Numerical simulation method of true triaxial test for coarse-grained soil based on principal stress effect

Abstract

This invention relates to the field of deep learning technology, specifically to a numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects. The method includes the following steps: acquiring three-dimensional geological parameters and boundary condition data of the coarse-grained soil material; and constructing a true triaxial finite element simulation model of the coarse-grained soil based on the three-dimensional geological parameters and boundary condition data. This invention utilizes a loading increment step size for trial calculations and calculates the reward function value based on the convergence state and iteration count of the trial calculation results to update the network parameters, enabling the control strategy to continuously evolve through interaction with the environment. This allows for the identification of dangerous regions with highly nonlinear constitutive relations or near-singular stiffness matrices. In these regions, the step size is automatically reduced to ensure computational convergence, while in stable regions, the step size is increased to improve computational efficiency. This solves the problem that traditional fixed step sizes or simple adaptive step sizes easily lead to computational divergence or excessive iterations under complex stress paths.

Description

Technical Field

[0001] This invention relates to the field of deep learning technology, and in particular to a numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects. Background Technology

[0002] Current techniques for numerical simulation of true triaxial tests on coarse-grained soils typically employ a fixed-step incremental method. However, when dealing with the complex dilatation, strain softening, and anisotropy characteristics of coarse-grained soils, a fixed step size struggles to balance computational accuracy and efficiency. Setting the step size too large can lead to non-convergence in the Newton-Raphson iteration, while setting it too small wastes computational resources. Furthermore, when the simulation enters critical stages of intense plastic flow or stress path inflection, it becomes difficult to detect the deterioration trend of the stiffness matrix. Continuing to apply the established loading strategy can easily lead to stiffness matrix singularities or unremovable residual forces, causing the calculation to enter a dead loop or even diverge and terminate. Therefore, improvements are needed. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: a numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects, comprising the following steps: Obtain the three-dimensional geological parameters and boundary condition data of coarse-grained soil material, and construct a true triaxial finite element simulation model of coarse-grained soil based on the three-dimensional geological parameters and boundary condition data; Construct a step-size adaptive control agent based on deep reinforcement learning, and define the state space, action space and reward function of the step-size adaptive control agent; The coarse-grained soil true triaxial finite element simulation model is run for loading simulation. In each loading analysis step, the current simulation state data is collected in real time. Bayesian neural network is used to perform uncertainty analysis on the simulation state data to generate the structural prediction cognitive uncertainty value. The simulation state data is combined with the constitutive prediction cognitive uncertainty value to form the current state vector. The current state vector is input into the step size adaptive control agent, and the strain loading increment step size of the current analysis step is output. The strain loading increment step size is used to perform trial calculations on the true triaxial finite element simulation model of the coarse-grained soil. The value of the reward function is calculated based on the convergence state and iteration number of the trial calculation results. The value of the reward function is used to update the network parameters of the step size adaptive control agent until the true triaxial finite element simulation model of the coarse-grained soil completes the simulation of all loading paths.

[0005] Preferably, the steps for obtaining the three-dimensional geological parameters and boundary condition data of the coarse-grained soil material, and constructing a true triaxial finite element simulation model of the coarse-grained soil based on the three-dimensional geological parameters and boundary condition data, are as follows: Initial void ratio, particle size distribution curve and relative density data of coarse-grained soil samples were collected; An initial nonlinear constitutive matrix is ​​established based on the initial void ratio, particle size distribution curve, and relative density data. The initial nonlinear constitutive relation matrix is ​​mapped to the finite element mesh nodes, and the displacement constraint boundaries of the three principal stress directions of the true triaxial loading chamber are set to generate the true triaxial finite element simulation model of the coarse-grained soil.

[0006] Preferably, the steps for constructing a step-size adaptive control agent based on deep reinforcement learning, and defining the state space, action space, and reward function of the step-size adaptive control agent, are as follows: The proximal policy optimization algorithm is adopted as the decision-making algorithm for the step size adaptive control agent, and an Actor-Critic dual neural network architecture containing an Actor network and a Critic network is constructed. The state space is defined to include the unbalanced force norm, tangent stiffness matrix condition number, triaxial principal stress ratio, and constitutive prediction cognitive uncertainty value of the current analysis step; The action space is defined as a continuous interval of values, and the values ​​correspond to the strain loading increment step size of the next increment step; Configure the reward function, which is used to minimize the number of nonlinear iterations.

[0007] Preferably, the loading simulation is performed by running the true triaxial finite element simulation model of the coarse-grained soil. In each loading analysis step, the current simulation state data is collected in real time, and the uncertainty analysis of the simulation state data is performed using a Bayesian neural network to generate the cognitive uncertainty value of the structure prediction. The specific steps are as follows: Extract the strain increment tensor and historical stress tensor of the true triaxial finite element simulation model of the coarse-grained soil at the current loading step to form the simulation state data. The simulation state data is input into a pre-trained Bayesian neural network; Multiple stress prediction samples are obtained by performing multiple forward propagations on the Bayesian neural network using the Monte Carlo Dropout sampling method. Calculate the statistical distribution characteristics of the multiple stress prediction samples, and quantify the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics.

[0008] Preferably, in the step of calculating the statistical distribution characteristics of the plurality of stress prediction samples and quantifying the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics, the constitutive prediction cognitive uncertainty value is calculated using the following cognitive uncertainty quantification formula: ; in, This represents the dimensionless constitutive prediction cognitive uncertainty value. Represents the stress normalization constant. This represents the total number of Monte Carlo samplings. Indicates the current sampling sequence number. Indicates the first The stress prediction scalar value obtained from the second sampling. This represents the average of all sampled stress prediction scalar values. This indicates the weight of the strain rate sensitivity coefficient. This represents the strain increment norm of the current analysis step. This represents the reference strain threshold constant.

[0009] Preferably, the steps of combining the simulation state data with the constitutive prediction cognitive uncertainty value to form a current state vector, inputting the current state vector into the step-size adaptive control agent, and outputting the strain loading increment step size of the current analysis step are as follows: The physical quantities in the simulation state data are normalized, and the normalized data is concatenated with the constitutive prediction cognitive uncertainty value to generate the current state vector. The current state vector is input into the Actor network of the step-size adaptive control agent; The original action values ​​are obtained from the output layer of the Actor network using a Gaussian distribution sampling strategy. The original action value is mapped to the range of the physically allowed minimum and maximum step size to obtain the strain loading increment step size of the current analysis step.

[0010] Preferably, the step of performing trial calculations on the true triaxial finite element simulation model of the coarse-grained soil using the strain loading increment step size, and calculating the value of the reward function based on the convergence state and iteration number of the trial calculation results, specifically includes: Perform Newton-Raphson iterative calculations and calculate the value of the reward function using the convergence efficiency reward scoring formula, which is as follows: ; in, This represents the value of the reward function. This represents the iteration efficiency weighting coefficient. This represents the actual number of iterations or the preset maximum penalty number when calculating divergence. This represents the expected number of preset optimal iterations. This represents the uncertainty avoidance weighting coefficient. This represents the constitutive prediction cognitive uncertainty value of the current analysis step. Represents the hyperbolic tangent function. This represents the divergence penalty coefficient. This represents the divergence state indicator factor, which is 1 when calculating divergence and 0 when calculating convergence.

[0011] Preferably, the step-size adaptive control agent includes an Actor network and a Critic network, and the step of updating the network parameters of the step-size adaptive control agent using the value of the reward function is specifically as follows: Store the current state vector, the strain loading increment step size, the value of the reward function, and the state vector at the next moment into the experience replay buffer; Randomly extract batches of sample data from the experience replay buffer; Calculate the advantage function and use the truncated objective function to calculate the policy gradient loss; The weight parameters of the Actor network and the Critic network in the step-size adaptive control agent are updated by the backpropagation algorithm to maximize the cumulative expected reward.

[0012] Compared with the prior art, the advantages and positive effects of the present invention are as follows: This invention constructs a finite element simulation model by acquiring three-dimensional geological parameters and boundary condition data of coarse-grained soil materials. During the loading simulation, simulation state data is collected in real time, and a Bayesian neural network is used for uncertainty analysis to generate a constitutive prediction cognitive uncertainty value, thereby quantifying the model's cognitive blind spot regarding the current stress-strain state. The simulation state data and cognitive uncertainty value are combined to form a current state vector, which is input into a deep reinforcement learning framework for decision-making. The optimal strain loading increment step size for the current analysis step is output, achieving dynamic adaptive adjustment of the loading rate. Trial calculations are performed using the loading increment step size, and the reward function value is calculated based on the convergence state and iteration count of the trial calculation results to update the network parameters, allowing the control strategy to continuously evolve through interaction with the environment. This mechanism can identify dangerous regions with highly nonlinear constitutive relations or near-singular stiffness matrices. In these regions, the step size is automatically reduced to ensure computational convergence, while the step size is increased in stable regions to improve computational efficiency. This solves the problem that traditional fixed step sizes or simple adaptive step sizes easily lead to computational divergence or excessive iterations under complex stress paths, improving the computational stability of true triaxial numerical simulations of coarse-grained soils. Attached Figure Description

[0013] Figure 1This is a schematic diagram of the steps of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0015] Please see Figure 1 This invention provides a technical solution: a numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects, comprising the following steps: Obtain the three-dimensional geological parameters and boundary condition data of coarse-grained soil material, and construct a true triaxial finite element simulation model of coarse-grained soil based on the three-dimensional geological parameters and boundary condition data; Construct a step-size adaptive control agent based on deep reinforcement learning, and define the state space, action space and reward function of the step-size adaptive control agent; A true triaxial finite element simulation model of coarse-grained soil was run to simulate loading. In each loading analysis step, the current simulation state data was collected in real time. Bayesian neural network was used to perform uncertainty analysis on the simulation state data to generate the cognitive uncertainty value of the structure prediction. The simulation state data is combined with the constitutive prediction cognitive uncertainty value to form the current state vector. The current state vector is input into the step size adaptive control agent and the strain loading increment step size of the current analysis step is output. The true triaxial finite element simulation model of coarse-grained soil was tested using the strain loading increment step. The value of the reward function was calculated based on the convergence state and iteration number of the test results. The network parameters of the step-size adaptive control agent were updated using the value of the reward function until the true triaxial finite element simulation model of coarse-grained soil completed the simulation of all loading paths.

[0016] In this embodiment, the steps for acquiring the three-dimensional geological parameters and boundary condition data of coarse-grained soil material and constructing a true triaxial finite element simulation model of coarse-grained soil based on the three-dimensional geological parameters and boundary condition data are as follows: collecting the initial void ratio, particle size distribution curve, and relative density data of the coarse-grained soil sample; establishing an initial nonlinear constitutive relation matrix based on the initial void ratio, particle size distribution curve, and relative density data; mapping the initial nonlinear constitutive relation matrix to the finite element mesh nodes; setting the displacement constraint boundaries of the three principal stress directions of the true triaxial loading chamber; and generating a true triaxial finite element simulation model of coarse-grained soil.

[0017] Specifically, in indoor testing environments or field surveys, a large true triaxial apparatus is used to test the physical and mechanical properties of selected coarse-grained soil samples. A high-precision laser particle size analyzer combined with sieving is used to determine the particle size distribution curve of the samples, recording the mass percentage of different particle size components to form a continuous distribution data stream. Simultaneously, the initial void ratio of the samples is determined using the vacuum saturation method. The minimum and maximum dry densities of the samples are measured using a relative density meter on a standard vibration table, and the relative density data is calculated. The obtained initial void ratio is set to a specific value between 0.3 and 0.8, for example, 0.55. The relative density is set to 0.65 to represent a medium-dense state. The non-uniformity coefficient and curvature coefficient are calculated based on the particle size distribution curve. Based on these physical indicators, nonlinear fitting is performed using the empirical formula of the Duncan-Chang EB model to calculate the tangent modulus and bulk modulus parameters. An initial model including the tangent elastic modulus, tangent bulk modulus, and stress level-related power exponent is constructed. A nonlinear constitutive relation matrix, a 6x6 tangent stiffness matrix, is used to describe the incremental stress-strain relationship of coarse-grained soil under the current stress state. Then, the mesh node coordinate file in the finite element analysis software is read, and the spatial coordinates of each hexahedral element node are traversed. The calculated initial nonlinear constitutive relation matrix is ​​discretized using shape function interpolation and assigned to each integration point, ensuring that each element has independent material properties. When setting boundary conditions, the six faces corresponding to the true triaxial loading chamber in the model are identified, the vertical displacement degree of freedom of the bottom face is locked, and the normal displacement degree of freedom of the sides is restricted. According to the stress path requirements of the true triaxial test, corresponding displacement constraint boundaries or force boundaries are applied in the three principal stress directions: the major principal stress direction, the intermediate principal stress direction, and the minor principal stress direction. For example, a constant confining pressure constraint is applied in the minor principal stress direction, and a fixed proportion of lateral pressure is applied in the intermediate principal stress direction, generating a true triaxial finite element simulation model of coarse-grained soil.

[0018] In this embodiment, the steps for constructing a step-size adaptive control agent based on deep reinforcement learning and defining the state space, action space, and reward function of the step-size adaptive control agent are as follows: A proximal policy optimization algorithm is used as the decision algorithm for the step-size adaptive control agent; an Actor-Critic dual neural network architecture containing an Actor network and a Critic network is constructed; the state space is defined to include the unbalanced force norm, tangent stiffness matrix condition number, triaxial principal stress ratio, and constitutive prediction cognitive uncertainty value of the current analysis step; the action space is defined as a continuous interval of values, corresponding to the strain loading increment step size of the next increment step; and a reward function is configured to minimize the number of nonlinear iterations.

[0019] Specifically, a deep learning framework based on Python is built, employing the Proximal Policy Optimization (PPO) algorithm as the core method for optimizing policy gradients. An Actor-Critic dual neural network architecture is established, where the Actor network is responsible for outputting action policies. Its structure is a fully connected neural network, with the number of neurons in the input layer matching the dimension of the state space, containing three hidden layers, each with 128 neurons. The ReLU activation function is used to increase non-linear mapping capability. The output layer contains two neurons representing the mean and standard deviation of a Gaussian distribution, used to generate continuous actions. The Critic network is responsible for evaluating state values, with a structure similar to the Act... The network is similar, but the output layer has only one neuron to output the predicted value V of the current state. When defining the state space, a data interface program is written to capture key indicators in real time during the finite element calculation process. The unbalanced force norm of the current analysis step is logarithmically processed to adapt to residual changes of different orders of magnitude. The ratio of the maximum to the minimum singular value obtained by the singular value decomposition (SVD) of the tangent stiffness matrix is ​​used as the condition number. The principal stress coefficient b value in the current calculation of the three principal stress components is extracted as the representation of the triaxial principal stress ratio. Combined with the cognitive uncertainty value obtained from subsequent calculations, the features of these four dimensions are combined into a state vector. The action space is defined as the interval [1e-6, The continuous floating-point values ​​within [1e-2] directly correspond to the strain loading increment step size of the next increment step in the finite element analysis. The normalized action values ​​output by the Actor network are transformed into this physical interval through linear mapping. For example, when the network output is 0, it is mapped to the baseline step size 1e-4. When configuring the reward function, the baseline reward value is set to the reciprocal of the number of iterations, that is, the fewer the number of nonlinear iterations, the higher the reward value. At the same time, a penalty term is set. When the condition number of the stiffness matrix exceeds the preset singular threshold, such as 1e12, a large negative reward, such as -100, is given. This guides the agent to choose the largest possible step size to reduce the total number of analysis steps while ensuring computational convergence. The reward function is used to minimize the number of nonlinear iterations.

[0020] In this embodiment, a true triaxial finite element simulation model of coarse-grained soil is run for loading simulation. In each loading analysis step, the current simulation state data is collected in real time. The steps of using a Bayesian neural network to perform uncertainty analysis on the simulation state data and generate constitutive prediction cognitive uncertainty value are as follows: extract the strain increment tensor and historical stress tensor of the true triaxial finite element simulation model of coarse-grained soil in the current loading step to form simulation state data. Input the simulation state data into a pre-trained Bayesian neural network. Perform multiple forward propagations on the Bayesian neural network using the Monte Carlo Dropout sampling method to obtain multiple stress prediction samples. Calculate the statistical distribution characteristics of the multiple stress prediction samples. Quantify the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics.

[0021] Specifically, after each incremental step calculation is completed using the post-processing interface of the finite element method software (such as Odb Access), the strain increment tensor at the key integration points in the model is extracted. This tensor contains three normal strain components and three shear strain components. Simultaneously, the cumulative historical stress tensor experienced at this integration point is read. These two second-order tensors are flattened into a one-dimensional array containing 12 components, which serves as the input features for a Bayesian neural network. This Bayesian neural network is pre-trained on an offline database containing various coarse-grained soil stress paths. The network structure includes a Dropout layer with a Dropout rate of 0.3, meaning that 30% of the neurons are randomly deactivated during each forward propagation. The assembled simulation state data is input into this network, and the Monte Carlo Dropout sampling procedure is initiated, maintaining... With the input data unchanged, the Dropout function in training mode is forcibly enabled, and forward propagation calculations are performed M times (e.g., 50 times). Each propagation generates a slightly different stress prediction sample due to the random sparsity of the neuron connection structure. These 50 stress prediction samples are collected to form a prediction set. For each sample in the set, the corresponding equivalent deviatoric stress or octahedral shear stress scalar value is calculated. The variance and standard deviation of these 50 scalar values ​​are calculated using statistical methods. The standard deviation reflects the degree of cognitive uncertainty of the model regarding the current input state. If the data distribution is compact, it indicates that the network is familiar with the state; otherwise, it indicates that it is in an unexplored region. The constitutive prediction cognitive uncertainty value is quantified based on the statistical distribution characteristics.

[0022] In this embodiment, in the step of calculating the statistical distribution characteristics of multiple stress prediction samples and quantifying the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics, the constitutive prediction cognitive uncertainty value is calculated using the following cognitive uncertainty quantification formula: ,in, This represents the dimensionless constitutive prediction cognitive uncertainty value. Represents the stress normalization constant. This represents the total number of Monte Carlo samplings. Indicates the current sampling sequence number. Indicates the first The stress prediction scalar value obtained from the second sampling. This represents the average of all sampled stress prediction scalar values. This indicates the weight of the strain rate sensitivity coefficient. This represents the strain increment norm of the current analysis step. This represents the reference strain threshold constant.

[0023] Specifically, the constitutive prediction cognitive uncertainty value is calculated using the following formula for quantifying cognitive uncertainty: ; in, This represents the dimensionless constitutive prediction cognitive uncertainty value. It is a scalar greater than or equal to 0, used to quantify the reliability of the current constitutive model's predictions; a larger value indicates a less reliable model. This represents the stress normalization constant, typically taken as the initial confining pressure at the start of the test, such as 300 kPa, or the standard atmospheric pressure of 100 kPa. It is used to eliminate the influence of the physical dimensions of stress, ensuring that the first term in the formula becomes a dimensionless coefficient. This represents the total number of Monte Carlo sampling iterations. In this embodiment, the number of iterations is set to 50 to ensure that the statistical results are sufficiently representative and the computational cost is controllable. This represents the current sampling sequence number, with a value ranging from 1 to... An integer, used to iterate through the result of each forward propagation. Indicates the first The stress prediction scalar value obtained from the second sampling, specifically referring to the first... The generalized shear stress is calculated from the stress tensor output by the sub-Monte Carlo Dropout forward propagation. Value, in kPa. This represents the average of all sampled stress prediction scalar values, i.e., by... All samples obtained from the second sampling Add and then divide The average value obtained, in kPa, represents the expected predicted output of the model under the current state. This represents the strain rate sensitivity coefficient weight, an empirical constant set according to the rate sensitivity of coarse-grained soil materials. For conventional coarse-grained soils, it can be set to a value between 0.5 and 2.0, for example, 1.0. This is used to adjust the amplification effect of the strain increment on uncertainty. This represents the strain increment norm of the current analysis step, i.e., the Frobenius norm of the strain increment tensor input in the current increment step, reflecting the severity of the current loading step. This represents the reference strain threshold constant, which is set to 0.001 (i.e., 0.1% strain) based on material testing experience. It serves as a benchmark for measuring the magnitude of strain increments to prevent the denominator from being too small, which could lead to numerical instability.

[0024] In this embodiment, the steps of combining the simulation state data with the constitutive prediction cognitive uncertainty value to form the current state vector, and inputting the current state vector into the step-size adaptive control agent to output the strain loading increment step size of the current analysis step are as follows: the physical quantities in the simulation state data are normalized, the normalized data is concatenated with the constitutive prediction cognitive uncertainty value to generate the current state vector, the current state vector is input into the Actor network of the step-size adaptive control agent, the original action value is obtained from the output layer of the Actor network through a Gaussian distribution sampling strategy, and the original action value is mapped to the physically allowed minimum and maximum step size range to obtain the strain loading increment step size of the current analysis step.

[0025] Specifically, the physical quantities in the simulation state data are standardized using the Z-score standardization method (subtracting the historical mean from the current value and then dividing by the historical standard deviation) or the Min-Max normalization method (mapping the unbalanced force norm to the 0-1 interval, mapping the logarithm of the condition number to the 0-1 interval, and directly using the triaxial principal stress ratio as a value between 0 and 1). These normalized physical characteristic data are then sequentially concatenated with the dimensionless constitutive prediction cognitive uncertainty value calculated in the previous step to form a dimensionless constitutive prediction cognitive uncertainty value. (For example The one-dimensional feature vector of the signal is used as the current state vector. This current state vector is input into the input layer of the Actor network for the step-size adaptive control agent. The signal is then propagated to the output layer after a linear transformation and ReLU activation in the hidden layer. The output layer outputs the mean of the action distribution. and logarithmic standard deviation By using a Gaussian distribution sampling strategy, Centered on Construct a normal distribution for the standard deviation, and randomly sample a value from it as the original action value. To ensure physical feasibility, the hyperbolic tangent function tanh is used to... Compress it to the interval (-1, 1), and then map it to the physically allowed minimum step size through a linear transformation. (e.g., 1e-6) and maximum step size (For example, within the range of 1e-3), the calculation formula is: This yields the strain loading increment step size for the current analysis step.

[0026] In this embodiment, the trial calculation of the true triaxial finite element simulation model of coarse-grained soil is performed using the strain loading increment step. The specific steps for calculating the reward function value based on the convergence state and iteration number of the trial calculation results are as follows: Newton-Raphson iteration calculation is performed, and the reward function value is calculated using the convergence efficiency reward scoring formula. The convergence efficiency reward scoring formula is as follows: ,in, This represents the value of the reward function. This represents the iteration efficiency weighting coefficient. This represents the actual number of iterations or the preset maximum penalty number when calculating divergence. This represents the expected number of preset optimal iterations. This represents the uncertainty avoidance weighting coefficient. This represents the constitutive prediction cognitive uncertainty value of the current analysis step. Represents the hyperbolic tangent function. This represents the divergence penalty coefficient. This represents the divergence state indicator factor, which is 1 when calculating divergence and 0 when calculating convergence.

[0027] Specifically, the calculated strain loading increment step size is submitted to the finite element solver, and Newton-Raphson iterative calculations are performed. In each iteration, the residual force norm is checked to see if it is less than the preset convergence tolerance (e.g., 1e-3). If the residual force meets the convergence criterion within the preset maximum number of iterations (e.g., 10), it is considered convergent; otherwise, it is considered divergent. The actual number of iterations required to reach the convergence criterion is recorded, and the value of the reward function is calculated using the convergence efficiency reward scoring formula. The convergence efficiency reward scoring formula is as follows: ; in, This represents the value of the reward function, which serves as an immediate feedback signal for reinforcement learning. This represents the iteration efficiency weighting coefficient, which takes a positive value, such as 2.0, and is used to adjust the proportion of computational efficiency in the total reward. This represents the actual number of iterations or the preset maximum penalty number when calculating divergence. When calculating convergence, it takes the actual number of iterations used (e.g., 3 steps); when calculating divergence, it takes the preset upper limit (e.g., 15 steps). This represents the expected number of iterations, typically set to 3 to 5 based on experience, representing the ideal convergence speed. This represents the uncertainty avoidance weighting coefficient, which takes a positive value, such as 1.5, and is used to incentivize the agent to operate in regions of lower uncertainty. This represents the constitutive prediction cognitive uncertainty value of the current analysis step, and its value is derived from the calculation results of the previous steps. This represents the hyperbolic tangent function, used to map uncertainty values ​​to the (0, 1) interval to facilitate the calculation of avoidance terms. This represents the divergence penalty coefficient, taken as a large positive number such as 10.0, used to severely punish divergent behavior. This represents the divergence state indicator factor, which is a Boolean indicator variable. It takes the value 1 when the finite element calculation fails to converge within the maximum number of iterations, resulting in divergence, and takes the value 0 when the calculation successfully converges.

[0028] In this embodiment, the step-size adaptive control agent includes an Actor network and a Critic network. The specific steps for updating the network parameters of the step-size adaptive control agent using the reward function are as follows: the current state vector, the strain loading increment step size, the reward function value, and the state vector at the next time step are stored in the experience replay buffer; a batch of sample data is randomly extracted from the experience replay buffer; the advantage function is calculated; the policy gradient loss is calculated using the truncated objective function; and the weight parameters of the Actor network and the Critic network in the step-size adaptive control agent are updated through the backpropagation algorithm to maximize the accumulated expected reward.

[0029] Specifically, after each simulation step, the current time step's state vector, the agent's action (i.e., the strain loading increment step size), the reward function value from the environmental feedback, the next time step's state vector, and a mask flag indicating whether the simulation has ended are combined to form a trajectory data set. This data is stored in an experience replay buffer with a capacity of 2048 data points. When the buffer is full, the parameter update process is initiated. A batch of 64 samples is randomly selected from the experience replay buffer, and the generalized advantage estimation (GAE) algorithm is used to calculate the advantage function. The discount factor is set. and GAE parameters Simultaneously, the mean squared error between the target value and the output value of the Critic network is calculated as the value loss. The policy gradient loss is calculated using the truncated objective function, and the truncation range is set. To limit the policy update magnitude, the total loss function is obtained by weighted summation of the policy gradient loss, value loss, and entropy regularization term. The gradient of the total loss with respect to the weights of the Actor and Critic networks is calculated using the backpropagation algorithm. The network parameters are then updated using the Adam optimizer with a learning rate of 3e-4. This process is repeated multiple times (e.g., 10 epochs) to maximize the cumulative expected reward.

[0030] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications 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 protection scope of the present invention.

Claims

1. A numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effects, characterized in that, Includes the following steps: Obtain the three-dimensional geological parameters and boundary condition data of coarse-grained soil material, and construct a true triaxial finite element simulation model of coarse-grained soil based on the three-dimensional geological parameters and boundary condition data; Construct a step-size adaptive control agent based on deep reinforcement learning, and define the state space, action space and reward function of the step-size adaptive control agent; The coarse-grained soil true triaxial finite element simulation model is run for loading simulation. In each loading analysis step, the current simulation state data is collected in real time. Bayesian neural network is used to perform uncertainty analysis on the simulation state data to generate the structural prediction cognitive uncertainty value. The simulation state data is combined with the constitutive prediction cognitive uncertainty value to form the current state vector. The current state vector is input into the step size adaptive control agent, and the strain loading increment step size of the current analysis step is output. The strain loading increment step size is used to perform trial calculations on the true triaxial finite element simulation model of the coarse-grained soil. The value of the reward function is calculated based on the convergence state and iteration number of the trial calculation results. The value of the reward function is used to update the network parameters of the step size adaptive control agent until the true triaxial finite element simulation model of the coarse-grained soil completes the simulation of all loading paths.

2. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 1, characterized in that, The specific steps for obtaining the three-dimensional geological parameters and boundary condition data of coarse-grained soil material, and constructing a true triaxial finite element simulation model of coarse-grained soil based on the three-dimensional geological parameters and boundary condition data are as follows: Initial void ratio, particle size distribution curve and relative density data of coarse-grained soil samples were collected; An initial nonlinear constitutive matrix is ​​established based on the initial void ratio, particle size distribution curve, and relative density data. The initial nonlinear constitutive relation matrix is ​​mapped to the finite element mesh nodes, and the displacement constraint boundaries of the three principal stress directions of the true triaxial loading chamber are set to generate the true triaxial finite element simulation model of the coarse-grained soil.

3. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 1, characterized in that, The specific steps for constructing a step-size adaptive control agent based on deep reinforcement learning, and defining the state space, action space, and reward function of the step-size adaptive control agent, are as follows: The proximal policy optimization algorithm is adopted as the decision-making algorithm for the step size adaptive control agent, and an Actor-Critic dual neural network architecture containing an Actor network and a Critic network is constructed. The state space is defined to include the unbalanced force norm, tangent stiffness matrix condition number, triaxial principal stress ratio, and constitutive prediction cognitive uncertainty value of the current analysis step; The action space is defined as a continuous interval of values, and the values ​​correspond to the strain loading increment step size of the next increment step; Configure the reward function, which is used to minimize the number of nonlinear iterations.

4. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 1, characterized in that, The coarse-grained soil true triaxial finite element simulation model is run for loading simulation. In each loading analysis step, the current simulation state data is collected in real time. The Bayesian neural network is used to perform uncertainty analysis on the simulation state data to generate the cognitive uncertainty value of the structure prediction. The specific steps are as follows: Extract the strain increment tensor and historical stress tensor of the coarse-grained soil true triaxial finite element simulation model at the current loading step to form the simulation state data. The simulation state data is input into a pre-trained Bayesian neural network; Multiple stress prediction samples are obtained by performing multiple forward propagations on the Bayesian neural network using the Monte Carlo Dropout sampling method. Calculate the statistical distribution characteristics of the multiple stress prediction samples, and quantify the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics.

5. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 4, characterized in that, In the step of calculating the statistical distribution characteristics of the multiple stress prediction samples and quantifying the constitutive prediction cognitive uncertainty value based on the statistical distribution characteristics, the constitutive prediction cognitive uncertainty value is calculated using the following cognitive uncertainty quantification formula: ； in, This represents the dimensionless constitutive prediction cognitive uncertainty value. Represents the stress normalization constant. This represents the total number of Monte Carlo samplings. Indicates the current sampling sequence number. Indicates the first The stress prediction scalar value obtained from the second sampling. This represents the average of all sampled stress prediction scalar values. This indicates the weight of the strain rate sensitivity coefficient. This represents the strain increment norm of the current analysis step. This represents the reference strain threshold constant.

6. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 3, characterized in that, The steps of combining the simulation state data with the constitutive prediction cognitive uncertainty value to form the current state vector, inputting the current state vector into the step-size adaptive control agent, and outputting the strain loading increment step size of the current analysis step are as follows: The physical quantities in the simulation state data are normalized, and the normalized data is concatenated with the constitutive prediction cognitive uncertainty value to generate the current state vector. The current state vector is input into the Actor network of the step-size adaptive control agent; The original action values ​​are obtained from the output layer of the Actor network using a Gaussian distribution sampling strategy. The original action value is mapped to the range of the physically allowed minimum and maximum step size to obtain the strain loading increment step size of the current analysis step.

7. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 5, characterized in that, The steps for performing trial calculations on the true triaxial finite element simulation model of the coarse-grained soil using the strain loading increment step size, and calculating the value of the reward function based on the convergence state and iteration number of the trial calculation results are as follows: Perform Newton-Raphson iterative calculations and calculate the value of the reward function using the convergence efficiency reward scoring formula, which is as follows: ； in, This represents the value of the reward function. This represents the iteration efficiency weighting coefficient. This represents the actual number of iterations or the preset maximum penalty number when calculating divergence. This represents the expected number of preset optimal iterations. This represents the uncertainty avoidance weighting coefficient. This represents the constitutive prediction cognitive uncertainty value of the current analysis step. Represents the hyperbolic tangent function. This represents the divergence penalty coefficient. This represents the divergence state indicator factor, which is 1 when calculating divergence and 0 when calculating convergence.

8. The numerical simulation method for true triaxial tests of coarse-grained soil materials based on principal stress effect according to claim 7, characterized in that, The step-size adaptive control agent includes an Actor network and a Critic network. The specific steps for updating the network parameters of the step-size adaptive control agent using the value of the reward function are as follows: Store the current state vector, the strain loading increment step size, the value of the reward function, and the state vector at the next moment into the experience replay buffer; Randomly extract batches of sample data from the experience replay buffer; Calculate the advantage function and use the truncated objective function to calculate the policy gradient loss; The weight parameters of the Actor network and the Critic network in the step-size adaptive control agent are updated by backpropagation algorithm to maximize the cumulative expected reward.

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