A robust adaptive algebraic multigrid linear solver for structural mechanics

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.Comment: 50 pages, 16 figures, submitted to CMAM

A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain

An adaptively stabilized monolithic finite element model is proposed to simulate the fully coupled thermo-hydro-mechanical behavior of porous media undergoing large deformation. We first formulate a finite-deformation thermo-hydro-mechanics field theory for non-isothermal porous media. Projection-based stabilization procedure is derived to eliminate spurious pore pressure and temperature modes due to the lack of the two-fold inf-sup condition of the equal-order finite element. To avoid volumetric locking due to the incompressibility of solid skeleton, we introduce a modified assumed deformation gradient in the formulation for non-isothermal porous solids. Finally, numerical examples are given to demonstrate the versatility and efficiency of this thermo-hydro-mechanical model

A simulation-based software to support the real-time operational parameters selection of tunnel boring machines

With the fact that the main operational parameters of the construction process in mechanized tunneling are currently selected based on monitoring data and engineering experience without exploiting the advantages of computer methods, the focus of this work is to develop a simulation-based real-time assistant system to support the selection of operational parameters. The choice of an appropriate set of these parameters (i.e., the face support pressure, the grouting pressure, and the advance speed) during the operation of tunnel boring machines (TBM) is determined by evaluating different tunneling-induced soil-structure interactions such as the surface settlement, the associated risks on existing structures and the tunnel lining behavior. To evaluate soil-structure behavior, an advanced process-oriented numerical simulation model based on the finite cell method is utilized. To enable the real-time prediction capability of the simulation model for a practical application during the advancement of TBMs, surrogate models based on the Proper Orthogonal Decomposition and Radial Basis Functions (POD-RBF) are adopted. The proposed approach is demonstrated through several synthetic numerical examples inspired by the data of real tunnel projects. The developed methods are integrated into a user-friendly application called SMART to serve as a support platform for tunnel engineers at construction sites. Corresponding to each user adjustment of the input parameters, i.e., each TBM driving scenario, approximately two million outputs of soil-structure interactions are quickly predicted and visualized in seconds, which can provide the site engineers with a rough estimation of the impacts of the chosen scenario on structural responses of the tunnel and above ground structures

Development of a Sensible Reduced-Order Modeling Framework for Geomechanics Simulation: With Application to Coupled Flow and Geomechanics Simulation

With the recent development of unconventional reservoirs, attention has been geared towards the integration of the geomechanical models with traditional flow simulation. A case in point is quantifying rock-fluid interactions in hydraulic fracturing operations. Although much effort has gone into the creation and advancement of commercial simulation software for coupled flow and geomechanics, it is still in its infancy. The models are considerably oversimplified and poorly representative of the problem’s complex nature. Throughout history, several contributions have been made into the development of efficient model-order reduction (MOR) techniques for “flow only” simulations. Yet – to date – contributions to the mechanical models in coupled simulations have been minimal. This study tackles this challenging aspect, by proposing a novel model reduction adaptive workflow, especially for the mechanics simulators, that (1) can be coupled with any simulator that can export mass, stiffness, and load matrices; (2) can achieve 2 orders of magnitude in computational time reduction; and (3) do not add more complexity to the solution. In the first part of this research, several – widely used – reduction techniques for structural mechanics were implemented based on the construction of the dynamic condensation matrix. Single-step reduction methods were first executed; in particular, Guyan DOFs based reduction techniques. Following that, two-step methods were implemented; where corrections were made to the results obtained from the former. Finally, iterative (three-step) reduction methods were applied; handling the problem of master DOFs selection through consistent updates of the dynamic condensation matrix until convergence is achieved. To that end, two schemes are presented; based on the convergence of the dynamic condensation matrix, as well as, the eigenvalues of the reduced-order model. In the second part of this research, we provide a rigorous framework for testing the completeness, efficiency, and convergence for all the presented reduction techniques. Regarding the completeness of the reduced models, two main criteria were investigated; namely, modal assurance criterion (MAC) and singular value decomposition (SVD). For efficiency testing, percent error (PE) of natural frequencies and the correlation coefficient for modal vector (CCFMV) values were considered. Finally, the efficiency of the convergent criterion was demonstrated through the errors associated with the column vectors of the condensation matrix. Several numerical examples are presented to show the efficiency of the presented framework, particularly for coupled simulations. Based on the adopted framework, we managed to reduce the scale of the finite element models to less than 9% of the full model with error as low as 1%. In terms of computational speed and runtime, we achieved substantial speedups; up to 20X. Given the proposed workflow, large-scale complex simulations – similar to those associated with hydraulic fracturing – could be more feasible and less costly. This, ultimately, would give allowance for incorporating the complex physics pertinent to unconventional reservoirs and motivate the advent of their development at no additional cost

Machine Learning-Based Constitutive Modelling for Granular Materials

As a material second only to liquids in nature, granular materials are widely used in hydraulic structures, roads, bridges 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 ultra-high 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 are described using non-linear or elastic-plastic theories. Yet, there is no unified theory to characterise all their constitutive properties. Constitutive modelling stands as a pivotal topic within mechanical calculations. Establishing an accurate description of the relationship between deformation and constitutive response serves as the foundation for Boundary Value Problem analysis. With the growing prominence of machine learning techniques in the data-driven realm, they are expected to enhance constitutive modelling and potentially surpass classical models based on simplifying assumptions. More and more endeavours have been dedicated to integrating machine learning into mechanical calculations and assessing its efficacy. This PhD thesis focuses on the use of machine learning techniques to investigate the feasibility of developing a constitutive model for granular materials and applying it in boundary value problem calculations. The main areas of research include the following aspects:1. In Chapter 2, we introduce a deep learning model designed to reproduce the macroscopic mechanical response of granular materials across various particle size distributions (PSDs) and initial states, considering different loading conditions. We start by extracting stress-strain data from massive DEM simulations and then proceed to capture the mechanical behaviour of these granular materials through the Long Short-Term Memory networks. The work contains three central issues: LSTM cell customisation, granular materials stress-strain sampling, and loading history pasteurisation. The validation results demonstrate that this deep learning model achieves good generalisation and a high level of prediction accuracy when tested on the true triaxial loading dataset.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 uncertainty given by activate learning method, the strain paths are evaluated without DEM simulations, from which the worst predicted paths are 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 single-cyclic loading datasets and performed quite well under multiple-cyclic loading paths.In order to circumvent the reliance on phenomenological assumptions in boundary value problem analysis, a computational framework coupled with FEM and neural network (FEM-NN) is proposed (Chapter 4). Building on the work in Chapter 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 on the integration points is collected. Part of them are subsequently, used to train the neural network. Material loading histories represented by encoded variables. Active learning is employed here again to assess the informativeness of the data points, according to which the points are resampled from the massive database. Two examples are provided to demonstrate the effectiveness of the implemented framework which provides considerable improvements in computational efficiency and the ability to reproduce the mechanical response of granular materials at the macroscopic scale.4. In Chapter 5 the trained network-based constitutive model is embedded 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 predicted tangential matrix is not accurate enough. Therefore, the explicit FEM solver is employed to circumvent non-linear iteration. The network is 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 ground truth results at the macroscopic level. However, the error accumulation problem resulting from a large number of steps is an-other challenge to the prediction accuracy and robustness of the data-driven model. A check-and-revision method is proposed to iteratively optimise the model by expanding the training range and improving the network generalisation.5. Chapter 6 focuses on evaluating the capacity and performance of a network-based material cell with physics extension against boundary-value problems. The proposed material cell aims to reproduce constitutive relationships learned from datasets generated by random loading paths following random Gaussian Process. The material cell demonstrates its effectiveness across three progressively complex constitutive models by incorporating physics-based basis functions as prior/assumptions. An adaptive linear transformation is introduced to mitigate the error caused by magnitude gaps between strain increments in training sets and finite element simulations. The mate- rial cell successfully reproduces constitutive relationships in FEM simulations, and its performance is comprehensively evaluated by comparing two different material cells: the sequentially trained gated recurrent unit (GRU)-based material cell and the one-to-one trained deep network-based material cell. The GRU-based material cell can be trained without prior knowledge about the internal variables. Consequently, this enables us to directly derive the constitutive model using stress-strain data obtained from experiments.6. A universal constitutive model has been introduced, combining the recurrent machine learning structure with traditional constitutive models in Chapter 7. A dramatic drop in prediction accuracy emerges when the input strain exceeds the training space because of the poor generalisation ability of the purely data-driven method. Therefore, we introduce the widely accepted elasticity theory, yielding, hardening and plastic flow as physical constraints to build a machine learning-based universal constitutive model. These constraints serve as priors/assumptions for the machine learning model. During the sample preparation stage, they alleviate the stringent demands for the completeness of data sampling. In the model calculations, they guide the model to make predictions, even for unseen loading paths. The proposed model has been calibrated and tested with FEM-DEM datasets

Model order reduction of coupled thermo-hydro-mechanical processes in geo-environmental applications

Tesi en modalitat de cotutela: Universitat Politècnica de Catalunya i Université libre de BruxellesIn a large number of geo-environmental applications, it is essential to model coupled processes that depend on several design parameters such as material properties and geometrical features. Thermo-hydro-mechanical (THM) processes are, among others, key effects to consider in critical applications such as deep geological repository of hazardous waste. This thesis proposes novel model order reduction strategies to evaluate the thermo-hydro-mechanical response of the material, taking into account the complexities involved in the coupled processes for such applications. To include variability of some design parameters, an a-posteriori model order reduction approach with reduced basis methods is applied to solve the high-dimensional parametric THM system. The reduction is based on an offline-online stage strategy. In the offline stage, reduced subspaces are constructed by a greedy adaptive procedure and in the online stage, multi-subspace projection is performed to quickly obtain the coupled THM response at any value of the design parameter. At the core of the greedy adaptive strategy is a goal-oriented error estimator that guides the selection of optimal design parameters where snapshots are evaluated. To tackle nonlinearity in the form of elasto-plastic material behaviour, the multi-subspace reduced basis method is combined with sub-structuring by domain decomposition. The effectiveness of the model reduction strategies are demonstrated on inverse problems involving large-scale geomodels that depict the coupled response of host rocks in potential deep geological repository sites. Two types of scenarios are considered: (i) the host rock undergoing geomorphological process is investigated as glacier advances over it for a period lasting over thousands of years and (ii) the clay response of an underground research laboratory is modelled numerically to support and validate in-situ heating experiments.En un gran número de aplicaciones geoambientales, es esencial modelar procesos acoplados que dependen de varios parámetros de diseño, como las propiedades de los materiales y las características geométricas. Los procesos termohidromecánicos (THM) son, entre otros, efectos clave a considerar en aplicaciones críticas como los depósitos geológicos profundos de residuos peligrosos. Esta tesis propone novedosas estrategias de reducción de orden del modelo para evaluar la respuesta termo-hidromecánica del material, teniendo en cuenta las complejidades que implican los procesos acoplados para dichas aplicaciones. Para incluir la variabilidad de algunos parámetros de diseño, se aplica un enfoque de reducción de orden del modelo a-posteriori con métodos de base reducida para resolver el sistema paramétrico THM de alta dimensión. La reducción se basa en una estrategia de etapas offline-online. En la etapa offline, los subespacios reducidos se construyen mediante un procedimiento adaptativo codicioso y en la etapa online, se realiza una proyección multisubespacio para obtener rápidamente la respuesta THM acoplada a cualquier valor del parámetro de diseño. El núcleo de la estrategia adaptativa 'greedy' es un 'goal-oriented error estimator' a objetivos que guía la selección de los parámetros de diseño óptimos donde se evalúan las 'snapshots'. Para hacer frente a la no linealidad en forma de comportamiento elastoplástico del material, se combina el método de bases reducidas multisuperficie con 'domain decomposition sub-structuring'. La eficacia de las estrategias de reducción de modelos se demuestra en problemas inversos de problemas inversos que implican geomodelos a gran escala que representan la respuesta acoplada de las rocas anfitrionas en posibles emplazamientos de depósitos geológicos profundos. Se consideran dos tipos de escenarios: (i) se investiga la roca sometida a un proceso geomorfológico a medida que el glaciar avanza sobre ella durante un período de miles de años y (ii) se modela numéricamente la respuesta de la arcilla de un laboratorio de investigación subterráneo para apoyar y validar los experimentos de "in situ heating"Postprint (published version

The Optimization of Geotechnical Site Investigations for Pile Design in Multiple Layer Soil Profiles Using a Risk-Based Approach

The testing of subsurface material properties, i.e. a geotechnical site investigation, is a crucial part of projects that are located on or within the ground. The process consists of testing samples at a variety of locations, in order to model the performance of an engineering system for design processes. Should these models be inaccurate or unconservative due to an improper investigation, there is considerable risk of consequences such as structural collapse, construction delays, litigation, and over-design. However, despite these risks, there are relatively few quantitative guidelines or research items on informing an explicit, optimal investigation for a given foundation and soil profile. This is detrimental, as testing scope is often minimised in an attempt to reduce expenditure, thereby increasing the aforementioned risks. This research recommends optimal site investigations for multi-storey buildings supported by pile foundations, for a variety of structural configurations and soil profiles. The recommendations include that of the optimal test type, number of tests, testing locations, and interpretation of test data. The framework consists of a risk-based approach, where an investigation is considered optimal if it results in the lowest total project cost, incorporating both the cost of testing, and that associated with any expected negative consequences. The analysis is statistical in nature, employing Monte Carlo simulation and the use of randomly generated virtual soils through random field theory, as well as finite element analysis for pile assessment. A number of innovations have been developed to assist the novel nature of the work. For example, a new method of producing randomly generated multiple-layer soils has been devised. This work is the first instance of site investigations being optimised in multiple-layer soils, which are considerably more complex than the single-layer soils examined previously. Furthermore, both the framework and the numerical tools have been themselves extensively optimised for speed. Efficiency innovations include modifying the analysis to produce re-usable pile settlement curves, as opposed to designing and assessing the piles directly. This both reduces the amount of analysis required and allows for flexible post-processing for different conditions. Other optimizations include the elimination of computationally expensive finite element analysis from within the Monte Carlo simulations, and additional minor improvements. Practicing engineers can optimise their site investigations through three outcomes of this research. Firstly, optimal site investigation scopes are known for the numerous specific cases examined throughout this document, and the resulting inferred recommendations. Secondly, a rule-of-thumb guideline has been produced, suggesting the optimal number of tests for buildings of all sizes in a single soil case of intermediate variability. Thirdly, a highly efficient and versatile software tool, SIOPS, has been produced, allowing engineers to run a simplified version of the analysis for custom soils and buildings. The tool can do almost all the analysis shown throughout the thesis, including the use of a genetic algorithm to optimise testing locations. However, it is approximately 10 million times faster than analysis using the original framework, running on a single-core computer within minutes.Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 202

Slope stability analysis of the west wall of LAB chrysotile mine in the vicinity of Road 112

Les pentes minières à proximité de routes publiques doivent être prises en compte lors du processus de conception de ces routes. Plusieurs mines à ciel ouvert sont actuellement en développement au Québec et certaines d'entre elles sont situées à proximité de routes nationales. Ce mémoire propose une revue de la littérature portant sur les pratiques mondiales actuelles en ce qui concerne la stabilité de pentes minières à proximité d’infrastructures publiques. Il examine ensuite la stabilité du mur ouest de la mine à ciel ouvert LAB Chrysotile à Thetford Mines (Québec) aux abords du nouveau tracé de la route 112. Les travaux de terrain effectués sur le site sont décrits. Des analyses déterministes et probabilistes sont effectuées à l'aide de la méthode de réduction de la résistance au cisaillement (SSR) implémentée dans un code d’éléments finis (FE) ainsi que l'analyse à l'équilibre limite (LE). L'impact du remplissage de la fosse et de sa vidange rapide ainsi que la stabilité à long terme de la pente sont également étudiés. Les résultats de toutes les analyses révèlent que cette pente respecte les limites acceptables des critères de conception étudiés.Mining slopes in the vicinity of public roads must be considered during the road design process. Several open-pit mines are currently in development in Quebec and some of them are located close to national highways. This M.Sc. thesis provides a review of the literature on some current practices around the world regarding mining slope design close to public infrastructures. It then investigates the stability of the west wall of the LAB Chrysotile open-pit mine in Thetford Mines (Quebec) in the vicinity of the new Road 112 location. The field work performed at the site is described. Deterministic and probabilistic analyses are conducted using finite element shear strength reduction (FE-SSR) and limit equilibrium (LE) methods. The impact of pit infilling and rapid dewatering, as well as long-term stability of the slope are also investigated. The results of all analyses reveal that the current mining slopes are within acceptable design criteria limits