Numerical modelling of stream–aquifer interaction: Quantifying the impact of transient streambed permeability and aquifer heterogeneity

Stream–aquifer interaction plays a vital role in the water cycle, and a proper study of this interaction is needed for understanding groundwater recharge, contaminants migration, and for managing surface water and groundwater resources. A model‐based investigation of a field experiment in a riparian zone of the Schwarzbach river, a tributary of the Rhine River in Germany, was conducted to understand stream–aquifer interaction under alternative gaining and losing streamflow conditions. An equivalent streambed permeability, estimated by inverting aquifer responses to flood waves, shows that streambed permeability increased during infiltration of stream water to aquifer and decreased during exfiltration. Aquifer permeability realizations generated by multiple‐point geostatistics exhibit a high degree of heterogeneity and anisotropy. A coupled surface water groundwater flow model was developed incorporating the time‐varying streambed permeability and heterogeneous aquifer permeability realizations. The model was able to reproduce varying pressure heads at two observation wells near the stream over a period of 55 days. A Monte Carlo analysis was also carried out to simulate groundwater flow, its age distribution, and the release of a hypothetical wastewater plume into the aquifer from the stream. Results of this uncertainty analysis suggest (a) stream–aquifer exchange flux during the infiltration periods was constrained by aquifer permeability; (b) during exfiltration, this flux was constrained by the reduced streambed permeability; (c) the effect of temporally variable streambed permeability and aquifer heterogeneity were found important to improve the accurate capture of the uncertainty; and (d) probabilistic infiltration paths in the aquifer reveal that such pathways and the associated prediction of the extent of the contaminant plume are highly dependent on aquifer heterogeneity.     

A semi‐analytical solution for groundwater responses to stream‐stage variations and tidal fluctuations in a coastal aquifer

A two‐dimensional semi‐analytical solution to analyse stream–aquifer interactions in a coastal aquifer where groundwater level responds to tidal effects is presented. The conceptual model considered is a two‐dimensional subsurface system with stream and coastline boundaries at right angles. The dimensional and non‐dimensional boundary value problems were solved for water level in the aquifer by successive application of Laplace and Fourier transform techniques, and the results were obtained by numerical inversion of the transformed solution. The solution was then verified by reducing the solutions to one‐dimensional known problems and comparing the results with those from previous studies. Hypothetical examples were used to examine the characteristics of water‐level variations due to the variations in stream stage and the fluctuations in tide level. Sensitivity analysis indicated that streambed leakance has no influence over the amplitude of groundwater fluctuations, but that the effect of stream stage increases with increasing leakance. Little difference was observed in the water level for different aquifer penetration ratios with narrow stream width. Increases in streambed leakance caused increases in the effect of aquifer penetration by the stream on the water level. An increased specific yield value resulted in decreased amplitude of water fluctuations and mean water level, and showed that water‐level variations due to stream and tidal boundaries are sensitive to specific yield. Copyright © 2006 John Wiley & Sons, Ltd.     

River–aquifer interactions in a semi‐arid environment stressed by groundwater abstraction

Rivers and aquifers are, in many cases, a connected resource and as such the interactions between them need to be understood and quantified for the resource to be managed appropriately. The objective of this paper is to advance the understanding of river–aquifer interactions processes in semi‐arid environments stressed by groundwater abstraction. This is performed using data from a specific catchment where records of precipitation, evapotranspiration, river flow, groundwater levels and groundwater abstraction are analysed using basic statistics, hydrograph analysis and a simple mathematical model to determine the processes causing the spatial and temporal changes in river–aquifer interactions. This combined approach provides a novel but simple methodology to analyse river–aquifer interactions, which can be applied to catchments worldwide. The analysis revealed that the groundwater levels have declined (~ 3 m) since the onset of groundwater abstraction. The decline is predominantly due to the abstraction rather than climatic changes (r = 0.84 for the relationship between groundwater abstraction and groundwater levels; r = 0.92 for the relationship between decline in groundwater levels and magnitude of seasonal drawdown). It is then demonstrated that, since the onset of abstraction, the river has changed from being gaining to losing during low‐flow periods, defined as periods with flow less than 0.5, 1.0 or 1.5 GL/day (1 GL/day = 1 × 10⁶ m³/day). If defined as < 1.0 GL/day, low‐flow periods constitute approximately 65% of the river flows; the periods where the river is losing at low‐flow conditions are thus significant. Importantly, there was a significant delay (> 10 years) between the onset of groundwater abstraction and the changeover from gaining to losing conditions. Finally, a relationship between the groundwater gradient towards the river and the river flow at low‐flow is demonstrated. The results have important implications for water management as well as water ecology and quality. Copyright © 2012 John Wiley & Sons, Ltd.     

Direct finite element method for nonlinear earthquake analysis of 3‐dimensional semi‐unbounded dam–water–foundation rock systems

A direct finite element method for nonlinear earthquake analysis of 2‐dimensional dam–water–foundation rock systems has recently been presented. The analysis procedure uses standard viscous‐damper absorbing boundaries to model the semi‐unbounded foundation‐rock and fluid domains and specifies the seismic input as effective earthquake forces at these boundaries. Presented in this paper is a generalization of the direct finite element method with viscous‐damper boundaries to 3‐dimensional dam–water–foundation rock systems. Step‐by‐step procedures for determining the effective earthquake forces starting from a ground motion specified at a control point on the foundation‐rock surface is developed, and several numerical examples are computed and compared with independent benchmark solutions to demonstrate the effectiveness of the analysis procedure for modeling 3‐dimensional systems.     

A conceptually based stochastic point process model for daily stream‐flow generation

Based on the stochastic and phenomenological aspects of hydrological processes, a conceptually based stochastic point process (SPP) model for daily stream‐flow generation is proposed in this paper. In which, storms are defined by a stochastic point process with marked values. All the random variables defining the process are assumed to be mutually independent, which constitutes a compound Poisson point process. The direct surface runoff is regarded as occurring from storage in a cascade of surface linear reservoirs and is responsible for the short‐term variation of the daily stream flows. The baseflow component is considered as coming from subsurface/groundwater storage and is responsible for the long‐term persistence of the storm time‐series. This type of model is proposed as a more realistic model of daily stream flow than models based on pure stochastic processes. Studies on the instantaneous unit hydrograph and the mechanism of baseflow could thereby provide some parameters for this model. Copyright © 2002 John Wiley & Sons, Ltd.     

Evaluation of water‐use policies for baseflow recovery during droughts in an agricultural intensive karst watershed: Case study of the lower Apalachicola–Chattahoochee–Flint River Basin,southeastern United States

The lower Apalachicola–Chattahoochee–Flint River Basin in the Southeast United States represents a major agricultural area underlain by the highly productive karstic Upper Floridan aquifer (UFA). During El Niño Southern Oscillation‐induced droughts, intense groundwater withdrawal for irrigation lowers streamflow in the Flint River due to its hydraulic connectivity with the UFA and threatens the habitat of the federally listed and endangered aquatic biota. This study assessed the compounding hydrologic effects of increased irrigation pumping during drought years (2010–2012) on stream–aquifer water exchange (stream–aquifer flux) between the Flint River and UFA using the United States Geological Survey modular finite element groundwater flow model. Principal component and K‐means clustering analyses were used to identify critical stream reaches and tributaries that are adversely affected by irrigation pumping. Additionally, the effectiveness of possible water restriction scenarios on stream–aquifer flux was also analysed. Moreover, a cost–benefit analysis of acreage buyout procedure was conducted for various water restriction scenarios. Results indicate that increased groundwater withdrawal in Water Year 2011 decreased baseflow in the lower Apalachicola–Chattahoochee–Flint River Basin, particularly, in Spring Creek, where irrigation pumping during April, June, and July changed the creek condition from a gaining to losing stream. Results from sensitivity analysis and simulated water restrictions suggest that reducing pumping in selected sensitive areas is more effective in streamflow recovery (approximately 78%) than is reducing irrigation intensity by a prescribed percentage of current pumping rates, such as 15% or 30%, throughout the basin. Moreover, analysis of acreage buyout indicates that restrictions on irrigation withdrawal can have significant impacts on stream–aquifer flux in the Basin, especially in critical watersheds such as Spring and Ichawaynochaway Creeks. The proposed procedure for ranking of stream reaches (sensitivity analysis) in this study can be replicated in other study areas/models. This study provides useful information to policymakers for devising alternate irrigation water withdrawal policies during droughts for maintaining flow levels in the study area.     

Soil–pile–structure interaction under SH wave excitation

A continuum model for the interaction analysis of a fully coupled soil–pile–structure system under seismic excitation is presented in this paper. Only horizontal shaking induced by harmonic SH waves is considered so that the soil–pile–structure system is under anti‐plane deformation. The soil mass, pile and superstructure were all considered as elastic with hysteretic damping, while geometrically both pile and structures were simplified as a beam model. Buildings of various heights in Hong Kong designed to resist wind load were analysed using the present model. It was discovered that the acceleration of the piled‐structures at ground level can, in general, be larger than that of a free‐field shaking of the soil site, depending on the excitation frequency. For typical piled‐structures in Hong Kong, the amplification factor of shaking at the ground level does not show simple trends with the number of storeys of the superstructure, the thickness and the stiffness of soil, and the stiffness of the superstructure if number of storeys is fixed. The effect of pile stiffness on the amplification factor of shaking is, however, insignificant. Thus, simply increasing the pile size or the superstructure stiffness does not necessarily improve the seismic resistance of the soil–pile–structure system; on the contrary, it may lead to excessive amplification of shaking for the whole system. Copyright © 2003 John Wiley & Sons, Ltd.     

Development and verification of a 3-D integrated surface water–groundwater model

Coupled modelling of surface and subsurface systems is a valuable tool for quantifying surface water–groundwater interactions. In the present paper, the 3-D non-steady state Navier–Stokes equations, after Reynolds averaging and with the assumption of a hydrostatic pressure distribution, are for the first time coupled to the 3-D saturated groundwater flow equations in an Integrated suRface watEr–grouNdwater modEl (IRENE). A finite-difference method is used for the solution of the governing equations of IRENE. A semi-implicit scheme is used for the discretisation of the surface water flow equations and a fully implicit scheme for the discretisation of the groundwater flow equations. The two sets of equations are coupled at the common interface of the surface water and groundwater bodies, where water exchange takes place, using Darcy’s law. A new approach is proposed for the solution of the coupled surface water and groundwater equations in a simultaneous manner, in such a fashion that gives computational efficiency at low computational cost. IRENE is verified against three analytical solutions of surface water–groundwater interaction, which are chosen so that different components of the model can be tested. The model closely reproduces the results of the analytical solutions and can therefore be used for analysing and predicting surface water–groundwater interactions in real-world cases.     

Modelling and experimental study of coupled exchange of p,p′‐DDE and colloids in a flume simulated stream–streambed system

Stream–subsurface exchange plays a significant role in the fate and transport of contaminants in streams. It has been modelled explicitly by considering fundamental processes such as hydraulic exchange, colloid filtration, and contaminant interactions with streambed sediments and colloids. The models have been successfully applied to simulate the transport of inorganic metals and nutrients. In this study, laboratory experiments were conducted in a recirculating flume to investigate the exchange of a hydrophobic organic contaminant, p,p′‐dichloro‐diphenyl‐dichloroethane (DDE), between a stream and a quartz sand bed. A previously developed process‐based multiphase exchange model was modified by accounting for the p,p′‐DDE kinetic adsorption to and desorption from the bed sediments/colloids and was applied to interpret the experimental results. Model input parameters were obtained by conducting independent small‐scale batch experiments. Results indicate that the immobilization of p,p′‐DDE in the quartz sand bed can occur under representative natural stream conditions. The observed p,p′‐DDE exchange was successfully simulated by the process‐based model. The model sensitivity analysis results show that the exchange of p,p′‐DDE can be sensitive to either the sediment sorption/desorption parameters or colloidal parameters depending on the experimental conditions tested. For the experimental conditions employed here, the effect of colloids on contaminant transport is expected to be minimal, and the stream–subsurface exchange of p,p′‐DDE is dominated by the interaction of p,p′‐DDE with bed sediment. The work presented here contributes to a better mechanistic understanding of the complex transport process that hydrophobic organic contaminants undergo in natural streams and to the development of reliable, predictive models for the assessment of impacted streams. Copyright © 2015 John Wiley & Sons, Ltd.     

Why permafrost rocks become unstable: a rock–ice‐mechanical model in time and space

In this paper, we develop a mechanical model that relates the destabilization of thawing permafrost rock slopes to temperature‐related effects on both, rock‐ and ice‐mechanics; and laboratory testing of key assumptions is performed. Degrading permafrost is considered to be an important factor for rock–slope failures in alpine and arctic environments, but the mechanics are poorly understood. The destabilization is commonly attributed to changes in ice‐mechanical properties while bedrock friction and fracture propagation have not been considered yet. However, fracture toughness, compressive and tensile strength decrease by up to 50% and more when intact water‐saturated rock thaws. Based on literature and experiments, we develop a modified Mohr–Coulomb failure criterion for ice‐filled rock fractures that incorporates fracturing of rock bridges, friction of rough fracture surfaces, ductile creep of ice and detachment mechanisms along rock–ice interfaces. Novel laboratory setups were developed to assess the temperature dependency of the friction of ice‐free rock–rock interfaces and the shear detachment of rock–ice interfaces. In degrading permafrost, rock‐mechanical properties may control early stages of destabilization and become more important for higher normal stress, i.e. higher magnitudes of rock–slope failure. Ice‐mechanical properties outbalance the importance of rock‐mechanical components after the deformation accelerates and are more relevant for smaller magnitudes. The model explains why all magnitudes of rock–slope failures can be prepared and triggered by permafrost degradation and is capable of conditioning long para‐glacial response times. Here, we present a synoptic rock‐ and ice‐mechanical model that explains the mechanical destabilization processes operating in warming permafrost rocks. Copyright © 2013 John Wiley & Sons, Ltd.     

A low‐dimensional hillslope‐based catchment model for layered groundwater flow

Despite the strong interaction between surface and subsurface waters, groundwater flow representation is often oversimplified in hydrological models. For instance, the interplay between local or shallow aquifers and deeper regional‐scale aquifers is typically neglected. In this work, a novel hillslope‐based catchment model for the simulation of combined shallow and deep groundwater flow is presented. The model consists of the hillslope‐storage Boussinesq (hsB) model representing shallow groundwater flow and an analytic element (AE) model representing deep regional groundwater flow. The component models are iteratively coupled via a leakage term based on Darcy's law, representing delayed recharge to the regional aquifer through a low conductivity layer. Simulations on synthetic single hillslopes and on a two‐hillslope open‐book catchment are presented, and the results are compared against a benchmark three‐dimensional Richards equation model. The impact of hydraulic conductivity, hillslope plan geometry (uniform, convergent, divergent), and hillslope inclination (0.2%, 5%, and 30%) under drainage and recharge conditions are examined. On the single hillslopes, good matches for heads, hydrographs, and exchange fluxes are generally obtained, with the most significant differences in outflows and heads observed for the 30% slope and for hillslopes with convergent geometry. On the open‐book catchment, cumulative outflows are overestimated by 1–4%. Heads in the confined and unconfined aquifers are adequately reproduced throughout the catchment, whereas exchange fluxes are found to be very sensitive to the hillslope drainable porosity. The new model is highly efficient computationally compared to the benchmark model. The coupled hsB/AE model represents an alternative to commonly used groundwater flow representations in hydrological models, of particular appeal when surface–subsurface exchanges, local aquifer–regional aquifer interactions, and low flows play a key role in a watershed's dynamics. Copyright © 2011 John Wiley & Sons, Ltd.     

Impact of lateral flow and spatial scaling on the simulation of semi‐arid urban land surfaces in an integrated hydrologic and land surface model

Understanding and representing hydrologic fluxes in the urban environment is challenging because of fine scale land cover heterogeneity and lack of coherent scaling relationships. Here, the impact of urban land cover heterogeneity, scale, and configuration on the hydrologic and surface energy budget (SEB) is assessed using an integrated, coupled land surface/hydrologic model at high spatial resolutions. Archetypes of urban land cover are simulated at varying resolutions using both the National Land Cover Database (NLCD; 30 m) and an ultra high‐resolution land cover dataset (0.6 m). The analysis shows that the impact of highly organized, yet heterogeneous, land cover typical of the urban domain can cause large variations in hydrologic and energy fluxes within areas of similar land cover. The lateral flow processes that occur within each simulation create variations in overland flow of up to ±200% and ±4% in evapotranspiration. The impact on the SEB is smaller and largely restricted to the wet season for our semi‐arid forcing scenarios. Finally, we find that this seasonal bias, predominantly caused by lateral flow, is displaced by a systematic diurnal bias at coarser resolutions caused by deficiencies in the method used for scaling of land surface and hydrologic parameters. As a result of this research, we have produced land surface parameters for the widely used NLCD urban land cover types. This work illustrates the impact of processes that remain unrepresented in traditional high‐resolutions land surface models and how they may affect results and uncertainty in modeling of local water resources and climate. Copyright © 2015 John Wiley & Sons, Ltd.     

A design‐variable‐based inelastic hysteretic model for beam–column connections

This paper presents a design‐variable‐based inelastic hysteretic model for beam–column connections. It has been well known that the load‐carrying capacity of connections heavily depends on the types and design variables even in the same connection type. Although many hysteretic connection models have been proposed, most of them are dependent on the specific connection type with presumed failure mechanisms. The proposed model can be responsive to variations both in design choices and in loading conditions. The proposed model consists of two modules: physical‐principle‐based module and neural network (NN)‐based module in which information flow from design space to response space is formulated in one complete model. Moreover, owing to robust learning capability of a new NN‐based module, the model can also learn complex dynamic evolutions in response space under earthquake loading conditions, such as yielding, post‐buckling and tearing, etc. Performance of the proposed model has been demonstrated with synthetic and experimental data of two connection types: extended‐end‐plate and top‐ and seat‐angle with double‐web‐angle connection. Furthermore, the design‐variable‐based model can be customized to any structural component beyond the application to beam–column connections. Copyright © 2007 John Wiley & Sons, Ltd.     

Analytical and statistical approach for evaluating the effects of a river barrage on river–aquifer interactions

The construction of a river barrage can increase groundwater levels upstream of the barrage during the rainy season. Analytical and statistical approaches were applied to evaluate the relationship between groundwater and river water at the Changnyeong–Haman river barrage in Korea using time series data of water level and electrical conductivity from June 2011 to September 2014. An artificial neural network based time series model was designed to filter out the effect of rainfall from the groundwater level data in the study area. Aquifer diffusivity and river resistance were estimated from the analytical solution of a one‐dimensional unit step response function by using the filtered groundwater level data. River resistance increased in response to groundwater level fluctuations. Cross‐correlation analyses between the groundwater and the river water showed that the lag time increased during the observation period for both the water level and the electrical conductivity while the cross‐correlation function declined for the same period. The results indicated that a constant river stage maintained at the river barrage can weaken the hydrologic stress and reduce the exchange of material between the river and the adjacent aquifer because of the deposition of fine sediment on the river bottom and walls. Copyright © 2016 John Wiley & Sons, Ltd.     

Predicting dry‐season flows with a monthly rainfall–runoff model: Performance for gauged and ungauged catchments

Hydrologic models are useful to understand the effects of climate and land‐use changes on dry‐season flows. In practice, there is often a trade‐off between simplicity and accuracy, especially when resources for catchment management are scarce. Here, we evaluated the performance of a monthly rainfall–runoff model (dynamic water balance model, DWBM) for dry‐season flow prediction under climate and land‐use change. Using different methods with decreasing amounts of catchment information to set the four model parameters, we predicted dry‐season flow for 89 Australian catchments and verified model performance with an independent dataset of 641 catchments in the United States. For the Australian catchments, model performance without catchment information (other than climate forcing) was fair; it increased significantly as the information to infer the four model parameters increased. Regressions to infer model parameters from catchment characteristics did not hold for catchments in the United States, meaning that a new calibration effort was needed to increase model performance there. Recognizing the interest in relative change for practical applications, we also examined how DWBM could be used to simulate a change in dry‐season flow following land‐use change. We compared results with and without calibration data and showed that predictions of changes in dry‐season flow were robust with respect to uncertainty in model parameters. Our analyses confirm that climate is a strong driver of dry‐season flow and that parsimonious models such as DWBM have useful management applications: predicting seasonal flow under various climate forcings when calibration data are available and providing estimates of the relative effect of land use on seasonal flow for ungauged catchments.     

Groundwater–surface water interactions in a large semi‐arid floodplain: implications for salinity management

Flow regulation and water diversion for irrigation have considerably impacted the exchange of surface water between the Murray River and its floodplains. However, the way in which river regulation has impacted groundwater–surface water interactions is not completely understood, especially in regards to the salinization and accompanying vegetation dieback currently occurring in many of the floodplains. Groundwater–surface water interactions were studied over a 2 year period in the riparian area of a large floodplain (Hattah–Kulkyne, Victoria) using a combination of piezometric surface monitoring and environmental tracers (Cl⁻, δ²H, and δ¹⁸O). Despite being located in a local and regional groundwater discharge zone, the Murray River is a losing stream under low flow conditions at Hattah–Kulkyne. The discharge zone for local groundwater, regional groundwater and bank recharge is in the floodplain within ∼1 km of the river and is probably driven by high rates of transpiration by the riparian Eucalyptus camaldulensis woodland. Environmental tracers data suggest that the origin of groundwater is principally bank recharge in the riparian zone and a combination of diffuse rainfall recharge and localized floodwater recharge elsewhere in the floodplain. Although the Murray River was losing under low flows, bank discharge occurred during some flood recession periods. The way in which the water table responded to changes in river level was a function of the type of stream bank present, with point bars providing a better connection to the alluvial aquifer than the more common clay‐lined banks. Understanding the spatial variability in the hydraulic connection with the river channel and in vertical recharge following inundations will be critical to design effective salinity remediation strategies for large semi‐arid floodplains. Copyright © 2005 John Wiley & Sons, Ltd.     

A novel predictor–corrector algorithm for sub‐structure pseudo‐dynamic testing

A new predictor–corrector (P–C) method for multi‐site sub‐structure pseudo‐dynamic (PSD) test is proposed. This method is a mixed time integration method in which computational components separable from experimental components are solved by implicit time integration method (Newmark β method). The experiments are performed quasi‐statically based on explicit prediction of displacement. The proposed P–C method has an important advantage as it does not require the determination of the initial stiffness values of experimental components and is thus suitable for representing elastic and inelastic systems. A parameter relating to quality of displacement prediction at boundaries nodes is introduced. This parameter is determined such that P–C method can be applicable to many practical problems. Error‐propagation characteristics of P–C method are also presented. A series of examples including linear and non‐linear soil–foundation–structure interaction problem demonstrate the performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd.     

A hybrid time frequency domain formulation for non-linear soil–structure interaction

Methods that combine frequency and time domain techniques offer an attractive alternative for solving Soil–Structure-interaction problems where the structure exhibits non-linear behaviour. In the hybrid-frequency-time-domain procedure a reference linear system is solved in the frequency domain and the difference between the actual restoring forces and those in the linear model are treated as pseudo-forces. In the solution scheme explored in this paper, designated as the hybrid-time-frequency-domain (HTFD) procedure, the equations of motion are solved in the time domain with due consideration for non-linearities and with the unbounded medium represented by frequency-independent springs and dampers. The frequency dependency of the impedance coefficients is introduced by means of pseudo-forces evaluated in the frequency domain at the end of each iteration. A criterion of stability for the HTFD approach is derived analytically and its validity is sustained numerically. As is often the case, the criterion takes the form of a limit of unity on the spectral radius of an appropriately defined matrix. Inspection of the terms in this matrix shows that convergence can be guaranteed by suitable selection of the reference impedance. The CPU times required to obtain converged solutions with the HTFD are found, in a number of numerical simulations, to be up to one order of magnitude less than those required by the alternative hybrid-frequency-time-domain approach. © 1998 John Wiley & Sons, Ltd.