Method for predicting steady-state creep curve of clay under freeze-thaw-dry-wet cycle

Abstract

The invention discloses a method for predicting a steady-state creep curve of clay under freeze-thaw-dry-wet cycle, which comprises the following steps: respectively carrying out creep tests on clay samples subjected to different freeze-thaw-dry-wet cycle times N to obtain a soil creep strain-time curve; establishing a creep model; fitting the measured creep strain-time curve to obtain model parameters respectively; respectively establishing quantitative relations between the model parameters and N; and establishing a prediction model of the steady-state creep curve of the clay after N times of freeze-thaw-dry-wet cycle effects. According to the method, creep model parameters and freeze-thaw-dry-wet cycle times are fitted through an exponential function with a simple form, and the established prediction model of the steady-state creep curve of the clay after the freeze-thaw-dry-wet cycle can continuously describe the change of creep characteristics along with the freeze-thaw-dry-wet cycle; the creep quantity of the clay under any freezing and thawing-wetting and drying cycle times can be reasonably predicted, and the creep behavior of the clay under the environmental action can be more truly and accurately described.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geotechnical engineering, and particularly relates to a method for predicting steady-state creep curves of clay under freeze-thaw-dry-wet cycles. BACKGROUND

[0002] The creep of soil refers to the phenomenon that the deformation of soil continuously increases with time under the action of constant stress. The development of creep strain is a key factor affecting the long-term deformation and stability of soil structures, and establishing a creep model for accurately predicting the creep curve of soil is an important basis for safety evaluation of soil structures.

[0003] In seasonal frozen regions such as northeast China and northwest China, the deformation characteristics of soil are affected by seasonal temperature and humidity cycles. Due to the presence of some hydrophilic clay minerals, clay is extremely sensitive to periodic freezing (frozen) - thawing (thawing) cycles and drying (dry) - wetting (wet) cycles. The alternating freeze-thaw-dry-wet cycles can destroy the cementation between clay particles, change the arrangement of particles and affect the internal pore structure, significantly improve the creep deformation capacity of clay, and may cause instability and damage of soil structures. Therefore, it is necessary to study the creep characteristics of clay under freeze-thaw-dry-wet cycles for accurate evaluation of structural stability.

[0004] Creep test is the most direct research means for measuring the creep curve of clay. Due to the influence of climate environment in natural state, the effect of temperature and humidity cycles of soil is not clear. In order to accurately reveal the creep characteristics of clay, it is inevitable to carry out a large number of creep tests under different freeze-thaw-dry-wet cycles, which consumes a lot of time, manpower and material resources, and the increase of test amount also leads to the increase of overall test error. Based on the measured creep curve under a small number of freeze-thaw-dry-wet cycles, establishing a creep model with simple operation and high precision to predict the creep characteristics of clay is an effective method to solve this problem, but the traditional creep model generally has low precision in describing creep curves with different development trends. SUMMARY

[0005] The purpose of the present application is to solve the problem of low precision of traditional creep model in describing creep curves with different development trends, and to provide a method for predicting steady-state creep curves of clay under freeze-thaw-dry-wet cycles.

[0006] In order to achieve the above-mentioned purpose, the technical scheme adopted by the present application is as follows: A method for predicting steady-state creep curves of clay under freeze-thaw-dry-wet cycles, comprising the following steps: 1) sample preparation; sample preparation under the set dry density and water content to obtain a plurality of initial clay samples; 2) take part of the initial clay samples, without freeze-thaw-dry-wet cycles, directly carry out creep test, and measure the soil creep strain-time curve; 3) Take part of the initial clay sample, respectively, through different times of freeze-thaw-dry-wet cycle, respectively, to carry out the same creep test under the conditions of step 2), and obtain the creep strain-time curve under different cycle times; 4) Take the Maxwell body and Kelvin body as the basic unit in series, and introduce the time-varying damage term D L , and obtain the creep model with damage; 5) Fit the creep strain-time curve measured in step 2) without freeze-thaw-dry-wet cycle to obtain the model parameters of the sample without freeze-thaw-dry-wet cycle E M 、 η M 、 E K 、 η K 、 D 0、 θ ; Fit the creep strain-time curve measured in step 3) under different freeze-thaw-dry-wet cycles 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) Fit the model parameters E M 、 η M 、 E K 、 η K 、 D 0、 θ with freeze-thaw-dry-wet cycle times N to establish the quantitative relationship between the model parameters and N ; 7) Combine the creep model of step 4) and the relationship between the model parameters and N of step 6), and thus establish the prediction model of the steady-state creep curve of clay after N freeze-thaw-dry-wet cycle.

[0007] Specifically, 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 steady state at this confining pressure; the deviatoric stress is gradually applied to a predetermined value at a set loading rate while the confining pressure remains unchanged, and the stress level is maintained constant for 7 days; during this period, the creep strain-time curve of the sample is recorded.

[0008] Further, 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, under the same deviatoric stress, the stress state of the samples is maintained constant for 7 days according to the loading mode described in step 2); the creep strain-time curves of the samples under different freeze-thaw-dry-wet cycle numbers are recorded.

[0009] Further, in step 4), considering that the physical properties of clay will change during creep, a time-varying degradation term is introduced to the model parameters D L = D 0(1- e -θt ), D 0 is the initial degradation factor, θ is the adjustment factor.

[0010] Because the Maxwell body is connected in series with the Kelvin body, the equivalent stress acting on the Maxwell body is equal to the equivalent stress acting on the Kelvin body, and the strain is superimposed, so the same stress symbol is used in formulas (1) and (2).

[0011] Then the constitutive equation of the Maxwell body is: In formula (1), E M is the elastic modulus of the Maxwell spring, η M is the viscosity coefficient of the Maxwell damping element, is the strain rate of the Maxwell body, i.e. ε M the derivative with respect to time; D L is the degradation term, σ d denotes the deviatoric stress, denotes the derivative of the deviatoric stress with respect to time.

[0012] Then the constitutive equation of the Kelvin body is:

[0013] In formula (2), E KE is the modulus of elasticity of the Kelvin spring, η K η is the viscosity coefficient of the Kelvin dashpot, γ is the strain rate of the Kelvin body, i.e. ε K the derivative with respect to time.

[0014] The creep model is obtained by combining the Maxwell body and the Kelvin body in series and solving equations (1) and (2) simultaneously as follows:

[0015] The derivation process of equation (3) is as follows: Since the Maxwell body and the Kelvin body are connected in series, the strain rate of the Maxwell body remains unchanged during the creep process; σ d ; For the Maxwell body, , i.e. the strain rate of the viscous dashpot in series is equal to the strain rate of the Maxwell unit, and the integral of this is: C is an integral constant determined by the initial condition; t = 0, ; ; For the Kelvin body, the solution of the differential equation is: C is an integral constant determined by the initial condition; t = 0, ; ; ; Further, step 5) is specifically: 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 the data analysis software to fit the scattered points in the creep strain-time coordinate system, to obtain the model parameters E M , η M , E K , η K , D 0, θ .

[0016] Further, in step 6), in order to describe the creep process from 0 to NThe change rule of model parameters between freeze-thaw-dry-wet cycles is established by exponential function as the quantitative relationship between model parameters and N

[0017] Φ N in formula (4) represents the model parameters of the sample after experiencing N freeze-thaw-dry-wet cycles, Φ0 represents the model parameters of the sample without experiencing freeze-thaw-dry-wet cycles, α β and a are function parameter values, and b is a fitting parameter, which is determined by nonlinear regression.

[0018] Under the action of freeze-thaw-dry-wet cycles, the internal micro-cracks of the material gradually expand, leading to rapid decay and tend to be stable in strength, modulus, etc. The typical process is as follows: Early stage: fast degradation rate (just experienced cycles, structure damage sensitive); Middle stage: the degradation rate gradually slows down; Later stage: tends to be a residual stable value (will not fall indefinitely).

[0019] This "fast → slow → stable" evolution process essentially conforms to the exponential decay / growth law.

[0020] For the change trend of different model parameters, in Matlab or origin software, the exponential decay function or the increasing exponential function is used by adopting the nonlinear fitting method, and the model parameters E M η M E K η K D 0, θ scatter points are fitted to establish the quantitative relationship between model parameters and N .

[0021] Further, in step 7), the quantitative relationship between model parameters and N established in step 6) is brought into formula (3) to establish a prediction model of clay steady-state creep curve under freeze-thaw-dry-wet cycles, that is, after experiencing N freeze-thaw-dry-wet cycles, the prediction model of clay steady-state creep curve is:

[0022] In the formula, f EM ( N ) and f ηM ​​​​​​( N ), f EK ( N ), f ηK ( N ), f D0 ( N ), f θ ( N ) represent the model parameters E M , η M , E K , η K , D 0、 θ and N The quantitative relationship.

[0023] Compared with the prior art, the present invention has the following beneficial effects: 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 , η 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.

[0024] 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.

[0025] 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

[0026] 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. 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. Figure 3The creep curve measured after different freeze-thaw-dry-wet cycle times under 50 kPa confining pressure in the embodiment of the present application; Figure 4 The change curve of the Maxwell body model parameter with freeze-thaw-dry-wet cycle times in the embodiment of the present application; Figure 5 The change curve of the Kelvin body model parameter with freeze-thaw-dry-wet cycle times in the embodiment of the present application; Figure 6 The change curve of the damage term model parameter with freeze-thaw-dry-wet cycle times in the embodiment of the present application; Figure 7 The creep curve measured under 12 kPa confining pressure in the embodiment of the present application; N The measured and predicted values of the creep curve when = 1, 4, 10; Figure 8 The creep curve measured under 25 kPa confining pressure in the embodiment of the present application; N The measured and predicted values of the creep curve when = 1, 4, 10; Figure 9 The creep curve measured under 50 kPa confining pressure in the embodiment of the present application; N The measured and predicted values of the creep curve when = 1, 4, 10. DETAILED DESCRIPTION

[0027] The method of the present application is described in detail below in combination with the drawings. The specific implementation cases described herein are only used to explain the present application and do not limit the present application.

[0028] A plurality of initial clay samples prepared at a set dry density and water content are subjected to 0, 1, 4, 10, etc. freeze-thaw-dry-wet cycle treatments, respectively, and then the samples are loaded into a triaxial apparatus. The samples are allowed to consolidate and stabilize under the initial stress state of a constant confining pressure, the confining pressure is kept unchanged, the deviatoric stress is loaded at a set loading rate, and after the deviatoric stress is loaded to a predetermined value, the overall stress state of the sample is kept constant for about 7 days, and the relationship curve of the axial creep strain and time is drawn.

[0029] For the measured creep curve under each freeze-thaw-dry-wet cycle time, the test data (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z) are substituted into formula (3), a nonlinear fitting tool or a ε c , t ) function is used, and the model parameter set (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z) is solved by using an iterative least square method. Origin Matlab lsqcurvefit E M , η M , E K , η K ​​​, D 0、 θ Repeat until the creep curve fitting is complete for all freeze-thaw-wet cycles.

[0030] Draw the model parameters respectively E M , η M , E K , η K , D 0、 θ 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 ), f EK ( 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.

[0031] 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.

[0032] 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. ε c With time t The creep curve is as follows Figure 1~Figure 3 As shown.

[0033] The test data ( ε c , t Substituting into formula (3), using Origin Data analysis software uses iterative least squares method to analyze... ε c - t By fitting the scattered points in the coordinate system, the model parameter values ​​can be obtained. E M , η M , E K , η K , D 0、 θ See Table 1.

[0034] Table 1. Fitting parameters and goodness of fit of the creep model under different freeze-thaw-wet cycles.

[0035] As shown in Table 1, the model parameters E M , η M , E K , η 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 θ Follow NThe increase of the model parameters with the increase of the freeze-thaw-dry-wet cycle times was fitted by the increasing exponential function using formula (4). The curves of the model parameters with the increase of the freeze-thaw-dry-wet cycle times and the corresponding fitting curves are shown in Figs. 2-4. Figure 4~Figure 6 The specific values of the fitting parameters are shown in Tables 2-4.

[0036] Table 2. Model parameters under 12 kPa confining pressure N Fitting parameter values and goodness of fit of the quantitative function

[0037] Table 3. Model parameters under 25 kPa confining pressure N Fitting parameter values and goodness of fit of the quantitative function

[0038] Table 4. Model parameters under 50 kPa confining pressure N Fitting parameter values and goodness of fit of the quantitative function

[0039] Taking 25 kPa confining pressure as an example, the quantitative functions of the model parameters E M , η M , E K , η K , D 0、 θ and N are respectively:

[0040] In the formula, the subscript 0 of the parameters represents the model parameter values without freeze-thaw-dry-wet cycle.

[0041] Substituting the functions f EM ( N )、 f ηM ( N )、 f EK ( N )、 f ηK ( N )、 f D0 ( N )、 f θ ( N ) into formula (5), the prediction model of the steady-state creep curve of clay under freeze-thaw-dry-wet action is obtained.

[0042] 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 that has undergone N a second freeze-thaw-wet-dry cycle.

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 cycles 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 bias stress loading mode as described in step 2); the creep strain of the samples under different freeze-thaw-dry-wet cycle times is recorded, and the change curve of the creep strain of the samples over time is obtained. σ d ε c 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, after experiencing N freeze-thaw-dry-wet cycles, the prediction model of the steady-state creep curve of clay is: ； wherein f EM , N ), f ηM , N ), f EK , N ), f ηK , N ), f D0 , N ), f θ , N are quantitative relationships of the model parameters E M , η M , E K , η K , D 0, θ and N .

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