A method for predicting stress and strain in discontinuous graded soil based on the coupling of discrete element method and machine learning

Abstract

This invention relates to a method for predicting stress-strain in discontinuously graded soil based on the coupling of discrete element method (DEM) and machine learning. The steps are as follows: S1. Obtain baseline stress-strain data; S2. Establish and validate a DEM model; S3. Construct DEM samples of discontinuously graded soil with different gradations; S4. Obtain stress-strain data for soils with different gradations; S5. Establish an initial database; S6. Divide the initial database; S7. Construct a random forest model; S8. Train the random forest model to obtain a predicted stress model; S9. Evaluate the trained random forest model; S10. Predict stress-strain data for discontinuously graded soil. This method can quickly predict the stress-strain curve of discontinuously graded soil directly through particle size distribution and fine particle content, improving efficiency.

Description

Technical Field

[0001] This invention relates to the field of stress-strain prediction technology, and in particular to a method for predicting stress-strain in discontinuous graded soil based on the coupling of discrete element method and machine learning. Background Technology

[0002] Under the influence of landslides, debris flows, and other similar events, coarse particles (gravel) and fine particles (silt) mix to form a discontinuously graded soil mixture. Discontinuously graded soils possess good drainage, stability, and compaction properties, and are widely used in hydraulic structures such as embankments and dams. The study of the physical and mechanical properties of discontinuously graded soils has become an important issue in engineering practice. Currently, the numerical values ​​of soil mechanical properties and design parameters almost entirely rely on in-situ geotechnical tests and laboratory geotechnical tests, but these are costly in terms of both economy and time. Therefore, constructing efficient and reliable constitutive prediction models for discontinuously graded soils is of great significance. Summary of the Invention

[0003] In view of the shortcomings of the prior art, the technical problem to be solved by the present invention is to provide a method for predicting the stress-strain of discontinuous graded soil based on the coupling of discrete element method and machine learning. This method can quickly predict the stress-strain curve of discontinuous graded soil directly through particle size ratio and fine particle content.

[0004] This invention is achieved by the following technical solution: a method for predicting stress and strain in discontinuous graded soil based on the coupling of discrete element method and machine learning, comprising the following steps:

[0005] S1. Obtain baseline stress-strain data.

[0006] A reference specimen is consolidated to saturation, sheared using a triaxial tester, and the axial force is measured through a verification ring and the deformation of the specimen surface is recorded through a digital image measurement system to obtain the stress-strain curve of the specimen and obtain the reference stress-strain data.

[0007] S2. Construct and validate the discrete element method model.

[0008] Using the same graded specimens as in S1, a conventional triaxial compression test model was established by constructing a discrete element method to simulate compression. The model was then compared with the baseline stress-strain data obtained in S1 to verify the accuracy of the conventional triaxial compression model using the discrete element method and to determine the particle parameters and loading conditions in the discrete element simulation model.

[0009] S3. Construct discrete element models of discontinuously graded soils with different gradations.

[0010] Adjust the particle size distribution of the simulated sample to establish discrete element samples containing different fine particle contents and particle size ratios;

[0011] S4. Obtain stress-strain data for specimens with different gradations.

[0012] Isotropic consolidation and conventional triaxial compression simulation tests were conducted on discrete element models with different gradations in S3 to obtain stress-strain data for different gradations.

[0013] S5. Establish the original database.

[0014] The stress-strain data obtained from the S4 simulation were preprocessed, and the corresponding fine particle content and particle size ratio characteristic values ​​were added to establish the original database.

[0015] S6. Divide the original database.

[0016] The original database was divided into a training set, a validation set, and a test set, with a data ratio of 8:1:1.

[0017] S7. Construct a random forest model.

[0018] The inputs to the random forest model include strain, particle size ratio, and fine particle content, and the output is strain;

[0019] S8. Train the random forest model to obtain the predicted stress model.

[0020] The validation set data is hyperparameter optimized using the Bayesian method to obtain and save the optimal parametric stress prediction model.

[0021] S9. Evaluate the trained random forest model.

[0022] The predicted stress random forest model trained in S8 is validated using test set data. The predicted data is compared with the original data, and the model performance is calculated to evaluate the accuracy of the obtained random forest model.

[0023] S10. Predicting stress data for discontinuous graded soil.

[0024] By inputting the different gradation parameters and axial strain of the discontinuous graded soil for which stress and strain need to be predicted into the stress prediction model trained in S8, the stress data of the discontinuous graded soil can be obtained.

[0025] The effects of this invention are as follows:

[0026] (1) This method is based on the discrete element method to simulate the stress-strain response of discontinuous graded soil with different gradations in conventional triaxial compression test, and uses machine learning and data-driven methods to establish the constitutive relationship of discontinuous graded soil.

[0027] (2) Traditional constitutive models are complex and have numerous parameters, which limits their application in describing the stress-strain relationship of soil. The machine learning method used in this paper is applied to the constitutive model of discontinuous graded soil without any assumptions. Machine learning can directly learn the stress-strain relationship from the original data. With the increase of the dataset, the machine learning-based model has significantly improved in terms of prediction accuracy and application scope. Attached Figure Description

[0028] Figure 1 This is a flowchart of the technical route in this invention;

[0029] Figure 2 This is a schematic diagram of model verification in this invention;

[0030] Figure 3 This is a schematic diagram of particle generation and isotropic consolidation in this invention;

[0031] Figure 4 This is a schematic diagram simulating conventional triaxial compression in this invention;

[0032] Figure 5 This is a schematic diagram of data preprocessing in this invention;

[0033] Figure 6 This is a schematic diagram of hyperparameter optimization in this invention;

[0034] Figure 7 This is a schematic diagram comparing the predicted and actual values ​​in this invention;

[0035] Figure 8 This is a schematic diagram illustrating the prediction of different particle size ratios and fine particle content in this invention. Detailed Implementation

[0036] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features, and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0037] Reference Figure 1-3 As shown, this invention provides a method for predicting stress and strain in discontinuous graded soil based on the coupling of discrete element method and machine learning, with the following steps:

[0038] S1. Obtain reference stress-strain data.

[0039] A reference specimen is consolidated to saturation, sheared using a triaxial testing apparatus, and the axial force is measured through a verification ring. The deformation of the specimen surface is recorded using a digital image measurement system to obtain the stress-strain curve of the specimen, thus obtaining the reference stress-strain data. Preferably, the specimen is a fully consolidated saturated quartz sand specimen with a relative density of 50%, and sheared using a triaxial testing apparatus at a constant strain rate of 0.2% / min.

[0040] S2. Construct and verify the discrete element simulation model.

[0041] Using specimens with the same gradation as those in S1, a conventional triaxial compression test model was established using the discrete element method (DEM). The model was then compared with the baseline stress-strain data obtained in S1 to verify its correctness and determine the particle parameters and loading conditions within the DEM model. The stress-strain curves from the numerical simulation and laboratory tests were compared, for example... Figure 2 As shown.

[0042] Specifically, in S2-1, when simulating a conventional triaxial test using the discrete element method, quasi-static conditions need to be met, so the moving speed of the upper and lower walls cannot be too fast; however, if the loading speed is too low, the computational cost will increase significantly. Therefore, the optimal loading speed for discrete element simulation is 0.0002 m / s.

[0043] S2-2, In order to maintain computational stability, the actual time step of the discrete element method simulation needs to be smaller than the limit time step, and the preferred time step is 2e-7s;

[0044] S2-3, to avoid boundary effects, the length of the sample before conventional triaxial compression is 10 times the diameter of the coarse particles.

[0045] S2-4, the numerical simulation of particles using the discrete element method includes a simulated Young's modulus of 70 GPa and a density of 2650 kg / m³. 3 Poisson's ratio 0.3, coefficient of restitution 0.2, coefficient of sliding friction 0.5, coefficient of rolling friction 0.1.

[0046] S3. Construct discrete element models of discontinuously graded soils with different gradations, adjust the particle gradation in the simulation model samples, and establish discrete element samples containing different fine particle contents and particle size ratios. The sample particles consist of coarse and fine particles.

[0047] Specifically, a sample with a specified fine particle content and particle size ratio can be generated within a 24mm x 24mm x 24mm simulation area, where the position of each particle is random. The particle size ratio is calculated using formula (1), and the fine particle content is determined using formula (2).

[0048]

[0049] In the above formula, SR represents the particle size ratio, and d max and d min These represent the diameters of the coarse and fine particles, respectively; FC represents the fine particle content; m fine and m all These represent the mass of the fine particles and the mass of all particles, respectively.

[0050] S4. Obtain stress-strain data for different gradations. Isotropic consolidation and conventional triaxial compression tests were performed on the discrete element models with different gradations in S3 to obtain stress-strain data for different gradations.

[0051] Specifically, the isotropic consolidation test simulation includes placing the sample in a six-sided servo wall, setting the sliding friction coefficient to 0, and simultaneously moving the six servo walls slowly towards the center until the initial confining pressure of 100 kPa is reached and maintained, thereby generating a dense and isotropic sample.

[0052] Isotropic specimens were subjected to conventional triaxial compression simulation tests. The interparticle friction coefficient was adjusted to 0.5, and the rolling friction coefficient was set to 0.1 to approximate the influence of irregular particle shapes. During loading, σ1 was achieved by uniformly moving the upper and lower walls, while the confining pressures σ2 and σ3 were maintained at a set value of 100 kPa by servo wall units, obtaining stress-strain data for different gradations.

[0053] S5. Establish the original database. Preprocess the stress-strain data obtained from the simulation in S4 to obtain simplified stress-strain curves. Add the corresponding fine particle content and particle size ratio characteristic values ​​to establish the original database.

[0054] Specifically, S5-1. Using unprocessed deviatoric stress-strain curves as input / output data for neural networks significantly increases the burden of model evaluation and consumes substantial computational resources. Therefore, this invention simplifies stress-strain curves through preprocessing, representing different stress-strain curves with the same abscissa value and different ordinates, resulting in a stress-strain curve expressed in two dimensions. The abscissa of this curve is divided into 100 equal parts, and 100 points at fixed intervals represent a set of stress-strain curves with different particle size ratios and fine particle contents (e.g.,...). Figure 5 As shown, a point is taken every 0.05.

[0055] S5-2, from S5-1, yields a stress-strain curve represented by 100 two-dimensional coordinates. Then, characteristic parameters of fine particle content and particle size ratio are added before each coordinate to obtain 100 four-dimensional coordinates, thus establishing the original database.

[0056] S6. Divide the original database into training set, validation set and test set, with a data ratio of 8:1:1.

[0057] Specifically, the original dataset is split using a Python script by importing the "train_test_split" function from the "sklearn.model_selection" module, and "random_state=42" is set to ensure that the results are reproducible.

[0058] S7. Construct a random forest model. The inputs to the random forest model include strain, particle size ratio, and fine particle content, and the output is strain.

[0059] Specifically, random forest is an ensemble technique that uses multiple decision trees. Its output is the average of all the trees. This method can effectively reduce overfitting and improve the model's generalization ability. Building a random forest model involves the following steps:

[0060] S7-1. Randomly select samples from the training set.

[0061] S7-2. Generate n decision trees. Using a Python script, the "RandomForestRegressor" class from the "sklearn.ensemble" module is called to create a random forest regressor.

[0062] S7-3. The data subset in each decision tree is generated by sampling based on the Bagging idea.

[0063] S7-4. Finally, the prediction results of all decision trees are averaged to obtain the final prediction value.

[0064] The convergence of random forest is expressed by the following formula (3):

[0065] mg(x,y)=av n I(f n (x)=y)-max j＝y av n I(f n (x)=j) (3)

[0066] In the formula f n (x) represents the decision tree, n represents the number of trees in the random forest, I(.) is the characteristic function, and av n It is the average value of the function; the larger the value of mg(x,y), the more accurate the prediction of the random forest.

[0067] S8. Train the random forest model to obtain the stress prediction model. Specifically, perform Bayesian hyperparameter optimization using the validation set to obtain and save the optimal parameter stress prediction model.

[0068] Bayesian hyperparameter optimization uses the "skopt" module of the "Scikit-Optimize" library and calls the "BayesSearchCV" function to perform Bayesian optimization. Compared with traditional grid search and random search, Bayesian optimization considers previous evaluation results, can explore the parameter space more efficiently, and usually requires fewer iterations to find better results. The Bayesian theorem is expressed as follows:

[0069]

[0070] In the formula, P(H|E) refers to the probability of target H given; P(E|H) is the probability of observing E after assuming target H; P(H) is the prior probability of assuming H without observing evidence E; and P(E) is the marginal likelihood of evidence E.

[0071] After tuning the parameters "n_estimators" and "max_depth", the Bayesian optimization results are as follows: Figure 6 As shown in Table 1.

[0072] Table 1

[0073]

[0074] S9. Evaluate the trained random forest model. Based on the hyperparameters determined by the Bayesian method in S8, the test set data is fed into the stress prediction model trained in S8 to obtain prediction data, and the model performance is calculated. The random forest model is evaluated using the test set. The model performance goodness of fit Rfit is also considered. 2

[0075] The formula for calculating the mean absolute error (MAE) is as follows:

[0076]

[0077] In the formula: y is the predicted value; y is the experimental value; n is the sample size.

[0078] From the appendix Figure 7 It can be seen that the predicted values ​​and the actual values ​​based on the prediction parameters of the random forest model can be compared. Figure 7 Chinese: R 2 MAE and 10% tolerance represent the coefficient of determination, mean absolute error, and prediction accuracy under a 10% tolerance, respectively. The horizontal and vertical axes represent the true and predicted values ​​of the deviatoric stress parameter, respectively. Figure 7 The closer a scatter point is to the diagonal, the closer the predicted value and the true value of the data corresponding to that scatter point are. The scatter points of the random forest model are all relatively close to the diagonal.

[0079] S10. Predict stress data for discontinuous graded soil. Input the different gradation parameters and axial strain of the discontinuous graded soil for which stress and strain need to be predicted into the stress prediction model trained in S8 to obtain the predicted stress data for the discontinuous graded soil.

[0080] like Figure 8 As shown, Figure 8 In the diagram, a represents particle size ratio 2 with a fine particle content of 22.5%; b represents particle size ratio 3 with a fine particle content of 12.5%; c represents particle size ratio 4 with a fine particle content of 10%; and d represents particle size ratio 6 with a fine particle content of 22.5%. This demonstrates that the random forest model effectively predicts the stress-strain curves of discontinuously graded soils with different gradations, and the predicted values ​​are largely consistent with the experimental values.

[0081] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for predicting stress and strain in discontinuous graded soil based on the coupling of discrete element method and machine learning, characterized by: The steps are as follows: S1. Obtain baseline stress-strain data. A reference specimen is consolidated to saturation, sheared using a triaxial tester, and the axial force is measured through a verification ring and the deformation of the specimen surface is recorded through a digital image measurement system to obtain the stress-strain curve of the specimen and obtain the reference stress-strain data. S2. Construct and validate the discrete element method model. Using the same graded specimens as in S1, a conventional triaxial compression test model was established by constructing a discrete element method to simulate compression. The model was then compared with the baseline stress-strain data obtained in S1 to verify the accuracy of the conventional triaxial compression model using the discrete element method and to determine the particle parameters and loading conditions in the discrete element simulation model. S3. Construct discrete element models of discontinuously graded soils with different gradations. Adjust the particle size distribution of the simulated sample to establish discrete element samples containing different fine particle contents and particle size ratios; S4. Obtain stress-strain data for specimens with different gradations. Isotropic consolidation and conventional triaxial compression simulation tests were conducted on discrete element models with different gradations in S3 to obtain stress-strain data for different gradations. S5. Establish the original database. The stress-strain data obtained from the S4 simulation were preprocessed, and the corresponding fine particle content and particle size ratio characteristic values ​​were added to establish the original database. S6. Divide the original database. The original database was divided into a training set, a validation set, and a test set, with a data ratio of 8:1:

1. S7. Construct a random forest model. The inputs to the random forest model include strain, particle size ratio, and fine particle content, and the output is strain; S8. Train the random forest model to obtain the predicted stress model. The validation set data is hyperparameter optimized using the Bayesian method to obtain and save the optimal parametric stress prediction model. S9. Evaluate the trained random forest model. The predicted stress random forest model trained in S8 is validated using test set data. The predicted data is compared with the original data, and the model performance is calculated to evaluate the accuracy of the obtained random forest model. S10. Predicting stress data for discontinuous graded soil. By inputting the different gradation parameters and axial strain of the discontinuous graded soil for which stress and strain need to be predicted into the stress prediction model trained in S8, the stress data of the discontinuous graded soil can be obtained.

2. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: S3 Medium particle size distribution is used to prepare particle samples with different fine particle content and particle size ratio. The sample particles are composed of coarse particles and fine particles. The particle size ratio is determined by formula (1), and the fine particle content is determined by formula (2). In the above formula, SR represents the particle size ratio, and d max and d min These represent the diameters of the coarse and fine particles, respectively; FC represents the fine particle content; m fine and m all These represent the mass of the fine particles and the mass of all particles, respectively.

3. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: S2 When simulating a conventional triaxial compression test using the discrete element method (DEM), the numerical values ​​for sand simulated by the DEM include a Young's modulus of 70 GPa and a density of 2650 kg / m³. 3 Poisson's ratio 0.3, coefficient of restitution 0.2, coefficient of sliding friction 0.5, coefficient of rolling friction 0.1, and discrete element method simulation was used with a loading speed of 0.0002 m / s and a time step size of 1e-7 s.

4. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: In the isotropic consolidation test in S4, a cubic specimen is placed in a six-sided servo wall, the sliding friction coefficient between the particles is set to 0, and the six servo walls are moved slowly toward the center at a speed of 0.025 m / s until the initial confining pressure of 100 kPa is reached and kept stable, thus generating a dense and isotropic specimen.

5. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 4, characterized in that: The isotropic specimens in S4 were subjected to conventional triaxial compression simulation tests. The interparticle friction coefficient was adjusted to 0.5, and the rolling friction coefficient was set to 0.

1. During the loading process, the upper and lower walls were moved at a constant speed, and the confining pressure was maintained at a set 100 kPa by the horizontal servo wall. Stress-strain data of specimens with different gradations were obtained.

6. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: S5 The stress-strain data is simplified by preprocessing different stress-strain curves using the same horizontal axis value and different vertical axes to obtain a stress-strain curve represented by two-dimensional coordinates. Then, the corresponding fine particle content and particle size ratio characteristic parameters are added before each coordinate to obtain a four-dimensional coordinate.

7. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: The steps to build a random forest model in S7 are as follows: 1) Randomly select samples from the training set; 2) Generate n decision trees, and the data subset in each decision tree is generated by sampling according to the Bagging idea; 3) Finally, take the average of the prediction results of all decision trees to obtain the final prediction value.

8. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 7, characterized in that: The convergence of random forest is expressed by the following formula (3): mg(x,y)=of n I(f n (x)=y)-max j＝y of n I(f n (x)=j) (3) In the formula f n (x) represents the decision tree, n represents the number of trees in the random forest, I(.) is the characteristic function, and av n It is the average value of the function; the larger the value of mg(x,y), the more accurate the prediction of the random forest.

9. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning as described in claim 1, characterized in that: S8 uses the Bayesian method for hyperparameter optimization, where Bayes' theorem is expressed as follows: In the formula, P(H|E) refers to the probability of target H given E; P(E|H) is the probability of observing E after assuming target H; P(H) is the prior probability of assuming H without observing evidence E; and P(E) is the marginal likelihood of evidence E.

10. The method for predicting stress and strain of discontinuous graded soil based on the coupling of discrete element method and machine learning according to claim 1, characterized in that: The sample in S1 is a quartz sand sample with a relative density of 50% that has been fully consolidated and saturated, and then sheared at a constant strain rate of 0.2% / min using a triaxial tester.

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