利用三维离散元法和卷积神经网络预测粒状土的压缩模量

Tongwei Zhang, Shuang Li, Huanzhi Yang, Fanyu Zhang*

(Key Laboratory of Mechanics on Disaster and Environment in Western China, MOE, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou,730000, China)

Abstract: To efficiently predict the mechanical parameters of granular soil based on its random micro-structure,this study proposed a novel approach combining numerical simulation and machine learning algorithms. Initially, 3500 simulations of one-dimensional compression tests on coarse-grained sand using the three-dimensional (3D) discrete element method (DEM) were conducted to construct a database. In this process, the positions of the particles were randomly altered, and the particle assemblages changed. Interestingly, besides confirming the influence of particle size distribution parameters, the stress-strain curves differed despite an identical gradation size statistic when the particle position varied. Subsequently, the obtained data were partitioned into training, validation, and testing datasets at a 7:2:1 ratio. To convert the DEM model into a multi-dimensional matrix that computers can recognize, the 3D DEM models were first sliced to extract multi-layer two-dimensional (2D) cross-sectional data. Redundant information was then eliminated via gray processing, and the data were stacked to form a new 3D matrix representing the granular soil’s fabric. Subsequently, utilizing the Python language and Pytorch framework, a 3D convolutional neural networks (CNNs) model was developed to establish the relationship between the constrained modulus obtained from DEM simulations and the soil’s fabric. The mean squared error (MSE) function was utilized to assess the loss value during the training process. When the learning rate (LR) fell within the range of 10^-5-10^-1, and the batch sizes (BSs) were 4, 8, 16, 32, and 64, the loss value stabilized after 100 training epochs in the training and validation dataset. For BS = 32 and LR = 10^-3, the loss reached a minimum. In the testing set, a comparative evaluation of the predicted constrained modulus from the 3D CNNs versus the simulated modulus obtained via DEM reveals a minimum mean absolute percentage error (MAPE) of 4.43% under the optimized condition, demonstrating the accuracy of this approach. Thus, by combining DEM and CNNs, the variation of soil’s mechanical characteristics related to its random fabric would be efficiently evaluated by directly tracking the particle assemblages.

Keywords: Soil structure；Constrained modulus；Discrete element model (DEM)；Convolutional neural networks (CNNs)；Evaluation of error

Fig. 3. Particle size distribution curves in DEM model: (a) d₅₀ = 0.8, 1, 1.2 and 1.4 mm; and (b) d = 0.9-1.1, 0.8-1.2, 0.7-1.3 and 0.6-1.4 mm.

Fig. 5. Modeling methodology and training process

Fig. 6. Architecture of CNNs in this study.

Fig. 7. Stress-strain curves of quartz sand using DEM simulation: (a) Effect of mean particle sizes, (b) Effect of particle size distribution ranges, and (c) Impact of random repetitions.

Fig. 8. Representative loss variation with epochs and batches when LR is 10^-5 and BS = 4, 8, 16, 32, 64: (a) Loss of each batch in the training set, and (b) Average loss of each epoch in the training and validation sets.

Fig. 9. Loss on validation set after model optimization of 100 epochs varying with BS and LR.

Fig. 10. Relationship between simulated and predicted constrained modulus of 350 testing samples in two groups (blue points: LR = 10^-5 and BS = 64; red points: LR = 10^-3 and BS = 32).

Zhang T et al., Prediction of constrained modulus for granular soil using 3D discrete element method and convolutional neural networks, Journal of Rock Mechanics and Geotechnical Engineering,

https://doi.org/10.1016/j.jrmge.2024.02.005