Characterisation and modelling of natural fracture networks: geometry, geomechanics and fluid flow

Natural fractures are ubiquitous in crustal rocks and often dominate the bulk properties of geological formations. The development of numerical tools to model the geometry, geomechanics and fluid flow behaviour of natural fracture networks is a challenging issue which is relevant to many rock engineering applications. The thesis first presents a study of the statistics and tectonism of a multiscale fracture system in limestone, from which the complexity of natural fractures is illustrated with respect to hierarchical topologies and underlying mechanisms. To simulate the geomechanical behaviour of rock masses embedded with natural fractures, the finite-discrete element method (FEMDEM) is integrated with a joint constitutive model (JCM) to solve the solid mechanics problems of such intricate discontinuity systems explicitly represented by discrete fracture network (DFN) models. This computational formulation can calculate the stress/strain fields of the rock matrix, capture the mechanical interactions of discrete rock blocks, characterise the non-linear deformation of rough fractures and mimic the propagation of new cracks driven by stress concentrations. The developed simulation tool is used to derive the aperture distribution of various fracture networks under different geomechanical conditions, based on which the stress-dependent fluid flow is further analysed. A novel upscaling approach to fracture network models is developed to evaluate the scaling of the equivalent permeability of fractured rocks under in-situ stresses. The combined JCM-FEMDEM model is further applied to simulate the progressive rock mass failure around an underground excavation in a crystalline rock with pre-existing discontinuities. The scope of this thesis covers the scenarios of both two-dimensional (2D) and three-dimensional (3D) fracture networks with pre-existing natural fractures and stress-induced new cracks. The research findings demonstrate the importance of integrating explicit DFN representations and conducting geomechanical computations for more meaningful assessments of the hydromechanical behaviour of naturally fractured rocks.Open Acces

A Liouville theorem for the fractional Ginzburg-Landau equation

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation \begin{equation*} u(x)=\int_{\mathbb{R}^{n}}\frac{u(1-|u|^{2})}{|x-y|^{n-\alpha}}dy, \end{equation*} where $u: \mathbb{R}^{n} \to \mathbb{R}^{k}$ with $k \geq 1$ and $1<\alpha<n/2$. We prove that $u \in L^2(\mathbb{R}^n) \Rightarrow u \equiv 0$ on $\mathbb{R}^n$, as long as $u$ is a bounded and differentiable solution.Comment: 7 page

New approach to improve the performance of fringe pattern profilometry using multiple triangular patterns for the measurement of objects in motion

Fringe pattern profilometry using triangular patterns and intensity ratios is a robust and computationally efficient method in three-dimensional shape measurement technique. However, similar to other multiple-shot techniques, the object must be kept static during the process of measurement, which is a challenging requirement for the case of fast-moving objects. Errors will be introduced if the traditional multiple-shot techniques are used directly in the measurement of a moving object. A new method is proposed to address this issue. First, the movement of the object is measured in real time and described by the rotation matrix and translation vector. Then, the expressions are derived for the fringe patterns under the influence of the two-dimensional movement of the object, based on which the normalized fringe patterns from the object without movement are estimated. Finally, the object is reconstructed using the existing intensity ratio algorithm incorporating the fringe patterns estimated, leading to improved measurement accuracy. The performance of the proposed method is verified by experiments

Hilbert expansion for kinetic equations with non-relativistic Coulomb collision

In this paper, we study the hydrodynamic limits of both the Landau equation and the Vlasov-Maxwell-Landau system in the whole space. Our main purpose is two-fold: the first one is to give a rigorous derivation of the compressible Euler equations from the Landau equation via the Hilbert expansion; while the second one is to prove, still in the setting of Hilbert expansion, that the unique classical solution of the Vlasov-Maxwell-Landau system converges, which is shown to be globally in time, to the resulting global smooth solution of the Euler-Maxwell system, as the Knudsen number goes to zero. The main ingredient of our analysis is to derive some novel interplay energy estimates on the solutions of the Landau equation and the Vlasov-Maxwell-Landau system which are small perturbations of both a local Maxwellian and a global Maxwellian, respectively. Our result solves an open problem in the hydrodynamic limit for the Landau-type equations with Coulomb potential and the approach developed in this paper can seamlessly be used to deal with the problem on the validity of the Hilbert expansion for other types of kinetic equations

Global Hilbert expansion for some non-relativistic kinetic equations

The Vlasov-Maxwell-Landau (VML) system and the Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this paper, we are concerned with the hydrodynamic limits of both the VML and the non-cutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or non-cutoff VMB system converges globally over time to the smooth global solution of the Euler-Maxwell system as the Knudsen number approaches zero. The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau-type equations and non-cutoff Boltzmann-type equations with a magnetic field. Furthermore, the approach developed in this paper can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations.Comment: 61 pages;Some statements of main theorems are adjusted;Partial results about the VML system was annouced in arxiv:2209.1520

Research of dimensionless index for fault diagnosis positioning based on EMD

Dimensionless index as a new theory tool has been applied in fault diagnosis study, which has shown some progress, however, it will cause some interference to the diagnosis results since no considering the influence of other noise jamming signal is given. Empirical Mode Decomposition (EMD) technique could extract effectively the fault characteristic signal of vibration data. In view of the noise jamming of dimensionless index in analyzing data, dimensionless index processing algorithms based on EMD is proposed. Firstly, EMD method is used to decompose the collected vibration signals, then the first few Intrinsic Mode Functions (IMF) components are obtained which contains the fault characteristic of vibration data, and the effects of other noise signal are removed at the same time. Secondly, fault diagnosis can be achieved by calculating dimensionless parameter values to the IMF components with characteristic signal of vibration data, and obtaining range of characteristic value of their dimensionless index, then diagnosing and analyzing fault characteristics of the equipment. The proposed method is applied to fault diagnosis test analysis of rotating machinery, and the experiment has shown that the proposed method is efficient and effective

Simultaneous manipulation of electromagnetic and elastic waves via glide symmetry phoxonic crystal waveguides

A phoxonic crystal waveguide with the glide symmetry is designed, in which both electromagnetic and elastic waves can propagate along the glide plane at the same time. Due to the band-sticking effect, super-cell bands of the waveguide degenerate in pairs at the boundary of the Brillouin zone, causing the appearance of gapless guided-modes in the bandgaps. The gapless guided-modes are single-modes over a relatively large frequency range. By adjusting the magnitude of the glide dislocation, the edge bandgaps of the guided-modes can be further adjusted, so as to achieve photonic and phononic single-mode guided-bands with relatively flat dispersion relationship. In addition, there exists acousto-optic interaction in the cavity constructed by the glide plane. The proposed waveguide has potential applications in the design of novel optomechanical devices.Comment: 16 pages, 9 figure

An Immune Detector-Based Method for the Diagnosis of Compound Faults in a Petrochemical Plant

Aiming at the serious overlap of traditional dimensionless indices in the diagnosis of compound faults in petrochemical plants, we use genetic programming to construct optimal indices for that purpose. In order to solve the problem of losing some useful fault feature information due to classification processing, during the generation of the dimensionless index immune detector, such as reduction and clustering, we propose an integrated diagnosis method using each dimensionless index immune detector. Simulation results show that this method has high diagnostic accuracy