Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Simplified multi-block constitutive model predicting earthquake-induced landslide triggering and displacement along slip surfaces of saturated sand

Slopes consisting of saturated sand have recently moved down-slope tens or hundreds of meters under the action of earthquakes. This paper presents a simplified but accurate method predicting the triggering and displacement of such landslides. For this purpose, a simplified constitutive model simulating soil response of saturated sands along slip surfaces is proposed and validated. Then, this constitutive model is coupled with the multi-block sliding system model to predict the triggering and displacement of such slides. The multi-block model considers a general mass sliding on a trajectory which consists of n linear segments. The steps needed to apply this method are described in detail. The method was applied successfully to predict the triggering, the motion and the final configuration of the well-documented (a) Higashi Takezawa, (b) Donghekou and (c) Nikawa earthquake-induced slides.     

Polygonal grain‐based distinct element modeling for mechanical behavior of brittle rock

The microstructure of rock was numerically reproduced by a polygonal grain‐based model, and its mechanical behavior was examined by performing the uniaxial compression test and Brazilian tests via the Universal Distinct Element Code. The numerical results of the model demonstrated good agreement with the experimental results obtained with rock specimens in terms of the stress–strain behavior, strength characteristics, and brittle fracture phenomenon. An encouraging result is that the grain‐based model‐Universal Distinct Element Code model can reproduce a low ratio of tensile to compressive strength of 1/20 to 1/10 without the need for an additional process. This finding is ascribed to the fact that the geometrical features of polygons can effectively capture the effects of angularity, finite rotation, and interlocking of grains that exist in reality. A numerical methodology to monitor the evolution of micro‐cracks was developed, which enabled us to examine the progressive process of the failure and distinguish the contribution of tensile cracking to the process from that of shear cracking. From the observations of the micro‐cracking process in reference to the stress–strain relation, crack initiation stress, and crack damage stress, it can be concluded that the failure process of the model closely resembles the microscopic observations of rock. We also carried out a parametric study to examine the relationships between the microscopic properties and the macroscopic behavior of the model. Depending on the micro‐properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics, the evolution of micro‐cracks, and the post‐peak behavior. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

The influence of coupled physical swelling and chemical reactions on deformable geomaterials

Coupled thermo‐hydro‐mechanical‐chemical modelling has attracted attention in past decades due to many contemporary geotechnical engineering applications (e.g., waste disposal, carbon capture and storage). However, molecular‐scale interactions within geomaterials (e.g., swelling and dissolution/precipitation) have a significant influence on the mechanical behaviour, yet are rarely incorporated into existing Thermal‐Hydro‐Mechanical‐Chemical (THMC) frameworks. This paper presents a new coupled hydro‐mechanical‐chemical constitutive model to bridge molecular‐scale interactions with macro‐physical deformation by combining the swelling and dissolution/precipitation through an extension of the new mixture‐coupling theory. Entropy analysis of the geomaterial system provides dissipation energy, and Helmholtz free energy gives the relationship between solids and fluids. Numerical simulation is used to compare with the selected recognized models, which demonstrates that the swelling and dissolution/precipitation processes may have a significant influence on the mechanical deformation of the geomaterials.     

Quantifying flows along hydrological pathways by applying a new filtering algorithm in conjunction with master recession curve analysis

Quantifying the proportion of the river hydrograph derived from the different hydrological pathways is essential for understanding the behaviour of a catchment. This paper describes a new approach using the output from master recession curve analysis to inform a new algorithm based on the Lyne and Hollick ‘one‐parameter’ signal analysis filtering algorithm. This approach was applied to six catchments (including two subcatchments of these) in Ireland. The conceptual model for each catchment consists of four main flow pathways: overland flow, interflow, shallow groundwater and deep groundwater. The results were compared with those of the master recession curve analysis, a recharge coefficient approach developed in Ireland and the semi‐distributed, lumped and deterministic hydrological model Nedbør‐Afstrømings‐Model. The new algorithm removes the ‘free variable’ aspect that is typically associated with filtering algorithms and provides a means of estimating the contribution of each pathway that is consistent with the results of hydrograph separation in catchments that are dominated by quick response pathways. These types of catchments are underlain by poorly productive aquifers that are not capable of providing large baseflows in the river. Such aquifers underlie over 73% of Ireland, ensuring that this new algorithm is applicable in the majority of catchments in Ireland and potentially in those catchments internationally that are strongly influenced by the quick‐responding hydrological pathways. Copyright © 2013 John Wiley & Sons, Ltd.     

Is there a superior conceptual groundwater model structure for baseflow simulation?

Previous work has shown that streamflow response during baseflow conditions is a function of storage, but also that this functional relationship varies among seasons and catchments. Traditionally, hydrological models incorporate conceptual groundwater models consisting of linear or non‐linear storage–outflow functions. Identification of the right model structure and model parameterization however is challenging. The aim of this paper is to systematically test different model structures in a set of catchments where different aquifer types govern baseflow generation processes. Nine different two‐parameter conceptual groundwater models are applied with multi‐objective calibration to transform two different groundwater recharge series derived from a soil‐atmosphere‐vegetation transfer model into baseflow separated from streamflow data. The relative performance differences of the model structures allow to systematically improve the understanding of baseflow generation processes and to identify most appropriate model structures for different aquifer types. We found more versatile and more aquifer‐specific optimal model structures and elucidate the role of interflow, flow paths, recharge regimes and partially contributing storages. Aquifer‐specific recommendations of storage models were found for fractured and karstic aquifers, whereas large storage capacities blur the identification of superior model structures for complex and porous aquifers. A model performance matrix is presented, which highlights the joint effects of different recharge inputs, calibration criteria, model structures and aquifer types. The matrix is a guidance to improve groundwater model structures towards their representation of the dominant baseflow generation processes of specific aquifer types. Copyright © 2014 John Wiley & Sons, Ltd.     

Including spatial distribution in a data‐driven rainfall‐runoff model to improve reservoir inflow forecasting in Taiwan

Multi‐step ahead inflow forecasting has a critical role to play in reservoir operation and management in Taiwan during typhoons as statutory legislation requires a minimum of 3‐h warning to be issued before any reservoir releases are made. However, the complex spatial and temporal heterogeneity of typhoon rainfall, coupled with a remote and mountainous physiographic context, makes the development of real‐time rainfall‐runoff models that can accurately predict reservoir inflow several hours ahead of time challenging. Consequently, there is an urgent, operational requirement for models that can enhance reservoir inflow prediction at forecast horizons of more than 3 h. In this paper, we develop a novel semi‐distributed, data‐driven, rainfall‐runoff model for the Shihmen catchment, north Taiwan. A suite of Adaptive Network‐based Fuzzy Inference System solutions is created using various combinations of autoregressive, spatially lumped radar and point‐based rain gauge predictors. Different levels of spatially aggregated radar‐derived rainfall data are used to generate 4, 8 and 12 sub‐catchment input drivers. In general, the semi‐distributed radar rainfall models outperform their less complex counterparts in predictions of reservoir inflow at lead times greater than 3 h. Performance is found to be optimal when spatial aggregation is restricted to four sub‐catchments, with up to 30% improvements in the performance over lumped and point‐based models being evident at 5‐h lead times. The potential benefits of applying semi‐distributed, data‐driven models in reservoir inflow modelling specifically, and hydrological modelling more generally, are thus demonstrated. Copyright © 2012 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.