A method for analyzing random seismic response of rockfill dam based on test database

Abstract

The application provides a rockfill dam seismic response randomness analysis method based on a test database, and belongs to the technical field of hydraulic engineering. First, a coarse-grained soil dynamic property database Geo-Gravel is constructed, and a deep learning model based on given physical parameters to generate corresponding dynamic parameters is trained; second, a finite element model and a material parameter random field are constructed, and the material parameter random field is assigned to the finite element model; third, the dam body dynamic response is obtained through calculation by using a finite element software; finally, the extreme values of the displacement and acceleration of the dam body dynamic response and the probability distribution thereof are counted, and the statistical results are analyzed to quantify the influence of the material physical parameter randomness on the dam body dynamic response. The application can effectively reduce the test cost, truly reflect the spatial variation characteristics of the rockfill material, and show through the probability distribution analysis that the parameter randomness significantly influences the dynamic response result, and the dispersion degree and the variation coefficient are positively correlated, thereby providing a reliable basis for seismic design.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology and relates to a method for analyzing the randomness of the seismic response of rockfill dams based on an experimental database. This method is used to accurately calculate the influence of the randomness of the physical parameters of the rockfill material on the dynamic response of the dam body. Background Technology

[0002] In existing dynamic analyses of earth-rock dams, constant parameters are often used to characterize the physical and mechanical properties of materials, neglecting the spatial variability of the physical and dynamic parameters of the rockfill, leading to biases in seismic response analysis results. Current techniques rely heavily on laboratory experiments to study the stochasticity of dynamic parameters, which is costly, inefficient, and makes it difficult to establish a nonlinear mapping relationship between physical and dynamic parameters.

[0003] To address the above issues, scholars both domestically and internationally have conducted extensive research and proposed several solutions. For example, Chinese invention patent (application number 2024112029305) uses Markov chain algorithm to predict rock strata characteristics within a borehole unit based on borehole measurement data. It then obtains corresponding material parameters based on the rock strata characteristics of each unit, establishes the correlation between rheological parameters and these material parameters, and derives a standard normal distribution random field for the rheological parameters of the rockfill dam foundation material. Another Chinese invention patent (application number 2025108618119) constructs a surrounding rock parameter database, uses the Akaike information criterion to determine the optimal edge distribution of different surrounding rock parameters, constructs a baseline numerical initial model, and generates a relevant standard uniform distribution random field.

[0004] The most important technical characteristic of deep learning is its ability to automatically extract features. These extracted features, also known as deep features or deep feature representations, are more powerful and robust than manually designed features. Deep learning techniques can be used to extract and process large amounts of data related to the physical and dynamic properties of rockfill materials, accurately and quickly establishing nonlinear mapping relationships between physical and dynamic parameters. Summary of the Invention

[0005] To address the shortcomings of existing technologies, such as insufficient consideration of the spatial variability of physical parameters of rockfill, high cost of obtaining dynamic parameters, and difficulty in modeling the nonlinear relationship between physical and dynamic parameters, this invention provides a method for analyzing the stochasticity of the seismic response of rockfill dams based on an experimental database. It establishes a nonlinear mapping relationship between the random field of physical parameters of the rockfill and the random field of dynamic parameters to accurately assess the impact of parameter randomness on the seismic response of the dam. Simultaneously, it constructs a spatial parameter random field to simulate the randomness of the rockfill parameters. This invention solves the problems of relying heavily on indoor experiments for obtaining the randomness of dynamic parameters, which is costly and inefficient, and the difficulty in establishing a nonlinear mapping relationship between physical and dynamic parameters. It also solves the challenge of predicting the impact of the randomness of rockfill physical parameters on the dynamic response of earth-rock dams.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for analyzing the stochasticity of seismic response of rockfill dams based on experimental databases includes the following steps:

[0008] The first step is to construct the Geo-Gravel database of coarse-grained soil dynamic properties and train a deep learning model that generates corresponding dynamic parameters based on given physical parameters; specifically:

[0009] Step 1.1: Based on existing publicly available literature and information, construct the Geo-Gravel database of coarse-grained soil dynamic properties. It mainly covers detailed data of drained triaxial tests of coarse-grained soil under monotonic shear conditions, including the physical and mechanical parameters of coarse-grained soil and the results of triaxial tests.

[0010] Step 1.2: The Seft-Net model was trained based on the established Geo-Gravel database of coarse-grained soil dynamic properties.

[0011] The Seft-Net model architecture includes an input module, a feature transformation module, a feature extraction module, a regression head module, and an output module. First, the input module upscales the input parameters into a high-dimensional matrix structure. Then, the feature transformation module groups these high-dimensional parameters based on their physical properties, resulting in a grouped high-dimensional data matrix. Next, the feature extraction module processes this grouped high-dimensional data matrix, fusing features from different levels through multi-scale convolution and branching structures to obtain high-dimensional features of the parameters. Then, the regression head module processes these high-dimensional features to reduce the feature dimensionality, resulting in dimensionality-reduced parameter features. Finally, the output module processes these dimensionality-reduced parameter features to obtain the predicted values ​​of the target parameters.

[0012] The training process of the Seft-Net model is as follows:

[0013] Fourteen physical parameters were selected as input variables, including shape irregularity. parent rock strength ,proportion porosity Soil characteristic particle size parameters , , , , , Inhomogeneity coefficient Cu, curvature coefficient Cc, effective mean principal stress p, and dynamic shear strain The output variables of the Seft-Net model are the dynamic shear modulus G and the damping ratio. .

[0014] Input variables into the input module. These variables are first arranged in the form of a 1×14 one-dimensional array, and then transformed into a 3×14 two-dimensional matrix structure through feature upscaling.

[0015] In the feature transformation module, the factors affecting dynamic shear modulus and damping ratio are summarized as particle properties, soil parameters, and external conditions; the particle properties include parent rock strength. Shape irregularity ,proportion The soil parameters include the void ratio. Particle characteristic size , , , , , The non-uniformity coefficient Cu; the external conditions include the mean principal stress p and the dynamic shear strain. .

[0016] In the feature extraction module, depthwise separable convolution integrals are used. Through multi-scale convolution and branching structures, features from different levels are fused, and the constructed feature space can effectively capture the dynamic shear modulus G and damping ratio of coarse-grained soil. The nonlinear correlation between the physical parameters of coarse-grained soil and the high-dimensional characteristics of the coarse-grained soil parameters is obtained.

[0017] The high-dimensional features of the successfully extracted coarse-grained soil parameters are passed to the regression head module and transformed into low-dimensional features of the coarse-grained soil parameters. The output module then converts these low-dimensional features into parameters related to the dynamic shear modulus G and damping ratio. The final prediction output.

[0018] The Geo-Gravel database of coarse-grained soil dynamic properties was divided into training and testing sets in a 5:1 ratio. During the Seft-Net model training phase, the training set was used to train the Seft-Net model, updating and adjusting the parameters to continuously reduce the loss function. Training stopped when the error value was less than 1e-6, resulting in the trained Seft-Net model. In the testing phase, the test set was used to verify the accuracy of the trained Seft-Net model. The trained Seft-Net model achieved high prediction accuracy on the test set, thus obtaining a Seft-Net model that generates corresponding dynamic parameters based on given physical parameters.

[0019] The second step is to construct the finite element model and the random field of material parameters, and then assign the random field of material parameters to the finite element model; specifically:

[0020] Step 2.1: Establish a finite element model based on the actual data of the dam using finite element software. Divide the finite element model into meshes to obtain finite element elements. Divide the finite element elements into partitions according to the actual structure of the dam. Assign uniform parameters to the entire partition for some partitions, and assign different parameters to each element for other partitions. That is, assign discretized material physical parameters random fields to obtain the finite element model to be assigned.

[0021] Step 2.2: Based on the node position information of the elements in the finite element model that require different parameters for each element, calculate the centroid coordinates of the finite element elements. Use the Gaussian autocorrelation function to calculate the correlation coefficient at the centroid coordinates of the finite element elements, thereby simulating the correlation of material physical parameters. The expression for the Gaussian autocorrelation function is as follows:

[0022] (1)

[0023] In the formula: The coordinates of the centroid of a finite element element and the horizontal distance between two points of the centroid coordinates of adjacent finite element elements are given. ; Let be the vertical distance between the centroid coordinates of the finite element elements and the centroid coordinates of two adjacent finite element elements. ; The horizontal autocorrelation distance; These are vertical autocorrelation distances, determined by soil properties.

[0024] Obtain the correlation coefficient matrix of the relevant random variables By sampling the correlation coefficient matrix of relevant random variables, the non-uniform characteristics of the spatial distribution of physical parameters are simulated, resulting in a discretized random field of material physical parameters.

[0025] (2)

[0026] The sampling process is as follows:

[0027] The Cholesky decomposition method makes ,in, Let n represent the correlation coefficient matrix, where n represents the dimension of the correlation coefficient matrix. Let the upper triangular matrix be the result of the correlation coefficient matrix decomposition; let Let be a column vector consisting of c independent random numbers that follow a normal distribution. Then the sample matrix of the relevant standard normal distributed random variable is... It is obtained through the following linear transformation:

[0028] (3)

[0029] In the formula: Let m be an upper triangular matrix; m is the number of simulations, c is the number of column vectors, and b is the number of subspaces, therefore b=c=n.

[0030] The sample matrix of the b-dimensional correlated normally distributed random variable for:

[0031] (4)

[0032] In the formula, Let be an m×b matrix with all elements equal to 1; This is the average value, obtained from actual measurements; The standard deviation is obtained from actual measurements.

[0033] Step 2.3: Using the Seet-Net model that generates corresponding dynamic parameters based on given physical parameters, the discretized random field of material physical parameters is transformed into a discretized random field of material dynamic parameters.

[0034] Step 2.4: Iterate through the finite element units, writing the discretized material dynamic parameter random field into each corresponding element of the finite element model to be assigned values. Each finite element unit is assigned a unique material number to avoid attribute conflicts, resulting in the finite element units with assigned discretized material dynamic parameter random fields. The remaining partitions are then uniformly assigned the corresponding dynamic parameters, which are obtained from actual measurements or empirical estimations, resulting in the assigned finite element model.

[0035] The third step is to use finite element software to calculate the dynamic response of the dam body.

[0036] The finite element model with assigned values ​​is read by the finite element software, and the seismic waves used to calculate the dynamic response of the dam are input into the finite element software to calculate the dynamic response of the dam. The seismic waves can be the measured seismic waves released by the earthquake bureau or simulated seismic waves. The dynamic response of the dam, including displacement and acceleration, is obtained.

[0037] The fourth step is to statistically analyze the extreme values ​​of displacement and acceleration in the dynamic response of the dam body, as well as the probability distribution of these extreme values, and to quantify the influence of the randomness of material physical parameters on the dynamic response of the dam body.

[0038] Furthermore, the extreme values ​​include both maximum and minimum values.

[0039] The beneficial effects of this invention are:

[0040] (1) By combining random field theory and deep learning, an efficient nonlinear mapping from physical parameters to dynamic parameters is achieved, reducing experimental costs.

[0041] (2) Taking into account the randomness of density and gradation characteristics, it more realistically reflects the spatial variation characteristics of rockfill.

[0042] (3) Quantify the degree of influence of randomness on seismic response to provide a more reliable basis for seismic design of engineering projects. Attached Figure Description

[0043] Figure 1 Statistical histogram of parameters for the Geo-Gravel database; Figure 1 (a) in the figure represents the statistical results of dry density; Figure 1 (b) in the figure represents the statistical results of the non-uniformity coefficient; Figure 1 (c) in the figure represents the statistical results of the curvature coefficient.

[0044] Figure 2 This is a two-dimensional finite element mesh diagram of a panel rockfill dam.

[0045] Figure 3 This is the time history curve of seismic acceleration along the river.

[0046] Figure 4 This represents the probability distribution of the maximum horizontal dynamic displacement at the dam crest. Figure 4 (a) in the figure represents the probability distribution of the maximum horizontal dynamic displacement of the dam crest in working condition one; Figure 4 (b) in the figure represents the probability distribution of the maximum horizontal dynamic displacement of the dam crest in working condition two.

[0047] Figure 5 This is a diagram showing the percentage of the maximum horizontal dynamic displacement at the dam crest. Figure 5 (a) represents the percentage of the maximum horizontal dynamic displacement at the dam crest under working condition 1; Figure 5 (b) represents the percentage of the maximum horizontal dynamic displacement of the dam crest under working condition two.

[0048] Figure 6 The probability distribution of the horizontal peak acceleration at the dam crest; Figure 6 (a) in the figure represents the probability distribution of the horizontal peak acceleration at the dam crest under working condition 1; Figure 6 (b) in the figure represents the probability distribution of the horizontal peak acceleration at the top of the dam under working condition two.

[0049] Figure 7 This is a probability distribution diagram of the peak horizontal acceleration at the dam crest. Figure 7 (a) represents the percentage of the horizontal peak value at the dam crest in working condition 1; Figure 7 (b) represents the percentage of the horizontal peak value at the top of the dam under working condition 2.

[0050] Figure 8 This is a flowchart of the present invention. Detailed Implementation

[0051] The present invention will be further described below with reference to specific implementation examples.

[0052] Taking a certain panel rockfill dam as an example, the specific steps are as follows:

[0053] The first step is to construct the Geo-Gravel database of coarse-grained soil dynamic properties and train a deep learning model that generates corresponding dynamic parameters based on given physical parameters; specifically:

[0054] Step 1.1: Based on existing publicly available literature and information, the Geo-Gravel database of coarse-grained soil dynamic properties is constructed. It mainly covers detailed data from drained triaxial tests of coarse-grained soil under monotonic shear conditions, including the physical and mechanical parameters of the coarse-grained soil and the results of the triaxial tests. Relevant statistical data can be found in [link to relevant statistics]. Figure 1 .

[0055] Step 1.2: The Seft-Net model was trained based on the established Geo-Gravel database of coarse-grained soil dynamic properties.

[0056] The Seft-Net model architecture includes an input module, a feature transformation module, a feature extraction module, a regression head module, and an output module. First, the input module upscales the input parameters into a high-dimensional matrix structure. Then, the feature transformation module groups these high-dimensional parameters based on their physical properties, resulting in a grouped high-dimensional data matrix. Next, the feature extraction module processes this grouped high-dimensional data matrix, fusing features from different levels through multi-scale convolution and branching structures to obtain high-dimensional features of the parameters. Then, the regression head module processes these high-dimensional features to reduce their dimensionality, resulting in dimensionality-reduced parameter features. Finally, the output module processes these dimensionality-reduced parameter features to obtain the predicted values ​​of the target parameters.

[0057] The training process of the Seft-Net model is as follows:

[0058] Fourteen physical parameters were selected as input variables, including shape irregularity. parent rock strength ,proportion porosity Soil characteristic particle size parameters , , , , , Inhomogeneity coefficient Cu, curvature coefficient Cc, effective mean principal stress p, and dynamic shear strain The output variables of the Seft-Net model are the dynamic shear modulus G and the damping ratio. .

[0059] Input variables into the input module. These variables are first arranged in the form of a 1×14 one-dimensional array, and then transformed into a 3×14 two-dimensional matrix structure through feature upscaling.

[0060] In the feature transformation module, the factors affecting dynamic shear modulus and damping ratio are summarized as particle properties, soil parameters, and external conditions; the particle properties include parent rock strength. Shape irregularity ,proportion The soil parameters include the void ratio. Soil characteristic particle size parameters , , , , , The non-uniformity coefficient Cu; the external conditions include the effective average principal stress p and the dynamic shear strain. .

[0061] In the feature extraction module, depthwise separable convolution integrals are used. Through multi-scale convolution and branching structures, features from different levels are fused, and the constructed feature space can effectively capture the dynamic shear modulus G and damping ratio of coarse-grained soil. The nonlinear correlation between the physical parameters of coarse-grained soil and the high-dimensional characteristics of the coarse-grained soil parameters is obtained.

[0062] The high-dimensional features of the successfully extracted coarse-grained soil parameters are passed to the regression head module and transformed into low-dimensional features of the coarse-grained soil parameters. The output module then converts these low-dimensional features into parameters related to the dynamic shear modulus G and damping ratio. The final prediction output.

[0063] The Geo-Gravel database of coarse-grained soil dynamic properties was divided into training and testing sets in a 5:1 ratio. During the Seft-Net model training phase, the training set was used to train the Seft-Net model, updating and adjusting the parameters to continuously reduce the loss function. Training stopped when the error value was less than 1e-6, resulting in the trained Seft-Net model. In the testing phase, the test set was used to verify the accuracy of the trained Seft-Net model. The trained Seft-Net model achieved high prediction accuracy on the test set, thus obtaining a Seft-Net model that generates corresponding dynamic parameters based on given physical parameters.

[0064] The model's performance metrics were evaluated using mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), coefficient of determination (R²), and mean square error (MSE). A nonlinear mapping relationship was established from a random field of physical parameters to a random field of dynamic parameters. Performance evaluation results showed that the model exhibited high-precision fitting on the training set (G: MAPE = 6.20%). The prediction error on the test set increased slightly (G: MAPE=8.75%), while the prediction error on the test set increased slightly (G: MAPE=9.42%). (MAPE=13.10%), the model's prediction error on the test set is higher than that on the training set, which is consistent with the general trend of deep learning models. This proves that the trained deep learning model has the ability to accurately analyze the nonlinear mapping relationship between the physical properties of coarse soil and the dynamic shear modulus-damping ratio.

[0065] The second step is to construct the finite element model and the random field of material parameters, and then assign the random field of material parameters to the finite element model; specifically:

[0066] Step 2.1: A finite element model of the dam is established using finite element software based on actual dam data. Model region X represents bedrock, region Y represents the rockfill area, the bedrock depth f is 150m, the dam height a is 100m, the dam base width c is 324m, the dam crest width e is 10m, the upstream and downstream slopes b and d are both 150m, and the upstream-downstream slope ratio Z is 1:1.6. (See...) Figure 2 .

[0067] The finite element model is meshed to obtain finite element elements, and the finite element elements are partitioned according to the actual structure of the dam. Some partitions are assigned uniform parameters to the entire partition, while other partitions are assigned different parameters to each element, that is, they are assigned discretized material physical parameters random fields, to obtain the finite element model to be assigned.

[0068] Step 2.2: Based on the node position information of the elements in the finite element model that require different parameters to be assigned to each element, the centroid coordinates of the finite element elements are calculated. The Gaussian autocorrelation function is used to calculate the correlation coefficient at the centroid coordinates of the finite element elements, thereby simulating the correlation of material physical parameters. The expression of the Gaussian autocorrelation function is shown in formula (1):

[0069] (1)

[0070] In the formula: The coordinates of the centroid of a finite element element and the horizontal distance between two points of the centroid coordinates of adjacent finite element elements are given. ; Let be the vertical distance between the centroid coordinates of the finite element elements and the centroid coordinates of two adjacent finite element elements. ; The horizontal autocorrelation distance is taken as 25m. The vertical autocorrelation distance is set to 5m.

[0071] Obtain the correlation coefficient matrix of the relevant random variables By sampling the correlation coefficient matrix of relevant random variables, the non-uniformity of physical parameters in spatial distribution is simulated, and the discretized random field of material physical parameters is obtained, as shown in formula (2).

[0072] The sampling process is as follows:

[0073] The Cholesky decomposition method makes ,in, Let n represent the correlation coefficient matrix, and n represent the dimension of the correlation coefficient matrix. Let the upper triangular matrix be the result of the correlation coefficient matrix decomposition; let Let be a column vector consisting of c independent random numbers that follow a normal distribution. Then the sample matrix of the relevant standard normal distributed random variable is... The linear transformation of formula (3) yields:

[0074] (3)

[0075] In the formula: Let m be an upper triangular matrix; m is the number of simulations, c is the number of column vectors, and b is the number of subspaces, therefore b=c=n.

[0076] The sample matrix of the b-dimensional correlated normally distributed random variable for:

[0077] (4)

[0078] In the formula, Let be an m×b matrix with all elements equal to 1; This is the average value, obtained from actual measurements; The standard deviation is obtained from actual measurements.

[0079] To illustrate the impact of the randomness of rockfill parameters (density, gradation characteristics) on the dynamic response of rockfill dams, this study focuses on comparing the dynamic response of rockfill dams under two different coefficients of variation. Two calculation conditions were set up. Specific data are shown in Table 1.

[0080] Table 1: Statistical Properties of Material Physical Parameters

[0081]

[0082] Step 2.3: Using the Seet-Net model that generates corresponding dynamic parameters based on given physical parameters, the discretized random field of material physical parameters is transformed into a discretized random field of material dynamic parameters.

[0083] Step 2.4: Iterate through the finite element units, writing the discretized material dynamic parameter random field into each corresponding element of the finite element model to be assigned values. Each finite element unit is assigned a unique material number to avoid attribute conflicts, resulting in the finite element units with assigned discretized material dynamic parameter random fields. The remaining partitions are then uniformly assigned the corresponding dynamic parameters, which are obtained from actual measurements or empirical estimations, resulting in the assigned finite element model.

[0084] The third step is to perform calculations using finite element software.

[0085] This calculation aims to investigate the impact of the randomness of rockfill parameters on the dynamic response analysis of earth-rock dams. By repeatedly generating a large number of random fields of material physical parameters, a finite element model with assigned values ​​is obtained for calculating the dynamic response of the dam body until the simulation results reach stability.

[0086] The pre-assigned finite element model was read into the finite element software, and the seismic wave used to calculate the dam's dynamic response was input into the software. The seismic wave can be either a measured seismic wave released by the earthquake bureau or a simulated seismic wave. The dam's dynamic response, including displacement and acceleration, was obtained. The peak ground acceleration of the downstream seismic wave used in this calculation was 0.45g. (See...) Figure 3 .

[0087] The Shen Zhujiang equivalent linear model is selected as the dynamic constitutive model. The Shen Zhujiang equivalent linear model uses the reciprocal of the dynamic shear modulus 1 / With dynamic shear strain Approximately using a straight line fit, let a and b be the intercept and slope of the fitted line, then the relationship between the dynamic shear modulus and the dynamic shear strain is expressed as:

[0088] (5)

[0089] Maximum dynamic shear modulus :

[0090] (6)

[0091] In the formula The confining pressure was obtained experimentally. The pressure was obtained experimentally. , n are parameters determined experimentally.

[0092] Shen Zhujiang's equivalent linear model incorporates a reference dynamic strain, thus correcting the equivalent linear model and eliminating the influence of confining pressure on the dynamic shear stress ratio and damping ratio, making it more convenient for dynamic calculations. The normalized dynamic strain is given by the following formula:

[0093] (7)

[0094] When normalized dynamic strain is used, the dynamic shear modulus decay curves generally converge on a single curve. For example, let... The dynamic shear strain at =0.5 is Then we have:

[0095] (8)

[0096] In the formula, The parameters were determined for the experiment.

[0097] Maximum damping ratio of soil It can be calculated using the following formula:

[0098] (9)

[0099] To better explore the impact of spatial variability of material physical parameters, a control group was established that did not consider spatial variability of material physical parameters. The parameter values ​​of the Shen Zhujiang equivalent linear model adopted for the control group are shown in Table 2.

[0100] Table 2: Material dynamic model parameters

[0101]

[0102] The same calculation steps were used for both working conditions and the control group. The static calculation simulated the dam construction process using a layered filling method. After the filling was completed, the water impoundment operation was carried out in stages. The dam body filling consisted of 33 steps, with each step filling approximately 3 meters. The water impoundment process was divided into 30 steps, with each step approximately 3 meters. The water pressure acted on the panel unit in the form of surface force.

[0103] To ensure the convergence of the number of calculations N in the numerical simulation, a dynamic mean criterion method is used for stability assessment. The specific process is as follows: After each numerical simulation iteration, key dynamic response indicators, such as the horizontal dynamic displacement of the dam crest and the horizontal acceleration of the dam body, are extracted, and their sample means are calculated. Let k be the current iteration number. When the relative error of the mean between two adjacent iterations satisfies the convergence criterion, it proves that the simulation results have reached a stable value. After 310 simulations, the calculation results for all working conditions can reach a stable value.

[0104] The fourth step is results evaluation;

[0105] The extreme values ​​of displacement and acceleration in the dynamic response of the dam body from the previous step were statistically analyzed, including the maximum and minimum values, and the probability distribution of the extreme values. The statistical results were analyzed to quantify the influence of the randomness of material physical parameters on the response results. 310 calculations were performed in this study.

[0106] Figure 4The diagram shows the probability distribution of the maximum horizontal dynamic displacement at the dam crest. The dashed line represents the calculation result using a fixed mean parameter value, which is 0.1071 m. The solid line represents the average value calculated considering the randomness of physical parameters, which are 0.1082 m and 0.1113 m for the two conditions, respectively. The results show that the distribution of the maximum horizontal dynamic displacement at the dam crest is basically consistent under both conditions. However, due to the greater coefficient of variation of the rockfill in condition two compared to condition one, the calculated results exhibit greater dispersion. Considering the randomness of the parameters, the maximum values ​​of the maximum horizontal dynamic displacement at the dam crest under both conditions can reach 0.1229 m and 0.1337 m, respectively, representing increases of 14.8% and 25.0% compared to the determined values.

[0107] Figure 5 The diagram shows the probability distribution of the maximum horizontal dynamic displacement of the dam crest. Compared with the determined value, when the randomness of the rockfill parameters is not considered, the maximum horizontal dynamic displacement of the dam crest is underestimated in 59.3% and 70.1% of the two working conditions, respectively.

[0108] Figure 6 The diagram shows the probability distribution of the peak horizontal acceleration at the dam crest. The dashed line represents the calculation results using fixed parameter values, which is 7.554 m / s² for both conditions. The solid line represents the calculated average values ​​considering the randomness of physical parameters, which are 7.400 m / s² and 7.683 m / s² for the two conditions, respectively. After considering the randomness of the parameters, the maximum horizontal acceleration at the dam crest for both conditions can reach 8.248 and 9.681 m / s², respectively, which is an increase of 9.2% and 28.2% compared to the determined values.

[0109] Figure 7 The diagram shows the probability distribution of the peak horizontal acceleration at the dam crest. Compared to the determined value, when the randomness of physical parameters is not considered, the maximum peak horizontal acceleration at the dam crest is underestimated in 48.7% and 44.2% of the two working conditions, respectively.

[0110] The results in summary indicate that the randomness of the physical parameters of the rockfill material significantly affects the dynamic response characteristics, as the dispersion of the response results is positively correlated with the coefficient of variation.

[0111] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for analyzing the stochasticity of seismic response of rockfill dams based on experimental databases, characterized in that, The method for analyzing the stochasticity of the seismic response of rockfill dams includes the following steps: The first step is to construct the Geo-Gravel database of coarse-grained soil dynamic properties. Based on the Geo-Gravel database, the Seft-Net model is trained to obtain a deep learning model that generates corresponding dynamic parameters based on given physical parameters. The architecture of the Seft-Net model includes an input module, a feature transformation module, a feature extraction module, a regression head module, and an output module. The training process of the Seft-Net model is as follows: Fourteen physical parameters were selected as input variables, including shape irregularity. parent rock strength ,proportion Porosity Soil characteristic particle size parameters , , , , , Inhomogeneity coefficient Cu, curvature coefficient Cc, effective mean principal stress p, and dynamic shear strain The output variables of the Seft-Net model are the dynamic shear modulus G and the damping ratio. ; Input variables are entered in the input module. The input variables are arranged in the form of a 1×14 one-dimensional array. They are then transformed into a 3×14 two-dimensional matrix structure through feature upscaling. In the feature transformation module, the factors affecting dynamic shear modulus and damping ratio are summarized as particle properties, soil parameters, and external conditions; the particle properties include parent rock strength. Shape irregularity ,proportion The soil parameters include the void ratio. Soil characteristic particle size parameters , , , , , The non-uniformity coefficient Cu; the external conditions include the effective average principal stress p and the dynamic shear strain. ; In the feature extraction module, depthwise separable convolution integrals are used. Through multi-scale convolution and branching structures, features from different levels are fused, and the constructed feature space can effectively capture the dynamic shear modulus G and damping ratio of coarse-grained soil. The nonlinear correlation between the physical parameters of coarse-grained soil and the high-dimensional characteristics of the coarse-grained soil parameters are obtained. The high-dimensional features of the successfully extracted coarse-grained soil parameters are passed to the regression head module and transformed into low-dimensional features of the coarse-grained soil parameters. The output module then transforms the low-dimensional features of the coarse-grained soil parameters into dynamic shear modulus G and damping ratio. The final prediction is output; the second step is to construct a finite element model and a random field of material parameters, and assign the random field of material parameters to the finite element model; specifically: Step 2.1: Establish a finite element model based on the actual data of the dam, divide the finite element model into meshes to obtain finite element elements, and then partition the mesh to obtain the finite element model to be assigned values. Step 2.2: Obtain the centroid coordinates of the finite element units based on the finite element model to be assigned values; and calculate the correlation coefficients at the centroid coordinates of the finite element units to finally obtain the discretized random field of material physical parameters. Step 2.3: Using the Seft-Net model that generates corresponding dynamic parameters based on given physical parameters, the discretized random field of material physical parameters is transformed into a discretized random field of material dynamic parameters. Step 2.4: Write the discretized material dynamic parameter random field into each corresponding finite element of the finite element model to be assigned values, and obtain the assigned finite element model. The third step is to use finite element software to calculate the dynamic response of the dam body; The finite element model that has been assigned values ​​in the second step is read by the finite element software, and the seismic wave used to calculate the dynamic response of the dam is input into the finite element model to calculate the dynamic response of the dam, including displacement and acceleration. The fourth step is to statistically analyze the extreme values ​​of displacement and acceleration in the dynamic response of the dam body, as well as their probability distribution, and to quantify the influence of the randomness of material physical parameters on the dynamic response of the dam body.

2. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 1, characterized in that, The first step is specifically as follows: Step 1.1: Construct the Geo-Gravel database of dynamic properties of coarse-grained soil, which covers detailed data of drained triaxial tests of coarse-grained soil under monotonic shear conditions, including the physical and mechanical parameters of coarse-grained soil and the results of triaxial tests. Step 1.2: Train the Seft-Net model; The Geo-Gravel database of coarse-grained soil dynamic properties was divided into a training set and a test set. During the Seft-Net model training phase, the Seft-Net model was trained using the training set, and the parameters were updated and adjusted to continuously reduce the loss function. Training was terminated when the error value was less than 1e-6, resulting in a trained Seft-Net model. During the testing phase, the accuracy of the trained Seft-Net model was verified using the test set, resulting in a Seft-Net model that generates corresponding dynamic parameters based on given physical parameters.

3. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 2, characterized in that, In step 1.2, firstly, the input module is used to increase the dimensionality of the input parameters into high-dimensional parameters of a matrix structure; then, the feature transformation module is used to group the high-dimensional parameters of the matrix structure based on the physical properties of the parameters, resulting in a grouped high-dimensional data matrix; next, the feature extraction module is used to process the grouped high-dimensional data matrix, fusing features from different levels through multi-scale convolution and branching structures to obtain high-dimensional features of the parameters; then, the regression head module is used to process the high-dimensional features of the parameters, reducing the feature dimension to obtain dimensionality-reduced parameter features; finally, the output module is used to process the dimensionality-reduced parameter features to obtain the predicted value of the target parameter.

4. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 1, characterized in that, In the second step mentioned above: In step 2.1, the finite element model is meshed to obtain finite element elements, and the finite element elements are divided into two regions according to the actual structure of the dam. One region is assigned a uniform parameter to the entire region, and the other region is assigned a different parameter to each element, that is, a discretized material physical parameter random field is assigned to obtain the finite element model to be assigned. In step 2.2, based on the node position information of the elements in the finite element model that require different parameters for each element, the centroid coordinates of the finite element elements are calculated; the Gaussian autocorrelation function is used to calculate the correlation coefficient at the centroid coordinates of the finite element elements, thereby simulating the correlation of material physical parameters; and the correlation coefficient matrix of the relevant random variables is obtained. By sampling the correlation coefficient matrix of relevant random variables, the non-uniformity of the spatial distribution of physical parameters is simulated to obtain a discretized random field of material physical parameters. In step 2.3, the discretized random field of material physical parameters is transformed into a discretized random field of material dynamic parameters by using the Seet-Net model that generates corresponding dynamic parameters based on given physical parameters. In step 2.4, the discretized material dynamic parameter random field is written into each corresponding finite element of the finite element model to be assigned value by cyclic finite element. Each finite element is assigned a unique material number, thus obtaining the finite element of the discretized material dynamic parameter random field. The remaining partitions are assigned corresponding dynamic parameters according to the partition, and the assigned finite element model is obtained.

5. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 4, characterized in that, In step 2.2, the Gaussian autocorrelation function is expressed as follows: （1）； In the formula: The coordinates of the centroid of a finite element element and the horizontal distance between two points of the centroid coordinates of adjacent finite element elements are given. ; Let be the vertical distance between the centroid coordinates of the finite element elements and the centroid coordinates of two adjacent finite element elements. ; The horizontal autocorrelation distance; These are vertical autocorrelation distances, determined by soil properties.

6. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 5, characterized in that, In step 2.2, the correlation coefficient matrix As shown below: （2）。 7. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 6, characterized in that, In step 2.2, the sampling process is as follows: The Cholesky decomposition method makes ,in, Let n represent the correlation coefficient matrix, and n represent the dimension of the correlation coefficient matrix. Let the upper triangular matrix be the result of the correlation coefficient matrix decomposition; let Let be a column vector consisting of c independent random numbers that follow a normal distribution. Then the sample matrix of the relevant standard normal distributed random variable is... It is obtained through the following linear transformation: （3）； In the formula: Let m be an upper triangular matrix; m is the number of simulations, c is the number of column vectors, and b is the number of subspaces; b = c = n; The sample matrix of the b-dimensional correlated normally distributed random variable for: （4）； In the formula, Let be an m×b matrix with all elements equal to 1; This is the average value, obtained from actual measurements; The standard deviation is denoted as .

8. The method for analyzing the stochasticity of seismic response of rockfill dams based on an experimental database according to claim 7, characterized in that, The seismic waves used in the third step are either measured seismic waves published by the earthquake bureau or simulated seismic waves.

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