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Isogeometric Analysis of Coupled Problems in Porous Media
Get PDFComputational modeling of coupled problems in porous media is essential in various disciplines of science and engineering. The porous media of interest here are soils subjected to different physical processes. In particular, hydraulic (H), coupled hydro-mechanical (HM) and thermo-hydro-mechanical (THM) processes are addressed. Development of a fully-coupled THM numerical model targets ground freezing phenomena as the main application problem. The governing equations for the various processes are derived based on porous media theory. The fundamentals of this theory are presented in a general form and discussed by focusing on soils and the application problems. Isogeometric analysis (IGA) is adopted for implementing the governing equations, leading to the development of a code for numerical simulations. One of the main reasons for choosing IGA as a computational framework is the smoothness of the basis functions, which is attractive for better continuity of field variables. The main concepts behind IGA, including its advantages compared to traditional finite element analysis (FEA), are briefly discussed.
The first problem studied is steady-state groundwater flow governed by Darcy’s law. Numerical challenges occur in the simulation of groundwater flow problems due to complex boundary conditions, varying material properties, presence of sources or sinks in the flow domain or a combination of these. Adaptive IGA using locally refined (LR) B-Splines is applied to address some of these problems. A posteriori error estimates are calculated to identify which B-Splines should be locally refined. The error estimates are calculated based on recovery of the L2-projected solution. The adaptive analysis method is first illustrated by performing simulation of benchmark problems with analytical solutions. Numerical applications to two-dimensional groundwater flow problems are then presented. The problems studied are flow around an impervious corner, flow around a cutoff wall and flow in a heterogeneous medium. The convergence rates obtained with adaptive analysis using local refinement were, in general, observed to be of optimal order in contrast to simulations with uniform refinement.
Classical problems in poroelasticity are next addressed using mixed IGA, i.e. using different polynomial degrees for displacement and pore pressure. The finite element method has been widely applied to such problems and the numerical behavior of the governing equations has been discussed by several researchers. Equal order IGA has recently been applied to poroelasticity. Pressure oscillations at small time steps have been known to be an issue in the simulation of poroelasticity problems. The performance of mixed IGA for smaller time steps is investigated by revisiting Terzaghi’s classical consolidation problem. A numerical study is also performed on the consolidation of a layered soil where a very low permeability layer is known to cause pressure oscillations. It is observed from the numerical studies that mixed IGA improves the accuracy of the pore pressure results compared to equal order simulations, as is known from traditional FEA. The pressure oscillations, however, are not completely removed but were observed to decrease with increasing polynomial degrees. Mixed simulations with a graded mesh refinement were observed to reduce the pore pressure oscillations, revealing the potential of adaptive refinement for such problems.
Fully coupled THM processes in ground freezing are then studied using mixed IGA. The governing linear momentum, mass and energy balance equations are formulated by assuming saturated conditions. Strain due to phase change is incorporated into the linear momentum balance equation. This is attained through a simple thermoelastic constitutive equation with temperature dependent strength parameters. The supplementary equations that complete the model include the soil-water characteristic curve and a hydraulic conductivity model. After spatial and temporal discretization, the governing and supplementary equations result in a strongly coupled and highly nonlinear system of equations, which are solved using Newton-Raphson iteration. Numerical studies are performed on one-dimensional freezing and a frost heave problem where experimental data is available. Good agreements were observed between the mixed IGA based simulation of a THM coupled problem in frost heave and the corresponding experimental data found from literature. The continuity of the basis functions in mixed IGA of THM coupled problems implies that prediction of derived quantities, such as fluxes, across knot spans (analogous to elements in traditional FEA) can be controlled and improved.
In general, the numerical implementation work resulted in H, HM and THM frameworks for simulation of poro/geomechanics problems using IGA. The frameworks are developed based on IFEM - an object-oriented isogeometric toolbox for the solution of partial differential equations. The developed numerical codes may be used and extended further. In addition to the various application problems studied, the numerical work mainly initiates application of IGA to THM coupled problems in porous media. The features of IGA that are computationally attractive in this context, such as the ability to perform higher-order simulations with ease, can thus be utilized
The Potential of Scientific Machine Learning in Geotechnics and Engineering Geology
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Physics-informed deep learning for one-dimensional consolidation
Get PDFNeural networks with physical governing equations as constraints have recently created a new trend in machine learning research. In this context, a review of related research is first presented and discussed. The potential offered by such physics-informed deep learning models for computations in geomechanics is demonstrated by application to one-dimensional (1D) consolidation. The governing equation for 1D problems is applied as a constraint in the deep learning model. The deep learning model relies on automatic differentiation for applying the governing equation as a constraint, based on the mathematical approximations established by the neural network. The total loss is measured as a combination of the training loss (based on analytical and model predicted solutions) and the constraint loss (a requirement to satisfy the governing equation). Two classes of problems are considered: forward and inverse problems. The forward problems demonstrate the performance of a physically constrained neural network model in predicting solutions for 1D consolidation problems. Inverse problems show prediction of the coefficient of consolidation. Terzaghi’s problem, with varying boundary conditions, is used as a numerical example and the deep learning model shows a remarkable performance in both the forward and inverse problems. While the application demonstrated here is a simple 1D consolidation problem, such a deep learning model integrated with a physical law has significant implications for use in, such as, faster real-time numerical prediction for digital twins, numerical model reproducibility and constitutive model parameter optimization
Isogeometric Analysis of Coupled Problems in Porous Media
No full textComputational modeling of coupled problems in porous media is essential in various disciplines of science and engineering. The porous media of interest here are soils subjected to different physical processes. In particular, hydraulic (H), coupled hydro-mechanical (HM) and thermo-hydro-mechanical (THM) processes are addressed. Development of a fully-coupled THM numerical model targets ground freezing phenomena as the main application problem. The governing equations for the various processes are derived based on porous media theory. The fundamentals of this theory are presented in a general form and discussed by focusing on soils and the application problems. Isogeometric analysis (IGA) is adopted for implementing the governing equations, leading to the development of a code for numerical simulations. One of the main reasons for choosing IGA as a computational framework is the smoothness of the basis functions, which is attractive for better continuity of field variables. The main concepts behind IGA, including its advantages compared to traditional finite element analysis (FEA), are briefly discussed.
The first problem studied is steady-state groundwater flow governed by Darcy’s law. Numerical challenges occur in the simulation of groundwater flow problems due to complex boundary conditions, varying material properties, presence of sources or sinks in the flow domain or a combination of these. Adaptive IGA using locally refined (LR) B-Splines is applied to address some of these problems. A posteriori error estimates are calculated to identify which B-Splines should be locally refined. The error estimates are calculated based on recovery of the L2-projected solution. The adaptive analysis method is first illustrated by performing simulation of benchmark problems with analytical solutions. Numerical applications to two-dimensional groundwater flow problems are then presented. The problems studied are flow around an impervious corner, flow around a cutoff wall and flow in a heterogeneous medium. The convergence rates obtained with adaptive analysis using local refinement were, in general, observed to be of optimal order in contrast to simulations with uniform refinement.
Classical problems in poroelasticity are next addressed using mixed IGA, i.e. using different polynomial degrees for displacement and pore pressure. The finite element method has been widely applied to such problems and the numerical behavior of the governing equations has been discussed by several researchers. Equal order IGA has recently been applied to poroelasticity. Pressure oscillations at small time steps have been known to be an issue in the simulation of poroelasticity problems. The performance of mixed IGA for smaller time steps is investigated by revisiting Terzaghi’s classical consolidation problem. A numerical study is also performed on the consolidation of a layered soil where a very low permeability layer is known to cause pressure oscillations. It is observed from the numerical studies that mixed IGA improves the accuracy of the pore pressure results compared to equal order simulations, as is known from traditional FEA. The pressure oscillations, however, are not completely removed but were observed to decrease with increasing polynomial degrees. Mixed simulations with a graded mesh refinement were observed to reduce the pore pressure oscillations, revealing the potential of adaptive refinement for such problems.
Fully coupled THM processes in ground freezing are then studied using mixed IGA. The governing linear momentum, mass and energy balance equations are formulated by assuming saturated conditions. Strain due to phase change is incorporated into the linear momentum balance equation. This is attained through a simple thermoelastic constitutive equation with temperature dependent strength parameters. The supplementary equations that complete the model include the soil-water characteristic curve and a hydraulic conductivity model. After spatial and temporal discretization, the governing and supplementary equations result in a strongly coupled and highly nonlinear system of equations, which are solved using Newton-Raphson iteration. Numerical studies are performed on one-dimensional freezing and a frost heave problem where experimental data is available. Good agreements were observed between the mixed IGA based simulation of a THM coupled problem in frost heave and the corresponding experimental data found from literature. The continuity of the basis functions in mixed IGA of THM coupled problems implies that prediction of derived quantities, such as fluxes, across knot spans (analogous to elements in traditional FEA) can be controlled and improved.
In general, the numerical implementation work resulted in H, HM and THM frameworks for simulation of poro/geomechanics problems using IGA. The frameworks are developed based on IFEM - an object-oriented isogeometric toolbox for the solution of partial differential equations. The developed numerical codes may be used and extended further. In addition to the various application problems studied, the numerical work mainly initiates application of IGA to THM coupled problems in porous media. The features of IGA that are computationally attractive in this context, such as the ability to perform higher-order simulations with ease, can thus be utilized
Vitenskapelig maskinlæring kan bidra til bedre løsninger innen geoteknikk og ingeniørgeologi
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Impact of Climate Change on Infrastructure in Longyearbyen. Case Study of Pile Foundations on Sloping Terrains
Get PDFThe effect of climate change on existing infrastructure in Longyearbyen, Svalbard is investigated in this study. Climate data recordings show that, over the past couple of years, record-breaking temperature and precipitations measurements are observed in this area. It is anticipated that this will pose a serious threat to existing infrastructure and will impose additional challenges for new developments. Adaptations of existing and future infrastructure to changes in climate for safety and serviceability is of paramount importance. The current study aims to contribute towards this initiative.
The particular focus of the study was slopes and buildings supported on sloping terrains in Longyearbyen. Changes in ground temperature are investigated based on existing temperature data and forecasts. The ground thermal regime is then used to evaluate the stability of representative slopes in the study area. The capacity of single piles on a slope is also investigated by considering various factors such as slope angle, location of pile on slope, pile material and geometry. The following findings are observed from the investigation:
The projected climate data show that temperatures will keep rising in Svalbard. Based on the analytical and numerical studies performed for the projected temperature data, it is observed that the active layer thickness will increase up to 2 m or more, depending on the thermal properties of the soil. The increase in ground temperatures also results in the warming of the permafrost underneath the active layer. The stability of slopes and the bearing capacity of existing infrastructure foundations is expected to be significantly affected by these changes.
Slope stability evaluations were performed for a representative slope in the study area by considering changing active layer thicknesses according to the projected ground temperature regime. The factor of safety against slope failure decreases with increasing active layer thickness. Under the specific assumptions made for the evaluation, the representative slope was found to be stable for active layer thicknesses of up to 2m. Sensitivity analyses show that the factor of safety is significantly affected by changes is material parameters such as cohesion and friction angle, which are associated with the ground thermal regime. Accurate estimation of material properties is required for a definitive slope stability evaluation.
The performance of single piles on a slope is investigated by performing various analytical and numerical studies. One of the effects of an increase in active layer thickness on sloping terrains is the risk of solifluction, which is a slow downward movement of soil. The soil movement exerts additional lateral forces on pile foundations, affecting the ultimate capacity of the piles. This is especially significant for building where the effect of solifluction is not considered in the original design. It is observed from the analyses that piles subjected to such additional lateral forces will experience increased deflections and internal forces. The deflections and internal forces increase with increasing slope angles and active layer thicknesses. Piles located in the middle of the slope are observed to experience larger deflections and internal forces than piles located at the toe of the slope. The effect of such increased deflections and internal forces is especially critical for timber piles where the capacity is expected (and shown) to reduce with aging.
Based on the observation from the current study, specific case study for a selected location was performed. The effects of increased lateral loads, as a result of thawing and warming permafrost, on the pile foundations of a selected building in Longyearbyen located on a slope are investigated through numerical analyses. A range of active layer thicknesses are considered in the analyses taking current and projected scenarios into account. The axial loads on the piles are estimated based on standard methods for residential buildings, and variations are considered to account for uncertainties. The lateral loads on the piles are assumed to mainly originate from slope movements (such as solifluction) and loads transferred from crest of the slope through earth pressure. The finite element simulations performed in a general way are used a basis to estimate the earth pressures on the piles and the loads are converted to an equivalent resultant system at the pile head for simplicity of the analyses. Variations in the lateral loads are considered corresponding to the range of active layer thicknesses. Analyses based on p-y curves are performed for the different active layer thicknesses and loads considered. The results are presented in terms of pile head deflections, bending moments and shear forces. It is shown that the pile head deflections are expected to increase as the active layer thicknesses increase. A similar trend of increase is observed in the internal forces generated in the piles.
In general, the study here highlights the importance of assessing the effect of climate change on existing infrastructure to ensure safety and serviceability. The knowledge gained from the study also highlights the necessity of the consideration of climate change in the design of new infrastructure to be built in affected areas
Pelefundamenter kan brukes til å utvinne og lagre geotermisk energi
Get PDFNorske bygninger kan bli mer energieffektive ved å utvinne grunnvarme og lagre termisk energi i pelefundamenter.publishedVersio
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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