Fracture Mechanism of Brazilian Discs with Multiple Parallel Notches Using PFC2D

This study presents crack initiation, propagation and coalescenceat or near pre-existing open cracks in a numericalmodel under Brazilian test. Firstly, Particle Flow Code intwo dimensions (PFC2d) was calibrated with respect to thedata obtained from experimental laboratory tests to ensurethe conformity of the simulated numerical models response.Brazilian discs contain one, two, three, four, and five parallelcentred cracks (45° to the horizontal) under compressiveline loading. Models containing two and three cracks havedifferent joint spacing and joint configuration. In model consistingone flaws, tensile cracks initiated from notch tip andpropagates in direction of compressive loading till coalescewith model edge. By increasing the number of notch, first typeof tensile crack initiated at the tips of outer flaws and coalescedwith model edge. Also second type of tensile cracksinitiates from middle of inner flaws and coalesce with tip ofthe neighbouring flaws. The results show that joint spacingand joint configuration has important effect on the failure patternin model consisting two and three notch. Experimentaland numerical results rendered by other researchers showed agood agreement with the numerical results in the coalescencecharacteristics in cracked model. In addition, crack initiationand coalescence stresses in models were analyzed and comparedwith those in the single-flawed model

SIMULACIJA SANACIJE VODONOSNIKA SLABOPROPUSNIH LEĆA FENOMENOM POVRATNE DIFUZIJE

Fluid flow in a dual permeable medium (DPM) is essential in solute transport in mining and aquifer studies. In this paper, water flushing into a contaminated DPM containing fine-grained lenses with different geometries was investigated with the Lattice Boltzmann Method (LBM). The LBM model used in this study was D2Q9 with a relaxation time of 1, a cohesion value of 3 for a fluid density of 1 (mu.Lu-3). The saturated fluid in the DPM was a contaminant that usually stays in low permeable lenses and after flushing, it is leaked into the porous medium by a second fluid (water). This phenomenon is predominant when the displacing fluid has a lower concentration than the contaminated fluid. Diffusion and advection are the main mechanisms that control fluid flow in the porous medium. The results of the simulations showed: (1) advection controlled solute transport through the flushing phase, and back-diffusion occurred after the change in phase; (2) the lenses’ geometry influenced the fluid flow pattern and the remediation process. As a result, aquifer remediation strategies based on the lenses’ geometry and their permeability can help us select the appropriate environmental protection.Protjecanje fluida kroz medije s dvostrukom propusnošću bitno je kod proučavanja transporta otopljene tvari u rudarstvu ili kroz vodonosnik. U ovome radu, s pomoću metode Boltzmannove rešetke, istraženo je ispiranje vodom medija dvostruke propusnosti koji sadržava sitnozrnate leće različite geometrije. Metoda Boltzmannove rešetke u ovome istraživanju uključivala je korištenje modela D2Q9 s vremenom otpuštanja 1 te vrijednošću kohezije 3 za fluid gustoće 1 (mu. Lu-3). Medij dvostruke propusnosti zasićen je fluidom koji je ujedno predstavljao i zagađivač koji se obično zadržavao u slabopropusnim lećama iz kojih se širio nakon ispiranja poroznoga medija sekundarnim fluidom (vodom). Ova je pojava prevladavajuća u slučaju kada istiskujući fluid ima manju koncentraciju od kontaminiranoga fluida, a difuzija i advekcija dva su osnovna mehanizma koja kontroliraju tok fluida kroz šupljikavu sredinu. Rezultati simulacije pokazuju da: (1) advekcija kontrolira transport otopljene tvari tijekom faze ispiranja, dok se povratna difuzija odvija nakon promjene u fazi; (2) geometrija leća utječe na oblik toka i proces sanacije. Rezultat je strategija sanacije vodonosnika bazirana na geometriji i propusnosti leća koja može pomoći u zaštiti okoliša

SIMULACIJA ZAGAĐENJA PODZEMNIH VODA S MJESTA ODLAGANJA RUDARSKOGA OTPADA

Mining wastes are a great source of pollutants. Open-pit backfill materials can be found as waste rock and as tailings. The aim of the current study was the investigation of the contaminant transportation pathways by groundwater flow from these waste materials through heterogeneous porous media. Numerical Lattice Boltzmann Method (LBM) was used for examining the effects of different factors on pollutant transportation through groundwater beneath the waste materials. Grain size, vertical and horizontal fracturing, and hydraulic pressure gradient were factors considered here. The results showed that contaminant transportation by the groundwater flow from the waste materials through porous media depends on primary and secondary matrix porosity of the open-pit material, heterogeneity in permeability of aquifer rock, and hydraulic head of groundwater.Rudarski otpad velik je izvor onečišćenja. Kao materijali za zatrpavanje otvorenih jama mogu se koristiti otpadne stijene i jalovina. Cilj ove studije bio je istražiti putove transporta onečišćenja podzemnim vodama iz ovih otpadnih materijala kroz heterogene porozne medije. Boltzmannova metoda numeričke rešetke (LBM) korištena je za određivanje učinaka različitih čimbenika na transport onečišćujućih tvari kroz podzemne vode ispod otpadnih materijala. Čimbenici koji su uzeti u obzir bili su veličina zrna, okomite i vodoravne pukotine te hidraulički gradijent tlaka. Rezultati su pokazali da prijenos onečišćenja protokom podzemnih voda iz otpadnih materijala kroz porozne medije ovisi o poroznosti primarne i sekundarne matrice otkopanih materijala, heterogenosti propusnosti stijene vodonosnika i hidrauličkom tlaku podzemne vode

Displacement Discontinuity Analysis of the Effects of Various Hydraulic Fracturing Parameters on the Crack Opening Displacement (COD)

The combination of horizontal drilling along with hydraulic fracturing has significantly improved the production of hydrocarbon reservoirs and made it possible to extract the relatively impermeable and uneconomical reservoirs. The production rate of oil and gas wells increases proportional to hydraulic fracture aperture or crack opening displacement (COD). This is an important parameter in fracture mechanics literature and hydraulic fracturing of hydrocarbon reservoirs. Despite the significance of COD there are a few analytical solutions for the estimation of COD under certain conditions. In this paper the effect of various parameters on COD is investigated semi-analytically. A higher order displacement discontinuity method is used to consider the effects of different parameters (Young’s modulus, Poisson’s ratio, internal pressure, maximum and minimum horizontal stresses, crack half-length and its inclination with maximum horizontal stress) on the COD in a hydraulic fracturing process under arbitrarily conditions. The coefficient of determination and standard error of the estimate were 94.35% and 4.37×10-4 respectively, showing a good agreement between the fitted equation and the numerical results. The effect of propagation and well radius on the maximum COD was also investigated. The results showed that COD increases almost linearly with the crack propagation and increase of well radius of hydraulic fractures (HFs). These effects are more significant when HFs are propagating in the direction of maximum horizontal stress. The proposed equation and the results from propagation of hydraulic fractures can be used in early stages of a hydraulic fracturing design</span

Modeling of cracks in rock fragmentation with a higher order displacement discontinuity method

Ph.D. - Doctoral Progra

A proper borehole pattern design for coal seam methane drainage in Tabas coal mine using Comsol Multiphysics

Optimizing the operational parameters of the borehole pattern in the coal seam includes the maximum amount of gas to be drained with the least amount of drilling, investment, and drainage time. The main purpose of this research is to properly design the drainage borehole pattern in the C1 coal seam of the Tabas coal mine. In this research, the Comsol Multiphysics software was used for numerical modeling of the boreholes. According to the method of diffusion of methane gas in a coal seam, the reduction of methane gas concentration and the amount of gas released from the coal blocks were approximated. For the gas drainage boreholes, the three patterns of the rectangular, parallelogram, and triangular forms were considered. Also, the boreholes were modeled with the three diameters of 76, 86, and 96 mm. This modeling was performed for 180 days of drainage operation and showed that the triangular pattern was more suitable than the other two patterns. The presented model is applicable in coal mines where gas drainage operations are necessary and helps engineers design the patterns of drainage boreholes to maximize their gas drainage efficiency

A Fourth Order Formulation of DDM for Crack Analysis in Brittle Solids

A fourth order formulation of the displacement discontinuity method (DDM) is proposed for the crack analysis of brittle solids such as rocks, glasses, concretes and ceramics. A fourth order boundary collocation scheme is used for the discretization of each boundary element (the source element). In this approach, the source boundary element is divided into five sub-elements each recognized by a central node where the displacement discontinuity components are to be numerically evaluated. Three different formulating procedures are presented and their corresponding discretization schemes are discussed. A new discretization scheme is also proposed to use the fourth order formulation for the special crack tip elements which may be used to increase the accuracy of the stress and displacement fields near the crack ends. Therefore, these new crack tips discretizing schemes are also improved by using the proposed fourth order displacement discontinuity formulation and the corresponding shape functions for a bunch of five special crack tip elements. Some example problems in brittle fracture mechanics are solved for estimating the Mode I and Mode II stress intensity factors near the crack ends. These semi-analytical results are compared to those cited in the fracture mechanics literature whereby the high accuracy of the fourth order DDM formulation is demonstrated