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The Laplace transform inversion is a well-known ill-conditioned problem and many numerical schemes in literature have investigated how to solve it. In this paper, we revise the Gaver-Stehfest method by using polyharmonic splines augmented with polynomials to approximate the Laplace transform into the numerical inversion formula. Theoretical accuracy bounds for the fitting model are given. Discussions on the effectiveness of the inversion algorithm are produced and confirmed by numerical experiments about approximation errors and inversion results. Comparisons with an existing model are also presented.

This paper addresses the hydromechanical postclosure behavior of an underground long cylindrical deep tunnel drilled into a massif (host medium) and backfilled at the end of its service life. It is concerned with the development of quasi-analytical Laplace transform solutions based on a simplified life cycle of the tunnel, idealized in four stages: (1) excavation, (2) pore-pressure dissipation before lining installation, (3) lining installation and tunnel exploitation, and (4) postclosure. The solutions proposed in this paper therefore extend the previous work of the authors, in this case by explicitly taking into consideration the excavation, waiting for lining installation, and tunnel exploitation stages of the life cycle. Results from a parametric study are also presented to highlight the hydromechanical responses of the tunnel over periods of its life cycle. The accuracy and correctness of the solutions from a finite-element model have been verified with the quasi-analytical results. The present solutions will be used later for benchmarking finite-element-based solutions currently under development, taking into account more complex material behaviors. © 2012 American Society of Civil Engineers.

This paper is an extension of earlier papers (Wong et al., 2008a, b) which sought to investigate the poroelastic and poro-viscoelastic behaviour of a ground medium following the closing of a spherical cavity, whereas the focus here is for a long horizontal tunnel with a circular section. It presents Laplace transform analytic solutions for the time dependent hydromechanical responses of a decommissioned and backfilled deep tunnel drilled into a poro-viscoelastic host medium. Both the backfill, which is assumed as poroelastic, and the host medium are supposed saturated with water. The solutions developed and inverted numerically to obtain the responses in time domain are used to study the effects of lining support deterioration, the backfill stiffness and of the host medium viscosity. The convergence of the tunnel leads to the expulsion of water from the backfill into the host medium resulting in corresponding transient responses. Each of the key parameters studied can have the effect of either attenuating or accentuating the transient and long term hydromechanical responses by delaying or shortening the dissipation period depending on the direction of change taken by the parameter value. The solutions presented in this paper permit an assessment of the relative importance of these parameters. Comparisons are also drawn between a tunnel and a spherical cavity of identical radius. Generally speaking, the implications of lining support, backfill stiffness and viscosity of ground medium are more significant in terms of the resulting hydromechanical responses, for the tunnel than for the spherical cavity.

This paper is interested in the hydro-mechanical behaviour of an underground cavity abandoned at the end of its service life. It is an extension of a previous study that accounted for a poro-elastic behaviour of the rock mass (Int. J. Comput. Geomech. 2007; DOI: 10.1016/j.compgeo.2007.11.003). Deterioration of the lining support with time leads to the transfer of the loading from the exterior massif to the interior backfill. The in situ material has a poro-visco-elastic constitutive behaviour while the backfill is poro-elastic, both saturated with water. This loading transfer is accompanied by an inward cavity convergence, thereby compressing the backfill, and induces an outward water flow. This leads to a complex space–time evolution of pore pressures, displacements and stresses, which is not always intuitive. In its general setting, a semi-explicit solution to this problem is developed, using Laplace transform, the inversion being performed numerically. Analytical inversion leading to a quasi-explicit solution in the time domain is possible by identifying the characteristic creep and relaxation times of volumetric strains with those of the deviatoric strains, on the basis of a parametric study. A few numerical examples are given to illustrate the hydro-mechanical behaviour of the cavity and highlight the influence of key parameters (e.g. stiffness of backfill, lining deterioration rate, etc.). Further studies accounting for more general material behaviours for the backfill and external ground are ongoing. Copyright © 2008 John Wiley & Sons, Ltd.

The first part of this thesis is devoted to the study randomly truncated stochastic algorithms as introduced by Chen and Zhu. The first study is concerned with the almost sure convergence. We continue the study with the convergence rate of the algorithm. We also consider a moving window version of the algorithm. Finally, we present a few applications to finance.The second part of the thesis is concerned with the pricing of Parisian options. The valuation technique is based on computing closed form formula for the Laplace transforms of the prices following the seminar work of Chesney, Jeanblanc and Yor on the topic. We determinethese formulae for the single and double barrier Parisian options. Then, prove the accuracy of the numerical inversion methods we use ton invert these Laplace transforms.; La première partie de cette thèse est consacrée à l'étude des algorithmes stochastiques aléatoirement tronqués de Chen et Zhu. La première étude de cet algorithme concerne sa convergence presque sûre. Dans le second chapitre, nous poursuivons l'étude de cet algorithme en nous intéressant à sa vitesse de convergence. Nous considérons également une version moyenne mobile de cet algorithme. Enfin nous terminons par quelques applications à la finance.La seconde partie de cette thèse s'intéresse à l'évaluation des options parisiennes en s'appuyant sur les travaux de Chesney, Jeanblanc et Yor. La méthode d'évaluation se base sur l'obtention de formules fermées pour les transformées de Laplace des prix par rapport à la maturité. Nous établissons ces formules pour les options parisiennes simple et double barrières. Nous étudions ensuite une méthode d'inversion numérique de ces transformées dont nous établissons la précision.

We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offline–online decomposition. A synthetic dataset is constructed offline by solving a parametric time-dependent partial differential equation for multiple input parameters, sampled from their probability distributions of natural variation. The collected time-signals, extracted at sensor locations, are used to train classifiers at such sensor locations, thus constructing multiple databases of healthy configurations. These datasets are then used to train one class Support Vector Machines (OC-SVMs) to detect anomalies. During the online stage, a new measurement, possibly obtained from a damaged configuration, is evaluated using the classifiers. Information on damage is provided in a hierarchical manner: first, using a binary feedback, the entire structure response is either classified as inlier (healthy) or outlier (damaged). Then, for the outliers, we exploit the outputs of multiple classifiers to retrieve information both on the severity and the spatial location of the damages. Because of the large number of signals needed to construct the datasets offline, a model order reduction strategy is implemented to reduce the computational burden. We apply this strategy to both 2D and 3D problems to mimic the vibrational behavior of complex structures under the effect of an active source and show the effectiveness of the approach for detecting and localizing cracks.