Hydraulic conductivity distribution in crystalline rocks, derived from inflows to tunnels and galleries in the Central Alps, Switzerland

Inflow data from 23 tunnels and galleries, 136km in length and located in the Aar and Gotthard massifs of the Swiss Alps, have been analyzed with the objective (1) to understand the 3-dimensional spatial distribution of groundwater flow in crystalline basement rocks, (2) to assess the dependency of tunnel inflow rate on depth, tectonic overprint, and lithology, and (3) to derive the distribution of fracture transmissivity and effective hydraulic conductivity at the 100-m scale. Brittle tectonic overprint is shown to be the principal parameter regulating inflow rate and dominates over depth and lithology. The highest early time inflow rate is 1,300l/s and has been reported from a shallow hydropower gallery intersecting a 200-m wide cataclastic fault zone. The derived lognormal transmissivity distribution is based on 1,361 tunnel intervals with a length of 100m. Such interval transmissivities range between 10−9 and 10−1m2/s within the first 200-400m of depth and between 10−9 and 10−4m2/s in the depth interval of 400-1,500m below ground surface. Outside brittle fault zones, a trend of decreasing transmissivity/hydraulic conductivity with increasing depth is observed for some schistous and gneissic geological units, whereas no trend is identified for the granitic unit

Initial value problem for one-dimensional rotating shallow water equations

In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we establish the local existence and the uniqueness of a solution to the hyperbolic system, as well as the global existence of a solution to the regularized system. In order to prove this, we use suitable variables that symmetrize the system

Hydraulic conductivity distribution in crystalline rocks, derived from inflows to tunnels and galleries in the Central Alps, Switzerland

Inflow data from 23 tunnels and galleries, 136 km in length and located in the Aar and Gotthard massifs of the Swiss Alps, have been analyzed with the objective (1) to understand the 3-dimensional spatial distribution of groundwater flow in crystalline basement rocks, (2) to assess the dependency of tunnel inflow rate on depth, tectonic overprint, and lithology, and (3) to derive the distribution of fracture transmissivity and effective hydraulic conductivity at the 100-m scale. Brittle tectonic overprint is shown to be the principal parameter regulating inflow rate and dominates over depth and lithology. The highest early time inflow rate is 1,300 l/s and has been reported from a shallow hydropower gallery intersecting a 200-m wide cataclastic fault zone. The derived lognormal transmissivity distribution is based on 1,361 tunnel intervals with a length of 100 m. Such interval transmissivities range between 10−9 and 10−1 m2/s within the first 200–400 m of depth and between 10−9 and 10−4 m2/s in the depth interval of 400–1,500 m below ground surface. Outside brittle fault zones, a trend of decreasing transmissivity/hydraulic conductivity with increasing depth is observed for some schistous and gneissic geological units, whereas no trend is identified for the granitic units.ISSN:1431-2174ISSN:1435-015

Thermal model reduction using the super-face concept

The objective of this presentation is to carry out thermal model reduction in the context of the finite element method. The finite element model is decomposed in several sets of adjacent faces called super-faces. Specialized algorithms such as the METIS partitioning algorithm are used to automatically generate the super-faces. Several constraints may be imposed, e.g., the size of the super-face, its aspect ratio or its aperture angle. Once the model is decomposed, view factors between super-faces are calculated with direct numerical integration or ray-tracing methods. This method offers a very substantial reduction of the computational burden compared to the full model, which is particularly interesting for pre-design studies or specific applications such as deployable structures

Use of the specific surface to measure the efficiency of grids of drillholes and classify the resources of a set of 2D mineral deposits

International audienceThe hole spacing is an essential element that controls the precision of estimatedresources, hence their categorisation. Generally, with a regular sampling grid, thesmaller the grid cell, the better the precision. However, for a given grid, the precision also depends on the spatial continuity, typically the variogram of the targetvariable. The specific surface (specific volume in 2D) has been designed to measurethe efficiency of a grid cell, depending on this variogram. This further allows toapproximate the precision of the resources contained in volumes made by blockscentered on the grid and having the size of the grid cell. Classification of resourcescan be deduced by considering a number of blocks corresponding to a nominal, forexample annual, production. It provides an objective method to evaluate the levelof confidence of resources, then to make comparison of different projects.This concept of specific surface has been used by Orano, a leader of uraniummining industry, for the classification of the resources of a set of deposits at variousstages of regular sampling. The present paper illustrates the methodology in theexample of one such deposit. It also shows how the method can be used to make asynthetic comparison of different projects at the level of a mining company

Proper Orthogonal Decomposition for Nonlinear Radiative Heat Transfer Problems

peer reviewedAnalysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlinear multiphysical systems. The paper focuses on Proper Orthogonal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The radiative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a raytracing method. A reduction procedure is proposed for this fully coupled nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic approach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes separately. The paper builds on previous work presented previously by the authors. The results are given for the RMS error between either approach and the original, full solution

Initial value problem for one-dimensional rotating shallow water equations

In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we establish the local existence and the uniqueness of a solution to the hyperbolic system, as well as the global existence of a solution to the regularized system. In order to prove this, we use suitable variables that symmetrize the system

Initial value problem for one-dimensional rotating shallow water equations

In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we establish the local existence and the uniqueness of a solution to the hyperbolic system, as well as the global existence of a solution to the regularized system. In order to prove this, we use suitable variables that symmetrize the system

Investigating the performance of model order reduction techniques for nonlinear radiative heat transfer problems

The problem of nonlinear radiative heat transfer is one of great importance to the aerospace industry. However, analysing large-scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally expensive. This provides motivation for the development of Model-Order Reduction (MOR) techniques capable of reducing simulation times without the loss of important information. The objective is to demonstrate the method of Proper Orthogonal Decompostition (POD) as a technique for nonlinear MOR. The nonlinear radiative exchanges between a linear benchmark beam within an external box (Figure 1) are analysed and a reduction procedure for this fully coupled, nonlinear, multiphysical, thermomechanical system is established. The solution to the strongly coupled, thermomechanical equations of motion is found by making use of an extended version of the implicit generalized-alpha scheme. In the reduced model, the residual of the unreduced system of equations need to be evaluated at each Newton iteration of each time step. In order to optimise the efficiency of the reduction method it is shown that the internal forces can be split into their linear and nonlinear counterparts. Only the nonlinear terms change at each time step, thus only these terms need to remain in the iterative loop significantly reducing the number of parameters that are to be computed at each step. These efficiency improvements to the method are discussed and the results are given