Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

Severe soil erosion during a 3‐day exceptional rainfall event: combining modelling and field data for a fallow cereal field

Exceptional rainfall events cause significant losses of soil, although few studies have addressed the validation of model predictions at field scale during severe erosive episodes. In this study, we evaluate the predictive ability of the enhanced Soil Erosion and Redistribution Tool (SERT‐2014) model for mapping and quantifying soil erosion during the exceptional rainfall event (~235 mm) that affected the Central Spanish Pyrenees in October 2012. The capacity of the simulation model is evaluated in a fallow cereal field (1.9 ha) at a high spatial scale (1 × 1 m). Validation was performed with field‐quantified rates of soil loss in the rills and ephemeral gullies and also with a detailed map of soil redistribution. The SERT‐2014 model was run for the six rainfall sub‐events that made up the exceptional event, simulating the different hydrological responses of soils with maximum runoff depths ranging between 40 and 1017 mm. Predicted average and maximum soil erosion was 11 and 117 Mg ha^?1 event^?1, respectively. Total soil loss and sediment yield to the La Reina gully amounted to 16.3 and 9.0 Mg event^?1. These rates are in agreement with field estimations of soil loss of 20.0 Mg event^?1. Most soil loss (86%) occurred during the first sub‐event. Although soil accumulation was overestimated in the first sub‐event because of the large amount of detached soil, the enhanced SERT‐2014 model successfully predicted the different spatial patterns and values of soil redistribution for each sub‐event. Further research should focus on stream transport capacity. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability analysis of tunnels driven in jointed rocks by means of a homogenized limit analysis approach

Conceived as a potential alternative to the classical design methods employed for analyzing the stability of underground structures driven in jointed rocks, the homogenization approach stems from the heuristic idea that, from a macroscopic point of view, a rock mass cut by a network of joints may be perceived as a homogenized continuum. The strength properties of the latter can be theoretically obtained from the failure conditions of its individual constituents: rock matrix and joint interfaces. At the material level, the limit analysis reasoning is used in the context of homogenization to formulate the homogenized strength criterion of a jointed rock mass in the particular situation of a single set of parallel joints. As it could be expected, the obtained closed‐form expressions show the strength anisotropy induced by joint preferential orientation. The support functions (π functions) associated with the homogenized strength criterion are also determined in both plane strain and three‐dimensional cases. This criterion is then applied to the investigation of stability analysis of a tunnel excavated in a jointed rock mass. Upper bounds estimated of the stability factor are derived from the implementation of the kinematic approach directly on the homogenized underground structure. Finally, the approach is applied to analyze and discuss the collapse of the Pinheiros subway station (São Paulo, Brazil). Copyright © 2014 John Wiley & Sons, Ltd.     

Elastoplastic model with loading memory surfaces (LMS) for monotonic and cyclic behaviour of geomaterials

A new elastoplastic model called loading memory surface based on the critical state concept and the multi‐surface framework is proposed for geomaterials. The model uses a hypoelastic formulation and two plastic mechanisms. The formulations of the model are made in three‐dimensional stress–strain space and work under both monotonic and cyclic loadings. A newly introduced formalism makes it possible to obtain the cyclic response directly from the monotonic loading one. This formalism gives a three‐dimensional generalization of the well‐known Masing rule. The model has been validated against test results of Hostun sand under several conditions: monotonic and cyclic, drained and undrained, tests in compression and in extension, and at different confining pressures and different densities. Copyright © 2014 John Wiley & Sons, Ltd.     

Response of suspended sediment particle size distributions to changes in water chemistry at an Andean mountain stream confluence receiving arsenic rich acid drainage

Acid drainage is an important water quality issue in Andean watersheds, affecting the sustainability of urban, agricultural, and industrial activities. Mixing zones receiving acid drainage are critical sites where changes in pH and chemical environment promote the formation and dissolution of iron and aluminum oxy/hydroxides. These particles can significantly change the speciation of toxic metals and metalloids throughout drainage networks via sorption, desorption, and settling processes. However, little is known about the behavior of particle size distributions (PSDs) in streams affected by acid drainage and their relationship to metal speciation. This work studied: (a) the PSDs for a wide range of mixing ratios found at a fluvial confluence affected by acid drainage, and (b) the response of PSDs and arsenic speciation to environmental changes found when the particles approach complete mixing conditions. The confluence between the Azufre River (pH ~ 2, high concentration of dissolved metals) and Caracarani River (pH = 8.6, low concentration of dissolved metals) was used as a representative model for study. Field measurements show a bimodal PSD with modal diameters of ~50 and 300 μm. At shorter distances from the junction, the smaller modes with smaller particle volumes were dominant across the stream cross‐sections. A systematic shift towards larger particle sizes and larger particle volumes occurred downstream. The analysis of laboratory PSDs for Azufre/Caracarani mixing ratios between 0.01 and 0.5 (pH from 6.2 to 2.3) showed a bimodal trend with ~15 and 50 μm characteristic diameters; larger particles formed at pH>4. When particle suspensions were transferred in laboratory experiments from very low pH to full mixing conditions (pH ~ 2.8 and mixing ratio ~ 0.25) particle sizes varied, and the dissolved arsenic concentration decreased. The observed reaction kinetics were slow compared to the time scale of advective transport, creating opportunities for engineered controls for arsenic. This work contributes to a better understanding of the chemical‐hydrodynamic interactions in watersheds affected by mining, and identifying opportunities to improve water quality at points of use.     

The supergene origin of ruthenian hexaferrum in Ni‐laterites

For two decades, the nature of Fe‐rich, oxygen‐bearing, Ru–Os compounds found in the supergene environment has been debated. Ru–Os–Fe‐oxides and nano‐intergrowths of ruthenium with magnetite have been proposed. We applied FE‐SEM, EMPA, μ‐Raman spectroscopy and synchrotron tts‐μXRD to Ru–Os–Fe compounds recovered from Ni‐laterites from the Dominican Republic. The results demonstrate that a significant portion of Fe exists in a common structure with the Ru–Os alloy, that is, ruthenian hexaferrum. This mineral occurs both as nanoparticles and as micrometric patches within a matrix of Fe‐oxide(s). Our data suggest that supergene ruthenian hexaferrum with a (Ru_0.4(Os,Ir)_0.1Fe_0.5)_?1.0 stoichiometry represents the most advanced weathering product of primary laurite within Ni‐laterites from the Dominican Republic.