Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.     

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.     

Evaluation of the temporal variations of groundwater storage and its interactions with climatic variables using GRACE data and hydrological models: A study from Turkey

Monitoring of the fluctuations of groundwater storage is particularly important in arid and semi-arid regions where water scarcity brings about various challenges. Remote sensing data and techniques play a preponderant role in developing solutions to environmental problems. The launch of Gravity Recovery and Climate Experiment (GRACE) satellites has eased the remote monitoring and evaluation of groundwater resources with an unprecedented precision over large scales. Within the scope of the current study, the latest release (RL06) of GRACE mass concentrations (Mascons) from Jet Propulsion Laboratory (JPL) dataset as well as Global Land Data Assimilation System (GLDAS) models of Noah and Catchment Land Surface Model (CLSM) were used to provide Groundwater Storage Anomalies (GWSA) over Turkey. The temporal interactions of the estimated GWSA with the climatic variables of precipitation and temperature (derived from the reanalysis datasets of CHELSA [Climatologies at High resolution for the Earth's Land Surface Areas] and FLDAS [the Famine Early Warning Systems Network Land Data Assimilation System], respectively) were investigated statistically. The results suggest that there is a descending trend (from 2003 to 2016) for Terrestrial Water Storage Anomalies (TWSA) and GWSA over Turkey with a total loss of 11 and 6 cm of water, respectively. The statistical analysis results also indicate that the monthly variations of GWSA over Turkey are highly correlated with precipitation and temperature at 2-month lag. The analysis of the climatology (long-term) values of monthly GWSA, precipitation and temperature also revealed high agreement between the variables.     

Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

We investigate our ability to assess transfer of hexavalent chromium, Cr(VI), from the soil to surface runoff by considering the effect of coupling diverse adsorption models with a two‐layer solute transfer model. Our analyses are grounded on a set of two experiments associated with soils characterized by diverse particle size distributions. Our study is motivated by the observation that Cr(VI) is receiving much attention for the assessment of environmental risks due to its high solubility, mobility, and toxicological significance. Adsorption of Cr(VI) is considered to be at equilibrium in the mixing layer under our experimental conditions. Four adsorption models, that is, the Langmuir, Freundlich, Temkin, and linear models, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes are associated with the highest release of Cr(VI) to runoff. We compare the relative abilities of the four models to interpret experimental results through maximum likelihood model calibration and four model identification criteria (i.e., the Akaike information criteria [AIC and AIC_C] and the Bayesian and Kashyap information criteria). Our study results enable us to rank the tested models on the basis of a set of posterior weights assigned to each of them. A classical variance‐based global sensitivity analysis is then performed to assess the relative importance of the uncertain parameters associated with each of the models considered, within subregions of the parameter space. In this context, the modelling strategy resulting from coupling the Langmuir isotherm with a two‐layer solute transfer model is then evaluated as the most skilful for the overall interpretation of both sets of experiments. Our results document that (a) the depth of the mixing layer is the most influential factor for all models tested, with the exception of the Freundlich isotherm, and (b) the total sensitivity of the adsorption parameters varies in time, with a trend to increase as time progresses for all of the models. These results suggest that adsorption has a significant effect on the uncertainty associated with the release of Cr(VI) from the soil to the surface runoff component.     

Predicting quantiles of water quality from catchment characteristics

Water quality is often highly variable both in space and time, which poses challenges for modelling the more extreme concentrations. This study developed an alternative approach to predicting water quality quantiles at individual locations. We focused on river water quality data that were collected over 25 years, at 102 catchments across the State of Victoria, Australia. We analysed and modelled spatial patterns of the 10th, 25th, 50th, 75th and 90th percentiles of the concentrations of sediments, nutrients and salt, with six common constituents: total suspended solids (TSS), total phosphorus (TP), filterable reactive phosphorus (FRP), total Kjeldahl nitrogen (TKN), nitrate-nitrite (NO_x), and electrical conductivity (EC). To predict the spatial variation of each quantile for each constituent, we developed statistical regression models and exhaustively searched through 50 catchment characteristics to identify the best set of predictors for that quantile. The models predict the spatial variation in individual quantiles of TSS, TKN and EC well (66%–96% spatial variation explained), while those for TP, FRP and NO_x have lower performance (37%–73% spatial variation explained). The most common factors that influence the spatial variations of the different constituents and quantiles are: annual temperature, percentage of cropping land area in catchment and channel slope. The statistical models developed can be used to predict how low- and high-concentration quantiles change with landscape characteristics, and thus provide a useful tool for catchment managers to inform planning and policy making with changing climate and land use conditions.     

Changes in hillslope hydrology in a perched,shallow soil system due to clearcutting and residual biomass removal

Sustainable fuels legislation and volatility in energy prices have put additional pressures on the forestry sector to intensify the harvesting of biomass for “advanced biofuel” production. To better understand how residual biomass removal after harvest affects forest hydrology in relatively low slope terrain, a Before-After-Control-Impact (BACI) study was conducted in the USDA Forest Service's Marcell Experimental Forest, Minnesota, USA. Hydrological measurements were made from 2010–2013 on a forested hillslope that was divided into three treatment blocks, where one block was harvested and residual biomass removed (Biomass Removed), the second was harvested and residual biomass left (Biomass Left), and the last block was left as an Unharvested Control. The pre-harvest period (2 years) was 2010–11 and post-harvest (2 years) was 2012–13. Water table elevation at the upslope and downslope position, subsurface runoff, and soil moisture were measured between May–November. Mixed effect statistical models were used to compare both the before-after and “control” treatment ratios (ratios between harvested hillslopes and the Unharvested Control hillslope). Subsurface runoff significantly increased (p < .05) at both harvested hillslopes but to a greater degree on the Biomass Left hillslope. Greater subsurface runoff volumes at both harvested hillslopes were driven by substantial increases during fall, with additional significant increases during summer on the Biomass Left hillslope. The hydrological connectivity, inferred from event runoff ratios, increased due to harvesting at both hillslopes but only significantly on the Biomass Left hillslope. The winter harvest minimized soil disturbance, resulting in no change to the effective hydraulic conductivity distribution with depth. Thus, the observed hydrological changes were driven by increased effective precipitation and decreased evapotranspiration, increasing the duration that both harvested hillslopes were hydrologically active. The harvesting of residual biomass appears to lessen hydrological connectivity relative to leaving residual biomass on the hillslope, potentially decreasing downstream hydrological impacts of similar forestry operations.     

Solution for a plane strain rough‐walled hydraulic fracture driven by turbulent fluid through impermeable rock

The impact of turbulent flow on plane strain fluid‐driven crack propagation is an important but still poorly understood consideration in hydraulic fracture modeling. The changes that hydraulic fracturing has experienced over the past decade, especially in the area of fracturing fluids, have played a major role in the transition of the typical fluid regime from laminar to turbulent flow. Motivated by the increasing preponderance of high‐rate, water‐driven hydraulic fractures with high Reynolds number, we present a semianalytical solution for the propagation of a plane strain hydraulic fracture driven by a turbulent fluid in an impermeable formation. The formulation uses a power law relationship between the Darcy‐Weisbach friction factor and the scale of the fracture roughness, where one specific manifestation of this generalized friction factor is the classical Gauckler‐Manning‐Strickler approximation for turbulent flow in a rough‐walled channel. Conservation of mass, elasticity, and crack propagation are also solved simultaneously. We obtain a semianalytical solution using an orthogonal polynomial series. An approximate closed‐form solution is enabled by a choice of orthogonal polynomials embedding the near‐tip asymptotic behavior and thus giving very rapid convergence; a precise solution is obtained with 2 terms of the series. By comparison with numerical simulations, we show that the transition region between the laminar and turbulent regimes can be relatively small so that full solutions can often be well approximated by either a fully laminar or fully turbulent solution.     

Modelling the poroelastoplastic behaviour of soils subjected to internal erosion by suffusion

Granular soils subjected to seepage flow may suffer suffusion, ie, a selective internal erosion. Extending the classical approach of poromechanics, we deduce a new form of the Clausius-Duhem inequality accounting for dissipation due to suffusion, and we deduce restrictions on the constitutive laws of the soil. We suggest (a) a possible coupling between the seepage forces and the suffusion kinetics and (b) an extension of an existing elastoplastic model for the skeleton mechanical behaviour. Numerical integrations of the elastoplastic model are carried out under drained axisymmetric triaxial and oedometric conditions. As a result, we prove that the extended model is able to qualitatively reproduce the suffusion induced strains and the strength reduction experimentally observed. Predictions on the oedometric behaviour of suffusive soils are also provided.     

A modified numerical model for moisture-salt transport in unsaturated sandy soil under evaporation

Soil salinization, caused by salt migration and accumulation underneath the soil surface, will corrode structures. To analyze the moisture-salt migration and salt precipitation in soil under evaporation conditions, a mathematical model consisting of a series of theoretical equations is briefly presented. The filling effect of precipitated salts on tortuosity factor and evaporation rate are taken into account in relevant equations. Besides, a transition equation to link the solute transport equation before and after salt precipitation is proposed. Meanwhile, a new relative humidity equation deduced from Pitzer ions model is used to modify the vapor transport flux equation. The results show that the calculated values are in good agreement with the published experimental data, especially for the simulation of volume water content and evaporation rate of Toyoura sand, which confirm the reliability and applicability of the proposed model.     

High energy phenomena in eta carinae

We have investigated with BeppoSAX the long term behaviour of the harder X-ray component of the supposed supermassive binary system η Car along its 5.52 year cycle. We have found that in March 1998 during egress from the last December 1997 eclipse, this component was the same as outside eclipse, but for a large (×3.5) increase of NH _h , that can be attributed to the presence or formation of opaque matter in front of the source near periastron. Unexpectedly, at that time the iron 6.7 keV emission line was 40% stronger. BeppoSAX has for the first time found ahard X-ray tail extending to at least 50 keV, that cannot be adequately fitted with an additional hotter thermal component. The 2–100 keV spectrum of η Car is instead well fitted with an absorbed powerlaw spectrum with photon index 2.53, suggesting non-thermal emission as an alternative model for the core source.