Permafrost constitutive model considering temperature and time effects and parameter calibration method

Abstract

The invention discloses a permafrost constitutive model considering temperature and time effects and a parameter calibration method. The method comprises the following steps: constructing a model basic framework; indoor test and core equation construction; an elastic-plastic constitutive relation is constructed; building a stress-strain relation by temperature and time effect; and carrying out model parameter inversion calibration. Through the progression and cooperation of the steps, the method realizes a systematic research and development process from a theoretical framework to experimental verification and then to parameter calibration, and effectively solves the problem of complex mechanical behavior modeling of frozen soil under the coupling action of temperature and time.

Description

Technical Field

[0001] The present invention belongs to the technical field related to geotechnical engineering, and particularly relates to a permafrost constitutive model and a parameter calibration method considering temperature and time effects. Background Art

[0002] my country is a country with a high permafrost burden, with permafrost covering 22.3% of its land area. The stability of permafrost has a significant impact on the construction and operation of local projects, such as roadbeds, bridges, and tunnels. Permafrost projects, such as high-speed railways in cold regions at high latitudes and the high-altitude Qinghai-Tibet Railway, are closely related to the properties and evolution of the permafrost they involve. In recent years, with the influence of climate warming and humidification, the average temperature on the Qinghai-Tibet Plateau has risen by 0.3-0.4°C per decade, and the permafrost temperature has generally increased by 0.13±0.07°C per decade, with the active layer thickness increasing by 59.9±12.7 cm per decade. This has intensified the degradation of permafrost, affecting the stability of permafrost projects and leading to deformation of roadbeds and other infrastructure, as well as increased thermal melt disasters. Permafrost is a complex, ice-cemented, multiphase system composed of soil, ice, and unfrozen water. It is highly sensitive to ambient temperature changes and its properties are highly variable, with significant temporal variations during warming. Under the influence of climate change or human activities, once permafrost warms up, it will experience a slow, complex and long-term deformation stage of permafrost creep, a phase change deformation and strength loss stage of permafrost thawing, and a large compression consolidation deformation stage under its own weight and additional stress after melting, causing a decrease in its own bearing capacity and an increase in deformation, which will have an adverse impact on railway engineering infrastructure.

[0003] Temperature-induced degradation of permafrost and deformation due to time are the core causes of long-term service degradation in permafrost projects. Existing empirical constitutive models that consider time effects, such as the Norton-Bailey model and the Sine-Hyperbolic model, are simple in form, but their establishment does not take into account the physical properties of permafrost and cannot directly describe volume changes. They also suffer from experimental dependence and limitations on specific creep behavior. Component models, such as the Maxwell model and the Kelvin-Voigt model, are simple in form and have clear physical meanings for their parameters, but they are numerous and difficult to determine, and therefore cannot effectively describe complex multi-directional loading situations. Elastic-viscoplastic models, such as the Perzyna model, Lai Yuanming's frozen sand model, Yao Yangping's negative creep model, and the Kachanov-Rabotnov damage creep model, can describe complex path loading, but their complexity makes them difficult to generalize. Existing permafrost constitutive models that consider temperature effects include the damaged elastic constitutive model, the Sevostianov-based constitutive model, and the cascade-correlated neural network-based constitutive model for artificially frozen soil. However, quantitative models that consider the time-dependent evolution of permafrost performance parameters after degradation are rare. Quantitative analysis of the time-varying mechanisms and multi-stage degradation patterns of high-temperature permafrost over the entire temperature range is lacking. There is an urgent need to develop a permafrost constitutive model that can simultaneously describe both temperature and time effects. Furthermore, due to differences in stress paths, initial confining pressures, and initial porosity, geomaterials can exhibit various phenomena, such as hardening or softening and particle crushing, resulting in extremely complex stress-strain relationships. Furthermore, the prediction of experimental data from the same material under different initial conditions must use the same set of parameters, resulting in varying sensitivity and magnitude between parameters and complex and diverse experimental variables. Therefore, when determining constitutive model parameters based on inversion of laboratory test data, high requirements are placed on the algorithm's adaptability, accuracy, and stability. Parameter calibration methods with global optimization capabilities and a unified input format are urgently needed. Existing technology, such as application number CN202211192200.2, discloses a creep deformation characterization method for lens-containing frozen soil and its application. This method, based on creep test results for lens-containing frozen soil of various structural types, constructs a creep data representation for lens-containing frozen soil that is compatible with structural damage. This model is validated through data fitting, inversion, and inversion. The model uses an exponential function related to stress and time to characterize the frozen soil hardening parameter. The creep damage parameter is characterized as a function of a Weibull distribution with a time factor. Furthermore, a generalized Kelvin and Bingham model is used to characterize the elastic, viscoelastic, and viscoplastic properties of lens-containing frozen soil throughout the creep process.The main shortcomings of this technical solution are: ① The 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 is unable to directly describe volume changes, and has limitations such as dependence on experimental laws and specific creep behavior; ② The model takes into account the influence of time factors in the creep hardening parameters and damage parameters of frozen soil, but does not consider the impact of temperature changes on the function form, parameter values, etc., and cannot simulate the differences in frozen soil deformation characteristics under different warming conditions.

[0004] Application No. CN202411456572.0 discloses a simulation method for a discrete element contact model of non-decaying creep of frozen soil. This method mainly addresses the limitations of conventional discrete element method (DEM) in simulating frozen soil creep. It establishes the Burgers first viscoelastic model of frozen soil, further introduces a damage element, connects the first viscoelastic model with the damage element in series, and establishes a discrete element contact model of non-decaying creep of frozen soil to achieve a good simulation of the three stages of initial creep, stable creep, and non-decaying creep in the process of frozen soil creep. In combination with the central difference method, a method and steps for using this model to carry out simulation calculations are proposed. The main shortcomings of this technical solution are: ① Its core model, the Burgers model, is mainly based on viscous elements and elastic elements in series, such as the Maxwell model and the Kelvin model. In essence, it still belongs to the category of component combination models and their improved models. Its form is simple and the physical meaning of each parameter is clear, but it cannot well describe complex multi-directional loading conditions; ② The model takes into account the time effect to a certain extent, that is, the stiffness K of the damage element D It decreases with time, but it needs to be modeled separately for the time period when the permafrost is not damaged and the time period when it is damaged, and the model unification of the entire time period is not achieved; ③ The model does not consider the influence of different temperature ranges and does not incorporate temperature effects.

[0005] Application No. CN202411531649.6 discloses a calculation method for the elastic-plastic model of shield-frozen reinforced rock and soil. This method mainly constructs an elastic-plastic constitutive model of the soil layer during freezing that considers the hardening parameters of the soil layer during freezing, and an elastic-plastic constitutive model of the soil layer during melting that considers the softening parameters of the soil layer during melting. Based on a sample library of rock and soil with water content and rock and soil temperature as input and hardening parameters and softening parameters as output, a support vector machine model is used for training to obtain the shear modulus and bulk modulus of the intelligent agent model, and then a stress-strain constitutive expression considering hardening and softening factors is constructed. The main shortcomings of this technical solution are: ① This method takes into account the temperature effects of freezing and thawing, but does not consider the influence of time factors on frozen soil parameters and deformation laws; ② The core hardening parameters H(w,t) and softening parameters S(w,t) of the model and the related model output results all rely on 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 tests and thawing tests. The sample library size 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 method. This method primarily addresses the optimization inversion problem of constitutive model parameters in conventional tests and provides a method for inverting soil constitutive model parameters based on a coupled optimization method, improving the speed, stability, and accuracy of the inversion calculation. Considering both known and unknown initial shear porosity ratios, a coupled optimization algorithm is formed using a local search operator based on a differential evolution algorithm and a state transition algorithm that considers the range of geotechnical constitutive parameters and sensitivity corrections. This algorithm enables convenient inversion calculations on a general Excel platform. The main deficiencies of this technical solution are: ① The Excel platform includes the Duncan-Zhang EB model, the modified Cambridge model, the Mohr-Coulomb model, and the CSUH model, but does not include a unified hardening constitutive model for permafrost that considers time and temperature effects; ② Because the unified hardening constitutive model for permafrost that considers time and temperature effects has additional time-related variables, its unified input format is no longer applicable to the unified hardening constitutive model for permafrost that considers time and temperature effects. Summary of the Invention

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

[0008] Step 1: Building the basic model framework

[0009] Establish an overall framework for a constitutive model of frozen soil that encompasses both temperature and time effects, clarifying the model's core modules (temperature and time effects) and their interactions. By defining the mechanisms by which temperature influences frozen soil strength, pre-consolidation pressure, and critical states, and a framework describing creep behavior based on time effects, this provides theoretical guidance for subsequent experimental design, equation construction, and parameter calibration.

[0010] Step 2: Indoor experiment and core equation construction

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

[0012] Correlation: Provide parameter basis for the elastic-plastic constitutive relationship in step 3, and provide data support for the creep model in step 4 and the parameter calibration in step 5.

[0013] Step 3: Construction of elastic-plastic constitutive relationship

[0014] Based on the unified hardening (UH) theoretical framework, an elastic-plastic constitutive relationship for 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 state stress ratio *M*~T~), dynamic simulation of the yield surface changes of frozen soil during warming or cooling processes is achieved.

[0015] Step 4: Construction of stress-strain relationship considering temperature and time effects

[0016] The time-hardening creep model is coupled with the elastic-plastic constitutive relation to establish a unified stress-strain increment relationship. A temperature-dependent creep rate equation is introduced to describe the creep characteristics of frozen soil under long-term load and temperature changes (e.g., initial creep, stable creep, and accelerated creep stages).

[0017] Step 5: Model parameter inversion and calibration

[0018] Global optimization algorithms (such as differential evolution coupled with state transition algorithms) are used to efficiently invert model parameters using multi-source test data (different temperatures and stress paths). By minimizing the error between model predictions and test data, the model's universality and accuracy in complex environments are ensured.

[0019] Beneficial effects

[0020] 1. The model achieves a quantitative description of temperature effects such as frozen soil strength and critical state, and achieves high-precision simulation of the yield surface changes of frozen soil in the phase transition range over the entire period, improving the applicability of the model under complex temperature conditions.

[0021] The introduction of temperature-related tensile strength parameter σ0 can accurately reflect the influence of temperature on the strength of frozen soil. The critical state parameter M considering temperature and pressure melting effect is proposed. T , the yield surface and plastic potential surface of the traditional model were modified to describe the critical state of frozen soil under different temperature and confining pressure conditions. A parabolic critical state line (CSL) including temperature effect was proposed to simulate the influence of temperature on strength and pressure melting phenomenon. A temperature loading line was established that uniformly considers positive and negative temperature ranges, and the temperature-related initial consolidation pressure parameter p was determined. xT , accurately depicting the influence of temperature on the stress-strain relationship, and introducing yield surface representation, realizing accurate simulation of the yield surface changes of frozen soil during heating and cooling processes.

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

[0023] A time-hardening creep model expression combining inverse exponential and typical power function factors was proposed. This model addresses the poor convergence of traditional models in the frozen soil phase transition range and enables high-precision simulation of creep rates across the entire phase transition temperature range and under the influence of moisture changes. By combining multi-source strain variables with the elastic-plastic constitutive relation, both temperature 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 parameter inversion and calibration method for a permafrost constitutive model considering temperature and time effects is proposed. A system of indicators for the model's undetermined parameters is defined, and an optimization algorithm is constructed based on a combination of a differential evolution algorithm and a local search operator within a state transition algorithm. The global search capability of the optimization algorithm is improved through multi-population collaboration and parameter adaptation. This improves the efficiency and accuracy of multi-parameter calibration in complex scenarios. The input format for parameter inversion is standardized, simplifying the calibration process. This overcomes the difficulty of rapidly implementing multi-parameter calibration in existing approaches under complex conditions considering temperature and time effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the basic process of permafrost constitutive model construction and parameter calibration considering temperature and time effects;

[0027] Figure 2Schematic diagram of the framework of the unified hardening constitutive model for permafrost considering temperature and time effects;

[0028] Figure 3 Schematic diagram of LY lines for frozen soil and thawed soil in positive and negative temperature ranges;

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

[0030] Figure 5 Schematic diagram of the relationship between normalized frozen soil shear strength and confining pressure;

[0031] Figure 6 The graph of cohesion changing with temperature;

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

[0033] Figure 8 is the 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 the prediction results of the critical state line (M = 1.39 MPa, σ0 = 2.75 MPa, p m =14.46 MPa);

[0035] Figure 10 Logic diagram of the elastic-plastic constitutive relationship

[0036] Figure 11 Flowchart of the process of inverting soil constitutive model parameters for the optimization algorithm;

[0037] Figure 12 This is the flow chart of the coupling optimization algorithm. DETAILED DESCRIPTION

[0038] The permafrost constitutive model and parameter calibration method considering temperature and time effects include the following steps:

[0039] Step 1: Construct the basic framework of the model: 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 interactions; by defining the influence mechanism of temperature on frozen soil strength, initial consolidation pressure, and critical state, as well as the description framework of time effect on creep behavior, establish a unified hardening constitutive model framework that includes elastic-plastic constitutive model and stress-strain increment relationship.

[0040] The main framework of the permafrost constitutive model considering temperature and time effects in this invention includes two sections: temperature influence and time influence. Figure 2 shown.

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

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

[0043] The elastic-plastic constitutive part of the model is expanded and updated based on the unified hardening UH constitutive model. The influence of temperature on the early consolidation pressure, strength, stress-deformation characteristics of frozen soil is 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 iterative relationship, the creep increment is obtained based on the time-hardening creep equation of frozen soil under different temperature and moisture content conditions, and the mapping relationship between the creep increment and the stress-strain increment and stiffness matrix in the elastic-plastic constitutive model is constructed, thereby realizing the unified coupling of time effect and temperature effect and constructing a permafrost constitutive model considering temperature and time effects.

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

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

[0046] The effect of temperature on the initial consolidation compressive stress is primarily determined based on confined compression tests of frozen soil at various temperatures. The tests employed a stepwise loading process. According to the "Standard for Geotechnical Test Methods," a constant load of 24 hours, or a displacement difference of ≤0.01 mm per hour, was used as the compression stability criterion. Based on the stress-deformation results of the specimens obtained at various temperatures, the double-logarithmic method (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 initial consolidation pressure.

[0047] Based on the relationship between the early consolidation compressive stress and temperature in the frozen soil and thawed soil stages, the functional relationship between the early consolidation pressure and temperature, namely the LY line expression, is proposed:

[0048] (1)

[0049] (2)

[0050] Where T is the current temperature; T0 is the initial temperature, and the subscript 0 indicates the initial meaning; p xT is the current initial consolidation stress, and the subscript xT represents the intersection of the yield surface and the x-axis at the current temperature T, i.e., the position of the initial consolidation pressure in the pq space; x is the initial consolidation stress at T0, the subscript x represents the intersection of the yield surface and the x-axis at the initial temperature, i.e., the initial consolidation pressure in pq space; γ is a model material parameter that reflects the extent to which temperature changes affect the initial consolidation compressive stress. Equation (1) represents the functional relationship between the initial consolidation pressure and temperature in frozen soil during the negative temperature stage, and Equation (2) represents the functional relationship between the initial consolidation pressure and temperature in frozen soil during the negative temperature stage.

[0051] The plastic volume strain at any two points on the LY line is equal. If it is assumed that the volume change caused by heating is irreversible, that is, the volume strain increases during heating (the porosity decreases), and the volume strain increment during cooling is zero (the porosity remains unchanged), then the plastic volume strain generated by the pure force compression and rebound process A→B→C is equal to the plastic volume strain generated by the heating, compression, rebound, and cooling process A→D→E→C→C'. BE is the LY line, p xT The corresponding point E is located on the rebound line BE passing through point B when the temperature is T0; the initial consolidation stress of point C after heating is p xT , the initial consolidation stress before heating is p x , and the LY line coincides with the rebound line, so the temperature effect can be converted into an overconsolidation effect, such as Figure 4 shown.

[0052] Based on the relationship between the early consolidation compressive stress of frozen soil and temperature in different temperature ranges, it can be seen that the early consolidation compressive stress increases as the temperature decreases. In order to uniformly describe the continuous change characteristics of frozen soil in the entire temperature range from positive to negative temperatures and avoid the convergence problem near 0°C, the following exponential formula is used:

[0053] (3)

[0054] Where T is the current temperature; p xT is the current pre-consolidation stress; p xmin and p xmax k is the asymptotic value corresponding to the high temperature and low temperature regions, i.e., the minimum and maximum values ​​of the early consolidation stress, with the subscript xmin representing the minimum value and xmax representing the maximum value. px is the slope of the section near T = 0 °C, and the subscript px represents the correlation curve of the early consolidation pressure.

[0055] When introducing the above core equation into the constitutive relationship, the key is to use the known pre-consolidation compressive stress p corresponding to a certain temperature T0. x , solve the early consolidation compressive stress p corresponding to any temperature T xT . Set (T0, p x )Substitute into the LY line:

[0056] (4)

[0057] We can get:

[0058] (5)

[0059] Therefore, containing p x The pre-consolidation compressive stress p corresponding to the temperature T of T0 xT Expressed as:

[0060] (6)

[0061] Where T is the current temperature; p xT is the early consolidation compressive stress corresponding to T; p x is the early consolidation compressive stress corresponding to temperature T0; k px is the slope of the section near T=0℃. xmax and k px 2 parameters, this formula can describe the key parameters of the early consolidation stress corresponding to the full temperature range of positive and negative temperatures in the freeze-thaw state, 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 primarily determined through triaxial tests of frozen soil at different temperatures. By testing the deformation and strength characteristics of frozen soil under different temperatures, confining pressures, and stresses, its internal mechanical behavior is analyzed. The test is equipped with a temperature control system to precisely maintain the specimens at the set temperature to simulate the behavior of frozen soil in its natural state. The strength parameters, cohesion and internal friction angle, are primarily calculated using the Mohr-Coulomb strength criterion. By plotting shear stress-normal stress curves from multiple sets of test data, the cohesion c can be obtained through linear fitting, and the friction angle ϕ can be calculated using the slope of the experimentally obtained failure envelope. A series of shear tests under different confining pressures measures the final stress state reached by the frozen soil during the shear process, allowing the critical state line to be plotted in the pq coordinate system of the effective mean 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 cementation of ice, and the strength is nonlinear due to the pressure melting phenomenon, such as Figure 5 shown.

[0065] like Figure 6As shown in Figure 2, considering the linear increase of cohesion with decreasing temperature, the tensile strength σ0 is expressed as:

[0066] (7)

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

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

[0069] (8)

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

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

[0072] (9)

[0073] Where q m and p m is the vertex coordinate of the parabola, the subscript m represents the vertex peak; a is related to the opening size of the parabola; the intersection of this parabola and the horizontal axis is (-σ0, 0). Substituting p = -σ0 and q = 0 into the above formula, we get:

[0074] (10)

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

[0076] (11)

[0077] (12)

[0078] (13)

[0079] Substituting into formula (10) we get:

[0080] (14)

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

[0082] (15)

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

[0084] When σ0 approaches 0 and p m When it approaches infinity, the frozen soil CSL degenerates into the thawed soil CSL:

[0085] (16)

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

[0087] (17)

[0088] (18)

[0089] The critical state line CSL and critical state parameter M obtained from the triaxial test results T like Figure 8 As shown in Figure 2, the predicted results are compared with the experimental results. Figure 9 shown.

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

[0091] The effects of temperature and time on deformation are primarily derived from frozen soil creep tests. Based on these test results, a time-hardening creep (THC) model was constructed. The effects of temperature and moisture content were also considered, and an improved time-hardening creep (TWTHC) model was constructed using a combination of an inverse exponential temperature factor and a typical power function moisture factor.

[0092] (19)

[0093] Where, represents the axial creep strain rate, the superscript cr indicates the meaning of creep; q represents the generalized shear stress, and under the uniaxial compressive stress path, the confining pressure is 0, at which point q is equal to the axial stress The subscript a indicates axial direction; t is time; T is temperature; w is water content; and A, n, m, d, and e represent the parameters of the time-hardening creep model. Integrating the above equation over time t yields the relationship between frozen soil strain and time under different stress, temperature, and water content conditions. This model can be expressed as either a strain rate or a strain variable.

[0094] The TWTHC model in the form of Equation (19) is only suitable for directly describing uniaxial compression creep tests. In order to describe the influence of different stress paths, the TWTHC model is three-dimensionalized according to the Prandtl-Reus plasticity theory:

[0095] (20)

[0096] Where, is the creep strain rate tensor; is the creep strain increment tensor, the superscript cr indicates the creep meaning, and the subscript ij indicates the direction corresponding to the component in the strain tensor; is the equivalent creep strain increment, which is equal to the uniaxial creep strain increment; is the equivalent stress, which is equal to q in the shear stress path; is the stress deviator tensor; p is the effective mean principal stress; is the Kronecker function, which is 1 when the subscripts i and j are equal, and 0 otherwise; is the stress tensor.

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

[0098] (twenty one)

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

[0100] When degenerated into a uniaxial stress path, the lateral stress ,at this time , generalized shear stress , then the axial creep strain is:

[0101] (twenty two)

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

[0103] (twenty three)

[0104] In the formula 、 and are the first, second and third principal stress increments, 、 and are the first, second and third principal strain increments, is the third-order stiffness matrix:

[0105] (twenty four)

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

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

[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 above stress-strain relationship, the theoretical stress-strain relationship for confined compression creep can be quickly calculated using numerical methods such as the forward Euler method. The derivation process for the incremental stress-strain relationship for 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 elastic-plastic constitutive relationship: Based on the unified hardening (UH) theoretical framework, the elastic-plastic constitutive relationship of frozen soil is constructed, and the temperature parameter influence term is introduced to realize the dynamic simulation of the yield surface, plastic potential surface and hardening law of frozen soil in the full temperature range;

[0112] The unified hardening (UH) constitutive model is adopted as the basic framework of the elastic-plastic constitutive part. By unifying the elastic-plastic theory and the hardening mechanism in modeling, it can simultaneously describe the behavior of geomaterials under complex stress states such as loading, unloading and reverse loading. In particular, it has strong adaptability to the coupling effects of isotropic hardening and kinematic hardening in cyclic loading.

[0113] The elastic-plastic constitutive part consists of three main parts: yield surface, plastic potential surface and hardening law, such as Figure 10 As shown. Based on the basic framework of the unified hardening constitutive model, there are current yield surface and reference yield surface. The current yield surface passes through the current stress point, and the reference yield surface passes through the corresponding normal consolidation state point. The relative position relationship between the two yield surfaces is expressed by the overconsolidation parameter R. The plastic potential surface determines the direction of plastic strain flow, that is, the plastic volume strain ε v p and plastic shear strain εd p The hardening law relates stress and plastic body strain. 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 permafrost constitutive model considering temperature and time effects in this invention introduces the influence of temperature and time effects on the basis of the unified hardening elastoplastic constitutive model. In the yield criterion, i.e., the current yield surface and the reference yield surface function, a critical state parameter M considering the influence of temperature and pressure melting is established. T , including the critical state parameter M of the melting soil, the tensile strength σ0 and the compressive melting stress p m , the influence of strength change on yield surface and elastic modulus E is realized, and the early consolidation pressure p is introduced into the overconsolidation parameter R. xT Considering the influence of temperature on stress and strain, a temperature loading line that uniformly considers the positive and negative temperature stages is established to describe the early consolidation compressive stress p in the positive and negative temperature stages. xT The yield surface changes with temperature; in the flow law, the plastic potential surface also considers the critical state parameter M T In the hardening law, the critical state parameter M is updated in the hardening parameter H. fT and M T , while considering the early consolidation compressive stress p in the full temperature range xT role.

[0115] (1) Yield function

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

[0117] (26) (27)

[0118] In the formula All superscript horizontal lines represent parameters related to the reference yield surface.

[0119] The critical state stress ratio related to temperature is expressed as:

[0120] (28)

[0121] Where σ0 is the intensity parameter including temperature effect:

[0122] (29)

[0123] Where c is the cohesion, φ is the internal friction angle, k is the slope parameter of the cohesion changing with temperature, and M is the critical stress ratio.

[0124] (2) Plastic potential function

[0125] Using the associated flow law, the plastic potential surface g and the yield surface have the same form and are expressed as:

[0126] (30)

[0127] (3) Hardening law

[0128] The reference yield surface corresponds to the normal consolidation state of the soil. On the same reference yield surface, the plastic volume strain ε caused by stress v p are equivalent, and its hardening law is the same as the modified Cambridge model, which can be expressed as:

[0129] (31)

[0130] Plastic volume strain ε v p As a hardening parameter, the superscript p represents plasticity, the subscript v represents volume-related parameters, and the reference yield surface is expressed as:

[0131] (32)

[0132] In the above formula, ; e0 is the initial porosity, the subscript 0 indicates the initial meaning; λ is the slope of the normal compression line of frozen soil when the temperature is T0 in the e-lnp plane; κ is the slope of the elastic rebound line of frozen soil when the temperature is T0 in the e-lnp plane; λ and κ are both constants; is the intersection of the initial yield surface and the p-axis.

[0133] The average principal stress at the reference stress point can be expressed as:

[0134] (33)

[0135] in .in According to the calculation formula (6) of the early consolidation compressive stress in the reference yield surface, we can obtain:

[0136] (34)

[0137] Since the current yield surface is geometrically similar to the reference yield surface, it can be expressed as:

[0138] (35)

[0139] Where H is the hardening parameter, expressed as:

[0140] (36)

[0141] Considering the potential intensity M of temperature fT Expressed as:

[0142] (37)

[0143] where R T is the overconsolidation parameter, combined with formula (33), it can be expressed as:

[0144] (38)

[0145] Step 4: Construct a stress-strain relationship considering temperature and time effects: Couple the time-hardening creep model with the elastic-plastic constitutive relation to establish a unified stress-strain increment relationship to describe the mechanical properties of frozen soil under long-term loads and temperature changes;

[0146] In this model, the total strain increment dε ij is the elastic strain increment dε e ij , plastic strain increment dε p ij and creep strain increment dε cr ij The sum of is expressed as follows

[0147] (39)

[0148] (1) Elastic strain increment

[0149] According to the generalized Hooke's law, the elastic strain increment is obtained as follows

[0150] (40)

[0151] (41)

[0152] Where E is the elastic modulus, v is Poisson's ratio, e0 is the initial void ratio, is the slope of the unloading line in the e-lnp space in the isotropic compression unloading test, p is the mean stress, and σ0 is the strength parameter including the temperature effect (see (29). According to the index notation and summation convention, That is, the sum of the three principal stress increments.

[0153] (2) Plastic strain increment

[0154] In the transformed stress space, the associated flow law is used, and its yield surface function and plastic potential surface function can be uniformly expressed as

[0155] (42)

[0156] In the formula is the average principal stress of the current stress point in the transformed stress space, is the average principal stress of the initial stress point in the transformed stress space, where the hardening parameter in the transformed stress space is and its inherent parameters 、 Satisfies the expressions of Equations (36) to (38).

[0157] According to the flow law, the plastic strain increment is:

[0158] (43)

[0159] (44)

[0160] (3) Creep strain increment

[0161] The creep strain increment is mainly calculated based on the modified time-hardening creep (TWTHC) model considering the influence of temperature and moisture, which is constructed based on the previous equations (19) to (20) and is expressed as:

[0162] , (45)

[0163] (4) Elastic-plastic constitutive tensor

[0164] According to the generalized Hooke's law, the relationship between the stress increment and the elastic strain increment is:

[0165] (46)

[0166] Among them, the elastic-plastic stiffness matrix Expressed as:

[0167] (47)

[0168] Where G and L are the Lamé constants:

[0169] (48)

[0170] Step 5: Model parameter inversion and calibration: Using a global optimization algorithm, we combine multi-source test data to efficiently invert model parameters. By minimizing the error between the model predictions and the test data, we ensure the universality and accuracy of the model in complex environments.

[0171] (1) Model parameters to be determined

[0172] Based on the previous model construction process, the undetermined parameters involved in the permafrost constitutive model considering temperature and time effects mainly include the critical state stress ratio, Poisson's ratio, the slopes of the unloading and compression lines, the pre-consolidation compressive stress corresponding to the initial temperature T0, the slope and maximum asymptotic value of the pre-consolidation pressure-temperature curve at point 0, the slope of the cohesion-temperature curve, the compressive stress at the peak point of the critical state line, and the time-hardening creep parameter, as shown in Table 1.

[0173] Table 1 Parameters of the permafrost constitutive model considering temperature and time effects

[0174]

[0175] (2) Constitutive model parameter inversion method

[0176] The process of determining the constitutive model parameters based on the inversion method is as follows: Figure 11 As shown, the main steps are as follows:

[0177] 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 iteration, the model parameters for all individuals or groups in the population are randomly generated. If it is in the second iteration or later, the model parameters for all individuals or groups in the population are generated by the optimization algorithm based on the error function values ​​of each set of model parameters.

[0178] ② Calculate the error function as the objective function value of the optimization problem. The constitutive model reads the model parameters transmitted by the optimization algorithm and the initial conditions known from the experiment to calculate the predicted stress-strain curve value. Then, the error function is calculated based on the predicted stress-strain curve value and the measured stress-strain curve value from the experiment. Finally, the error function value is returned to the optimization algorithm as the objective function value.

[0179] ③ The optimization algorithm attempts to generate a better solution based on the error function value corresponding to the outgoing parameters, in order to make the value of the error function smaller, thereby making the predicted value of the stress-strain curve closer to the measured value of the stress-strain curve in the experiment.

[0180] ④ The above process repeats until the termination condition is met. The termination condition may be that the optimization algorithm reaches the maximum number of iterations, or the value of the error function does not decrease after a specified number of iterations in the optimization algorithm, or the number of error function calls reaches the set maximum value, or the error function is less than the set value.

[0181] (3) Model parameter inversion coupled optimization algorithm

[0182] The inversion of constitutive model parameters by using optimization algorithms based on indoor tests places high demands on the accuracy and stability of the optimization algorithms. The present invention uses an optimization algorithm coupled with a differential evolution algorithm and a state transfer algorithm local search operator to invert the constitutive model parameters. Figure 12 As shown, the main steps of the algorithm are as follows:

[0183] ① Determine the algorithm control parameters of the differential evolution algorithm and the modified local search operator. The control parameters of the differential evolution algorithm include: population size N p , the maximum number of calls of the error function F esmax , the maximum iteration number G, the MLS algorithm control parameters include the calculation of coupling probability p g Parameters, rotation factor control parameters Ω, etc.

[0184] ② Based on the Sobol method, the initial population is randomly generated and evaluated, that is, the mean relative error (MRE) of each individual in the initial population is calculated, and the evolutionary generation g = l is set.

[0185] (49)

[0186] Where, and They represent the model prediction value and the experimental measurement value respectively, the superscript i represents the serial number, the subscript m represents the model value, and the subscript e represents the experimental value; N represents or The number of vectors Represents a set of constitutive model parameters.

[0187] ③ Determine whether the termination condition or the maximum number of evolutionary generations has been reached: If so, evolution terminates and the optimal individual at that point is output as the solution; otherwise, proceed to the next step. During the optimization process, if the objective function value does not decrease after 0.02×G iterations, half of the poorer individuals in the population are re-initialized uniformly and randomly to increase diversity and avoid premature maturation.

[0188] ④ Dynamically adjust the mutation operator control parameter F and the crossover operator control parameter CR of the differential evolution algorithm, then perform mutation and crossover operations, process the boundary conditions, and obtain a temporary population.

[0189] (50)

[0190] (51)

[0191] Where g nThe subscript n represents the current generation, and G represents the maximum number of generations allowed for optimization. The mutation operator starts at 1 and ends at a value close to 0.5. The rand function generates a uniform random number between 0 and 1.

[0192] ⑤ Evaluate the temporary population, calculate the objective function value of each individual in the temporary population, and summarize the original population and the temporary population to obtain the global optimal constitutive model parameters.

[0193] ⑥ Calculate the coupling probability p based on the parameters of the optimal constitutive model of the last few generations g , if the coupling probability p g A random number between 0 and 1 performs a local search for the global optimal model parameters. The modified local search operator attempts to find better parameters near the global optimal constitutive model parameters. If a better parameter is found, the previous global optimal constitutive model parameters are overwritten.

[0194] 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.

[0195] ⑧Evolutionary algebra g = g+1, go to step ④.

[0196] (4) Data format

[0197] This paper proposes a parameter calibration method for a permafrost constitutive model that considers temperature and time effects. The data area includes specimen information data, parameter and error data, test data, optimization process and sensitivity data, simulation prediction output, and plot data. The data format should support the test data input tables for 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), confined consolidation test (4_K0), and drained shear test with constant p stress path (5_ConstP). The input format for all five tests is the same, consisting of a comment line, an initial condition area, a test data area, and an operation button area.

[0198] The test data area varies with the test type, including the average stress , volumetric strain , porosity ratio e, axial strain , axial stress , shear stress The data also includes columns for time and temperature effects, i.e., time t (s) and temperature T (°C). Parameter and error data include the error between the experimental curve for each set of tests and the curve predicted by the constitutive model simulation, as well as the optimal parameters and corresponding error values ​​for each generation during the inversion process, and the decrease in error with the number of optimization generations. The optimization process and sensitivity data include the error function type, constitutive model type, parameter signs, upper and lower limits, number of decimal places, initial values, and optimal optimization parameters. Model prediction output and plot data include the constitutive model calculation results and prediction curves.

[0199] The invention points are as follows:

[0200] The present invention describes the influence of temperature on the strength of frozen soil, the early consolidation compressive stress and the critical state through a model, proposes a tensile strength parameter σ0 considering the temperature correlation, and innovatively introduces a critical state parameter M considering the influence of temperature and pressure melting. T The critical stress ratio M in the yield surface and plastic potential surface of the traditional model is replaced by M T Replacement, overconsolidation parameter R T , potential strength M f The critical stress ratio M considering the temperature is used in both the hardening parameter H and the critical stress ratio M considering the temperature. T The new tensile strength σ0 and compressive melting stress p are proposed. m The parabolic critical state line (CSL) of two temperature effect parameters enables strength and critical state simulation considering temperature effects.

[0201] The model establishes a temperature loading line that uniformly considers positive and negative temperatures throughout the entire period, breaking through the limitation of the existing frozen soil pre-consolidation compressive stress model that can only consider positive or negative temperatures. The newly established pre-consolidation compressive stress p xT The yield surface changes across the phase change temperature range over the entire period can be considered, achieving a unified description of the simulation of yield surface changes across the phase change temperature range during the time-varying process of frozen soil warming.

[0202] This paper proposes an improved time-hardening creep model that comprehensively considers the effects of temperature and moisture content. By combining inverse exponential and typical power function factors, this model overcomes the lack of convergence in traditional models within the phase transition range. This model achieves high-precision creep rate simulation across the entire phase transition temperature range and the effects of moisture content. By combining multi-source strain variables with the elastic-plastic constitutive relation, a stress-strain relationship simulation method is constructed that uniformly considers temperature and long-term time effects.

[0203] This paper proposes a parameter inversion and calibration method for a permafrost constitutive model that accounts for temperature and time effects. This method utilizes an optimization algorithm coupled with a differential evolution algorithm and a local search operator within a state transition algorithm, resulting in a robust global search capability. The model features a unified input format that facilitates batch writing, saving, reading, and plotting of various data from various stress path tests, such as isotropic compression tests, 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.

[0204] The above shows and describes 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 above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A constitutive model of permafrost and a parameter calibration method considering temperature and time effects are characterized by: Step 1: Build the basic framework of the model: Establish an overall framework for the constitutive model of frozen soil that covers both temperature and time effects, clarify the core modules of the model and their interactions; define the mechanisms by which temperature influences frozen soil strength, pre-consolidation pressure, and critical state, and define a framework for describing creep behavior based on time effects; Step 2: Indoor test and core equation construction: Through systematic indoor experiments, we obtain the key mechanical parameters of frozen soil under different temperatures and stress paths, and establish the core equations describing the temperature and time effects based on the experimental data. Step 3: Construction of elastic-plastic constitutive relationship: Based on the unified hardening (UH) theoretical framework, the elastic-plastic constitutive relationship of frozen soil is constructed. By introducing temperature-sensitive parameters, the dynamic simulation of the yield surface change of frozen soil during heating or cooling is realized. Step 4: Construct the stress-strain relationship considering the temperature and time effects: The time-hardening creep model is coupled with the elastic-plastic constitutive relation to establish a unified stress-strain increment relationship. By introducing a temperature-dependent creep rate equation, the creep characteristics of frozen soil under long-term load and temperature changes are described. Step 5: Model parameter inversion and calibration: A global optimization algorithm is used to efficiently invert model parameters in combination with multi-source test data; by minimizing the error between the model prediction value and the test data, the universality and accuracy of the model in complex environments are ensured.

2. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 1, wherein step 2 further comprises the following: (1) Effect of temperature on pre-consolidation compressive stress: Based on the relationship between the pre-consolidation compressive stress of frozen soil and temperature in different temperature ranges, 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 is the asymptotic value corresponding to the high and low temperature regions, i.e., the minimum and maximum values ​​of the early consolidation stress, k px is the slope of the section near T=0℃; (2) Effect of temperature on strength: Through a series of shear tests under different confining pressures, the final stress state reached by frozen soil during the shear process is measured, and the critical state line is drawn in the pq coordinate system space of the effective mean stress p and the deviatoric stress q; (3) Influence of temperature and time factors on deformation: Based on the test results, a time hardening creep (THC) model was constructed. The improved time hardening creep (TWTHC) model was constructed by combining the inverse exponential temperature influence factor and the typical power function water content influence factor: （19） Where, represents the axial creep strain rate; q represents the generalized shear stress. Under the uniaxial compressive stress path, the confining pressure is 0, and q is equal to the axial stress ; t is time; T is temperature; w is water content; A, n, m, d and e represent the time hardening creep model parameters; integrating the above formula over time t can obtain the relationship between the strain of frozen soil and time under different stress, temperature and water content conditions, that is, the model can be expressed in the form of strain rate or in the form of strain variable.

3. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 1 is characterized by: The step 3 further includes the following contents: introducing the influence of temperature and time effect, establishing the critical state parameter M considering the influence of temperature and pressure melting in the yield criterion, i.e., the current yield surface and the reference yield surface function. T , including the critical state parameter M of the melting soil, the tensile strength σ0 and the compressive melting stress p m , the influence of strength change on yield surface and elastic modulus E is realized by introducing the early consolidation pressure p in the overconsolidation parameter R xT Considering the influence of temperature on stress and strain, a temperature loading line that uniformly considers the positive and negative temperature stages is established to describe the early consolidation compressive stress p in the positive and negative temperature stages. xT The yield surface size changes with temperature; in the flow law, the plastic potential surface considers the critical state parameter M T In the hardening law, the critical state parameter M is updated in the hardening parameter H. fT and M T , while considering the early consolidation compressive stress p in the full temperature range xT role.

4. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 1, wherein step 4 further comprises the following: Total strain increment dε ij is the elastic strain increment dε e ij , plastic strain increment dε p ij and creep strain increment dε cr ij The sum of is expressed as follows ； in: 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 subscript ij represents the direction of the component in the strain tensor, the superscript e represents elasticity, p represents plasticity, and cr represents creep characteristics.

5. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 1 is characterized by: The step 5 further includes the following contents: Undetermined model parameters: The undetermined parameters involved in the permafrost constitutive model considering temperature and time effects include the critical state stress ratio, Poisson's ratio, the slope of the unloading line and the compression line, the early consolidation compressive stress corresponding to the initial temperature T0, the slope of the early consolidation pressure at point 0 and the maximum asymptotic value of the temperature change curve, the slope of the cohesion changing with temperature, the compressive stress at the peak point of the critical state line, and the time hardening creep parameter.

6. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 5, characterized in that: Step 5 further includes the following content: The main steps of the process of determining the constitutive model parameters based on the inversion method are as follows: ① The optimization algorithm reads the number and range of parameters to be optimized and generates multiple groups 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 later, the model parameters of all individuals or all groups in the population are generated by the optimization algorithm based on the error function value feedback of each group of model parameters. ② Calculate the error function as the objective function value of the optimization problem: The overall architecture of the constitutive model consists of an elastic-plastic constitutive model that considers temperature and time effects, as well as 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 law, yield function, and flow law, and then couples the creep increment obtained by the time-hardening creep equation to construct a total stress-strain mapping relationship. When performing error calculations, the constitutive model reads the model parameters transmitted from the optimization algorithm and calculates the predicted values ​​of the stress-strain curve based on the initial conditions known from the experiment. The error function is then calculated based on the predicted values ​​of the stress-strain curve and the measured values ​​of the experimental stress-strain curve. Finally, the error function value is returned to the optimization algorithm as the objective function value. 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; 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 value of the error function does not decrease after the specified number of iterations in the optimization algorithm, or the number of error function calls reaches the set maximum value, or the error function is less than the set value.

7. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 6 is characterized by: The step 5 further includes the following contents: Model parameter inversion coupled optimization algorithm: Inversion of constitutive model parameters is performed based on an optimization algorithm coupled with a local search operator of a differential evolution algorithm and a state transfer algorithm. 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 the initial population based on the Sobol method and evaluate the initial population; ③ Determine whether the termination condition or the maximum evolutionary generation is reached: If so, the evolution terminates and the best individual at this time is output as the solution; otherwise, proceed 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 and crossover operations, process the boundary conditions, and obtain a temporary population: （50） （51） In the formula, g represents the current generation, G represents the maximum generation allowed for optimization; the mutation operator is set to 1 at the beginning and close to 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 summarize the original population and the temporary population to obtain the global optimal constitutive model parameters; ⑥ Calculate the coupling probability p based on the parameters of the optimal constitutive model of the last few generations g , if the coupling probability p g A random number greater than 0 and between 1 performs a local search operation on the global optimal model parameters; 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; ⑧Evolutionary algebra g = g+1, go to step ④.

8. The permafrost constitutive model and parameter calibration method considering temperature and time effects according to claim 7 is characterized by: Step 5 further includes the following: the data format should be able to support the test data input form of five stress paths, including the isotropic compression test (1_IsoCom), the drained triaxial shear test with constant confining pressure (2_CD), the undrained triaxial shear test with constant confining pressure (3_CU), the confined consolidation test (4_K0), and the drained shear test with constant p stress path (5_ConstP); the input format of the five tests is the same, including a note line, an initial condition area, a test data area, and an operation button area; The test data area varies with the test type, including the average stress , volumetric strain , porosity ratio e, axial strain , axial stress , shear stress , and contains time and temperature effect columns, namely time t (s) and temperature T (℃).

9. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is executed, the device where the non-volatile storage medium is located is controlled to execute the method according to claim 1.

10. A terminal device, characterized in that: 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 communicate with 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, so as to execute the method as described in claim 1 above.

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