well as the descriptive framework for the time effect on creep behavior, theoretical guidance was provided for subsequent experimental design, equation construction, and parameter calibration.

[0010] Step 2: Indoor Experiments and Core Equation Construction

[0011] Through systematic indoor tests (such as lateral confined compression tests, triaxial shear tests, and creep tests), key mechanical parameters of frozen soil under different temperatures and stress paths (such as preconsolidation pressure, cohesion, and critical state line) are obtained, and core equations describing the effects of temperature and time are established based on the test data.

[0012] Correlation: It provides parameter basis for the elastoplastic constitutive relation in step 3, and provides data support for the creep model in step 4 and the parameter calibration in step 5.

[0013] Step 3: Constructing Elastoplastic Constitutive Relations

[0014] Based on the unified hardening (UH) theoretical framework, the elastoplastic constitutive relation of frozen soil is constructed, including the temperature-dependent yield function, plastic potential function, and hardening law. By introducing temperature-sensitive parameters (such as the critical stress ratio *M*~T~), dynamic simulation of the yield surface change of frozen soil during heating or cooling is achieved.

[0015] Step 4: Constructing the stress-strain relationship considering temperature and time effects

[0016] By coupling the time-hardening creep model with the elastoplastic constitutive relation, a unified stress-strain increment relationship is established. By introducing a temperature-dependent creep rate equation, the creep characteristics of frozen soil under long-term load and temperature changes (such as the initial creep, steady creep, and accelerated creep stages) are described.

[0017] Step 5: Model parameter inversion and calibration

[0018] A global optimization algorithm (such as a coupling of differential evolution and state transition algorithms) is employed to efficiently invert model parameters using multi-source experimental data (different temperatures and stress paths). By minimizing the error between model predictions and experimental data, the universality and accuracy of the model in complex environments are ensured.

[0019] Beneficial effects

[0020] 1. It achieves a quantitative description of temperature effects such as frozen soil strength and critical state, and realizes high-precision simulation of the yield surface change of frozen soil throughout the phase transition range, thus improving the applicability of the model under complex temperature conditions.

[0021] Introducing the temperature-dependent tensile strength parameter σ0 can accurately reflect the influence of temperature on the strength of frozen soil. A critical state parameter M considering both temperature and pressure-melt effects is proposed. T This paper corrects the yield surface and plastic potential surface of traditional models, enabling the description of the critical state of frozen soil under different temperature and confining pressure conditions. A parabolic critical state line (CSL) incorporating temperature effects is proposed, simulating the influence of temperature on strength and pressure-melt phenomena. A temperature loading line considering both positive and negative temperature ranges is established, and the temperature-dependent pre-consolidation pressure parameter p is determined. xT It accurately characterizes the effect of temperature on stress-strain relationship and introduces yield surface characterization, realizing precise simulation of yield surface changes in frozen soil during temperature rise and fall.

[0022] 2. The proposed improved time-hardening creep model achieves high-precision prediction of permafrost creep behavior across the entire temperature range and under varying moisture conditions, overcoming the problem that existing technologies cannot uniformly consider temperature and long-term time effects.

[0023] A time-hardening creep model expression combining inverse exponential and typical power function factors is proposed, solving the problem of poor convergence of traditional models in the frozen soil phase transition range. This achieves high-precision simulation of creep rate across the entire temperature range of the phase transition and under the influence of moisture variations. By combining multi-source strain with elastoplastic constitutive relations, temperature effects and long-term time effects are uniformly considered.

[0024] 3. A multi-parameter calibration method for temperature and time effects is proposed to improve the efficiency of model parameter inversion.

[0025] A method for parameter inversion and calibration of constitutive models for permafrost considering temperature and time effects is proposed. The index system for undetermined model parameters is clarified, and an optimization algorithm based on a combination of differential evolution and state transition algorithms with local search operators is constructed. The global search capability of the optimization algorithm is improved through multi-group collaboration and parameter adaptation. This enhances the efficiency and accuracy of multi-parameter calibration under complex conditions. The parameter inversion input format is standardized, simplifying the calibration process. This method addresses the difficulty of rapidly achieving multi-parameter calibration in existing schemes under complex conditions considering temperature and time effects. Attached Figure Description

[0026] Figure 1 A schematic diagram illustrating the basic process of constructing and calibrating a constitutive model for permafrost that takes into account temperature and time effects;

[0027] Figure 2A schematic diagram of a unified constitutive model framework for permafrost hardening that takes into account temperature and time effects.

[0028] Figure 3 This is a schematic diagram of the LY line for frozen soil and thawed soil in the positive and negative temperature ranges;

[0029] Figure 4 A schematic diagram of the LY line in the e–ln p space;

[0030] Figure 5 This is a schematic diagram showing the relationship between normalized frozen soil shear strength and confining pressure.

[0031] Figure 6 This is a graph showing the change in cohesion as a function of temperature.

[0032] Figure 7 For parabolic CSL (M=1.2, p m =850, q m =528);

[0033] Figure 8 Critical state line CSL and parameter M T (M=1.39 MPa, σ0 = 2.75 MPa, p m =14.46 MPa).

[0034] Figure 9 Comparison of critical state line prediction results (M=1.39 MPa, σ0 = 2.75 MPa, p) m =14.46 MPa).

[0035] Figure 10 Logical block diagram of elastoplastic constitutive relations

[0036] Figure 11 Flowchart of the process for optimizing the algorithm to invert the constitutive model parameters of soil;

[0037] Figure 12 This is a flowchart of the coupling optimization algorithm. Detailed Implementation

[0038] Constitutive models and parameter calibration methods for permafrost considering temperature and time effects include the following steps:

[0039] Step 1: Construction of the basic model framework: Establish the overall architecture of the frozen soil constitutive model covering temperature and time effects, and clarify the core modules of the model and their interaction relationships; by defining the influence mechanism of temperature on frozen soil strength, pre-consolidation pressure, and critical state, as well as the descriptive framework of time effect on creep behavior, establish a unified hardening constitutive model framework that includes elastoplastic constitutive and stress-strain increment relationships.

[0040] The constitutive model for permafrost considering temperature and time effects described in this invention mainly comprises two modules: temperature influence and time influence, as follows: Figure 2 As shown.

[0041] Regarding the influence of temperature, the loading lines of frozen soil at different temperatures are obtained mainly based on lateral compression tests of frozen soil at different temperatures, and constitutive core parameters and expressions under the influence of temperature and different stress paths are constructed. On the other hand, the influence of key parameters such as strength and cohesion on frozen soil at different temperatures is obtained through triaxial tests of frozen soil at different temperatures, and the critical state lines are obtained and the corresponding critical state parameters are constructed.

[0042] Regarding the effects of time, the long-term creep deformation characteristics of frozen soil are obtained mainly based on compression creep tests under different loading stress conditions, and a time-hardening creep equation is constructed.

[0043] The elastoplastic constitutive part of the model is an extension and update based on the unified hardening UH constitutive model. The effects of temperature on the early consolidation pressure, strength, and stress-deformation characteristics of frozen soil are reflected in the hardening law, yield function, and flow law, respectively. The influence of temperature on the elastic modulus is also considered in the elastic constitutive model. In the stress-strain increment iteration relationship, the creep increment is obtained based on the time hardening creep equation of frozen soil under different temperature and water content conditions. The mapping relationship between the creep increment and the stress-strain increment and stiffness matrix in the elastoplastic constitutive model is constructed, thereby realizing the unified coupling of time effect and temperature effect, and constructing a constitutive model of permafrost that considers temperature and time effects.

[0044] Step 2: Indoor Experiments and Core Equation Construction: Through systematic indoor experiments, the key mechanical parameters and deformation laws of frozen soil under different temperatures, times and stress paths are obtained, and core equations describing the effects of temperature and time are established based on the experimental data.

[0045] (1) Effect of temperature on early consolidation compressive stress

[0046] The influence of temperature on preconsolidation compressive stress was mainly obtained from confined compression tests of frozen soil at different temperatures. The tests employed a progressively increasing loading process, and according to the "Standard for Geotechnical Testing Methods," a constant load of 24 hours, or a displacement difference ≤0.01 mm per hour, was used as the compressive stability standard. For the stress-deformation results of the samples obtained under different temperature conditions, the double logarithmic method of ln(1+e) −lg p was used to describe the frozen soil compression curve; the stress corresponding to the intersection of the two straight lines is the preconsolidation pressure.

[0047] Based on the relationship between pre-consolidation compressive stress and temperature in frozen soil and thawing soil stages respectively, a functional relationship between pre-consolidation pressure and temperature, i.e., the LY line expression, is proposed:

[0048] (1)

[0049] (2)

[0050] In the formula, T is the current temperature; T0 is the initial temperature, and the subscript 0 indicates the initial state; p xT The current pre-consolidation stress is represented by the subscript xT, indicating the location of the intersection of the yield surface and the x-axis at the current temperature T, i.e., the pre-consolidation pressure, in space pq; p x γ represents the pre-consolidation stress at T0, and the subscript x indicates the position of the pre-consolidation pressure in pq space at the intersection of the yield surface and the x-axis at the initial temperature; γ is the model material parameter, reflecting the degree of influence of temperature change on the pre-consolidation compressive stress. Equation (1) represents the functional relationship between the pre-consolidation pressure and temperature of frozen soil in the negative temperature stage, and Equation (2) represents the functional relationship between the pre-consolidation pressure and temperature of frozen soil in the negative temperature stage.

[0051] The plastic volumetric strain is equal at any two points on the LY line; if we assume that the volume change caused by heating is irreversible, that is, the volumetric strain increases (porosity decreases) during heating and the volumetric strain increment is zero (porosity remains unchanged) during cooling, then the plastic volumetric strain produced by the purely force-driven compression and springback process A→B→C is equal to that produced by the heating, compression, springback, and cooling process A→D→E→C→C'; BE is the LY line, p xT The corresponding point E is located on the springback line BE passing through point B at temperature T0; the pre-consolidation stress at point C after heating is p. xT The initial consolidation stress before heating is p x Furthermore, the LY line coincides with the springback line, thus the temperature effect can be converted into a superconsolidation effect, such as... Figure 4 As shown.

[0052] Based on the relationship between the pre-consolidation compressive stress of frozen soil and temperature in different temperature ranges, it can be seen that the pre-consolidation compressive stress generally increases as the temperature decreases. In order to uniformly describe the continuous variation characteristics of frozen soil across the entire temperature range from positive to negative, and to avoid convergence problems near 0℃, the following exponential formula is used:

[0053] (3)

[0054] In the formula, T is the current temperature; p xT This represents the current pre-consolidation stress; p xmin and p xmax These are the asymptotic values ​​corresponding to the high and low temperature regions, i.e., the minimum and maximum values ​​of the early consolidation stress. The subscript xmin indicates the minimum value and xmax indicates the maximum value. k px The slope is the curve near T=0℃, and the subscript px indicates the correlation curve of the early consolidation pressure.

[0055] When incorporating the aforementioned core equations into the constitutive relation, the key lies in applying the known pre-consolidation compressive stress p at a given temperature T0. x Solve for the pre-consolidation compressive stress p at any temperature T. xT . (T0, p x Substitute into the LY line:

[0056] (4)

[0057] We can obtain:

[0058] (5)

[0059] Therefore, containing p x The pre-consolidation compressive stress p corresponding to temperature T0. xT Represented as:

[0060] (6)

[0061] In the formula, T is the current temperature; p xT p represents the pre-consolidation compressive stress corresponding to T. x k represents the pre-consolidation compressive stress corresponding to temperature T0. px Let p be the slope of the segment near T=0℃. xmax and k px With two parameters, this formula can describe the key parameters of the early consolidation stress corresponding to the entire temperature range of positive and negative temperatures under freeze-thaw conditions, so as to reflect the influence of temperature effect on frozen soil.

[0062] (2) Effect of temperature on strength

[0063] The effect of temperature on strength is mainly based on triaxial tests of frozen soil at different temperatures. The deformation and strength characteristics of frozen soil are tested under different temperatures, confining pressures, and stress conditions to analyze its internal mechanical behavior. A temperature control system is used to precisely maintain the samples under the set temperature conditions to simulate the behavior of frozen soil in its natural state. Strength parameters cohesion and internal friction angle are mainly calculated using the Mohr-Coulomb strength criterion. Shear stress-normal stress curves are plotted using multiple sets of test data. Cohesion c can be obtained through linear fitting, and the friction angle ϕ is calculated using the slope of the failure envelope obtained from the tests. Through a series of shear tests under different confining pressures, the final stress state reached by the frozen soil during shearing is measured, and the critical state line can be plotted in the pq coordinate system space of the effective average stress p and deviatoric stress q.

[0064] The critical state line of frozen soil does not pass through the origin of the pq coordinate system due to the cementing effect of ice, and the strength exhibits nonlinearity due to the pressure-melt phenomenon, such as... Figure 5 As shown.

[0065] like Figure 6As shown, considering the linear increase in cohesion with decreasing temperature, the tensile strength σ0 is expressed as:

[0066] (7)

[0067] Where σ0 is the tensile strength, and the subscript 0 indicates the limit value; c is the cohesion. is the internal friction angle, and k is the slope parameter of cohesion as a function of temperature.

[0068] When the frozen soil stress p is small, the critical state line is close to a straight line. The internal friction angle is calculated using the critical state stress ratio M under the linear assumption. :

[0069] (8)

[0070] Where M is the critical stress ratio. This is the internal friction angle when the critical state line is close to a straight line, and the subscript 0 indicates the meaning of the limit value.

[0071] The nonlinearity of intensity that occurs when p is large can be represented by a parabola of the following form:

[0072] (9)

[0073] In the formula q m and p m Let be the coordinates of the vertex of the parabola, with the subscript m indicating the peak value; 'a' is related to the size of the parabola's opening; the intersection of this parabola and the horizontal axis is (-σ0, 0). Substituting p = -σ0 and q = 0 into the above equation, we get:

[0074] (10)

[0075] The slope of the parabola at the point (-σ0, 0) is the critical stress ratio M. Differentiation yields:

[0076] (11)

[0077] (12)

[0078] (13)

[0079] Substituting into equation (10), we get:

[0080] (14)

[0081] Substituting equations (13) and (14) into equation (9), we obtain the expression for the critical state line CSL:

[0082] (15)

[0083] The key parameters involved in the formula are strength σ0, critical stress ratio M, and peak value p. m .

[0084] When σ0 approaches 0 and p m As the value approaches infinity, the permafrost CSL degenerates into the thawed CSL.

[0085] (16)

[0086] The critical stress ratio M of frozen soil, considering temperature effects, is calculated based on the slope of the straight line between two points (p, q) and (-σ0, 0) on the critical state line CSL. T The subscript T indicates the effect of temperature:

[0087] (17)

[0088] (18)

[0089] The critical state line CSL and critical state parameter M were obtained based on the triaxial test results. T like Figure 8 As shown, the comparison between the predicted results and the experimental results is as follows: Figure 9 As shown.

[0090] (3) The influence of temperature and time on deformation

[0091] The effects of temperature and time on deformation were mainly obtained from frozen soil creep tests. Based on the test results, a time-hardening creep (THC) model was constructed. The effects of temperature and water content were also considered in the model. An improved time-hardening creep (TWTHC) model was constructed by combining an inverse exponential temperature influence factor and a typical power function water content influence factor.

[0092] (19)

[0093] In the formula, The axial creep strain rate is represented by the superscript cr, which indicates the creep process; q represents the generalized shear stress. Under uniaxial compressive stress, the confining pressure is zero, at which point q equals the axial stress. The subscript 'a' indicates axial direction; 't' represents time; 'T' represents temperature; 'w' represents water content; and A, n, m, d, and e represent parameters of the time-hardening creep model. Integrating the above equation over time 't' yields the relationship between the strain of frozen soil and time under different stresses, temperatures, and water contents. That is, the model can be expressed in the form of strain rate or strain variable.

[0094] The TWTHC model in the form of Equation (19) is only suitable for directly describing uniaxial compression creep tests. To describe the effects of different stress paths, the TWTHC model is made three-dimensional based on Prandtl-Reus plasticity theory:

[0095] (20)

[0096] In the formula, For creep strain rate tensor; For creep strain increment tensor, the superscript cr indicates the creep meaning, and the subscript ij indicates the direction of the component in the strain tensor; This is the equivalent creep strain increment, which is equal to the uniaxial creep strain increment here; The equivalent stress is equal to q in the shear stress path; p is the stress deviatoric tensor; p is the effective mean principal stress. This is the Kronecker function, which has a value of 1 when the indices i and j are equal, and 0 otherwise. Let be the stress tensor.

[0097] When the above tensor degenerates into a three-dimensional principal stress form:

[0098] (twenty one)

[0099] In the formula, , and These represent the first, second, and third principal strain rates of creep, respectively, with subscripts 1, 2, and 3 indicating the directions of the principal stress strains; , and These are the first, second, and third principal stresses, respectively. The subscripts 1, 2, and 3 indicate the direction of the principal stress strain. In a uniaxial creep test, the first principal stress... Equal to axial stress .

[0100] When degenerating into a uniaxial stress path, lateral stress ,at this time Generalized shear stress Then the axial creep strain is:

[0101] (twenty two)

[0102] Combining the time-hardening creep model that considers the effects of temperature and moisture content with the isotropic linear elastic model, the stress-strain increment relationship in the principal stress form is as follows:

[0103] (twenty three)

[0104] In the formula , and These are the increments of the first, second, and third principal stresses, respectively. , and These are the first, second, and third principal strain increments, respectively. It is a third-order stiffness matrix:

[0105] (twenty four)

[0106] In the formula This is a third-order elastic stiffness matrix, where the superscript e indicates elasticity, and E and v are the elastic modulus and Poisson's ratio, respectively.

[0107] For the stress-strain relationship under the commonly used laterally confined compression (K0) stress path, substituting the creep stress condition and the boundary condition of the K0 path into equation (23) yields:

[0108] (25)

[0109] In the formula is the element in the i-th row and j-th column of the third-order stiffness matrix.

[0110] Based on the stress-strain relationship described above, the theoretical stress-strain relationship for laterally confined compression creep can be quickly calculated using numerical methods such as the forward Euler method. The derivation process for the stress-strain increment relationship of other stress paths is similar, that is, the boundary conditions of the stress path to be determined and equation (23) are solved simultaneously.

[0111] Step 3: Construction of elastoplastic constitutive relation: Based on the unified hardening (UH) theoretical framework, the elastoplastic constitutive relation of frozen soil is constructed, and the influence term of temperature parameter is introduced to realize the dynamic simulation of the yield surface, plastic potential surface and hardening law of frozen soil in the temperature range of the whole time period.

[0112] The Unified Hardening (UH) constitutive model is adopted as the basic framework of the elastoplastic constitutive part. By unifying the modeling of elastoplastic theory and hardening mechanism, it can simultaneously describe the behavior of soil and rock materials under complex stress states such as loading, unloading and reverse loading. In particular, it has a strong adaptability to the coupling effect of isotropic hardening and kinematic hardening in cyclic loading.

[0113] The elastoplastic constitutive part consists of three main components: the yield surface, the plastic potential surface, and the hardening law, such as... Figure 10 As shown. Based on the unified hardening constitutive framework, there exist a current yield surface and a reference yield surface. The current yield surface passes through the current stress point, and the reference yield surface passes through the corresponding normally consolidated point. The relative positional relationship between the two yield surfaces is represented by the overconsolidation parameter R. The plastic potential surface determines the direction of plastic strain flow, i.e., the strain ε in the plastic body. v p and plastic shear strain εd p The ratio. The hardening law relates stress and strain in the plastic body. The hardening parameter in the hardening law used for the current yield surface is H, and the hardening parameter in the hardening law used for the reference yield surface is ε. v p .

[0114] The constitutive model for permafrost considering temperature and time effects described in this invention, based on a unified hardening elastoplastic constitutive model, introduces the influence of temperature and time effects, and establishes a critical state parameter M considering the effects of temperature and pressure melting in the yield criterion, i.e., the current yield surface and the reference yield surface function. T It includes the critical state parameter M of the molten soil, the tensile strength σ0, and the compressive molten stress p. m The effect of strength variation on yield surface and elastic modulus E was realized, and the pre-consolidation pressure p was introduced into the overconsolidation parameter R. xT The influence of temperature on stress and strain is considered, and a unified temperature loading line considering both positive and negative temperature stages is established to describe the consolidation compressive stress p in the early stage of both positive and negative temperature stages. xT The yield surface size changes with temperature; in the flow law, the plastic potential surface also considers the critical state parameter M. T The influence of hardening on the critical state parameter M in the hardening parameter H is updated in the hardening process. fT and M T Simultaneously, the early consolidation compressive stress p in the temperature range throughout the entire time period was considered. xT Its function.

[0115] (1) Yield function

[0116] Based on the UH model theoretical framework, the current yield surface and the reference yield surface are used to describe the overconsolidation and normal consolidation states of frozen soil, respectively. Current yield function. and reference yield function It is expressed as follows:

[0117] (26)

[0118] (27)

[0119] In the formula All superscripts indicate parameters related to the reference yield surface.

[0120] The temperature-dependent critical state stress ratio is expressed as:

[0121] (28)

[0122] Where σ0 is the intensity parameter including temperature effect:

[0123] (29)

[0124] In the formula, c is the cohesive force, φ is the internal friction angle, k is the slope parameter of the cohesive force as a function of temperature, and M is the critical stress ratio.

[0125] (2) Plastic potential function

[0126] Using the associated flow rule, the plastic potential surface g and the yield surface have the same form, expressed as:

[0127] (30)

[0128] (3) Hardening Law

[0129] The reference yield surface corresponds to the normal consolidation state of the soil. On the same reference yield surface, the stress-induced plastic volumetric strain ε... v p They are equivalent, and their hardening law is the same as that of the modified Cambridge model, expressed as:

[0130] (31)

[0131] With plastic volumetric strain ε v p As a hardening parameter, its superscript 'p' indicates plasticity, and its subscript 'v' indicates a volume-related parameter. The reference yield surface is represented as follows:

[0132] (32)

[0133] In the above formula, e0 is the initial void ratio, and the subscript 0 indicates the initial meaning; λ is the slope of the normal compression line of frozen soil at temperature T0 in the e-lnp plane; κ is the slope of the elastic rebound line of frozen soil at temperature T0 in the e-lnp plane; λ and κ are both constants; This is the intersection of the initial yield surface and the p-axis.

[0134] The mean principal stress at the reference stress point can be expressed as:

[0135] (33)

[0136] in .in Based on the formula (6) for calculating the early consolidation compressive stress in the reference yield surface, the following is obtained:

[0137] (34)

[0138] Since the current yield surface is geometrically similar to the reference yield surface, it can be represented as:

[0139] (35)

[0140] Where H is the hardening parameter, expressed as:

[0141] (36)

[0142] Considering the potential intensity M at temperature fT Represented as:

[0143] (37)

[0144] Where R T The overconsolidation parameter, combined with equation (33), is expressed as:

[0145] (38)

[0146] Step 4: Constructing the stress-strain relationship considering temperature and time effects: Couple the time-hardening creep model with the elastoplastic constitutive relation to establish a unified stress-strain increment relationship to describe the mechanical properties of frozen soil under long-term load and temperature changes.

[0147] In this model, the total strain increment dε ij The elastic strain increment dε e ij Plastic strain increment dε p ij and creep strain increment dε cr ij The sum, its expression is as follows:

[0148] (39)

[0149] (1) Elastic strain increment

[0150] The elastic strain increment is obtained according to the generalized Hooke's law as follows:

[0151] (40)

[0152] (41)

[0153] In the formula, E is the elastic modulus, v is Poisson's ratio, and e0 is the initial void ratio. Let be the slope of the unloading line in the e-lnp space during the isotropic compression unloading test, p be the average stress, and σ0 be the strength parameter including temperature effects (see (29)). According to the indexing method and summation convention, That is, the sum of the increments of the three principal stresses.

[0154] (2) Increment of plastic strain

[0155] When the associated flow rule is applied in the transformed stress space, its yield surface function and plastic potential surface function can be uniformly expressed as follows:

[0156] (42)

[0157] In the formula To transform the average principal stress at the current stress point in the stress space, Let be the average principal stress at the initial stress point in the transformed stress space, where is the hardening parameter of the transformed stress space. and its contained parameters , The expressions satisfy equations (36) to (38).

[0158] According to the flow law, the increment of plastic strain is:

[0159] (43)

[0160] (44)

[0161] (3) Creep strain increment

[0162] The creep strain increment is mainly calculated based on the improved time-hardening creep (TWTHC) model considering the effects of temperature and moisture, constructed from the preceding equations (19) to (20), and is expressed as:

[0163] , (45)

[0164] (4) Elastoplastic constitutive tensor

[0165] According to the generalized Hooke's law, the relationship between the stress increment and the elastic strain increment is as follows:

[0166] (46)

[0167] Among them, the elastic-plastic stiffness matrix Represented as:

[0168] (47)

[0169] In the formula, G and L are Lamé constants:

[0170] (48)

[0171] Step 5: Model parameter inversion and calibration: A global optimization algorithm is used to efficiently invert the model parameters by combining multi-source experimental data; by minimizing the error between the model predictions and the experimental data, the universality and accuracy of the model in complex environments are ensured.

[0172] (1) Undetermined parameters of the model

[0173] Based on the preceding model construction process, the undetermined parameters involved in the constitutive model of permafrost considering temperature and time effects mainly include the critical stress ratio, Poisson's ratio, slopes of the unloading line and compression line, pre-consolidation compressive stress corresponding to the initial temperature T0, the slope of the pre-consolidation pressure curve at point 0 and its maximum asymptotic value, the slope of cohesion as a function of temperature, the peak compressive stress at the critical state line, and time-hardening creep parameters. These are shown in Table 1.

[0174] Table 1. Parameter list of constitutive models for permafrost considering temperature and time effects.

[0175]

[0176] (2) Constitutive model parameter inversion method

[0177] The process of determining constitutive model parameters based on inversion methods is as follows: Figure 11 As shown, the main steps are as follows:

[0178] ① The optimization algorithm reads in the number and range of parameters to be optimized and generates multiple sets of model parameters. If the optimization algorithm is in the first generation, the model parameters of all individuals or all groups in the population are randomly generated. If it is the second generation or subsequent iterations, the model parameters of all individuals or all groups in the population are generated by the optimization algorithm based on the feedback of the error function values ​​of each set of model parameters.

[0179] ② Calculate the error function as the objective function value of the optimization problem. The constitutive model reads the model parameters from the optimization algorithm and the predicted values ​​of the stress-strain curves based on the initial conditions known from the experiment. Then, it calculates the error function based on the predicted values ​​of the stress-strain curves and the measured values ​​of the experimental stress-strain curves. Finally, the error function value is returned to the optimization algorithm as the objective function value.

[0180] ③ The optimization algorithm attempts to generate a better solution based on the error function value corresponding to the output parameters, in order to make the error function value smaller, thereby making the predicted value of the stress-strain curve closer to the measured value of the stress-strain curve in the experiment.

[0181] ④ The above process is repeated until the termination condition is met. The termination condition may be that the optimization algorithm reaches its maximum number of iterations, or the value of the error function does not decrease after the specified number of iterations in the optimization algorithm, or the number of times the error function is called reaches the set maximum value, or the error function is less than the set value.

[0182] (3) Model parameter inversion coupled optimization algorithm

[0183] Determining constitutive model parameters through inversion using optimization algorithms from indoor experiments places high demands on the accuracy and stability of the optimization algorithms. This invention employs an optimization algorithm coupled with a local search operator in a state transition algorithm to invert constitutive model parameters. For example... Figure 12 As shown, the main steps of the algorithm are as follows:

[0184] ① Determine the algorithm control parameters for the differential evolution algorithm and the modified local search operator. The control parameters for the differential evolution algorithm include: population size N. p Maximum number of calls to the error function F esmax The maximum number of iterations G, and the algorithm control parameters of MLS include calculating the coupling probability p. g Parameters such as rotation factor control parameter Ω.

[0185] ② The initial population is randomly generated based on the Sobol method, and the initial population is evaluated by calculating the mean relative error (MRE) of each individual in the initial population and setting the number of generations g = l.

[0186] (49)

[0187] In the formula, and These represent the model predicted value and the experimental measured value, respectively. The superscript i indicates the sequence number, the subscript m indicates the model value, and the subscript e indicates the experimental value; N represents... or The number of vectors; It represents a set of constitutive model parameters.

[0188] ③ Determine if the termination condition or the maximum number of generations has been reached: If yes, the evolution terminates, and the best individual at this point is output as the solution; otherwise, continue to the next step. During the optimization process, if the objective function value does not decrease after 0.02×G iterations, half of the worse individuals in the population are re-initialized uniformly and randomly to increase diversity and avoid premature convergence.

[0189] ④ The mutation operator control parameter F and the crossover operator control parameter CR of the differential evolution algorithm are dynamically adjusted, and then mutation and crossover operations are performed to process the boundary conditions and obtain a temporary population.

[0190] (50)

[0191] (51)

[0192] In the formula, g nThe index n represents the current generation, and G represents the maximum number of generations allowed for optimization. The mutation operator is initially set to 1 and ends close to 0.5. The rand function generates a uniformly distributed random number between 0 and 1.

[0193] ⑤ Evaluate the temporary population, calculate the objective function value of each individual in the temporary population, and summarize the parameters of the original population and the temporary population to obtain the globally optimal constitutive model.

[0194] ⑥ Calculate the coupling probability p based on the parameters of the most recent generations of optimal constitutive models. g If the coupling probability p g Random numbers greater than 0 and 1 are used to perform a local search operation on the globally optimal model parameters. The modified local search operator attempts to find better parameters near the globally optimal constitutive model parameters, and if better parameters are found, they overwrite the previous globally optimal constitutive model parameters.

[0195] ⑦ Perform a one-to-one selection operation on the individuals in the temporary population and the corresponding individuals in the original population to obtain a new population.

[0196] ⑧ Evolutionary generation g = g+1, go to step ④.

[0197] (4) Data format

[0198] This invention proposes a method for calibrating parameters of a constitutive model for permafrost that considers temperature and time effects. The data area includes sample information data, parameter and error data, experimental data, optimization process and sensitivity data, simulation prediction output, and plotting data. The data format should support input tables for experimental data of five commonly used stress paths: isotropic compression test (1_IsoCom), drained triaxial shear test with constant confining pressure (2_CD), undrained triaxial shear test with constant confining pressure (3_CU), lateral confinement test (4_K0), and drained shear test with constant p stress path (5_ConstP). The input format for all five tests is the same, including a remarks line, an initial condition area, an experimental data area, and an operation button area.

[0199] The data types in the experimental data range will vary depending on the type of experiment, including mean stress. Volumetric strain void ratio e, axial strain Axial stress Shear stress The data includes time and temperature effects, specifically time t (s) and temperature T (°C). Parameter and error data include the error between the experimental curves and the constitutive model's simulated prediction curves for each set of experiments, as well as the optimal parameters and corresponding error values ​​for each generation during the inversion process, showing the decrease in error with each optimization generation. Optimization process and sensitivity data include the error function type, constitutive model type, parameter signs, upper and lower limits, decimal places, initial values, and optimal optimization parameters. Model prediction output and plotting data include the calculation results and prediction curves of the constitutive model.

[0200] The inventive points are as follows:

[0201] This invention characterizes the effects of temperature on the strength, pre-consolidation compressive stress, and critical state of frozen soil through a model, proposes a tensile strength parameter σ0 that considers temperature correlation, and innovatively introduces a critical state parameter M that considers the effects of temperature and compressive melting. T The critical stress ratio M in the yield surface and plastic potential surface of the traditional model is represented by M. T Replacement, overconsolidated parameter R T Potential strength M f Both the hardening parameter H and the critical state stress ratio M, which takes temperature into account, are used. T A description is provided. New tensile strength σ0 and compressive stress p are proposed. m The parabolic critical state line (CSL) with two temperature effect parameters enables the simulation of intensity and critical state considering the temperature effect.

[0202] The model establishes a unified temperature loading line that considers both positive and negative temperatures throughout the entire time period, overcoming the limitation of existing models for pre-consolidation compressive stress in frozen soil that can only consider positive or negative temperatures. The newly established pre-consolidation compressive stress p xT The variation of the yield surface across the entire phase transition temperature range can be considered, thus achieving a unified description of the yield surface variation across the phase transition temperature range during the time-varying process of permafrost warming.

[0203] This invention proposes an improved time-hardening creep model that comprehensively considers the effects of temperature and moisture content. It employs a combination of inverse exponential and typical power function factors, addressing the insufficient convergence of traditional models in the phase transition range. This achieves high-precision creep rate simulation across the entire temperature range of the phase transition and the influence of moisture variations. Furthermore, by combining multi-source strain with elastoplastic constitutive relations, a stress-strain relationship simulation method that uniformly considers temperature and long-term time effects is constructed.

[0204] This invention proposes a parameter inversion calibration method for constitutive models of permafrost considering temperature and time effects. It also proposes an optimization algorithm-based inversion calibration method coupled with a local search operator of a differential evolution algorithm and a state transition algorithm, possessing powerful global search capabilities. The model has a unified input format, supporting convenient batch writing, saving, reading, and plotting of various data under different stress path test conditions, such as isotropic compression tests, laterally confined compression tests, and triaxial tests with constant confining pressure. In addition to strain and stress columns, the input format also includes time and temperature columns.

[0205] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention. The scope of protection claimed by the appended claims and their equivalents is defined.

Claims

1. A method for constitutive model of permafrost considering temperature and time effects, characterized in that: Step 1, model basic framework construction: Establish the overall framework of the permafrost constitutive model covering temperature effects and time effects, and clarify the core modules of the model and their interaction; define the influence mechanism of temperature on the strength of permafrost, the pre-consolidation pressure, and the critical state, and the description framework of time effects on creep behavior; Step 2, laboratory test and core equation construction: Through systematic laboratory tests, obtain the key mechanical parameters of permafrost under different temperatures and stress paths, and establish the core equation to describe the temperature and time effects based on the test data; Step 3, construction of elastic-plastic constitutive relationship: Based on the unified hardening UH theory framework, the elastic-plastic constitutive relationship of permafrost is constructed, and the dynamic simulation of the yield surface change of permafrost in the process of temperature rise or fall is realized by introducing temperature sensitive parameters; Step 4, construction of stress-strain relationship considering temperature and time effects: Couple the time hardening creep model with the elastic-plastic constitutive relationship to establish a unified stress-strain increment relationship, and describe the creep characteristics of permafrost under long-term load and temperature change by introducing temperature-related creep rate equation; Step 5, model parameter inversion calibration: Using global optimization algorithm, combine multi-source test data to efficiently inverse the model parameters; minimize the error between the model prediction value and the test data to ensure the universality and accuracy of the model in complex environment; The step 2 further includes the following contents: (1) Temperature effect on pre-consolidation pressure: based on the relationship between pre-consolidation pressure of permafrost and temperature in different temperature intervals, the following exponential formula is used to describe it: （3） where T is the current temperature; p xT is the current pre-consolidation stress; p xmin and p xmax are the asymptotic values corresponding to the high and low temperature regions, i.e. the minimum and maximum values of the pre-consolidation stress, k px is the slope of the segment around T = 0°C; (2) Temperature effect on strength: through a series of shear tests under different confining pressures, the final stress state reached by permafrost in the shearing process is measured, and the critical state line is plotted in the p-q coordinate system of effective mean stress p and deviatoric stress q; (3) Temperature and time factors on deformation: based on the test results, the time hardening creep THC model is constructed, and the improved time hardening creep TWTHC model is constructed by combining the inverse exponential temperature influence factor and the typical power function type water content influence factor: （19） wherein represents the axial creep strain rate; q represents the generalized shear stress, which is equal to the axial stress when the confining pressure is 0 under the uniaxial compression stress path ; t is time; T is temperature; w is water content; A, n, m, d, and e represent time hardening creep model parameters; the above equation is integrated with respect to time t to obtain the relationship between the strain of frozen soil and time under different stress, temperature, and water content conditions, i.e., the model is expressed in the form of strain rate, and can also be expressed in the form of strain amount; Step 3 further includes the following: incorporating the effects of temperature and time, establishing a critical state parameter M that considers the effects of temperature and pressure melting in the yield criterion, i.e., the current yield surface and the reference yield surface function. T It includes the critical state parameter M of the molten soil, the tensile strength σ0, and the compressive molten stress p. m To realize the effect of strength variation on yield surface and elastic modulus E, the pre-consolidation pressure p is introduced into the overconsolidation parameter R. xT Considering the influence of temperature on stress and strain, a unified temperature loading line was established that takes into account both positive and negative temperature stages, to describe the consolidation compressive stress p in the early stage of both positive and negative temperature stages. xT The relationship between temperature and yield surface size changes; in flow laws, the plastic potential surface considers the critical state parameter M. T The influence of hardening on the critical state parameter M in the hardening parameter H is updated in the hardening process. fT and M T Simultaneously, the early consolidation compressive stress p in the temperature range throughout the entire time period was considered. xT Its function; The step 4 further includes the following contents: the total strain increment dε ij is the elastic strain increment dε e ij , the plastic strain increment dε p ij and the creep strain increment dε cr ij whose expression is given by ； wherein: dε ij is the total strain increment, dε e ij is the elastic strain increment, dε p ij is the plastic strain increment, dε cr ij is the creep strain increment; the lower index ij represents the directions corresponding to the components of the strain tensor, the upper index e indicates elasticity, p indicates plasticity, and cr indicates creep.

2. The multi-year frozen soil constitutive model and parameter calibration method considering temperature and time effects according to claim 1, characterized in that: The step 5 further includes the following contents: model parameters to be determined: the parameters to be determined involved in the constitutive model of permafrost considering temperature and time effects include critical state stress ratio, Poisson's ratio, unloading line and compression line slope, pre-consolidation pressure corresponding to initial temperature T0, slope and maximum asymptotic value of pre-consolidation pressure curve at 0 point, temperature-dependent cohesion, critical state line peak point pressure, and time hardening creep parameters. 3.The method for constitutive model of permafrost considering temperature and time effects according to claim 2, characterized in that: the step 5 further includes the following contents: the main steps of determining the constitutive model parameters based on the inversion method are as follows: ① The optimization algorithm reads in the number and range of the parameters to be optimized and generates multiple sets of model parameters; if the optimization algorithm is in the first generation, all individuals or all sets of model parameters in the population are randomly generated; if it is the second generation and subsequent iteration numbers, all individuals or all sets of model parameters in the population are generated by the optimization algorithm according to the error function value feedback of each set of model parameters; ② Calculate the error function as the objective function value of the optimization problem: the overall architecture of the constitutive model is composed of an elastic-plastic constitutive model considering temperature and time effects and a stress-strain increment relationship; the elastic-plastic constitutive model obtains the elastic-plastic stress-strain increment and stiffness matrix based on the generalized Hooke's law, hardening rule, yield function and flow rule, and then couples the creep increment obtained from the time hardening creep equation to construct the total stress-strain mapping relationship; when calculating the error, the constitutive model reads in the model parameters transmitted from the optimization algorithm and calculates the stress-strain curve prediction value according to the initial conditions known from the test, and calculates the error function according to the stress-strain curve prediction value and the measured stress-strain curve; finally, the error function value is returned to the optimization algorithm as the objective function value; ③ The optimization algorithm tries to generate better solutions according to the error function value corresponding to the transmitted parameters, in order to make the error function value smaller, so that the stress-strain curve prediction value is closer to the measured stress-strain curve in the test; ④ The above process is repeated until the termination condition is met: the termination condition may be that the optimization algorithm reaches the maximum number of iterations, or the error function value does not decrease after a specified number of iterations in the optimization algorithm, or the error function call number reaches the maximum set value, or the error function is less than the set value.

4. The multi-year frozen soil constitutive model and parameter calibration method considering temperature and time effects according to claim 3, characterized by: The step 5 further comprises the following contents: model parameter inversion coupled with optimization algorithm: the optimization algorithm based on the differential evolution algorithm and the local search operator of the state transition algorithm is coupled to invert the constitutive model parameters, and the main steps of the algorithm are as follows: ① Determine the algorithm control parameters of the differential evolution algorithm and the modified local search operator; ② Randomly generate an initial population based on the Sobol method, and evaluate the initial population; ③ Determine whether the termination condition is reached or the maximum evolution number is reached: if yes, the evolution is terminated, and the best individual at this time is output as the solution; otherwise, continue to the next step; ④ Dynamically adjust the mutation operator control parameter F and the crossover operator control parameter CR of the differential evolution algorithm, then perform mutation operation and crossover operation, and process the boundary conditions to obtain a temporary population: （50） （51） wherein g represents the current generation number, and G represents the maximum generation number allowed for optimization; the mutation operator is taken as 1 at the beginning and approaches 0.5 at the end; The rand function represents a uniform random number between 0 and 1; ⑤ Evaluate the temporary population, calculate the objective function value of each individual in the temporary population, and obtain the global optimal constitutive model parameters by summarizing the original population and the temporary population; (6) Calculate the coupling probability p according to the parameters of the most optimal constitutive model of the last several generations g If the coupling probability p g is greater than a random number between 0 and 1, then perform a local search operation on the global optimal model parameters; ⑦ Perform "one-to-one" selection operation on the individuals in the temporary population and the corresponding individuals in the original population to obtain a new population; ⑧ Evolution number g = g + 1, go to step ④.

5. The multi-year frozen soil constitutive model and parameter calibration method considering temperature and time effects according to claim 4, characterized by: The step 5 further includes the following: the data format should be able to support the test data input table of 5 stress paths, including isotropic compression test 1_IsoCom, constant confining pressure drained triaxial shear test 2_CD, constant confining pressure undrained triaxial shear test 3_CU, side limit consolidation test 4_K0, and equal p stress path drained shear test 5_ConstP; the input formats of the 5 tests are the same, and all include a remark line, an initial condition area, a test data area, and an operation button area; where the experimental data region varies with the type of experiment, including average stress p, units: kPa, volumetric strain , void ratio e, axial strain , axial stress , units: kPa, shear stress q, units: kPa, and includes columns for time and temperature effects, namely time t, units: s, temperature T, °C.

6. A non-volatile storage medium, characterized by The non-volatile storage medium includes a stored program, wherein the program, when executed, controls a device in which the non-volatile storage medium is located to perform the method of any one of claims 1-5.

7. A terminal device, characterized by comprising: The terminal device includes a processor, a memory, a communication interface, and a bus; the processor, the memory, and the communication interface are connected through the bus and complete communication among each other; the memory stores executable program code; the processor runs a program corresponding to the executable program code by reading the executable program code stored in the memory, to execute the method of any one of claims 1-5.

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