A coupled hydro-mechanical analysis for prediction of hydraulic fracture propagation in saturated porous media using EFG mesh-less method

The details of the Element Free Galerkin (EFG) method are presented with the method being applied to a study on hydraulic fracturing initiation and propagation process in a saturated porous medium using coupled hydro-mechanical numerical modelling. In this EFG method, interpolation (approximation) is based on nodes without using elements and hence an arbitrary discrete fracture path can be modelled.The numerical approach is based upon solving two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Displacement increment and pore water pressure increment are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system of equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on the penalty method. In order to model discrete fractures, the so-called diffraction method is used.Examples are presented and the results are compared to some closed-form solutions and FEM approximations in order to demonstrate the validity of the developed model and its capabilities. The model is able to take the anisotropy and inhomogeneity of the material into account. The applicability of the model is examined by simulating hydraulic fracture initiation and propagation process from a borehole by injection of fluid. The maximum tensile strength criterion and Mohr-Coulomb shear criterion are used for modelling tensile and shear fracture, respectively. The model successfully simulates the leak-off of fluid from the fracture into the surrounding material. The results indicate the importance of pore fluid pressure in the initiation and propagation pattern of fracture in saturated soils. © 2013 Elsevier Ltd.

Differentiate performance of eight filter media in vertical flow constructed wetland: Removal of organic matter, nitrogen and phosphorus

A comparative study was conducted to reveal the differentiate effects of eight different filter media including gravel, zeolites, anthracite, shale, vermiculite, ceramic filter media, blast furnace steel slag and round ceramsite. The study mainly related to the eight different filter media's removal performances of organic matter, nitrogen and phosphorus in the vertical flow constructed wetland simulated system, which treating wastewater at hydraulic loading rate of 1000-2500 mm/d. The results indicated that the removal effects were closely related to the physical and chemical properties of medium materials. Anthracite-filled system had the highest removal rate for the total organic carbon (TOC), up to 70%, and the removal rates of other systems ranged from 20% to 30%. As for the five-day biochemical oxygen demand (BOD5), anthracite-filled and steel slag-filled systems had the highest removal rates, also up to 70%, as well as other systems all exceeded 50%. At the same time, for the total nitrogen (TN) and NH4(+)-N, the zeolites-filled and ceramic-filled systems had the best performances with the removal rates of more than 70%, the other way round, the removal rates of other systems were only about 20%. The distinguishable effects were also observed in removal performances of total phosphorus (TP) and total dissoluble phosphorus (TDP). The removal rates of TP and TDP in steel slag-filled systems were more than 90%, a much higher value, followed by that of the anthracite-filled system, more than 60%, but those of other systems being the less. Our study provided a potential mechanism to optimize the filter media design for the vertical flow constructed wetlands.

Status and trends of short pulse generation using mode-locked lasers based on advanced quantum-dot active media

In this review, the potential of mode-locked lasers based on advanced quantum-dot ( QD) active media to generate short optical pulses is analysed. A comprehensive review of experimental and theoretical work on related aspects is provided, including monolithic-cavity mode-locked QD lasers and external-cavity mode-locked QD lasers, as well as mode-locked solid-state and fibre lasers based on QD semiconductor saturable absorber mirrors. Performance comparisons are made for state-of-the-art experiments. Various methods for improving important characteristics of mode-locked pulses such as pulse duration, repetition rate, pulse power, and timing jitter through optimization of device design parameters or mode-locking methods are addressed. In addition, gain switching and self-pulsation of QD lasers are also briefly reviewed, concluding with the summary and prospects.

One-dimensional incoherently coupled grey solitons in two-photon photorefractive media

We show that grey solitons, grey-grey soliton pairs, and multi-component grey solitons can be realized in two-photon photorefractive media. The results for soliton pairs and multi-component solitons are derived under the assumption that the carrier beams share the same polarization, wavelength, and are mutually incoherent.

Dark incoherent spatial solitons in logarithmically saturable nonlinear media

This paper studies numerically the dark incoherent spatial solitons propagating in logarithmically saturable nonlinear media by using a coherent density approach and a split-step Fourier approach for the first time. Under odd and even initial conditions, a soliton triplet and a doublet are obtained respectively for given parameters. Simultaneously, coherence properties associated with the soliton triplet and doublet are discussed. In addition, if the values of the parameters are properly chosen, five and four splittings from the input dark incoherent spatial solitons can also form. Lastly, the grayness of the soliton triplet and that of the doublet are studied, in detail.

Evolution of Localized Damage Zone in Heterogeneous Media

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.