Method for characterizing the creep deformation of a frozen soil containing a lens and applications thereof

Abstract

The application discloses a kind of frozen soil containing lens creep deformation characterization method and application thereof, based on the data-oriented multi-factor collaborative construction of experimental factors, data expression model construction factors, data fitting inversion factors and other associated factors to the quantification and data characterization of frozen soil containing lens creep deformation, while building quantitative data characterization formula, the dynamic construction damage effect of frozen soil, frozen soil creep hardening effect, frozen soil attenuation creep stage lens ice geometry effect, frozen soil stable creep stage lens ice geometry effect, frozen soil accelerated creep stage lens ice geometry effect and other associated effects are data-based built-in compatible characterization, and the obtained data characterization formula is verified by post fitting as needed, to realize the long-term dynamic settlement and deformation of construction in cold region foundation Quantitative prediction.

Description

Technical Field

[0001] This invention relates to the field of cold-region building engineering technology, specifically to a method for characterizing creep in lenticular frozen soil considering structural damage and its application in predicting long-term dynamic settlement and deformation of foundations in cold regions. Background Technology

[0002] During the complex heat and mass exchange between permafrost and the atmosphere, unfrozen water within the permafrost freezes into ice upon encountering sub-zero temperatures during migration and accumulation, resulting in a complex structure. The state of the unfrozen water during freezing depends on the temperature gradient and stress magnitude within the soil. These factors determine the spatial arrangement of ice crystals or ice layers with soil particles, thus forming different cryogenic structures in permafrost. This complex spatial arrangement leads to a diverse range of cryogenic structures in permafrost. Its most distinctive feature compared to ordinary soil is not only the cementing effect of ice crystals on soil particles but also the presence of lenticular ice within the permafrost, exhibiting a complex structure. The influence of lenticular ice within permafrost on its deformation characteristics under different temperature and stress conditions has attracted considerable attention from scholars.

[0003] Permafrost, as a crucial material in foundation engineering in cold regions, plays a vital role in the stability of these projects due to its deformation characteristics. After the completion of engineering facilities in cold regions, the original thermal equilibrium of the foundation is disturbed, the internal structure of the permafrost changes, and the overall deformation of the foundation exhibits a creep effect over time. This can lead to instability or even failure of the foundation after a considerable period. Therefore, the creep characteristics of permafrost have a significant impact on the stability of foundations in cold-region engineering projects. Due to the influence of complex geological environments and special thermodynamic conditions, lenticular ice within permafrost is distributed in layers or sheets; moreover, the unique bonding and structure between lenticular ice and soil (rock) gives it strong structural properties. However, current research on permafrost creep models by domestic and international scholars treats permafrost as an isotropic homogeneous material, neglecting the influence of internal lenticular ice and other cold-formed structures on its deformation. This leads to significant errors in predicting foundation settlement and deformation. With increasingly stringent requirements for foundation settlement and deformation in cold-region engineering structures, the calculation results of traditional permafrost creep models are no longer sufficient to meet the needs of engineering design. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for characterizing creep deformation of frozen soil containing lenses and its application in predicting long-term dynamic settlement and deformation of foundations of structures in cold regions, so as to objectively and accurately reflect the deformation of foundations of structures in cold regions.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows.

[0006] A method for characterizing creep deformation in permafrost containing lensing ice is proposed. This method is based on a data-driven multi-factor collaborative construction of creep data experimental factors, data expression model construction factors, data fitting and inversion factors, and other related factors to quantify and quantify the creep deformation of permafrost containing lensing ice. At the same time, when constructing the quantitative data characterization formula, the dynamic structural damage effect of permafrost, the creep hardening effect of permafrost, the lensing ice geometric effect in the permafrost decay creep stage, the lensing ice geometric effect in the permafrost stable creep stage, the lensing ice geometric effect in the permafrost accelerated creep stage, and other related effects are built-in compatible data characterization. The obtained data characterization formula is then subjected to post-fit verification as needed to achieve quantitative prediction of long-term dynamic settlement and deformation of foundations of structures in cold regions.

[0007] As a preferred technical solution of the present invention, the implementation steps of the method include: ① constructing data on the hardening variables and structural damage variables of lenticular frozen soil during the creep process; ② constructing a creep data characterization formula for lenticular frozen soil that is compatible with structural damage, based on the mechanism of hardening effect and damage effect of lenticular frozen soil with different structural types during the creep process.

[0008] As a preferred technical solution of the present invention, the implementation steps of the method further include: ① For the obtained creep data characterization formula of lenticular frozen soil with compatible structural damage, the parameters of the data characterization formula are post-constructed by data fitting inversion based on the creep test results of lenticular frozen soil with different structural types; ② The obtained creep data characterization formula of lenticular frozen soil with compatible structural damage is post-fitted and verified.

[0009] As a preferred embodiment of the present invention, the hardening parameters of frozen soil are constructed through the following data process:

[0010] Setting H as the character identifier for the hardening parameter and representing it using an exponential function related to stress and time, we obtain:

[0011] H(σ,t)=f(σ)[1-e -t (1)

[0012] In the formula: f(σ) is a function representing the degree of hardening related to the stress level, obtained by curve fitting based on creep test; t is the creep time.

[0013] The structural damage parameters of permafrost were constructed using the following data processing procedure:

[0014] Let D be the character identifier for the hardening parameter. During the creep process of frozen soil, the damage caused by the propagation of internal micro-cracks is related to stress and time. A Weibull distribution function is used to characterize the creep damage parameter, resulting in:

[0015]

[0016] In the formula: g(σ) is a function representing the degree of damage related to the stress level, obtained by curve fitting based on creep test; m is a parameter related to the rate of damage development in frozen soil during creep; t is the creep time.

[0017] Further constructing damage parameters for the creep process of lens-containing permafrost considering tectonic damage, we obtain:

[0018]

[0019] In the formula: D1(σ,t) is the damage parameter without considering the influence of lens ice inside the permafrost; D2 is the structural damage parameter considering the influence of lens ice inside the permafrost.

[0020] Furthermore, structural damage parameters of permafrost containing lens ice were constructed under the condition of considering the crack propagation at the lens ice tip due to stress concentration effects, and the following results were obtained:

[0021]

[0022] In the formula: τ eff The effective stress at the ice-frozen soil interface is related to the interfacial friction coefficient, the lens ice tilt angle, and the confining pressure; B, a are the lens ice thickness and half-length perpendicular to the plane; V, θ are the volume of the frozen soil sample and the crack initiation angle at the lens ice tip, where θ = 60-80°; spherical stress σ m = (σ1 + 2σ3) / 3; deviatoric stress σ1 and σ3 are the axial load and confining pressure, respectively; ν is the Poisson's ratio of the frozen soil.

[0023] As a preferred technical solution of the present invention, when constructing the data characterization formula for lenticular frozen soil creep based on the following conditions: when lenticular frozen soil undergoes creep, the hardening effect and damage effect run through the entire creep process, and the degree of their exertion is different at different stages. The data characterization of the elasticity, viscoelasticity and viscoplasticity of the object covers the entire creep process.

[0024] As a preferred technical solution of the present invention, the generalized Kelvin and Bingham models are used to characterize the elasticity, viscoelasticity and viscoplasticity of lens-containing frozen soil throughout the creep process.

[0025] As a preferred embodiment of the present invention, the further data processing steps include: firstly, introducing a hardening parameter H into the viscoplastic element of the viscoelastic element in the generalized Kelvin model and Bingham model; then, applying a damage parameter D to the entire creep deformation calculated based on the hardening effect. 12 By reducing the data, a complete progressive process of creep data based on hardening and damage effects is constructed, resulting in a characterization formula for creep data of lenticular frozen soil with compatible structural damage.

[0026] As a preferred embodiment of the present invention, the complete creep data progression process includes:

[0027] A. When 0 < σ < σ s At that time, it was mainly viscoelastic, and a generalized Kelvin data model was adopted. As deformation progressed, the hardening effect intensified, and the following settings were made: The viscosity coefficient of a viscoelastic element considering the hardening effect is expressed as:

[0028]

[0029] In the formula: is the initial viscosity coefficient of the viscoelastic element.

[0030] For the generalized Kelvin model, data analysis of its constitutive equation yields the viscoelastic strain considering the hardening effect, expressed as:

[0031]

[0032] In the formula: E0 is the initial elastic modulus; E1 is the viscoelastic modulus; σ is the deviatoric stress during the creep process.

[0033] B. When σ > σ s At this stage, the damage effect is brought into play by a series connection of the generalized Kelvin model and the Bingham model; decaying creep, steady-state creep, and accelerated creep are all included. Similarly, the viscosity coefficient of a viscoelastic element considering the hardening effect is expressed as:

[0034]

[0035] In the formula: is the initial viscosity coefficient of the viscoplastic element.

[0036] For the Bingham model, data analysis of its constitutive equation yields the viscoplastic strain considering the hardening effect, expressed as:

[0037]

[0038] In the formula: σ is the deviatoric stress during the creep process; σ s This refers to the long-term strength of the frozen soil.

[0039] According to the principle of strain superposition, we get σ > σ s The strain at time is expressed as:

[0040]

[0041] Furthermore, based on the presence of lens ice in the frozen soil, the initial structural damage value is not zero. Under load, the damage gradually increases with creep time, and the damage effect exists throughout the entire creep process. Therefore, the creep deformation of frozen soil containing lens ice considering the damage effect is:

[0042] ε(t)=ε H (t)[1-D 12 (σ,t)] (10).

[0043] As a preferred technical solution of the present invention, based on Equations 6, 9, and 10, a characterization formula for creep data of lens-containing permafrost with compatible structural damage is constructed, resulting in:

[0044]

[0045] In the formula: G0 is the initial shear modulus; σ s G1 is the long-term strength; G2 is the viscoelastic shear modulus. The initial viscoelastic viscosity coefficient; σ0 represents the initial viscoplastic viscosity coefficient; σ1 and σ3 represent the axial load and confining pressure, respectively; D0 12 (t) represents the damage parameter during the creep process of lens-containing permafrost, taking into account structural damage.

[0046] As a preferred embodiment of the present invention, the parameters in the obtained characterization formula of lens-containing permafrost creep data compatible with structural damage are obtained through the following known methods: measurement, manuals, measurement-based data curve fitting, data fitting inversion, reliable tangible documents, reliable online documents, and other reliable public data carriers or data channels; among them, the elastic modulus G0 and long-term strength σ s Determined based on creep curves.

[0047] As a preferred embodiment of the present invention, the method for characterizing creep deformation of lens-containing frozen soil generally includes the following steps:

[0048] Step 1: Triaxial creep tests were conducted on frozen soil containing lens ice under different deviatoric stresses to obtain creep curves of the frozen soil under different deviatoric stresses. In this step, a cylinder with a height of 200 mm and a diameter of 100 mm was prepared using a layered compaction method. After demolding, the sample was placed in a pre-made cylindrical mold, and then a crack with a length of 60 mm, a width of 10 mm, and an angle of 60° with the horizontal was cut at the center of the sample using a hollow knife. After the sample was formed, it was first frozen in an environment of -20℃ for 12 hours. Then, pre-cooled distilled water was injected into the pre-made crack in batches, and freezing continued for another 12 hours to form frozen soil samples containing lens ice. Triaxial creep tests were then conducted under different deviatoric stresses.

[0049] Step two: Based on the creep curves of frozen soil containing lenses under different deviatoric stresses, the long-term strength of the frozen soil is determined using the Vyalov (С.С.) model. In this step, the long-term strength of the frozen soil serves as the threshold for determining whether the sample has failed during the creep process. To determine the long-term strength of frozen soil with different structural types, this paper adopts the first inflection point method of the creep curve, that is, finding the point in the creep curve where decaying creep transitions to constant-rate creep. To reduce the subjectivity in point selection, the creep curve is fitted using the Vyalov (С.С.) model, and the model expression is:

[0050]

[0051] In the formula: ε is the creep strain, σ is the deviatoric stress; T is the temperature, t is the creep time; A, B, C, and D are model parameters.

[0052] First, the test results of frozen soil with different structural types are fitted using Equation 1. Then, the first derivative of the fitted curve of the creep test results is obtained to determine the relationship between strain rate and time. The time point corresponding to the decrease of strain rate to constant is the first inflection point in the creep curve. The long-term strength of the corresponding frozen soil can be determined according to the relationship between different deviatoric stresses and inflection points.

[0053] Step 3: When the deviatoric stress is less than the long-term strength, the adjustment of internal stress in the frozen soil during creep leads to structural reinforcement, and the hardening effect plays a dominant role, thus decay creep is the main characteristic. When the deviatoric stress is greater than the long-term strength, the propagation of lens ice end cracks inside the frozen soil leads to structural weakening greater than strengthening, and the damage effect plays an important role in the creep process, thus isochronous creep and accelerated creep are the main characteristics. Over time, the frozen soil sample fails and loses strength. In order to quantitatively describe the hardening characteristics of the frozen soil structure over time during decay creep under triaxial stress, the expression for the hardening parameter in the frozen soil creep process was determined. In order to quantitatively describe the deterioration characteristics of the frozen soil structure over time due to stress concentration at the lens ice end during the isochronous creep and accelerated creep stages under triaxial stress, the expression for the damage parameter in the frozen soil creep process was determined based on the principles of continuous damage mechanics and strain energy.

[0054] In this step, for frozen soil containing lens ice, the components involved in creep are mainly the soil skeleton, ice crystals, lens ice, unfrozen water, and microcracks. Under external load, the increased stress at the solid-solid contact points within the frozen soil causes compression of microcracks and plastic flow of ice crystals. Soil particles rearrange and form new connections, increasing cohesion and friction between particles, thus enhancing the strength of the frozen soil and producing a hardening effect. On the other hand, stress concentration at the ends of lens ice in the frozen soil leads to the initiation and propagation of microcracks, simultaneously disrupting the original connections between soil particles, causing a decrease in frozen soil strength and producing a damage effect. When the stress is less than the long-term strength of the frozen soil, the adjustment of internal stress during creep leads to structural reinforcement, with the hardening effect playing a dominant role; therefore, decay creep is the primary characteristic. When the stress exceeds the long-term strength of the frozen soil, the propagation of internal cracks leads to structural weakening outweighing strengthening. The damage effect plays a significant role in the creep process, thus isolating and accelerating creep are the main characteristics. Over time, the frozen soil sample fails, losing strength. Therefore, when establishing the creep constitutive model of frozen soil, this invention fully considers the hardening and damage effects of frozen soil under different stress levels.

[0055] The hardening effect arises from the frozen soil's resistance to further deformation, typically occurring during the plastic deformation stage, and primarily characterizing the gradual increase in the frozen soil's strength over time. The hardening parameter H(σ,t) generally satisfies the following: when t→0, H(σ,t)→0; and when t→∞, H(σ,t)→constant. The hardening parameter H(σ,t) satisfying these conditions can be represented by an exponential function related to stress and time, in the form:

[0056] H(σ,t)=f(σ)[1-e -t (2)

[0057] In the formula: f(σ) is a function representing the degree of hardening, which is related to the stress level and can be obtained by fitting the creep curve; t is the creep time.

[0058] During the creep process of frozen soil, when the stress level exceeds the long-term strength, the bonds of the frozen soil skeleton gradually break down with increasing strain, the skeleton begins to disintegrate, and slippage occurs between particles. The deformation behavior of frozen soil exhibits viscoplastic creep characteristics. Moreover, as creep continues, the micro-cracks in the frozen soil continuously propagate and penetrate. Since the damage caused by the propagation of micro-cracks inside the frozen soil during creep is time-dependent, the creep damage parameter is described by a function in the form of a Weibull distribution, which can be expressed as:

[0059]

[0060] In the formula: g(σ) is a function representing the degree of damage and is related to the stress level, which can be obtained by fitting the creep curve; m is a parameter representing the rate of damage development in frozen soil during creep; t is the creep time.

[0061] Furthermore, the presence of lens ice within the permafrost and the initiation and propagation of cracks caused by stress concentration at the lens ice ends during loading also weaken the strength of the permafrost. Therefore, the deterioration of the mechanical properties of permafrost during creep is also caused by the coupling between the lens ice structure and the propagation of microscopic cracks within the permafrost. Based on the principle of equivalent strain, the damage parameters of permafrost containing lens ice during creep, considering tectonic damage, are as follows:

[0062]

[0063] In the formula: D1(σ,t) is the damage parameter without considering the influence of lens ice inside the frozen soil; D2 is the structural damage parameter of frozen soil containing lens ice considering the influence of lens ice. For type 1 frozen soil, D2=0. Based on the principles of continuous damage mechanics and strain energy, under the condition of considering the crack propagation at the lens ice tip under stress concentration effect, the structural damage parameter of frozen soil containing lens ice can be derived as follows:

[0064]

[0065] In the formula: τ eff The effective stress at the ice-frozen soil interface is related to the interfacial friction coefficient, the lens ice tilt angle, and the confining pressure; B, a are the lens ice thickness and half-length perpendicular to the plane; V, θ are the volume of the frozen soil sample and the crack initiation angle at the lens ice tip, where θ = 70.5°; spherical stress σ m = (σ1 + 2σ3) / 3; deviatoric stress σ1 and σ3 are the axial load and confining pressure applied to the specimen; ν is the Poisson's ratio of the frozen soil.

[0066] Step four: By introducing mechanical elements describing the elasticity, viscoelasticity, and viscoplasticity of materials, and taking long-term strength as the critical point, and combining the hardening and damage effects of lensed frozen soil during the creep process, a creep model structure for lensed frozen soil is constructed. In this step, based on the experimental results of step one, it can be found that when the shear stress is lower than the long-term strength, the curve shows decaying creep. When the shear stress is higher than the long-term strength, the curve shows non-decaying creep, and the three stages are fully demonstrated in the creep process. The creep model constructed in this patent has the following characteristics: (1) When the stress is less than the long-term strength σ s When the creep curve tends to stabilize with increasing time, it belongs to viscoelastic strain and is described by the generalized Kelvin model; (2) when the stress is greater than the long-term strength σ sAs time increases, the deformation of the frozen soil increases, which is a viscoelastic-plastic strain. The entire creep process is divided into three stages, which are described by a series of the generalized Kelvin model and the Bingham model.

[0067] Step five: Subsequently, based on the triaxial creep test results of lensed frozen soil under different deviatoric stresses, the model parameters can be determined through fitting and inversion, and the rationality of the model can be verified. The model has a total of 8 parameters, mainly the elastic modulus G0 and the long-term strength σ. s The shear modulus G1 and initial viscosity coefficient in the Kelvin model Initial viscosity coefficient in the Bingham model The hardening degree function f(σ), the damage degree function g(σ), and the damage development rate parameter m are given. Among these, the elastic modulus G0 and the long-term strength σ are also considered. s The parameters can be determined based on the creep curve, and the remaining parameters can be determined through fitting and inversion.

[0068] Applications of the creep deformation characterization method for frozen soil with lenses: for the dynamic and long-term settlement and deformation characterization and prediction of foundations of cold-region structures under external loads.

[0069] The beneficial effects of adopting the above technical solution are as follows:

[0070] Overall, this invention establishes a creep model of permafrost containing lenses under triaxial loads, which can comprehensively characterize the creep process of permafrost containing lenses, considering the structural incompleteness caused by lens ice cutting and stress concentration effects induced by stress concentration. This has important practical significance for tunnel, slope and foundation deformation and related engineering construction in permafrost areas.

[0071] Specifically, this invention first prepared lenticular ice-containing frozen soils with different structural types and obtained triaxial creep curves under different deviatoric stresses; secondly, based on the creep curves and combined with the Vyarov (S.C.) model, the long-term strength of the frozen soil was determined; thirdly, based on the creep characteristics of the frozen soil under different deviatoric stresses in the experiment, the roles of hardening and damage effects in the creep process of lenticular ice-containing frozen soil were explained; fourthly, based on the principles of continuous damage mechanics and strain energy, the hardening parameters and structural damage parameters considering lenticular ice in the creep process of frozen soil were determined; fifthly, based on the relationship between the hardening and damage effects in the creep process of lenticular ice-containing frozen soil, mechanical elements describing the elasticity, viscoelasticity, and viscoplasticity of the material were introduced and modified, and a creep model of lenticular ice-containing frozen soil considering structural damage was constructed, and the expression of the model was proposed; sixthly, based on the creep test results of lenticular ice-containing frozen soil, the corresponding model parameters were determined. The creep model of frozen soil with lens ice established in this invention uses long-term strength as the threshold. The model not only considers the influence of hardening and damage effects during creep and the influence of lens ice geometric parameters on the three stages of creep (decay creep stage, stable creep stage and accelerated creep stage), but also overcomes the defect of artificially determining long-term strength during creep, making the model more accurate in prediction. Attached Figure Description

[0072] Figure 1 Schematic diagrams of lens-containing frozen soil samples of different structural types.

[0073] Figure 2 The graphs show creep test curves for frozen soil with lenses of different structural types.

[0074] Figure 3 The graph shows the relationship between deviatoric stress and initial strain in lens-containing frozen soils of different structural types.

[0075] Figure 4 This is a schematic diagram showing the long-term strength of lenticular frozen soil with different structural types.

[0076] Figure 5 This is a graph showing the changes in hardening and damage parameters over time during creep.

[0077] Figure 6 This is a diagram showing the relationship between hardening parameters, damage parameters, and stress in the model.

[0078] Figure 7 This is a comparison chart of the results of creep tests on frozen soil with model calculations for different structural types. Detailed Implementation

[0079] The following embodiments illustrate the present invention in detail. In the description of the following embodiments, specific details of the technology are set forth for illustrative purposes and not for limitation, so as to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that the present application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known prior art methods have been omitted so as not to obscure the description of this application with unnecessary detail. It should be understood that, as used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. It should be understood that, as used in this specification and the appended claims, the term "and / or" refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0080] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]." Furthermore, in the description of this specification and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0081] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0082] Example 1: Triaxial creep test of frozen soil with lens structure of different types

[0083] Cylindrical specimens with a height of 200 mm and a diameter of 100 mm were prepared using a layered compaction method. After demolding, the specimens were placed in a pre-made cylindrical mold, and then 60 mm long and 10 mm wide cracks were cut at pre-designed locations on the specimens using a hollow knife. After molding, the specimens were first frozen at -20°C for 12 hours, followed by the injection of pre-cooled distilled water into the pre-made cracks and a further 12 hours of freezing, resulting in five different types of frozen soil structures, such as... Figure 1 As shown. To ensure good bonding between the lens ice formed during freezing and the surrounding soil, the entire sample was first wrapped tightly with plastic wrap and sealed with tape. Then, pre-cooled distilled water was injected five times at 0°C into the corners of the cracks using a syringe, with each injection spaced 3 hours apart. During the final injection, the injection was stopped when the plastic wrap around the cracks bulged, and the micropores were quickly sealed with tape. The sample was then left to freeze for another 12 hours. After freezing, any excess ice on the surface of the specimen was scraped off and stored in a constant-temperature environment at the test temperature.

[0084] Then, triaxial creep tests were conducted on the prepared samples under different deviatoric stresses. The confining pressure was kept constant at 90 kPa, and the deviatoric stresses were set to 100 kPa, 400 kPa, 700 kPa, and 1000 kPa, respectively. The creep curves of frozen soils of different structural types under different deviatoric stresses are shown below. Figure 2 As shown, the frozen soil exhibits instantaneous deformation in the initial stage of loading, followed by time-dependent deformation as the load duration increases. Except for Type 2 frozen soil, the other types of frozen soil show three stages of creep under deviatoric stresses of 1000 kPa and 700 kPa: decaying creep, constant-rate creep, and accelerated creep. Furthermore, the creep failure time is shorter at 1000 kPa than at 700 kPa. At a deviatoric stress of 400 kPa, all five structural types of frozen soil exhibit decaying creep and constant-rate creep; while at a deviatoric stress of 100 kPa, all exhibit decaying creep.

[0085] Example 2: Initial elastic modulus and long-term strength of frozen soil

[0086] In the initial stage of creep, elastic deformation occurs within a short period of time, and the corresponding modulus is the initial elastic modulus, which is an important parameter in the creep model. The initial elastic strain is the intercept of the creep curve with the vertical axis when the creep time approaches zero. The relationship between deviatoric stress and initial strain, and the initial modulus, for frozen soils of different structural types are shown below. Figure 3As shown in the figure, the relationship between the two can be fitted using a linear relationship. Therefore, the initial elastic moduli of the lenticular frozen soils of structures 1-5 are determined to be 519.6 kPa, 313.1 kPa, 409.9 kPa, 788.6 kPa, and 759.9 kPa, respectively. It can be seen that the relationship between the initial elastic moduli of the five structural types of frozen soil and the relationship between the structural types of frozen soil is not obvious, indicating that in the initial deformation stage, the strength of the frozen soil is less affected by the structural characteristics.

[0087] The experiments revealed that the creep failure process of frozen soil involves a transition from decaying creep to constant-rate creep and finally to accelerated creep. For the creep process to fully reflect these three stages, a high level of deviatoric stress is required in the experiment. While a moderate level of deviatoric stress is sufficient to transition from decaying creep to constant-rate creep, the specimen's failure is only a matter of time as deformation accumulates. Therefore, whether a specimen fails depends on whether the applied deviatoric stress exceeds the critical value for the transition from decaying creep to constant-rate creep. If the deviatoric stress exceeds this critical value, the specimen will eventually fail; if it is below, the deformation will eventually stabilize over time, and the specimen will not fail. This critical value can be defined as long-term strength. Long-term strength, as the threshold for determining whether a specimen will fail during creep, is a crucial parameter in the creep model. To determine the long-term strength of frozen soils with different structural types, this paper adopts the first inflection point method of creep curve, that is, finding the point in the creep curve where decaying creep transitions to constant-rate creep. To reduce the arbitrariness of manually selecting points, the creep curve is fitted using the Vyarov (Вялов, С.С.) model. The expression of the model is as follows:

[0088]

[0089] In the formula: ε is creep strain; σ is deviatoric stress; T is temperature; t is creep time; A, B, C, and D are model parameters.

[0090] First, Equation 1 is used to fit the test results of frozen soils with different structural types. Then, the first derivative of the fitted curve of the creep test results is obtained to determine the relationship between strain rate and time. The time point corresponding to the strain rate decreasing to a constant is the first inflection point in the creep curve. The relationship curves between time and deviatoric stress corresponding to the inflection point under different deviatoric stresses are plotted, as shown below. Figure 4 As shown, this curve has an asymptote, and the intercept of this asymptote with the vertical axis represents the long-term strength. Based on the relationship between the inflection point and the deviatoric stress, it is easy to see that when the creep time t = 0, the corresponding deviatoric stress is infinite, and as t approaches infinity, the deviatoric stress tends to a stable value, which is the long-term strength. Based on this property, an exponential function q = a / (1-e^(-t / t)) is constructed. -btThe curves were fitted, where a and b are parameters and t is time. The fitting results for different structural types of frozen soil are shown in Equation 2. From the equation, it can be seen that the long-term strengths of frozen soil types 1 to 5 are 276.9 kPa, 271.6 kPa, 252.7 kPa, 263.3 kPa, and 256.1 kPa, respectively. Therefore, the better the structural type of frozen soil, the greater its long-term strength, while the worse the structural type, the smaller its long-term strength.

[0091]

[0092] Example 3: Hardening and damage parameters during creep of lens-containing frozen soil

[0093] Based on the creep characteristics of permafrost of different structural types under different stress levels, it can be found that the creep process is a continuous process of stress adjustment, hardening effect, and damage effect interacting and developing within the permafrost. For permafrost containing lens ice, the components involved in creep are mainly the soil skeleton, ice crystals, lens ice, unfrozen water, and microcracks. Under external loads, the increased stress at the solid-solid contact points within the permafrost causes compression of microcracks and plastic flow of ice crystals. Soil particles rearrange and form new connections between them, increasing the cohesion and friction between soil particles, enhancing the strength of the permafrost, and producing a hardening effect. On the other hand, stress concentration at the ends of lens ice in the permafrost leads to the initiation and propagation of microcracks, while simultaneously disrupting the original connections between soil particles, causing a decrease in the strength of the permafrost and producing a damage effect.

[0094] The deformation of frozen soil under constant load exhibits time-dependent characteristics, and its deformation behavior is closely related to the load. The entire creep process can be divided into three stages: decay, steady state, and acceleration. In the decay creep stage, the micropores within the frozen soil gradually close under load, the hardening effect plays a significant role, the strain rate gradually decreases, and the curve approximately exhibits a convex shape. In the steady-state creep stage, viscoplastic flow occurs during deformation development, the closure and propagation of internal microcracks are in competition, the strain increases linearly, and the strain rate remains constant. In the acceleration stage, the creep curve becomes concave, the slope of the curve gradually increases, the microcracks in the frozen soil propagate rapidly, and the damage effect dominates.

[0095] Based on the experimental results of Examples 1-2, it can be determined that when the stress is less than the long-term strength of the frozen soil, the adjustment of internal stress during creep leads to structural reinforcement, with the hardening effect playing a dominant role; therefore, decay creep is the primary characteristic. When the stress exceeds the long-term strength of the frozen soil, the propagation of internal cracks results in structural weakening exceeding strengthening, and the damage effect plays a significant role in the creep process; therefore, constant-rate creep and accelerated creep are the main characteristics. Over time, the frozen soil sample fails, losing strength. Therefore, this section fully considers the hardening and damage effects under different stress levels when establishing the creep constitutive model of frozen soil.

[0096] To quantitatively describe the effects of hardening and damage on creep characteristics, a hardening parameter H and a damage parameter D are introduced to reflect the strengthening and weakening of frozen soil structures under load. The hardening effect arises from the frozen soil's resistance to further deformation and typically occurs during the plastic deformation stage, mainly characterizing the gradual increase in the strength of the frozen soil over time. The hardening parameter H(σ,t) generally satisfies the following: when t→0, H(σ,t)→0; and when t→∞, H(σ,t)→constant. The hardening parameter H(σ,t) satisfying the above conditions can be represented by an exponential function related to stress and time, in the form:

[0097] H(σ,t)=f(σ)[1-e -t (3)

[0098] In the formula: f(σ) is a function representing the degree of hardening, which is related to the stress level and can be obtained by fitting the creep curve; t is the creep time.

[0099] During the creep process of frozen soil, when the stress level exceeds the long-term strength, the bonds of the frozen soil skeleton gradually break down with increasing strain, the skeleton begins to disintegrate, and slippage occurs between particles. The deformation behavior of frozen soil exhibits viscoplastic creep characteristics. Moreover, as creep continues, the micro-cracks in the frozen soil continuously propagate and penetrate. Since the damage caused by the propagation of micro-cracks inside the frozen soil during creep is time-dependent, the creep damage parameter is described by a function in the form of a Weibull distribution, which can be expressed as:

[0100]

[0101] In the formula: g(σ) is a function representing the degree of damage and is related to the stress level, which can be obtained by fitting the creep curve; m is a parameter representing the rate of damage development in frozen soil during creep; t is the creep time.

[0102] Furthermore, the presence of lens ice within the permafrost and the initiation and propagation of cracks caused by stress concentration at the lens ice ends during loading also weaken the strength of the permafrost. Therefore, the deterioration of the mechanical properties of permafrost during creep is also caused by the coupling between the lens ice structure and the propagation of microscopic cracks within the permafrost. Based on the principle of equivalent strain, the damage parameter for permafrost containing lens ice during creep, considering tectonic damage, is proposed as follows:

[0103]

[0104] In the formula: D1(σ,t) is the damage parameter without considering the influence of lens ice inside the frozen soil; D2 is the structural damage parameter of the frozen soil containing lens ice considering the influence of lens ice. Based on the principles of continuous damage mechanics and strain energy, under the condition of considering the crack propagation at the lens ice tip under stress concentration effect, the structural damage parameter of the frozen soil containing lens ice can be derived as follows:

[0105]

[0106] In the formula: τ eff The effective stress at the ice-frozen soil interface is related to the interfacial friction coefficient, the lens ice tilt angle, and the confining pressure; B, a are the lens ice thickness and half-length perpendicular to the plane; V, θ are the volume of the frozen soil sample and the crack initiation angle at the lens ice tip, where θ = 70.5°; spherical stress σ m = (σ1 + 2σ3) / 3; deviatoric stress σ1 and σ3 are the axial load and confining pressure applied to the specimen; ν is the Poisson's ratio of the frozen soil.

[0107] The above analysis describes the structural damage parameters under triaxial compression when the permafrost contains only one lensing ice. When multiple lensing ices are present, a weighted method is needed to determine the equivalent structural damage parameters. First, the area fraction S of each lensing ice layer is calculated. i =φL j L j =t i / d represents the thickness fraction of the lens ice in the permafrost; φ = 2a / b represents the connectivity of the lens ice, t i Let be the thickness of the lens ice, d be the spacing between the rows of lens ice, a be the half-length of the lens ice, and b be the distance between the centers of two adjacent lens ice segments. Since... Therefore, by weighting the damage parameters according to the area fraction occupied by each lens ice, the equivalent damage parameter of the frozen soil containing multiple lens ices can be obtained, and its expression is:

[0108]

[0109] In the formula D i The damage parameters are for a single lens ice.

[0110] The relationship between hardening parameters and damage parameters is as follows: Figure 5As shown in the figure, the hardening parameter, initially zero, increases non-linearly with time in the early stages of creep, then stabilizes, indicating that the permafrost hardens to a certain extent and then stabilizes. The damage parameter, due to structural damage caused by lenticular ice, has a non-zero initial value and increases with creep time, eventually approaching 1. Comparing the hardening and damage parameters during creep, it can be found that in the early stages of creep, the hardening parameter is greater than the damage parameter. Around 2.3 hours, the hardening and damage parameters are equal, after which the damage parameter is greater than the hardening parameter. This indicates that in the early stages of creep, the hardening effect dominates, and the permafrost exhibits mainly decaying creep. As time increases, the damage effect begins to dominate, and the permafrost mainly undergoes isochronous or accelerated creep.

[0111] Example 4: Creep Model of Lens-Containing Frozen Soil Considering Tectonic Damage

[0112] Based on the experimental results, it can be found that when the shear stress is lower than the long-term strength, the curve exhibits decaying creep. When the shear stress is higher than the long-term strength, the curve exhibits non-decaying creep, and the creep process fully demonstrates three stages. The creep model proposed in this section has the following characteristics: (1) When the stress is less than the long-term strength σ s When the creep curve tends to stabilize with increasing time, it belongs to viscoelastic strain and is described by the Kelvin model; (2) when the stress is greater than the long-term strength σ s As time increases, the deformation of the permafrost increases, exhibiting viscoelastic-plastic strain. The entire creep process is divided into three stages, described using the Kelvin and Bingham cascade model. According to... Figure 5 Analysis shows that hardening and damage effects are present throughout the entire creep process, but their extent varies at different stages. To reflect the hardening and damage effects throughout the creep process, a hardening parameter H is first introduced into the viscosity coefficient of the viscoelastic element in the Kelvin and Bingham models. Then, the entire creep deformation calculated based on the hardening effect is reduced using the damage parameter D. This yields a complete creep model structure based on hardening and damage effects.

[0113] (1) When 0 < σ < σ s At this stage, the material is primarily viscoelastic, and the model consists of a generalized Kelvin model. As deformation progresses, the hardening effect intensifies. The viscosity coefficient of a viscoelastic element considering the hardening effect can be expressed as:

[0114]

[0115] In the formula: is the initial viscosity coefficient of the viscoelastic element.

[0116] For springs:

[0117]

[0118] In the formula, E0 is the initial elastic modulus, and σ is the deviatoric stress during the creep process.

[0119] For the Kelvin model, the viscoelastic strain considering the hardening effect can be expressed as:

[0120]

[0121] In the formula, E1 is the viscoelastic modulus; σ is the deviatoric stress during the creep process.

[0122] According to the principle of strain superposition, then σ < σ s The strain at that time is:

[0123]

[0124] (2) When σ>σ s At this stage, the model is composed of a cascaded generalized Kelvin model and a Bingham model, where the damage effect plays a crucial role. Decaying creep, steady-state creep, and accelerated creep are all included. Similarly, the viscosity coefficient of a viscoelastic element considering the hardening effect can be expressed as:

[0125]

[0126] In the formula: is the initial viscosity coefficient of the viscoplastic element.

[0127] For the Bingham model, solving its constitutive equations yields the viscoplastic strain considering the hardening effect as follows:

[0128]

[0129] In the formula: σ is the deviatoric stress during the creep process; σ s This refers to the long-term strength of the frozen soil.

[0130] According to the principle of strain superposition, then σ > σ s The strain at that time is:

[0131]

[0132] The analysis of Example 3 shows that due to the presence of lens ice in the frozen soil, the structural damage value is not zero. Under load, the damage gradually increases with creep time, indicating that the damage effect exists throughout the entire creep process. Therefore, considering the damage effect, the creep deformation of the frozen soil containing lens ice is:

[0133] ε(t)=εH (t)[1-D 12 (σ,t)] (15)

[0134] Based on equations 11, 14, and 15, the expression for the three-dimensional creep model considering hardening and damage effects can be obtained using elastoplastic theory:

[0135]

[0136] In the formula: G0 is the initial shear modulus; σ s G1 is the long-term strength; G2 is the viscoelastic shear modulus. The initial viscoelastic viscosity coefficient; σ0 represents the initial viscoplastic viscosity coefficient; σ1 and σ3 represent the axial load and confining pressure, respectively; D0 12 (t) represents the damage parameter during the creep process of lens-containing permafrost, taking into account structural damage.

[0137] Equation 16 contains eight parameters, including the elastic modulus G0 and the long-term strength σ. s As determined in Example 2, the remaining 6 parameters are the shear modulus G1 and the initial viscosity coefficient in the Kelvin model. Initial viscosity coefficient in the Bingham model The six parameters—f(σ)—representing the degree of hardening, g(σ) representing the degree of damage, and m—representing the damage development rate, can be identified through inversion. Among these, the shear modulus G1 and the initial viscoelastic viscosity coefficient are important parameters for different structural types of lenticular frozen soils. Initial viscosity coefficient of viscoplastic The damage development rate parameter m is shown in Table 1.

[0138] Table 1 Model parameters for frozen soils with different structural types

[0139]

[0140] The relationship between the hardening degree function f(σ) and the damage degree function g(σ) and the deviatoric stress during the creep process of frozen soil is as follows: Figure 6 As shown, the relationship between the hardening degree function and stress is f(σ)=a+b(σ1-σ3). The values ​​of the hardening function parameters a and b for different structural types of frozen soil are shown in [reference needed]. Figure 6 (a); the relationship between the damage degree function and stress is g(σ)=mexp[b(σ1-σ3)], and the values ​​of the damage function parameters m and n for different structural types of frozen soil are shown in [reference]. Figure 6 (b)

[0141] from Figure 6The results show that the hardening degree function f(σ) decreases with increasing deviatoric stress, and the stronger the permafrost structure, the larger the hardening parameter. This indicates that the hardening effect is dominant at low stress levels, and weakens as the stress level increases. The damage degree function g(σ) increases with increasing deviatoric stress and decreases with increasing permafrost structure, indicating that the stronger the structure, the more difficult it is to fail. Under low stress conditions, the damage effect of permafrost is small, and the damage increases with increasing stress level. Furthermore, the growth rate of g(σ) increases with increasing deviatoric stress.

[0142] Substituting the corresponding model parameters into Equation 16 yields the calculation results. When the deviatoric stress is less than the long-term strength, the formula σ1-σ3<σ in Equation 16 is used. s For formula fitting under the given conditions, when the deviatoric stress is greater than the long-term strength, the formula σ1-σ3≥σ in Equation 16 is adopted. s Formula fitting under given conditions. Comparison of model calculation results with experimental results. Figure 7 As shown in the figure, it can be seen that the model proposed in this paper can simulate the creep characteristics of permafrost of different structural types very well, especially the nonlinear deformation characteristics caused by the propagation of cracks at the end of lens ice.

[0143] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0144] As demonstrated in the above implementation examples, this invention conducts triaxial creep tests on lenticular frozen soils of different structural types under different deviatoric stresses to obtain corresponding creep curves; determines the elastic modulus and long-term strength of frozen soils of different structural types; determines the expressions for hardening and tectonic damage variables of lenticular frozen soils during the creep process; and constructs a creep model for lenticular frozen soils considering tectonic damage based on the mechanisms of hardening and damage effects during creep in lenticular frozen soils of different structural types. Based on the creep test results of lenticular frozen soils of different structural types, the parameters of the creep model are determined through fitting and inversion, and the rationality of the model is verified. This invention, through the establishment of a frozen soil creep model considering tectonic damage, can predict the creep deformation of lenticular frozen soils with complex structures under external loads and can be applied to long-term deformation studies in relevant engineering projects.

[0145] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for characterizing creep deformation in frozen soil containing lenses, characterized in that: This method is based on the data-driven multi-factor collaborative construction of creep data experimental factors, data expression model construction factors, and data fitting inversion factors to quantify and quantify the creep deformation of frozen soil containing lens ice. At the same time, when constructing the quantitative data representation formula, the dynamic structural damage effect of frozen soil, the creep hardening effect of frozen soil, the lens ice geometric effect of frozen soil decay creep stage, the lens ice geometric effect of frozen soil stable creep stage, and the lens ice geometric effect of frozen soil accelerated creep stage are built-in compatible data representations. The obtained data representation formula is then subjected to post-fit verification as needed to achieve quantitative prediction of long-term dynamic settlement and deformation of foundations of structures in cold regions. The implementation steps of this method include: ① constructing data on the hardening parameters and structural damage parameters of lenticular frozen soil during the creep process; ② constructing a creep data characterization formula for lenticular frozen soil compatible with structural damage based on the mechanism of hardening and damage effects of lenticular frozen soil with different structural types during the creep process. The hardening parameters of frozen soil were constructed through the following data processing procedure: Setting H as the character identifier for the hardening parameter and representing it using an exponential function related to stress and time, we obtain: （1） In the formula: The function representing the degree of hardening related to stress level is obtained by curve fitting based on creep tests; t is the creep time. The structural damage parameters of permafrost were constructed using the following data processing procedure: Let D be the character identifier for the hardening parameter. During the creep process of frozen soil, the damage caused by the propagation of internal micro-cracks is related to stress and time. A Weibull distribution function is used to characterize the creep damage parameter, resulting in: （2） In the formula: is a function representing the degree of damage related to the stress level, obtained by curve fitting based on creep tests; m is a parameter related to the rate of damage development in frozen soil during creep; t is the creep time. Damage parameters for the creep process of lens-containing permafrost soil considering tectonic damage were constructed, and the following results were obtained: （3） In the formula: D1 represents the damage parameter without considering the influence of lens ice inside the permafrost; D2 represents the structural damage parameter considering the influence of lens ice inside the permafrost. The structural damage parameters of frozen soil containing lens ice were constructed under the condition of considering the crack propagation at the tip of the lens ice due to stress concentration effect, and the following results were obtained: （4） In the formula: τ eff The effective stress at the ice-frozen soil interface is related to the interfacial friction coefficient, the lens ice tilt angle, and the confining pressure; B, a are the lens ice thickness and half-length perpendicular to the plane; V, θ are the volume of the frozen soil sample and the crack initiation angle at the lens ice tip, where θ = 60-80°; spherical stress. ; deviatoric stress σ1 and σ3 are the axial load and confining pressure, respectively; ν is the Poisson's ratio of the frozen soil.

2. The method for characterizing creep deformation of lens-containing frozen soil according to claim 1, characterized in that: The data characterization formula for creep data of lens-containing frozen soil is constructed based on the following conditions: when lens-containing frozen soil undergoes creep, the hardening effect and damage effect run through the entire creep process, and the degree of their exertion varies at different stages. The data characterization of the object's elasticity, viscoelasticity and viscoplasticity covers the entire creep process.

3. The method for characterizing creep deformation of lens-containing frozen soil according to claim 2, characterized in that: The generalized Kelvin and Bingham models were used to characterize the elasticity, viscoelasticity, and viscoplasticity of lensed permafrost throughout the creep process.

4. The method for characterizing creep deformation of lens-containing frozen soil according to claim 3, characterized in that: The data characterization process includes: first, introducing a hardening parameter H into the viscoplastic element of the viscoelastic element in the generalized Kelvin model and Bingham model; then, reducing the entire creep deformation calculated based on the hardening effect using a damage parameter, thereby constructing a complete progressive process of creep data based on hardening and damage effects, and obtaining a characterization formula for creep data of lenticular frozen soil with compatible structural damage.

5. The method for characterizing creep deformation of lens-containing frozen soil according to claim 4, characterized in that: The complete creep data progression process includes: A. When 0 < σ < σ s At this time, viscoelasticity is the primary property, and a generalized Kelvin data model is adopted. As deformation progresses, the hardening effect intensifies. ŋ1(H) is set as the viscosity coefficient of the viscoelastic element considering the hardening effect, expressed as: （5） In the formula: The initial viscosity coefficient of the viscoelastic element; For the generalized Kelvin model, data analysis of its constitutive equation yields the viscoelastic strain considering the hardening effect, expressed as: （6） In the formula: E0 is the initial elastic modulus; E1 is the viscoelastic modulus; σ is the deviatoric stress during the creep process; B, when At this stage, the damage effect is achieved by connecting the generalized Kelvin model and the Bingham model in series; decay creep, steady-state creep, and accelerated creep are all included. ŋ2(H) is also the viscosity coefficient of the viscoelastic element considering the hardening effect, expressed as: （7） In the formula: The initial viscosity coefficient of the viscoplastic element; For the Bingham model, data analysis of its constitutive equation yields the viscoplastic strain considering the hardening effect, expressed as: （8） In the formula: σ is the deviatoric stress during the creep process; σ s The long-term strength of frozen soil; According to the principle of strain superposition, we obtain The strain at time is expressed as: （9） Due to the presence of lens ice in the frozen soil, the initial structural damage value is not zero. Under load, the damage gradually increases with creep time, and the damage effect exists throughout the entire creep process. Therefore, the creep deformation of frozen soil containing lens ice considering the damage effect is: （10）。 6. The method for characterizing creep deformation of lens-containing frozen soil according to claim 5, characterized in that: Based on Equations 6, 9, and 10, a characterization formula for creep data of lens-containing permafrost with compatible structural damage is constructed, yielding: （11） In the formula: G0 is the initial shear modulus; σ s G1 is the long-term strength; G1 is the viscoelastic shear modulus; ŋ1 0 ŋ2 is the initial viscoelastic viscosity coefficient; 0 σ0 represents the initial viscoplastic viscosity coefficient; σ1 and σ3 represent the axial load and confining pressure, respectively; D0 12 (σ,t) represents the damage parameters during the creep process of lens-containing frozen soil, taking into account structural damage.

7. The method for characterizing creep deformation of lens-containing frozen soil according to claim 6, characterized in that: The parameters in the obtained characterization formula for lenticular permafrost creep data with compatible structural damage were obtained through the following known methods: measurement, manuals, measurement-based data curve fitting, data fitting inversion, reliable tangible literature, and reliable online literature; among them, the elastic modulus G0 and long-term strength σ are... s Determined based on creep curves.

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