Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

A new approach for the dynamic modelling of the human knee

Mathematical models of the knee joint are important tools which have both theoretical and practical applications. They are used by researchers to fully understand the stabilizing role of the components of the joint, by engineers as an aid for prosthetic design, by surgeons during the planning of an operation or during the operation itself, and by orthopedists for diagnosis and rehabilitation purposes. The principal aims of knee models are to reproduce the restraining function of each structure of the joint and to replicate the relative motion of the bones which constitute the joint itself. It is clear that the first point is functional to the second one. However, the standard procedures for the dynamic modelling of the knee tend to be more focused on the second aspect: the motion of the joint is correctly replicated, but the stabilizing role of the articular components is somehow lost. A first contribution of this dissertation is the definition of a novel approach — called sequential approach — for the dynamic modelling of the knee. The procedure makes it possible to develop more and more sophisticated models of the joint by a succession of steps, starting from a first simple model of its passive motion. The fundamental characteristic of the proposed procedure is that the results obtained at each step do not worsen those already obtained at previous steps, thus preserving the restraining function of the knee structures. The models which stem from the first two steps of the sequential approach are then presented. The result of the first step is a model of the passive motion of the knee, comprehensive of the patello-femoral joint. Kinematical and anatomical considerations lead to define a one degree of freedom rigid link mechanism, whose members represent determinate components of the joint. The result of the second step is a stiffness model of the knee. This model is obtained from the first one, by following the rules of the proposed procedure. Both models have been identified from experimental data by means of an optimization procedure. The simulated motions of the models then have been compared to the experimental ones. Both models accurately reproduce the motion of the joint under the corresponding loading conditions. Moreover, the sequential approach makes sure the results obtained at the first step are not worsened at the second step: the stiffness model can also reproduce the passive motion of the knee with the same accuracy than the previous simpler model. The procedure proved to be successful and thus promising for the definition of more complex models which could also involve the effect of muscular forces.

Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

New mechanisms for modelling the motion of the human ankle complex

The relevance of human joint models was shown in the literature. In particular, the great importance of models for the joint passive motion simulation (i.e. motion under virtually unloaded conditions) was outlined. They clarify the role played by the principal anatomical structures of the articulation, enhancing the comprehension of surgical treatments, and in particular the design of total ankle replacement and ligament reconstruction. Equivalent rigid link mechanisms proved to be an efficient tool for an accurate simulation of the joint passive motion. This thesis focuses on the ankle complex (i.e. the anatomical structure composed of the tibiotalar and the subtalar joints), which has a considerable role in human locomotion. The lack of interpreting models of this articulation and the poor results of total ankle replacement arthroplasty have strongly suggested devising new mathematical models capable of reproducing the restraining function of each structure of the joint and of replicating the relative motion of the bones which constitute the joint itself. In this contest, novel equivalent mechanisms are proposed for modelling the ankle passive motion. Their geometry is based on the joint’s anatomical structures. In particular, the role of the main ligaments of the articulation is investigated under passive conditions by means of nine 5-5 fully parallel mechanisms. Based on this investigation, a one-DOF spatial mechanism is developed for modelling the passive motion of the lower leg. The model considers many passive structures constituting the articulation, overcoming the limitations of previous models which took into account few anatomical elements of the ankle complex. All the models have been identified from experimental data by means of optimization procedure. Then, the simulated motions have been compared to the experimental one, in order to show the efficiency of the approach and thus to deduce the role of each anatomical structure in the ankle kinematic behavior.

Numerical modelling of fluid-structure interaction with application in hemodynamics

The thesis deals with numerical algorithms for fluid-structure interaction problems with application in blood flow modelling. It starts with a short introduction on the mathematical description of incompressible viscous flow with non-Newtonian viscosity and a moving linear viscoelastic structure. The mathematical model consists of the generalized Navier-Stokes equation used for the description of fluid flow and the generalized string model for structure movement. The arbitrary Lagrangian-Eulerian approach is used in order to take into account moving computational domain. A part of the thesis is devoted to the discussion on the non-Newtonian behaviour of shear-thinning fluids, which is in our case blood, and derivation of two non-Newtonian models frequently used in the blood flow modelling. Further we give a brief overview on recent fluid-structure interaction schemes with discussion about the difficulties arising in numerical modelling of blood flow. Our main contribution lies in numerical and experimental study of a new loosely-coupled partitioned scheme called the kinematic splitting fluid-structure interaction algorithm. We present stability analysis for a coupled problem of non-Newtonian shear-dependent fluids in moving domains with viscoelastic boundaries. Here, we assume both, the nonlinearity in convective as well is diffusive term. We analyse the convergence of proposed numerical scheme for a simplified fluid model of the Oseen type. Moreover, we present series of experiments including numerical error analysis, comparison of hemodynamic parameters for the Newtonian and non-Newtonian fluids and comparison of several physiologically relevant computational geometries in terms of wall displacement and wall shear stress. Numerical analysis and extensive experimental study for several standard geometries confirm reliability and accuracy of the proposed kinematic splitting scheme in order to approximate fluid-structure interaction problems.

Computational Modelling of Cardiac Electrophysiology: from Cell to Bedside

Heart diseases are the leading cause of death worldwide, both for men and women. However, the ionic mechanisms underlying many cardiac arrhythmias and genetic disorders are not completely understood, thus leading to a limited efficacy of the current available therapies and leaving many open questions for cardiac electrophysiologists. On the other hand, experimental data availability is still a great issue in this field: most of the experiments are performed in vitro and/or using animal models (e.g. rabbit, dog and mouse), even when the final aim is to better understand the electrical behaviour of in vivo human heart either in physiological or pathological conditions. Computational modelling constitutes a primary tool in cardiac electrophysiology: in silico simulations, based on the available experimental data, may help to understand the electrical properties of the heart and the ionic mechanisms underlying a specific phenomenon. Once validated, mathematical models can be used for making predictions and testing hypotheses, thus suggesting potential therapeutic targets. This PhD thesis aims to apply computational cardiac modelling of human single cell action potential (AP) to three clinical scenarios, in order to gain new insights into the ionic mechanisms involved in the electrophysiological changes observed in vitro and/or in vivo. The first context is blood electrolyte variations, which may occur in patients due to different pathologies and/or therapies. In particular, we focused on extracellular Ca2+ and its effect on the AP duration (APD). The second context is haemodialysis (HD) therapy: in addition to blood electrolyte variations, patients undergo a lot of other different changes during HD, e.g. heart rate, cell volume, pH, and sympatho-vagal balance. The third context is human hypertrophic cardiomyopathy (HCM), a genetic disorder characterised by an increased arrhythmic risk, and still lacking a specific pharmacological treatment.

MODELLING β2AR REGULATION

The β2 adrenergic receptor (β2AR) regulates smooth muscle relaxation in the vasculature and airways. Long- and Short-acting β-agonists (LABAs/SABAs) are widely used in treatment of chronic obstructive pulmonary disorder (COPD) and asthma. Despite their widespread clinical use we do not understand well the dominant β2AR regulatory pathways that are stimulated during therapy and bring about tachyphylaxis, which is the loss of drug effects. Thus, an understanding of how the β2AR responds to various β-agonists is crucial to their rational use. Towards that end we have developed deterministic models that explore the mechanism of drug- induced β2AR regulation. These mathematical models can be classified into three classes; (i) Six quantitative models of SABA-induced G protein coupled receptor kinase (GRK)-mediated β2AR regulation; (ii) Three phenomenological models of salmeterol (a LABA)-induced GRK-mediated β2AR regulation; and (iii) One semi-quantitative, unified model of SABA-induced GRK-, protein kinase A (PKA)-, and phosphodiesterase (PDE)-mediated regulation of β2AR signalling. The various models were constrained with all or some of the following experimental data; (i) GRK-mediated β2AR phosphorylation in response to various LABAs/SABAs; (ii) dephosphorylation of the GRK site on the β2AR; (iii) β2AR internalisation; (iv) β2AR recycling; (v) β2AR desensitisation; (vi) β2AR resensitisation; (vii) PKA-mediated β2AR phosphorylation in response to a SABA; and (viii) LABA/SABA induced cAMP profile ± PDE inhibitors. The models of GRK-mediated β2AR regulation show that plasma membrane dephosphorylation and recycling of the phosphorylated β2AR are required to reconcile with the measured dephosphorylation kinetics. We further used a consensus model to predict the consequences of rapid pulsatile agonist stimulation and found that although resensitisation was rapid, the β2AR system retained the memory of prior stimuli and desensitised much more rapidly and strongly in response to subsequent stimuli. This could explain tachyphylaxis of SABAs over repeated use in rescue therapy of asthma patients. The LABA models show that the long action of salmeterol can be explained due to decreased stability of the arrestin/β2AR/salmeterol complex. This could explain long action of β-agonists used in maintenance therapy of asthma patients. Our consensus model of PKA/PDE/GRK-mediated β2AR regulation is being used to identify the dominant β2AR desensitisation pathways under different therapeutic regimens in human airway cells. In summary our models represent a significant advance towards understanding agonist-specific β2AR regulation that will aid in a more rational use of the β2AR agonists in the treatment of asthma.

A Case Study of Geometric Modelling via 3-D Point Interpolation for the Bathymetry of the Rabasa Lakes (Alicante, Spain)

The interpolation of points by means of Information Technology programs appears as a technical tool of some relevancy in the hydrogeology in general and in the study of the humid zones in particular. Our approach has been the determination of the 3-D geometry of the humid zones of major depth of the Rabasa Lakes. To estimate the topography of the lake bed, we proceed to acquire information in the field by means of sonar and GPS equipment. A total of 335 points were measured both on the perimeter and in the lake bed. In a second stage, this information was used in a kriging program to obtain the bathymetry of the wetland. This methodology is demonstrated as one of the most reliable and cost-efficient for the 3-D analysis of this type of water masses. The bathymetric study of the zone allows us to characterize the mid- and long-term hydrological evolution of the lakes by means of depth-area-volume curves.

Applied continuous modelling in the study of pyrotechnic shock propagation on Ariane 5

This paper deals with the theoretical method and the modelling problems on the analysis of the Pyrotechnic Shock Propagation in the Vehicle Equipment Bay Structure of the ARIANE 5 during the separation of the upper stage. This work has been developed under a contract with the Spanish Firm Construcciones Aeronáuticas S.A. From all the analysis and the studies it can be concluded that: 1.- The mathematical method used for the study of the pyrotechnic shock phenomena is very well suited for conducting parametric studies. 2.- A careful model of the structure should be developed taking into account the realistic stiffness and dissipation properties at the junctions. 3.- The load produced by the pyrotechnic device should be carefully calibrated to reach a good agreement between theoretical and test results. 4.- In any case with the adquired experience it can be said that with the modelling of continuous elements the order of magnitude of the accelerations can be predicted with the accuracy needed in practical applications.

Criteria for mathematical model selection for satellite vibro-acoustic analysis depending on frequency range

Satellites and space equipment are exposed to diffuse acoustic fields during the launch process. The use of adequate techniques to model the response to the acoustic loads is a fundamental task during the design and verification phases. Considering the modal density of each element is necessary to identify the correct methodology. In this report selection criteria are presented in order to choose the correct modelling technique depending on the frequency ranges. A model satellite’s response to acoustic loads is presented, determining the modal densities of each component in different frequency ranges. The paper proposes to select the mathematical method in each modal density range and the differences in the response estimation due to the different used techniques. In addition, the methodologies to analyse the intermediate range of the system are discussed. The results are compared with experimental testing data obtained in an experimental modal test.

Modelling of landslides propagation with SPH : effects of rheology and pore water pressure

El estudio desarrollado en este trabajo de tesis se centra en la modelización numérica de la fase de propagación de los deslizamientos rápidos de ladera a través del método sin malla Smoothed Particle Hydrodynamics (SPH). Este método tiene la gran ventaja de permitir el análisis de problemas de grandes deformaciones evitando operaciones costosas de remallado como en el caso de métodos numéricos con mallas tal como el método de los Elementos Finitos. En esta tesis, particular atención viene dada al rol que la reología y la presión de poros desempeñan durante estos eventos. El modelo matemático utilizado se basa en la formulación de Biot-Zienkiewicz v - pw, que representa el comportamiento, expresado en términos de velocidad del esqueleto sólido y presiones de poros, de la mezcla de partículas sólidas en un medio saturado. Las ecuaciones que gobiernan el problema son: • la ecuación de balance de masa de la fase del fluido intersticial, • la ecuación de balance de momento de la fase del fluido intersticial y de la mezcla, • la ecuación constitutiva y • una ecuación cinemática. Debido a sus propiedades geométricas, los deslizamientos de ladera se caracterizan por tener una profundidad muy pequeña frente a su longitud y a su anchura, y, consecuentemente, el modelo matemático mencionado anteriormente se puede simplificar integrando en profundidad las ecuaciones, pasando de un modelo 3D a 2D, el cual presenta una combinación excelente de precisión, sencillez y costes computacionales. El modelo propuesto en este trabajo se diferencia de los modelos integrados en profundidad existentes por incorporar un ulterior modelo capaz de proveer información sobre la presión del fluido intersticial a cada paso computacional de la propagación del deslizamiento. En una manera muy eficaz, la evolución de los perfiles de la presión de poros está numéricamente resuelta a través de un esquema explicito de Diferencias Finitas a cada nodo SPH. Este nuevo enfoque es capaz de tener en cuenta la variación de presión de poros debida a cambios de altura, de consolidación vertical o de cambios en las tensiones totales. Con respecto al comportamiento constitutivo, uno de los problemas principales al modelizar numéricamente deslizamientos rápidos de ladera está en la dificultad de simular con la misma ley constitutiva o reológica la transición de la fase de iniciación, donde el material se comporta como un sólido, a la fase de propagación donde el material se comporta como un fluido. En este trabajo de tesis, se propone un nuevo modelo reológico basado en el modelo viscoplástico de Perzyna, pensando a la viscoplasticidad como a la llave para poder simular tanto la fase de iniciación como la de propagación con el mismo modelo constitutivo. Con el fin de validar el modelo matemático y numérico se reproducen tanto ejemplos de referencia con solución analítica como experimentos de laboratorio. Finalmente, el modelo se aplica a casos reales, con especial atención al caso del deslizamiento de 1966 en Aberfan, mostrando como los resultados obtenidos simulan con éxito estos tipos de riesgos naturales. The study developed in this thesis focuses on the modelling of landslides propagation with the Smoothed Particle Hydrodynamics (SPH) meshless method which has the great advantage of allowing to deal with large deformation problems by avoiding expensive remeshing operations as happens for mesh methods such as, for example, the Finite Element Method. In this thesis, special attention is given to the role played by rheology and pore water pressure during these natural hazards. The mathematical framework used is based on the v - pw Biot-Zienkiewicz formulation, which represents the behaviour, formulated in terms of soil skeleton velocity and pore water pressure, of the mixture of solid particles and pore water in a saturated media. The governing equations are: • the mass balance equation for the pore water phase, • the momentum balance equation for the pore water phase and the mixture, • the constitutive equation and • a kinematic equation. Landslides, due to their shape and geometrical properties, have small depths in comparison with their length or width, therefore, the mathematical model aforementioned can then be simplified by depth integrating the equations, switching from a 3D to a 2D model, which presents an excellent combination of accuracy, computational costs and simplicity. The proposed model differs from previous depth integrated models by including a sub-model able to provide information on pore water pressure profiles at each computational step of the landslide's propagation. In an effective way, the evolution of the pore water pressure profiles is numerically solved through a set of 1D Finite Differences explicit scheme at each SPH node. This new approach is able to take into account the variation of the pore water pressure due to changes of height, vertical consolidation or changes of total stress. Concerning the constitutive behaviour, one of the main issues when modelling fast landslides is the difficulty to simulate with the same constitutive or rheological model the transition from the triggering phase, where the landslide behaves like a solid, to the propagation phase, where the landslide behaves in a fluid-like manner. In this work thesis, a new rheological model is proposed, based on the Perzyna viscoplastic model, thinking of viscoplasticity as the key to close the gap between the triggering and the propagation phase. In order to validate the mathematical model and the numerical approach, benchmarks and laboratory experiments are reproduced and compared to analytical solutions when possible. Finally, applications to real cases are studied, with particular attention paid to the Aberfan flowslide of 1966, showing how the mathematical model accurately and successfully simulate these kind of natural hazards.

Modelling of short runout propagation landslides and debris flows

This paper proposes an extension of methods used to predict the propagation of landslides having a long runout to smaller landslides with much shorter propagation distances. The method is based on: (1) a depth-integrated mathematical model including the coupling between the soil skeleton and the pore fluids, (2) suitable rheological models describing the relation between the stress and the rate of deformation tensors for fluidised soils and (3) a meshless numerical method, Smooth Particle Hydrodynamics, which separates the computational mesh (or set of computational nodes) from the mesh describing the terrain topography, which is of structured type – thus accelerating search operations. The proposed model is validated using two examples for which there are analytical solutions, and then it is applied to two short runout landslides which happened in Hong Kong in 1995, for which there is available information.

Inception of debris avalanches: remarks on geomechanical modelling

Debris avalanches are complex phenomena due to the variety of mechanisms that control the failure stage and the avalanche formation. Regarding these issues, in the literature, either field evidence or qualitative interpretations can be found while few experimental laboratory tests and rare examples of geomechanical modelling are available for technical and/or scientific purposes. As a contribution to the topic, the paper firstly highlights as the problem can be analysed referring to a unique mathematical framework from which different modelling approaches can be derived based on limit equilibrium method (LEM), finite element method (FEM), or smooth particle hydrodynamics (SPH). Potentialities and limitations of these approaches are then tested for a large study area where huge debris avalanches affected shallow deposits of pyroclastic soils (Sarno-Quindici, Southern Italy). The numerical results show that LEM as well as uncoupled and coupled stress–strain FEM analyses are able to individuate the major triggering mechanisms. On the other hand, coupled SPH analyses outline the relevance of erosion phenomena, which can modify the kinematic features of debris avalanches in their source areas, i.e. velocity, propagation patterns and later spreading of the unstable mass. As a whole, the obtained results encourage the application of the introduced approaches to further analyse real cases in order to enhance the current capability to forecast the inception of these dangerous phenomena.

Depth Averaged Models for Fast Landslide Propagation: Mathematical, Rheological and Numerical Aspects

This paper presents an overview of depth averaged modelling of fast catastrophic landslides where coupling of solid skeleton and pore fluid (air and water) is important. The first goal is to show how Biot-Zienkiewicz models can be applied to develop depth integrated, coupled models. The second objective of the paper is to consider a link which can be established between rheological and constitutive models. Perzyna´s viscoplasticity can be considered a general framework within which rheological models such as Bingham and cohesive frictional fluids can be derived. Among the several alternative numerical models, we will focus here on SPH which has not been widely applied by engineers to model landslide propagation. We propose an improvement, based on combining Finite Difference meshes associated to SPH nodes to describe pore pressure evolution inside the landslide mass. We devote a Section to analyze the performance of the models, considering three sets of tests and examples which allows to assess the model performance and limitations: (i) Problems having an analytical solution, (ii) Small scale laboratory tests, and (iii) Real cases for which we have had access to reliable information

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.