Intermittent graded soil stress-strain prediction method based on discrete element method and machine learning coupling

Abstract

The invention relates to an intermittent graded soil stress-strain prediction method based on discrete element method and machine learning coupling, and the method comprises the following steps: S1, obtaining reference stress-strain data; s2, establishing a discrete element method model and verifying the discrete element method model; s3, constructing discontinuous graded soil discrete element method samples of different grades; s4, obtaining stress-strain data of different graded soil; s5, establishing an original database; s6, dividing an original database; s7, constructing a random forest model; s8, training the random forest model to obtain a prediction stress model; s9, evaluating the trained random forest model; and S10, predicting the stress-strain data of the discontinuous graded soil. According to the method, the discontinuous graded soil stress-strain curve can be quickly and directly predicted through the particle size ratio and the fine particle content, and the efficiency is improved.

Description

Technical Field

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

[0002] Under the action of landslides, debris flows, etc., coarse particles (sand and gravel) and fine particles (silt) will mix with each other to form a discontinuously graded soil particle mixture. Discontinuously graded soil has good drainage, stability and compaction, and is widely used in hydraulic structures such as embankments and dams. The study of the physical and mechanical properties of discontinuously graded soil has become an important issue in engineering practice. At present, the values ​​of the mechanical properties and design parameters of soil bodies almost entirely rely on in-situ geotechnical tests and indoor geotechnical tests, but the economic and time costs are high. Therefore, it is of great significance to construct an efficient and reliable constitutive prediction model for discontinuously graded soil. Summary of the invention

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

[0004] The present invention is completed by adopting the following technical scheme: a stress-strain prediction method for discontinuous graded soil based on the coupling of discrete element method and machine learning, the steps are as follows:

[0005] S1. Obtain benchmark stress-strain data,

[0006] Take a benchmark sample for consolidation saturation, shear it with a triaxial tester, measure the axial force with a verification ring, and record the deformation of the sample surface with a digital image measurement system to obtain the stress-strain curve of the sample and obtain benchmark stress-strain data;

[0007] S2. Construct discrete element method model and verify it.

[0008] The same graded samples as those in S1 were used to establish a conventional triaxial compression test model by constructing the discrete element method, and compression simulation was performed. The data were compared with the benchmark stress-strain data obtained in S1 to verify the accuracy of the conventional triaxial compression model of the discrete element method and determine the particle parameters and loading conditions in the discrete element simulation model.

[0009] S3. Construct discrete element model of discontinuous graded soil with different gradations.

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

[0011] S4. Obtain stress-strain data of samples with different gradations,

[0012] The isotropic consolidation and conventional triaxial compression simulation tests were carried out on the discrete element models of different gradations in S3 to obtain stress-strain data of different gradations.

[0013] S5. Establish the original database,

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

[0015] S6. Divide the original database,

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

[0017] S7. Build a random forest model,

[0018] The inputs of 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 hyper-parameter optimized by Bayesian method to obtain and save the optimal parameter stress prediction model;

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

[0022] The predicted stress random forest model trained in S8 is verified with the 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. Prediction of stress data of discontinuous graded soil,

[0024] Different grading parameters and axial strains of the discontinuous graded soil for which stress and strain prediction is required are input into the stress prediction model trained in S8 to obtain the stress data of the discontinuous graded soil.

[0025] The effects of the present invention are as follows:

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

[0027] (2) The traditional constitutive model is complex and has many parameters, which limits its application in describing the stress-strain relationship of soil. The machine learning method used in this method is applied to the constitutive modeling of discontinuous graded soil without any assumptions. Machine learning can directly learn the stress-strain relationship from the original data. With the increase of data sets, the prediction accuracy and application scope of the model based on machine learning have been significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a technical route flow chart of the present invention;

[0029] Figure 2 It is a schematic diagram of model verification in the present invention;

[0030] Figure 3 It is a schematic diagram of particle generation and isotropic consolidation in the present invention;

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

[0032] Figure 5 It is a schematic diagram of data preprocessing in the present invention;

[0033] Figure 6 It is a schematic diagram of hyperparameter optimization in the present invention;

[0034] Figure 7 It is a schematic diagram comparing the predicted value and the actual value in the present invention;

[0035] Figure 8 It is a schematic diagram for predicting different particle size ratios and fine particle contents in the present invention. DETAILED DESCRIPTION

[0036] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation mode, structure, characteristics and effects of the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments.

[0037] Reference Figure 1-3 As shown, the present invention provides a stress-strain prediction method for discontinuous graded soil based on the coupling of discrete element method and machine learning, and the steps are as follows:

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

[0039] A reference sample is consolidated and saturated, sheared by a triaxial tester, and the axial force is measured by a verification ring and the deformation of the sample surface is recorded by a digital image measurement system to obtain a stress-strain curve of the sample and obtain reference stress-strain data. The sample is preferably a quartz sand sample with a relative density of 50% that is fully consolidated and saturated, and sheared by a triaxial tester at a constant strain rate of 0.2% / min.

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

[0041] The same graded samples as those in S1 were used to establish a conventional triaxial compression test model using the discrete element method. The model was compared with the benchmark stress-strain data obtained in S1 to verify the correctness of the discrete element simulation model and determine the particle parameters and loading conditions in the discrete element simulation model. Figure 2 shown.

[0042] Specifically, S2-1, when simulating conventional triaxial tests by discrete element method, quasi-static conditions need to be met, so the movement speed of the upper and lower walls cannot be too fast; however, if the loading speed is too low, the calculation cost will be greatly increased. Therefore, the loading speed of discrete element simulation is preferably 0.0002m / s;

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

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

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

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

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

[0048]

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

[0050] S4. Obtain stress-strain data of different gradations. The discrete element models of different gradations in S3 are simulated by isotropic consolidation and conventional triaxial compression tests to obtain stress-strain data of different gradations.

[0051] Specifically, the isotropic consolidation test simulation includes placing the sample in six servo walls, setting the sliding friction coefficient to 0, and slowly moving the six servo walls toward the center at the same time until the set initial confining pressure of 100 kPa is reached and remains stable, thereby generating a dense and isotropic sample.

[0052] The isotropic specimens were subjected to conventional triaxial compression simulation tests, the inter-particle friction coefficient was adjusted to 0.5, and the rolling friction coefficient was set to 0.1 to approximately consider the influence of irregular particle shape. During the loading process, σ1 was achieved by moving the upper and lower walls at a uniform speed, and the confining pressures σ2 and σ3 were maintained at a set 100 kPa by the servo wall unit to obtain stress-strain data of different gradations.

[0053] S5. Establishing an original database. Preprocessing the stress-strain data obtained by simulation in S4 to obtain a simplified stress-strain curve. Adding the corresponding fine particle content and particle size ratio characteristic values ​​to establish an original database.

[0054] Specifically, S5-1. If the unprocessed deviatoric stress-strain curve is used as the input and output data of the neural network, it will significantly increase the burden of model evaluation and consume a lot of computing resources. In view of this, the present invention simplifies the stress-strain curve by preprocessing, represents different stress-strain curves with the same horizontal coordinate value and different vertical coordinates, and obtains a stress-strain curve represented by two-dimensional coordinates. The horizontal coordinate of the curve is divided into 100 equal parts, and the corresponding 100 fixed-interval horizontal coordinate points are taken to represent a group of stress-strain curves with different particle size ratios and fine particle contents (such as Figure 5 As shown, a point is taken every 0.05).

[0055] S5-2, a stress-strain curve represented by 100 two-dimensional coordinates is obtained from S5-1, and then characteristic parameters of fine particle content and particle size ratio are added before each coordinate to obtain 100 four-dimensional coordinates and establish an original database.

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

[0057] Specifically, the original data set is divided into the data set by importing the “train_test_split” function from the “sklearn.model_selection” module through a Python script, and “random_state=42” is set to ensure that the results are reproducible.

[0058] S7. Construct a random forest model, wherein the input of the random forest model includes strain, particle size ratio and fine particle content, and the output is strain.

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

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

[0061] S7-2. Generate n decision trees. Use Python script to call the “RandomForestRegressor” class from the “sklearn.ensemble” module 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] Where f n (x) represents the decision tree, n represents the number of trees in the random forest, I(.) is the indicator function, av n It is the average value of the function. The larger the mg(x,y) value is, the more accurate the random forest prediction is.

[0067] S8. Train the random forest model to obtain a stress prediction model. Specifically, perform Bayesian hyperparameter optimization on 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 for Bayesian optimization. Compared with traditional grid search and random search, Bayesian optimization takes into account previous evaluation results and can explore parameter space more effectively, usually requiring fewer iterations to find better results. Among them, the Bayesian theorem is expressed as follows:

[0069]

[0070] Where P(H|E) is the probability of the target H given E; P(E|H) is the probability of observing E assuming the target H; P(H) is the prior probability of assuming H when no evidence E is observed; and P(E) is the marginal likelihood of evidence E.

[0071] Adjust the parameters of "n_estimators" and "max_depth". The Bayesian optimization results are as follows Figure 6 And 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 passed into the stress prediction model trained in S8 to obtain the predicted data, and the model performance is calculated. The random forest model is evaluated through the test set. Among them, the model performance goodness of fit R 2

[0075] The mean absolute error (MAE) is calculated as follows:

[0076]

[0077] Where: is the predicted value; y is the experimental value; n is the number of samples.

[0078] By the attached Figure 7 It can be seen that the predicted values ​​and true values ​​of the prediction parameters based on the random forest model are compared. Figure 7 Middle: R 2 , MAE and 10% tolerance represent the determination coefficient, mean absolute error and prediction accuracy under 10% tolerance, respectively. The horizontal and vertical axes represent the true value and predicted value of the deviator stress parameter, respectively. Figure 7 The closer the scatter points are to the diagonal line, the closer the predicted value and the true value of the data corresponding to the scatter points are. The scatter points of the random forest model are all closer to the diagonal line.

[0079] S10. Predicting stress data of discontinuous graded soil. Inputting different gradation parameters and axial strains of the discontinuous graded soil for which stress and strain prediction is required into the stress prediction model trained in S8, obtains predicted stress data of the discontinuous graded soil.

[0080] like Figure 8 As shown, Figure 8 a is particle size ratio 2-fine particle content 22.5%; b is particle size ratio 3-fine particle content 12.5%; c is particle size ratio 4-fine particle content 10%; d is particle size ratio 6-fine particle content 22.5. It can be seen that the random forest model has a good prediction effect on the stress-strain curve of different discontinuous grading soils, and the predicted values ​​are basically consistent with the experimental values.

[0081] The above is only the preferred embodiment of the present invention, and does not limit the present invention in any form. Although the present invention has been disclosed as the preferred embodiment, it is not used to limit the present invention. Any technical personnel in the field can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any brief modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention still fall within the scope of the technical solution of the present invention.

Claims

1. A stress-strain prediction method for discontinuous graded soil based on the coupling of discrete element method and machine learning, characterized by: The steps are as follows, S1. Obtain benchmark stress-strain data, Take a benchmark sample for consolidation saturation, shear it with a triaxial tester, measure the axial force with a verification ring, and record the deformation of the sample surface with a digital image measurement system to obtain the stress-strain curve of the sample and obtain benchmark stress-strain data; S2. Construct discrete element method model and verify it. The same graded samples as those in S1 were used to establish a conventional triaxial compression test model by constructing the discrete element method, and compression simulation was performed. The data were compared with the benchmark stress-strain data obtained in S1 to verify the accuracy of the conventional triaxial compression model of the discrete element method and determine the particle parameters and loading conditions in the discrete element simulation model. S3. Construct discrete element model of discontinuous graded soil with different gradations. Adjust the particle size distribution of the simulated sample to establish discrete element samples with different fine particle contents and particle size ratios; S4. Obtain stress-strain data of samples with different gradations, The isotropic consolidation and conventional triaxial compression simulation tests were carried out on the discrete element models of different gradations in S3 to obtain stress-strain data of different gradations. S5. Establish the original database, The stress-strain data obtained by simulation in S4 are preprocessed, and the corresponding fine particle content and particle size ratio characteristic values ​​are added to establish the original database; S6. Divide the original database, The original database is divided into training set, validation set and test set, with a data ratio of 8:1:1; S7. Build a random forest model, The inputs of 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 hyper-parameter optimized by Bayesian method to obtain and save the optimal parameter stress prediction model; S9. Evaluate the trained random forest model. The predicted stress random forest model trained in S8 is verified with the 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. Prediction of stress data of discontinuous graded soil, Different grading parameters and axial strains of the discontinuous graded soil for which stress and strain prediction is required are input into the stress prediction model trained in S8 to obtain the stress data of the discontinuous graded soil.

2. The stress-strain prediction method for discontinuous-graded soil based on the coupling of discrete element method and machine learning according to claim 1 is characterized in that: S3 The medium particle grading is to prepare particle samples with different fine particle contents and particle size ratios. The sample particles are composed of coarse particles and fine particles. The particle size ratio is calculated by formula (1) and the fine particle content is determined by formula (2). In the above formula, SR represents the particle size ratio, d max and d min Represent the diameters of coarse particles and fine particles respectively, FC represents the fine particle content, m fine and m all Represent the mass of fine particles and all particles respectively.

3. The stress-strain prediction method for discontinuous-graded soil based on the coupling of discrete element method and machine learning according to claim 1 is characterized in that: S2 When the conventional triaxial compression test is simulated by discrete element method, the values ​​of the simulated sand by discrete element method include the simulated particle Young's modulus of 70GPa and the density of 2650kg / m 3 , Poisson's ratio 0.3, restitution coefficient 0.2, sliding friction coefficient 0.5, rolling friction coefficient 0.1, discrete element simulation loading speed 0.0002m / s and time step size 1e-7s.

4. The stress-strain prediction method for discontinuous-graded soil based on the coupling of discrete element method and machine learning according to claim 1 is characterized by: In the isotropic consolidation test in S4, the cubic specimen is placed in six servo walls, the sliding friction coefficient between the particles is set to 0, and the six servo walls are slowly moved toward the center at a speed of 0.025 m / s until the set initial confining pressure of 100 kPa is reached and remains stable, 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 according to claim 4 is characterized by: The isotropic specimens in S4 were subjected to conventional triaxial compression simulation tests, and the inter-particle 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 uniform speed, and the confining pressure was maintained at a set 100 kPa by the servo wall in the horizontal direction to obtain the stress-strain data of specimens with different gradations.

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

7. The stress-strain prediction method for discontinuous-graded soil based on the coupling of discrete element method and machine learning according to claim 1 is characterized by: The construction of the random forest model in S7 includes the following steps: 1) randomly selecting samples from the training set; 2) generating n decision trees, and the data subset in each decision tree is generated by sampling based on the bagging idea; 3) finally averaging 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 according to claim 7 is characterized by: 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) Where f n (x) represents the decision tree, n represents the number of trees in the random forest, I(.) is the indicator function, av n It is the average value of the function. The larger the mg(x,y) value is, the more accurate the random forest prediction is.

9. 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: S8 uses the Bayesian method for hyperparameter optimization, where the Bayesian theorem is expressed as follows: Where P(H|E) is the probability of target H given E; P(E|H) is the probability of observing E given target H; P(H) is the prior probability of assuming H when no evidence E is observed; and P(E) is the marginal likelihood of evidence E.

10. The stress-strain prediction method for 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 was made of quartz sand with a relative density of 50% and fully consolidated and saturated, and sheared with a triaxial tester at a constant strain rate of 0.2% / min.

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