A method for predicting steady-state creep curves of clay under freeze-thaw-dry-wet cycles

Abstract

The application discloses a method for predicting clay steady-state creep curves under freeze-thaw-dry-wet cycles, which comprises the following steps: carrying out creep tests on clay samples with different freeze-thaw-dry-wet cycle times N , respectively, to obtain soil creep strain-time curves; establishing a creep model; fitting the obtained creep strain-time curves to obtain model parameters, respectively; establishing quantitative relationships between the model parameters and N ; and establishing a prediction model for clay steady-state creep curves after N times of freeze-thaw-dry-wet cycles. The prediction model for clay steady-state creep curves after freeze-thaw-dry-wet cycles is established by fitting the creep model parameters and freeze-thaw-dry-wet cycle times with a simple exponential function, and can continuously describe the change of creep characteristics with freeze-thaw-dry-wet cycles, so that the creep amount of clay under any freeze-thaw-dry-wet cycle can be reasonably predicted, and the creep behavior of clay under environmental action can be more truly and accurately described.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering technology, specifically to a method for predicting the steady-state creep curve of clay under freeze-thaw-wet cycles. Background Technology

[0002] Soil creep refers to the phenomenon where deformation of soil increases continuously over time under constant stress. The development of creep strain is a key factor affecting the long-term deformation and stability of geotechnical structures, and establishing a creep model that accurately predicts the creep curve of soil is an important basis for conducting safety assessments of geotechnical structures.

[0003] In seasonally frozen soil regions such as Northeast and Northwest my country, soil deformation characteristics are influenced by seasonal temperature and humidity cycles. Due to the presence of some hydrophilic clay minerals, clay is extremely sensitive to periodic freezing-thawing and dehumidification-wetting cycles. Alternating freeze-thaw and wet-dry cycles disrupt the cementation between clay particles, alter particle arrangement, and affect internal pore structure, significantly increasing the creep deformation capacity of clay and potentially leading to instability and failure of geotechnical structures. Therefore, studying the creep characteristics of clay under freeze-thaw and wet-dry cycles is essential for accurately evaluating structural stability.

[0004] Creep testing is the most direct research method for measuring the creep curve of clay. Due to the influence of climate and environment under natural conditions, the effects of temperature and humidity cycles on soil are not clearly defined. Accurately revealing the creep characteristics of clay inevitably requires conducting numerous creep tests under different freeze-thaw and wet-dry cycles, which consumes significant time, manpower, and resources. Furthermore, increasing the number of tests also leads to an increase in overall experimental error. Establishing a simple and accurate creep model based on creep curves measured under a small number of freeze-thaw and wet-dry cycles to predict the creep characteristics of clay is an effective way to solve this problem. However, traditional creep models generally suffer from low accuracy in describing creep curves with different development trends. Summary of the Invention

[0005] The purpose of this invention is to solve the problem that traditional creep models are not accurate enough in describing creep curves with different development trends, and to provide a method for predicting the steady-state creep curve of clay under freeze-thaw-wet cycles.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A method for predicting the steady-state creep curve of clay under freeze-thaw-wet cycles includes the following steps:

[0008] 1) Sample preparation; Prepare several initial clay samples at the set dry density and moisture content.

[0009] 2) Take a portion of the initial clay sample, and without subjecting it to freeze-thaw and wet-dry cycles, directly conduct creep tests to obtain the soil creep strain-time curve;

[0010] 3) Take some initial clay samples and subject them to different numbers of freeze-thaw and wet-dry cycles. Conduct creep tests on each sample under the same conditions as in step 2) to obtain creep strain-time curves for different number of cycles.

[0011] 4) Using Maxwell and Kelvin bodies connected in series as the basic unit, and introducing a time-varying depreciation term. D L This yields a creep model with damage;

[0012] 5) Fit the creep strain-time curve obtained in step 2) without the freeze-thaw-wet cycle to obtain the model parameters of the sample without the freeze-thaw-wet cycle. E M , or M , E K , or K , D 0、 i ;

[0013] By fitting the creep strain-time curves obtained from different freeze-thaw-wet cycles in step 3), model parameters of the specimens under different freeze-thaw-wet cycles are obtained. E M , or M , E K , or K , D 0、 i ;

[0014] 6) Model parameters based on exponential functions E M , or M , E K , or K , D 0、 i With the number of freeze-thaw-wet cycles N Fit the change curves and establish model parameters and... N Quantitative relationship;

[0015] 7) Combining the creep model from step 4) and the model parameters from step 6) with N Relationships, thereby establishing experiencesN Predictive model for steady-state creep curve of clay after one freeze-thaw-wet cycle.

[0016] Specifically, the implementation process of step 2) is as follows:

[0017] The initial clay sample was loaded to a constant confining pressure and consolidated to a stable state under that pressure. Under the condition that the confining pressure remained unchanged, a deviatoric stress was gradually applied to a predetermined value at a set loading rate and maintained at this stress level for 7 days. During this period, the creep strain of the sample was recorded as a function of time.

[0018] Further, in step 3), a portion of the initial clay samples were taken and divided into three groups, and each group of samples was subjected to 1, 4 and 10 freeze-thaw-wet cycles, respectively. Then, according to the loading method described in step 2), the stress state of the samples was kept constant for 7 days under the same deviatoric stress conditions. The creep strain of the samples over time was recorded under different freeze-thaw-wet cycles.

[0019] Furthermore, in step 4), considering that the physical properties of clay will change during creep, a time-varying loss term is introduced into the model parameters. D L = D 0(1- e -θt ), D 0 is the initial loss factor. i It is a regulating factor.

[0020] Because the Maxwell body and the Kelvin body are connected in series, the equivalent stress acting on the Maxwell body is equal to the equivalent stress acting on the Kelvin body, and the strains are superimposed. Therefore, the same stress symbol is used in formulas (1) and (2).

[0021] The constitutive equation of the Maxwell body is:

[0022]

[0023] In formula (1), E M The elastic modulus of the Maxwell spring. or M The viscosity coefficient of the Maxwell damping element. The strain rate of the Maxwell body is, i.e. e M The derivative with respect to time; D L For losses, s d Indicates deviatoric stress. This represents the derivative of the deviatoric stress with respect to time.

[0024] The constitutive equation of the Kelvin body is:

[0025]

[0026] In formula (2), E K The elastic modulus of the Kelvin spring. or K The viscosity coefficient of the Kelvin damping element. The strain rate of the Kelvin body, i.e. e K The derivative with respect to time.

[0027] Connecting the Maxwell body and the Kelvin body in series and combining equations (1) and (2), the creep model is obtained as follows:

[0028]

[0029] The derivation of formula (3) is as follows:

[0030] Due to series connection, During creep s d Remain unchanged;

[0031] For Maxwell bodies , That is, the strain rate of the sticky pot in series is equal to the strain rate of the Maxwell element. Integrating this, we get:

[0032] C is the integration constant, determined by the initial conditions;

[0033] At t=0,

[0034] ;

[0035] ;

[0036] For Kelvin body, Solving the differential equation yields:

[0037] C is the integration constant, determined by the initial conditions;

[0038] At t=0, ;

[0039] ;

[0040] ;

[0041] Further, step 5) specifically involves substituting the creep strain and time obtained in steps 2) and 3) into the creep model formula, and using the iterative least squares method in data analysis software to fit the scatter points in the creep strain-time coordinate system to obtain the model parameters. E M , or M , E K , or K , D 0、 i .

[0042] Furthermore, in step 6), to describe from 0 to... N The variation of model parameters between freeze-thaw and wet-dry cycles was investigated using an exponential function to establish the relationship between model parameters and... N Quantitative relationship:

[0043]

[0044] In formula (4) Φ N Indicates experience N Model parameters of the sample after one freeze-thaw-wet cycle, where Φ0 represents the model parameters of the sample that did not undergo freeze-thaw-wet cycle. α , β is the function parameter value, and is the fitting parameter, determined through nonlinear regression.

[0045] Under freeze-thaw and wet-dry cycles, microcracks within the material gradually expand, leading to a rapid decline and eventual stabilization of strength, modulus, and other properties. Typical process:

[0046] Early stage: Rapid degradation rate (has just undergone a cycle, and the structure is sensitive to damage).

[0047] Mid-term: The rate of degradation gradually slows down;

[0048] Later stage: It tends to reach a residual stable value (it will not decrease indefinitely).

[0049] This evolutionary process of "fast → slow → stable" essentially conforms to the exponential decay / growth law.

[0050] Regarding the changing trends of different model parameters, Matlab or origin The software employs a nonlinear fitting method, using either a decaying exponential function or an increasing exponential function, to adjust the model parameters obtained in step 6). E M , or M , E K, or K , D 0、 i Scatter points were fitted, and model parameters were established respectively. N The quantitative relationship.

[0051] Furthermore, in step 7), the model parameters established in step 6) are compared with... N Substituting the quantitative relationship into formula (3), a prediction model for the steady-state creep curve of clay under freeze-thaw-wet cycles is established, that is, after experiencing... N The prediction model for the steady-state creep curve of clay after one freeze-thaw-wet cycle is as follows:

[0052]

[0053] In the formula, f EM ( N ), f ηM ( N ), f EK ( N ), f ηK ( N ), f D0 ( N ), f θ ( N ) represent the model parameters E M , or M , E K , or K , D 0、 i and N The quantitative relationship.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] This invention considers the changes in the physical and mechanical properties of clay during creep, by connecting Maxwell bodies and Kelvin bodies in series, and by uniformly introducing the loss term into four parameters ( E , or The established creep model can more accurately and effectively describe the development of clay creep strain over time, and has stronger adaptability to predict different trends.

[0056] This invention measures creep curves under a limited number of freeze-thaw and wet-dry cycles. Based on this, a predictive model for the steady-state creep curve of clay after freeze-thaw and wet-dry cycles can be established by fitting the creep model parameters with the number of freeze-thaw and wet-dry cycles using a simple exponential function. This effectively reduces the amount of experiments required to study the creep characteristics of clay under freeze-thaw and wet-dry conditions and lowers experimental costs.

[0057] The method proposed in this invention can continuously describe the changes in creep characteristics with freeze-thaw and wet-dry cycles, which facilitates reasonable prediction of the creep of clay under any number of freeze-thaw and wet-dry cycles, and more realistically and accurately describes the creep behavior of clay under environmental influences. Attached Figure Description

[0058] Figure 1 These are creep curves measured after different freeze-thaw-wet cycles under a confining pressure of 12 kPa in this embodiment of the invention.

[0059] Figure 2 These are creep curves measured after different freeze-thaw-wet cycles under a confining pressure of 25 kPa in this embodiment of the invention.

[0060] Figure 3 These are creep curves measured after different freeze-thaw-wet cycles under a confining pressure of 50 kPa in this embodiment of the invention.

[0061] Figure 4 This is a curve showing the variation of Maxwell volume model parameters with the number of freeze-thaw-wet cycles in an embodiment of the present invention;

[0062] Figure 5 This is a curve showing the variation of Kelvin body model parameters with the number of freeze-thaw-wet cycles in an embodiment of the present invention;

[0063] Figure 6 This is a curve showing the change of the loss item model parameters with the number of freeze-thaw-wet cycles in an embodiment of the present invention;

[0064] Figure 7 In the embodiment of the present invention, under a confining pressure of 12 kPa... N Measured and predicted values ​​of creep curves at values ​​of 1, 4, and 10;

[0065] Figure 8 In the embodiment of the present invention, under a confining pressure of 25 kPa... N Measured and predicted values ​​of creep curves at values ​​of 1, 4, and 10;

[0066] Figure 9 In this embodiment of the invention, under a confining pressure of 50 kPa... N Measured and predicted values ​​of creep curves at values ​​of 1, 4, and 10. Detailed Implementation

[0067] The method of the present invention will be described in detail below with reference to the accompanying drawings. The specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0068] Several initial clay samples prepared at set dry density and moisture content were subjected to multiple freeze-thaw and wet-dry cycles of 0, 1, 4, and 10, respectively. The samples were then placed in a triaxial apparatus. Under constant confining pressure, the samples were allowed to consolidate and stabilize. While maintaining the confining pressure, the deviatoric stress was applied at a set rate to a predetermined value. The overall stress state of the samples was kept constant for approximately 7 days, and the axial creep strain versus time curve was plotted.

[0069] For the creep curves measured under each freeze-thaw-wet cycle, the experimental data ( e c , t Substituting into formula (3), using Origin Nonlinear fitting tools or Matlab of lsqcurvefit The function uses the iterative least squares method to solve for the model parameter set. E M , or M , E K , or K , D 0、 i Repeat until the creep curve fitting is complete for all freeze-thaw-wet cycles.

[0070] Draw the model parameters respectively E M , or M , E K , or K , D 0、 i With the number of freeze-thaw-wet cycles N A scatter plot of changes, in Origin or Matlab The software uses a nonlinear regression fitting method, employing either the decay exponential function or the increase exponential function in formula (4) to fit the decaying or increasing model parameters respectively, determining the specific function parameter values, and establishing the model parameters and... N Quantitative function f EM ( N ), f ηM ( N ), fEK ( N ), f ηK ( N ), f D0 ( N ), f θ ( N Substituting the aforementioned quantitative function into formula (5), a prediction model for the steady-state creep curve of clay under freeze-thaw-wet conditions can be obtained, which can effectively predict the creep curve of clay under any number of freeze-thaw-wet cycles.

[0071] Example 1: The method for predicting the steady-state creep curve of clay under freeze-thaw-wet-dry cycles according to the present invention is further illustrated below with specific soil samples.

[0072] The soil sample used in this embodiment is a low liquid limit clay. The soil sample was divided into four groups. The first group of initial clay samples did not undergo freeze-thaw-wet-dry cycles; the second group of initial clay samples underwent one freeze-thaw-wet-dry cycle; the third group of initial clay samples underwent four freeze-thaw-wet-dry cycles; and the fourth group of initial clay samples underwent ten freeze-thaw-wet-dry cycles. The samples were then placed in a triaxial apparatus for creep testing. Under constant confining pressure, the samples were allowed to consolidate and stabilize. Maintaining the confining pressure, the deviatoric stress was applied at a set rate to a predetermined value. The overall stress state of the samples was kept constant for approximately 7 days. Based on the axial strain data measured during the test, the axial creep strain was plotted. e c With time t The creep curve is as follows Figure 1~Figure 3 As shown.

[0073] The test data ( e c , t Substituting into formula (3), using Origin Data analysis software uses iterative least squares method to analyze... e c - t By fitting the scattered points in the coordinate system, the model parameter values ​​can be obtained. E M , or M , E K , or K , D 0、 i See Table 1.

[0074] Table 1. Fitting parameters and goodness of fit of the creep model under different freeze-thaw-wet cycles.

[0075]

[0076] As shown in Table 1, the model parameters E M , or M , E K , or K Follow N The decrease is due to the increase of the initial loss factor, and the decay exponential function of formula (4) is used for fitting; D 0 N The increase of remains almost constant, and the function parameters in formula (4) β Set to 0. α It can take any value; adjustment factor i Follow N The value increases with the increase of the value, and the model is fitted using the exponential function of formula (4). The curves showing the change of model parameters with the number of freeze-thaw-wet cycles and the corresponding fitting curves are as follows: Figure 4~Figure 6 As shown in the table. The specific values ​​of the fitting parameters are shown in Tables 2 to 4.

[0077] Table 2.12 kPa confining pressure model parameters - N Quantitative function fitting parameter values ​​and goodness of fit

[0078]

[0079] Table 3. Model parameters under 25 kPa confining pressure - N Quantitative function fitting parameter values ​​and goodness of fit

[0080]

[0081] Table 4. Model parameters under 50 kPa confining pressure - N Quantitative function fitting parameter values ​​and goodness of fit

[0082]

[0083] Taking a confining pressure of 25 kPa as an example, the model parameters E M , or M , E K , or K , D 0、 i and N The quantitative functions are expressed as follows:

[0084]

[0085] In the formula, parameters with a subscript of 0 represent model parameter values ​​that have not undergone freeze-thaw-wet cycles.

[0086] Function f EM ( N ), f ηM ( N ), f EK ( N ), f ηK ( N ), f D0 ( N ), f θ ( N Substituting into formula (5), we obtain the prediction model of the steady-state creep curve of clay under freeze-thaw and wet-dry conditions.

[0087] Based on the creep curve of the sample that has not undergone freeze-thaw-wet cycle, the model parameters and N The model parameter values ​​under different freeze-thaw-wet cycles were calculated using the quantitative function, and then substituted into formula (5) to calculate the predicted creep curves corresponding to different N values, such as... Figure 7~Figure 9 As shown, the predicted curves are highly similar in morphology to the creep curves of samples subjected to freeze-thaw and wet-dry cycles, with only minor differences in curve amplitude and creep rate. This indicates that the established prediction model can accurately maintain the basic morphological characteristics of the clay creep curve, while effectively reflecting the deformation aggravation caused by parameter deterioration under freeze-thaw and wet-dry cycles, thus verifying the rationality of the model structure and the reliability of the prediction method. Furthermore, compared to the Burgers model which only connects Maxwell and Kelvin bodies in series, the prediction model proposed in this invention significantly improves the prediction accuracy of the creep curve after freeze-thaw and wet-dry cycles, and its long-term prediction effect on clay steady-state creep is significantly better than that of the Burgers model.

Claims

1. A method of predicting steady-state creep curves of clay under freeze-thaw- wet-dry cycles, characterized in that: Comprising the following steps: 1) sample preparation; sample preparation under a set dry density and water content, to obtain several initial clay samples; 2) take part of the initial clay samples, without freeze-thaw-dry-wet cycle, directly carry out creep test, measure the soil creep strain-time curve; 3) take part of the initial clay samples, respectively experience different times of freeze-thaw-dry-wet cycle, carry out the same creep test under the same conditions of step 2) for each sample, obtain the creep strain-time curve under different cycle times; 4) Maxwell body and Kelvin body in series as the basic unit, and the introduction of time-varying loss term D L , get the creep model with damage 5) fitting the creep strain-time curve measured for step 2) without freeze-thaw-dry-wet cycles to obtain the model parameters of the sample without freeze-thaw-dry-wet cycles E M 、 η M 、 E K 、 η K 、 D 0、 θ ; The creep strain-time curves measured for step 3) under different freeze-thaw-dry-wet cycles are fitted to obtain the model parameters of the sample under different freeze-thaw-dry-wet cycles E M 、 η M 、 E K 、 η K 、 D 0、 θ ; 6) Model parameters based on exponential function E M , η M , E K , η K , D 0、 θ With the number of freeze-thaw-dry-wet cycle N The change curve is fitted, and the quantitative relationship between the model parameters and N is established respectively; 7) the creep model of step 4) and the relationship between the model parameters of step 6) and N thereby establishing a predictive model of the steady-state creep curve of clay after N the effect of n freeze-thaw-dry-wet cycles, the predictive model of the steady-state creep curve of clay after the effect of n freeze-thaw-dry-wet cycles being: wherein f EM ( N ), f ηM ( N ), f EK ( N ), f ηK ( N ), f D0 ( N ), f θ ( N ) are the quantitative relationships of the model parameters E M , η M , E K , η K , D 0, θ and N .

2. The method of predicting the steady-state creep curve of clay under freeze-thaw- wet-dry cycling of claim 1, wherein: The specific implementation process of step 2) is as follows: The initial clay sample is loaded to a constant confining pressure and consolidated to a stable state under the confining pressure; under the condition that the confining pressure remains unchanged, the bias stress is gradually applied at a set loading rate to a predetermined value, and the stress level is maintained constant for 7 days; during this period, the change curve of the creep strain of the sample with time is recorded.

3. The method of predicting the steady-state creep curve of clay under freeze-thaw- wet-dry cycling according to claim 2, characterized in that: In step 3), part of the initial clay sample is taken and divided into three groups, and each group of samples is subjected to 1, 4 and 10 freeze-thaw-dry-wet cycles, respectively; then, the stress state of the samples is kept constant for 7 days under the same deviatoric stress σ d loading mode described in step 2); the creep strain of the samples under different freeze-thaw-dry-wet cycle numbers is recorded ε c over time t .

4. The method of predicting the steady-state creep curve of clay under freeze-thaw- wet-dry cycling of claim 1, wherein: The creep model in step 4) is: wherein D L is a time-dependent impairment term, D L D 0(1- e -θt D 0 is an initial impairment factor, θ is an adjustment factor; E M is the modulus of elasticity of the Maxwell spring, η M is the coefficient of viscosity of the Maxwell damping element, σ d denotes the deviatoric stress, E K is the modulus of elasticity of the Kelvin spring, η K is the coefficient of viscosity of the Kelvin damping element.​​ 5. The method of predicting the steady state creep curve of clay under freeze-thaw- wet-dry cycling of claim 1, wherein: The creep strain and time obtained in step 2) and step 3) are substituted into the creep model formula in step 5), and the scattered points in the creep-time coordinate system are fitted using the iterative least square method in the data analysis software to obtain the model parameters E M 、 η M 、 E K 、 η K 、 D 0、 θ .

6. The method of predicting the steady-state creep curve of clay under freeze-thaw- wet-dry cycling of claim 1, wherein: In the step 6), to describe the change rule of the model parameters between the freeze-thaw and dry-wet cycles, an exponential function is used to establish the quantitative relationship between the model parameters and the freeze-thaw and dry-wet cycles. N N the freeze-thaw and dry-wet cycles:​ ； where Φ N denotes the model parameters of the specimen after experiencing N the freeze-thaw-dry-wet cycle, and Φ0denotes the model parameters of the specimen without experiencing the freeze-thaw-dry-wet cycle, α , β are the function parameter values, and are the fitting parameters determined by the nonlinear regression.

7. The method of predicting the steady-state creep curve of clay under freeze-thaw- wet-dry cycling of claim 1, wherein: The step 7) is to bring the quantitative relationship between the model parameters established in step 6) and N into the creep model formula, to establish a prediction model of the steady-state creep curve of clay under freeze-thaw-dry-wet cycles, that is, the prediction model of the steady-state creep curve of clay after experiencing N freeze-thaw-dry-wet cycles.

Images