SUMMARYThis paper presents the development of a computationally efficient finite element tool for the analysis of 3D steady state heat flow in geothermal heating systems. Emphasis is placed on the development of finite elements for vertical borehole heat exchangers and the surrounding soil layers. Three factors have contributed to the computational efficiency: the proposed mathematical model for the heat exchanger, the discretization of the spatial domain using the Petrov-Galerkin method and the sequential numerical algorithm for solving the resulting system of non-linear equations. These have contributed in reducing significantly the required number of finite elements necessary for describing the involved systems. Details of the mathematical derivations and some numerical examples are presented.

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While reliability methods have already been widely adopted in civil engineering, the efficiency and robustness of finite element-based reliability assessments of quay walls are still fairly low. In this paper, the reliability indices of structural and geotechnical failure modes of two real-life quay walls are determined by coupling probabilistic methods with finite element models, taking into account a large number of stochastic variables. The reliability indices found are within the range of the targets suggested in the design codes presently in use. Nevertheless, neglecting model uncertainty and correlations between stochastic variables leads to an underestimation of the probability of failure. In addition, low sensitivity factors are found for time-independent variables, such as material properties and model uncertainty. Furthermore, the results are used to reflect on the partial factors used in the original design. Important variables, such as the angle of internal friction, are subjected to a sensitivity analysis in order to illuminate their influence on the reliability index. Port authorities and terminal operators might be able to use the findings of this paper to derive more insight into the reliability of their structures and to optimise their service life and functionality, for example by deepening berths or increasing operational loads.