Interpretation of Core Extrusion Measurements When Tunnelling Through Squeezing Ground

Squeezing intensity in tunnelling often varies over short distances, even where there is no change in the excavation method or lithology. Reliable predictions of the ground conditions ahead of the face are thus essential to avoid project setbacks. Such predictions would enable adjustments to be made during construction to the temporary support, to the excavation diameter and also to the final lining. The assessment of the behaviour of the core ahead of the face, as observed by means of extrusion measurements, provides some indications as to the mechanical characteristics of the ground. If the ground exhibits a moderate time-dependent behaviour and the effects of the support measures are taken into account, the prediction of convergence is feasible. If the ground behaviour is pronouncedly time-dependent, however, convergence predictions become very difficult, because core extrusion is governed by the short-term characteristics of the ground, which may be different from the long-term properties that govern final convergence. The case histories of the Gotthard Base Tunnel and of the Vasto tunnel show that there is a weak correlation between the axial extrusions and the convergences of the tunnel. By means of the case histories of the Tartaiguille tunnel and Raticosa tunnel, it is shown that to identify potentially weak zones on the basis of the extrusion measurements, careful processing of the monitoring data is essential: the analysis of the data has to take account of the effects of tunnel support and time, and has to eliminate errors caused by the monitoring proces

Operational Planning of Active Distribution Grids under Uncertainty

Modern distribution system operators are facing constantly changing operating conditions caused by the increased penetration of intermittent renewable generators and other distributed energy resources. Under these conditions, the distribution system operators are required to operate their networks with increased uncertainty, while ensuring optimal, cost-effective, and secure operation. This paper proposes a centralized scheme for the operational planning of active distribution networks under uncertainty. A multi-period optimal power flow algorithm is used to compute optimal set-points of the controllable distributed energy resources located in the system and ensure its security. Computational tractability of the algorithm and feasibility of the resulting flows are ensured with the use of an iterative power flow method. The system uncertainty, caused by forecasting errors of renewables, is handled through the incorporation of chance constraints, which limit the probability of insecure operation. The resulting operational planning scheme is tested on a low-voltage distribution network model using real forecasting data for the renewable energy sources. We observe that the proposed method prevents insecure operation through efficient use of system controls

Predicting Fracture in the Proximal Humerus using Phase Field Models

Proximal humerus impacted fractures are of clinical concern in the elderly population. Prediction of such fractures by CT-based finite element methods encounters several major obstacles such as heterogeneous mechanical properties and fracture due to compressive strains. We herein propose to investigate a variation of the phase field method (PFM) embedded into the finite cell method (FCM) to simulate impacted humeral fractures in fresh frozen human humeri. The force-strain response, failure loads and the fracture path are compared to experimental observations for validation purposes. The PFM (by means of the regularization parameter $l_0$) is first calibrated by one experiment and thereafter used for the prediction of the mechanical response of two other human fresh frozen humeri. All humeri are fractured at the surgical neck and strains are monitored by Digital Image Correlation (DIC). Experimental strains in the elastic regime are reproduced with good agreement ($R^2 = 0.726$), similarly to the validated finite element method [9]. The failure pattern and fracture evolution at the surgical neck predicted by the PFM mimic extremely well the experimental observations for all three humeri. The maximum relative error in the computed failure loads is $3.8\%$. To the best of our knowledge this is the first method that can predict well the experimental compressive failure pattern as well as the force-strain relationship in proximal humerus fractures

Local spectroscopy and atomic imaging of tunneling current, forces and dissipation on graphite

Theory predicts that the currents in scanning tunneling microscopy (STM) and the attractive forces measured in atomic force microscopy (AFM) are directly related. Atomic images obtained in an attractive AFM mode should therefore be redundant because they should be \emph{similar} to STM. Here, we show that while the distance dependence of current and force is similar for graphite, constant-height AFM- and STM images differ substantially depending on distance and bias voltage. We perform spectroscopy of the tunneling current, the frequency shift and the damping signal at high-symmetry lattice sites of the graphite (0001) surface. The dissipation signal is about twice as sensitive to distance as the frequency shift, explained by the Prandtl-Tomlinson model of atomic friction.Comment: 4 pages, 4 figures, accepted at Physical Review Letter

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Local Anisotropy of Fluids using Minkowski Tensors

Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices $0\leq \beta_\nu^{a,b}\leq 1$ of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from $\beta_\nu^{a,b}\approx 0.3$ for vapor phases to $\beta_\nu^{a,b}\to 1$ for ordered solids. We find that for fluids, local anisotropy decreases monotonously with increasing free volume and randomness of particle positions. Furthermore, the local anisotropy indices $\beta_\nu^{a,b}$ are sensitive to structural transitions in these simple fluids, as has been previously shown in granular systems for the transition from loose to jammed bead packs

Studies of the dose-effect relation

Dose-effect relations and, specifically, cell survival curves are surveyed with emphasis on the interplay of the random factors — biological variability, stochastic reaction of the cell, and the statistics of energy deposition —that co-determine their shape. The global parameters mean inactivation dose, , and coefficient of variance, V, represent this interplay better than conventional parameters. Mechanisms such as lesion interaction, misrepair, repair overload, or repair depletion have been invoked to explain sigmoid dose dependencies, but these notions are partly synonymous and are largely undistinguishable on the basis of observed dose dependencies. All dose dependencies reflect, to varying degree, the microdosimetric fluctuations of energy deposition, and these have certain implications, e.g. the linearity of the dose dependence at small doses, that apply regardless of unresolved molecular mechanisms of cellular radiation action