published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

No description available.

published_or_final_version / abstract / Civil Engineering / Doctoral / Doctor of Philosophy

In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework. The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales. To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing. To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques.

Not available / text

Computer simulations for civil and mechanical engineering that efficiently leverage computational resources to solve boundary value problems have pervasive impacts on many aspects of civilization, including manufacturing, communication, transportation, medicine, and defense. Conventionally, a solver that predicts the mechanical behaviors of solids requires constitutive laws that represent mechanisms not directly derived from balance principles. These mechanisms are often characterized by mathematical models validated and tested via tabulated data, organized in grids or, more broadly, within normed Euclidean space (e.g., principle stress space, Mohr circle). These mathematical models often involved mapping between/among normed vector spaces that adhere to physical constraints. This methodology has manifested frameworks such as hyperelastic energy functional, elastoplasticity models with evolving internal variables, cohesive zone models for fracture, etc. However, the geometry of material data plays a crucial role in the efficiency, accuracy, and robustness of predictions. This thesis introduces a collection of mathematical models, tools, algorithms, and frameworks that, when integrated, may unleash the potential of leveraging data geometry to advance solid mechanics modeling. In the first part of the thesis, we introduce the concept of treating constitutive data as a manifold. This idea leads to a novel data-driven paradigm called “Manifold Embedding Data-Driven Mechanics,” which incorporates the manifold structure of data into the distance minimization model-free method. By training an invertible artificial neural network (ANN) to embed nonlinear constitutive data onto a hyperplane, we replace the costly combinatoric optimization necessary for the classical model-free paradigm with a projection and, as a result, significantly improve the efficiency and robustness of the model-free approach with a distance measure consistent with the data geometry. This method facilitates consistent interpolation on the manifold, which improves the accuracy when data is limited. To handle noisy data, we relax the invertibility constraint of the designed ANN and construct the desired embedding space via a geometric autoencoder. Unlike the classical autoencoder, which compresses data by reducing the data dimensionality in the latent space, our design focuses on reducing the dimensionality of the data by imposing constraints. This technique enables us to learn a noise-free embedding through a simple projection by assuming the orthogonality between the data and noise. To improve the interpretability and, ultimately, the trustworthiness of machine learning-derived constitutive models, we abandon the design of the fully connected neural networks and instead introduce polynomials in feature space that enable us to turn neural network parametrized black-box models back into mathematical models understandable by engineers. We present geometrically inspired structures in a feature space spanned by univariate ANNs and then learn a sparse representation of the data using these acquired features. Our divide-and-conquer scheme takes advantage of the learned univariate functions to perform parallel symbolic regression, ultimately extracting human-readable equations for material modeling. Our approach mitigates the well-known computational burden associated with symbolic regression for high-dimensional data and data that must adhere to physical constraints. We demonstrate the interpretability, accuracy, and computational efficiency of our algorithm in discovering constitutive models for hyperelastic materials and plastic yield surfaces.

Soil nail walls are a form of mechanical earth stabilization for cut situations. They consist of the introduction of passive inclusions (nails) into soil cut lifts. These nailed lifts are then tied together with a structural facing (usually shotcrete) . The wall lifts are constructed incrementally from the top of cut down. Soil nail walls are being recognized as having potential for large cost savings over other alternatives. The increasing need to provide high capacity roadways in restricted rights of way under structures such as bridges will require increasing use of techniques such as combined soil nail and piling walls. The Swift Delta Soil Nail wall required installing nails between some of the existing pipe piling on the Oregon Slough Bridge. This raised questions of whether the piling would undergo internal stress changes due to the nail wall construction. Thus, it was considered necessary to understand the soil nail wall structure interaction in relation to the existing pile supported abutment. The purpose of this study was to investigate the Swift Delta Wall using finite element (FE) modeling techniques. Valuable data were available from the instrumentation of the swift Delta Wall. These data were compared with the results of the FE modeling. This study attempts to answer the following two questions: 1. Is there potential for the introduction of new bending stresses to the existing piling? 2. Is the soil nail wall system influenced by the presence of the piling? A general purpose FE code called ABAQUS was used to perform both linear and non-linear analyses. The analyses showed that the piling definitely underwent some stress changes. In addition they also indicated that piling influence resulted in lower nail stresses. Comparison of measured data to predicted behavior showed good agreement in wall face deflection but inconsistent agreement in nail stresses. This demonstrated the difficulty of modeling a soil nail due to the many variables resulting from nail installation.

We develop a dual-purpose damage model (DPDM) that can simultaneously model intralayer damage (ply failure) and interlayer damage (delamination) as an alternative to conventional practices that models ply failure by continuum damage mechanics (CDM) and delamination by cohesive elements. From purely computational point of view, if successful, the proposed approach will significantly reduce computational cost by eliminating the need for having double nodes at ply interfaces. At the core, DPDM is based on the regularized continuum damage mechanics approach with vectorial representation of damage and ellipsoidal damage surface. Shear correction factors are introduced to match the mixed mode fracture toughness of an analytical cohesive zone model. A predictor-corrector local-nonlocal regularization scheme, which treats intralayer portion of damage as nonlocal and interlayer damage as local, is developed and verified. Two variants of the DPDM are studied: a single- and two- scale DPDM. For the two-scale DPDM, reduced-order-homogenization (ROH) framework is employed with matrix phase modeled by the DPDM while the inclusion phase modeled by the CDM. The proposed DPDM is verified on several multi-layer laminates with various ply orientations including double-cantilever beam (DCB), end-notch-flexure (ENF), mixed-mode-bending (MMB), and three-point-bending (TPB). The simulation is executed in the platform of FOOF (Finite element solver based on Object-Oriented Fortran). The objective of FOOF is to develop a new architecture of the nonlinear multiphysics finite element code in object oriented Fortran environment. The salient features of FOOF are reusability, extensibility, and performance. Computational efficiency stems from the intrinsic optimization of numerical computing intrinsic to Fortran, while reusability and extensibility is inherited from the support of object-oriented programming style in Fortran 2003 and its later versions. The shortcomings of the object oriented style in Fortran 2003 (in comparison to C++) are alleviated by introducing the class hierarchy and by utilizing a multilevel programming style.

The loads applied to pile foundations installed offshore vary greatly from those encountered onshore, with more substantial lateral and torsional loads. For combined axial and lateral loading the current design practice involves applying an axial load to a deep foundation and assessing the pile behaviour and then considering a lateral load separately. For the problem of an altering directions of lateral loads (e.g. due to changes in the wind directions acting on offshore wind turbines) a clear design procedure is not available. There is thus a need for a clearly established methodology to effectively introduce the interaction between the four different loading directions (two lateral, one axial and one torsional). In this thesis, a model is presented that introduces a series of Winkler elasto-plastic elements coupled between the different directions via local interaction yield surfaces along the pile. The energy based method that is used allows the soil-pile system to be defined explicitly using two equations: the energy potential and the dissipation potential. One of the most interesting applications of this model is to piles subjected to a change in lateral loading direction, where the loading history can significantly influence the pile behaviour. This effect was verified by a series of experimental tests, undertaken using the Geotechnical Centrifuge at UWA. The same theory was then applied to cyclic loading in two dimensions, leading to some very useful conclusions regarding shakedown behaviour. A theoretically based relationship was applied to the local yielding behaviour for a pile subjected to a combination of lateral and axial loading, allowing predictions to be made of the influence of load inclination on the pile behaviour. The ability of this model to represent interaction between four degrees of freedom allows a more realistic approach to be taken to this problem than that considered in current design practice.