A long-term settlement prediction method for high-speed railway subgrade under cyclic train loads

Abstract

A method for predicting the long-term settlement of high-speed railway subgrade under cyclic train loads comprises the following steps: (1) observing the existing settlement data of the subgrade and the load on the surface layer of the subgrade bed to obtain the compression modulus of the subgrade soil; (2) fitting the observed data into a logarithmic function to obtain the parameter values required in the calculation; (3) substituting the parameter values obtained in the previous two steps into the constitutive equation; (4) discretizing the constitutive equation by the finite difference method and substituting the load on the surface layer of the subgrade bed; (5) solving the equation obtained by the finite difference method by the iteration method to calculate the settlement of the subgrade under the long-term high-speed railway train loads; (6) continuously verifying and correcting the parameter values according to the real-time observed data, so as to make the predicted value of the subgrade settlement more accurate. The present invention first uses the state evolution constitutive model to predict the settlement deformation of the high-speed railway subgrade under long-term train loads. This method is simple, easy to implement and accurate, and has good popularization and application value.

Description

Technical Field

[0001] The present invention relates to a method for predicting long-term settlement of high-speed railway subgrade under cyclic train loads, belonging to the technical field of high-speed railway subgrade. Background Technique

[0002] With the development of China's social economy and the improvement of people's living standards, China's high-speed rail technology has been continuously developing and has reached the world's leading level. To ensure the safety and stability of high-speed rail trains running at high speeds, the requirements for controlling the settlement of high-speed railway subgrades are very strict. The long-term cyclic dynamic loads of high-speed rail trains have a great impact on the settlement of high-speed railway subgrades and cannot be ignored. Therefore, great attention is paid to the long-term settlement deformation of high-speed railway subgrades in engineering. At present, in the research on predicting the long-term settlement of high-speed railway subgrades, conventional methods are limited to numerical simulation methods. This method requires a large amount of time and effort, consumes huge computer resources, and the prediction results are overly dependent on the values of model parameters. In addition, the fixed-point and regular observations at the high-speed railway subgrade engineering site can only reflect the settlement situation of the subgrade at that time and cannot effectively predict the settlement of the subgrade under long-term train loads.

[0003] Therefore, it is a technical problem with great engineering application value to propose a method for predicting the long-term settlement of high-speed railway subgrades under cyclic train loads, which can predict and warn the future settlement amount of the subgrade through the existing settlement observation data of high-speed railway subgrades, and then prevent the possibility of engineering risks. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for predicting the long-term settlement of high-speed railway subgrades under cyclic train loads to solve the problem that the existing technology cannot effectively predict the settlement of subgrades under long-term train loads.

[0005] The technical solution implemented by the present invention is as follows. A method for predicting the long-term settlement of high-speed railway subgrades under cyclic train loads, and the steps of the method are as follows:

[0006] (1) Observe the existing settlement data of the subgrade and the load on the surface layer of the subgrade bed, and conduct basic geotechnical tests to obtain the compression modulus of the subgrade soil.

[0007] (2) Fit the observed data into a logarithmic function to obtain the parameter values required for calculation.

[0008] (3) Substitute the parameter values obtained in the previous step into the constitutive equation.

[0009] (4) Discretize the constitutive equation using the finite difference method and substitute the load on the surface layer of the subgrade bed obtained by observation.

[0010] (5) Solve the equation obtained by the finite difference method through the iterative method, and finally predict the settlement of the subgrade under the long-term high-speed rail train load.

[0011] (6) According to the on-site real-time observation data, continuously verify and correct the parameter values obtained in step (2), and then correct the calculation results of the method of the present invention, so that the predicted value of the subgrade settlement is more accurate.

[0012] The fitted logarithmic function is:

[0013] w = C1 log(1 + C2t)

[0014] In the formula: w is the settlement value of the high-speed rail subgrade; t is the time; C1 and C2 are undetermined coefficients. By fitting the curve of the logarithmic function according to the observed subgrade settlement data changing with time, C1 and C2 can be obtained.

[0015] The constitutive equation is:

[0016]

[0017]

[0018] In the formula: σ is the dynamic stress on the surface layer of the subgrade; is the first derivative of the dynamic stress on the surface layer of the subgrade with respect to time, which can be obtained from the load on the surface layer of the subgrade bed observed; E is the compression modulus of the subgrade, which is measured through basic geotechnical tests; γ is the subgrade strain; is the first derivative of the subgrade strain with respect to time (hereinafter referred to as the strain rate); D is the fluidization parameter in the model; is the first derivative of the fluidization parameter in the model with respect to time; γ c is the characteristic strain; is the model parameter, usually or smaller;

[0019] According to the fitted C1 and C2, the initial value D0 of the fluidization parameter and the characteristic strain γ can be obtained through the following formula c :

[0020]

[0021]

[0022] In the formula: σ0 is the static load on the subgrade, which can be obtained from the load on the surface layer of the subgrade bed observed.

[0023] The process of discretizing the constitutive equation by using the finite difference method is as follows:

[0024] For the first derivative of the subgrade strain with respect to time and the first derivative of the fluidization parameter with respect to time Perform time discretization:

[0025]

[0026]

[0027] Where: is the subgrade strain rate at the nth moment; γ n+1 is the subgrade strain at the (n + 1)th moment; γ n is the subgrade strain at the nth moment; is the value of the first derivative of the fluidization parameter with respect to time at the nth moment; D n+1 is the value of the fluidization parameter at the (n + 1)th moment; D n is the value of the fluidization parameter at the nth moment; Δt is the time step calculated by the finite difference method;

[0028] Substitute the above formula into After derivation, it can be obtained:

[0029]

[0030]

[0031] Where: D n is the fluidization parameter at the nth moment, σ n is the dynamic stress value at the nth moment; is the value of the first derivative of the dynamic stress value with respect to time at the nth moment.

[0032] The process of solving the above equation by the iterative method is as follows:

[0033] (1) When other parameters are known through fitting or geotechnical tests, substitute the initial value D0 of the fluidization parameter obtained by fitting into to calculate D1;

[0034] (2) Then, successively iterate to calculate D2, D3,..., D n ;

[0035] (3) According to the initial subgrade strain γ0 = 0, substitute it into to calculate γ1, and then successively iterate to calculate γ2, γ3,..., γ n ;

[0036] (4) According to the relationship between the subgrade settlement w = H·γ, obtain the settlement value of the subgrade changing with time under the long-term train cyclic load, where H is the subgrade height.

[0037] The beneficial effects of the present invention are as follows: The state evolution constitutive model is first adopted in the present invention to predict the settlement deformation of high-speed railway subgrades under long-term train loads. The finite difference method is used to discretize the constitutive equation, and iterative solution is carried out to obtain the subgrade settlement value. At the same time, the parameters can be corrected according to the on-site real-time observation data to obtain more accurate prediction values. This method is simple, easy to implement and accurate, and has good popularization and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is a flowchart of the method for predicting the long-term settlement of high-speed railway subgrades under cyclic train loads according to the present invention;

[0039] Figure 2 is a calculation model diagram of the method of the present invention;

[0040] Figure 3 are the measured strain data of the soil body obtained under the cyclic load of 1200 seconds in this embodiment;

[0041] Figure 4 are the strain data calculated by using the method of the present invention for the soil body under the cyclic load of 1200 seconds in this embodiment;

[0042] Figure 5 is the strain curve calculated by using the method of the present invention for the soil body after 2400 seconds of cyclic load in this embodiment;

[0043] In the figure: 1 is the high-speed railway subgrade; 2 is the subgrade height; 3 is the dynamic load on the surface layer of the subgrade bed. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] The calculation process of a method for predicting the long-term settlement of a high-speed railway subgrade under cyclic train loads in this embodiment is as Figure 1 shown. This embodiment is described with test data, and the specific steps are as follows:

[0045] First step: Observe the existing settlement data of the subgrade and the load on the surface layer of the subgrade bed, and conduct basic geotechnical tests to obtain the compression modulus of the subgrade soil body:

[0046] Figure 3 are the strain data of the subgrade obtained under the cyclic load of 1200 seconds. The load on the surface layer of the subgrade bed is The compression modulus of the subgrade soil body is: E = 140 MPa.

[0047] Second step: Fit the observed data into a logarithmic function to obtain the parameter values required in the calculation:

[0048] The logarithmic function curve fitted according to the observed data is: y = 1.52×10 -4 log(1 + 2.58×103 x);

[0049] where C1 = 1.52×10 -4 and C2 = 2.58×10 3 At this time, the initial values D0 of the fluidization parameters and the characteristic strain γ are obtained according to Equations (1) and (2). c :

[0050]

[0051]

[0052] In the formula: σ0 = 100 kPa, Taking 0.001, D0 = 10 and γ are calculated c = 1.52×10 -4 .

[0053] Step 3: Based on the state evolution constitutive model, substitute the parameter values obtained in the first two steps into the constitutive equations (3) and (4):

[0054]

[0055]

[0056] Step 4: Discretize the constitutive equation using the finite difference method to obtain Equations (5) and (6), and substitute the load on the surface layer of the subgrade bed

[0057]

[0058]

[0059] In this example, the calculation step size Δt is taken as 0.0005 s, and appropriate supplements can be selected according to the required calculation accuracy and speed for actual prediction.

[0060] Step 5: Solve the equations obtained by the finite difference method through the iteration method to calculate the settlement of the subgrade under the long-term high-speed train load.

[0061] Substitute the initial value D0 = 10 of the fluidization parameter obtained by fitting into Equation (6) to calculate D1, and then calculate D2, D3,..., D iteratively in turn n ; then, according to the initial strain γ0 = 0 of the subgrade, substitute it into Equation (5) to calculate γ1, and then calculate γ2, γ3,..., γ iteratively in turn n .

[0062] Step 6: Continuously verify and correct the parameter values according to the real-time observation data, so as to make the predicted value of the subgrade settlement more accurate.

[0063] Compare the calculated subgrade strain data with the real-time observed strain data, and adjust the values of the three parameters of γ c , D0 and so that the calculation results are closer to the actual observed values, and then obtain more accurate prediction values. After comparing and correcting with the actual data, the corrected γ c = 1.52×10 -4 , D0 = 6.80×10 -3 , At this time, the calculated subgrade strain curve is as shown in Figure 4 .

[0064] Compare Figure 3 with Figure 4 , it can be seen that the calculated value is in good agreement with the measured value. At this time, predict the subgrade settlement according to the corrected parameters. Figure 5 This is the strain curve of the predicted settlement deformation of the subgrade calculated by this method after 2400 seconds of cyclic loading. It can be seen that the strain generated by the subgrade at 2400 seconds is 0.0026. According to the subgrade filling height of 2700 mm, the subgrade settlement value is w = H·γ = 2700×0.0026 = 7.02 mm. After observing the actual settlement data of the subgrade after 2400 seconds of cyclic loading, the parameters can be further corrected and then continue to predict.

[0065] The above embodiments only represent one implementation mode of the present invention, and its description is relatively specific and detailed, but it should not be understood as a limitation of the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements are made, and these all belong to the protection scope of the present invention.

Claims

1. A long-term settlement prediction method for high-speed railway subgrade under cyclic train loads, characterized in that The method steps are as follows: (1) Observe the existing settlement data of the subgrade and the surface load of the subgrade bed, and conduct basic geotechnical tests to obtain the compression modulus of the subgrade soil. (2) Fit the observed data into a logarithmic function to obtain the parameter values required in the calculation. (3) Substitute the parameter values obtained in the previous step into the constitutive equation. (4) Discretize the constitutive equation using the finite difference method and substitute the observed surface load of the subgrade bed. (5) Solve the equation obtained by the finite difference method through the iteration method, and finally predict the settlement of the subgrade under the long-term high-speed train load. (6) Continuously verify and correct the parameter values obtained in step (2) according to the on-site real-time observation data, and then correct the calculation results of the method of the present invention to make the predicted value of the subgrade settlement more accurate. The logarithmic function obtained by fitting is: w = C1log(1 + C2t) In the formula: w is the settlement value of the high-speed railway subgrade; t is the time; C1 and C2 are undetermined coefficients. By fitting the curve of the above logarithmic function according to the observed subgrade settlement data changing with time, C1 and C2 can be obtained.

2. A long-term settlement prediction method for high-speed railway subgrade under cyclic train loads according to claim 1, characterized in that, The constitutive equation is: Where: σ is the dynamic stress on the subgrade surface; is the first derivative of the dynamic stress on the subgrade surface with respect to time, which can be obtained from the load on the subgrade bed surface measured by observation; E is the compression modulus of the subgrade, which is measured by basic geotechnical tests; γ is the subgrade strain; is the first derivative of the subgrade strain with respect to time; D is the fluidization parameter in the model; is the first derivative of the fluidization parameter in the model with respect to time; γ c is the characteristic strain; is a model parameter, usually or less; Based on the obtained C1 and C2 from fitting, the initial value D0 of the fluidization parameter and the characteristic strain γ can be obtained through the following formula c : In the formula: σ0 is the static load on the subgrade, which can be obtained from the observed surface load of the subgrade bed.

3. A long-term settlement prediction method for high-speed railway subgrade under cyclic train loads according to claim 1, characterized in that The process of discretizing the constitutive equation using the finite difference method is as follows: The first derivative of subgrade strain with respect to time and the first derivative of fluidization parameters with respect to time Perform time discretization: In the formula: is the subgrade strain rate at the nth moment; γ n+1 is the subgrade strain at the (n + 1)th moment; γ n is the subgrade strain at the nth moment; is the first derivative of the fluidization parameter with respect to time at the nth moment; D n+1 is the value of the fluidization parameter at the (n + 1)th moment; D n is the value of the fluidization parameter at the nth moment; Δt is the time step calculated by the finite difference method; Substitute the above formula into After derivation, it can be obtained that: Where: D n is the fluidization parameter at the nth moment, and σ n is the dynamic stress value at the nth moment; is the first derivative value of the dynamic stress value at the nth moment with respect to time.

4. A long-term settlement prediction method for high-speed railway subgrade under cyclic train loads according to claim 3, characterized in that, The process of solving the above equation by the iteration method is: (1)When other parameters are all known through fitting or geotechnical tests, substitute the initial fluidization parameter value D0 obtained by fitting into to calculate D1; (2) Then, iterate the calculations in sequence to obtain D2, D3,..., D n ; (3) Substitute the initial subgrade strain γ0 = 0 into to calculate γ1, and then iteratively calculate γ2, γ3,..., γ n ; (4) According to the relationship between the subgrade settlement w = H·γ, obtain the settlement value of the subgrade changing with time under the long-term train cyclic load, where H is the subgrade height.

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