Data-Driven Multiscale Constitutive Modelling Of Dam-Building Granular Materials

As a material second only to liquids in nature,granular materials are widely used in hydraulic structures,roads,bridges and etc.Dam-building granular materials are complex systems of pore structures and continuously graded rock particles.An accurate description of their mechanical properties is essential for the safety analysis of ultrahigh rockfill dams.At the microscopic scale,granular materials are discrete elementary systems aggregated by complex internal interactions,and their microscopic mechanical structure and statistical characteristics influence the macroscopic mechanical properties;at the macroscopic scale,especially in engineering-scale computational analysis,granular materials are often regarded as continuous media and their constitutive relationship is by non-linear or elastic-plastic theory,however,there is no unified theory to characterize all their stress-deformation properties.The constitutive modelling is one of the most crucial topics in macro-mechanical calculations.An accurate description of the relationship between deformation and mechanical response is the basis for BVP analysis.Due to the rise of machine learning methods in regression analysis,they are expected to improve the constitutive modelling and outperform the classical mathematical formula-based models.Massive efforts has been made to introduce machine learning into mechanics calculations and evaluating its performance.This Ph D thesis centers on the use of machine learning methods to investigate the possibilities of constructing a constitutive model of granular materials and utilize it in BVP calculations.The main research includes the following aspects:1.We present a deep learning model for reproducing the macroscopic mechanical response of granular materials with different PSD and initial states under different loading paths(Chapter 2).The granular material stress-strain data are extracted from DEM simulations and then the mechanical behavior of the granular material is learnt from the material dataset using the long short term memory network LSTM.Three main issues are involved: modification of the LSTM cell,stress-strain sampling of the granular material and parameterization of the loading history.2.For the different loading and unloading paths in the conventional triaxial simulation of the DEM,an Active Learning approach is introduced to guide the sampling(Chapter 3).Based on the positive correlation between the prediction error and the variance of the multi-model predictions,the strain paths were evaluated without DEM unloading simulations,from which the worst predicted paths were selected for sampling.To prevent data redundancy,points in the vicinity of one selected point will not be selected for the current resampling round.The model was trained on singlecyclic loading datasets and demonstrated excellent prediction accuracy under multiplecyclic loadings.3.In order to circumvent the reliance on phenomenological assumptions in BVP analysis,a computational framework coupled with FEM and ML(FEM-ML)is proposed(Chapter 4).Building on the work in Chapters 2 and 3,we further introduce FEM-DEM multiscale simulations by employing the Random Gaussian Process to generate macroscopic random loading paths to be applied to the macro-scale model.A large amount of stress-strain data is collected from the Gauss points of the FEM model and they(part of them)are subsequently,used to train the neural network.Parametric material deformation histories are used to represent the loading histories.Active learning is employed here again to assess the informativeness of the data points,according which the points are effectively resampled from the massive database.Two examples are provided to demonstrate the effectiveness of the implemented FEM-ML framework.The results show that the FEM-ML framework provides considerable improvements in computational efficiency and ability to reproduce the mechanical response of granular materials at the macroscopic scale.4.In Chapter 5 we embed the trained network-based constitutive model into the explicit FEM solver.In implicit FEM solvers for non-linear static problems,a global equilibrium solution is typically obtained via Newton-Raphson iteration.However,the non-linear iterations may not converge when the neural network is not sufficiently accurate in predicting the tangential matrix.Therefore,we integrated the explicit FEM solver over time,circumventing non-linear iteration.The network was trained and investigated on data generated from two constitutive models(IME model and CSUH model)separately.The trained network is able to reproduce almost exactly the results of the two classical constitutive models at the macroscopic level,however,the error accumulation problem resulting from large number of steps in time integration is another challenge to the prediction accuracy and robustness of the data-driven constitutive model.A check-and-revision method is proposed to iteratively optimize the model by expanding the training range and improving the network generalization capability.5.A machine learning material cell is proposed based on the recurrent structure and traditional constitutive model.Thanks to the powerful mapping capability of neural networks,the purely data-driven approach,is able to accurately reproduce the constitutive response of materials without introducing assumptions,but once the input strain exceeds the training space,the prediction accuracy drops dramatically to an unacceptable level.Therefore,we introduce the widely accepted elasticity theory,yielding,hardening and plastic flow as physical constraints in the intrinsic constitutive model to build a material cell-based machine learning constitutive model.This constraint acts as an a priori condition for the machine learning model: at the sample preparation stage,it can alleviate the stringent requirements for sample preparation completeness;at the model calculation,it can guide the model to calculate the mechanical response based on the a priori condition for different loading paths.The proposed model is calibrated on rigid strip footing and biaxial simulations respectively,and then tested on retaining wall simulations.