Inverse Modeling Approach to Allogenic Karst System Characterization

Allogenic karst systems function in a particular way that is influenced by the type of water infiltrating through river water losses, by karstification processes, and by water quality. Management of this system requires a good knowledge of its structure and functioning, for which a new methodology based on an inverse modeling approach appears to be well suited. This approach requires both spring and river inflow discharge measurements and a continuous record of chemical parameters in the river and at the spring. The inverse model calculates unit hydrographs and the impulse responses of fluxes from rainfall hydraulic head at the spring or rainfall flux data, the purpose of which is hydrograph separation. Hydrograph reconstruction is done using rainfall and river inflow data as model input and enables definition at each time step of the ratio of each component. Using chemical data, representing event and pre-event water, as input, it is possible to determine the origin of spring water (either fast flow through the epikarstic zone or slow flow through the saturated zone). This study made it possible to improve a conceptual model of allogenic karst system functioning. The methodology is used to study the Bas-Agly and the Cent Font karst systems, two allogenic karst systems in Southern France.     

Hydraulic modeling of flood pulses in the Middle Bussento Karst System (MBSKS), UNESCO Cilento Global Geopark,southern Italy

Karst systems provide water for domestic and industrial uses and for generating hydropower, but they can also create fluvial hazards, such as upstream back‐flooding and downstream karst flash‐flood events. However, these hazards are difficult to foresee due to the complex recharge‐discharge processes as well as the lack of information on the inside of the system, which has often not been completely surveyed by speleologists or explored by boreholes. To overcome these difficulties, hydro‐chemical data from the monitoring system in the Middle Bussento Karst System (MBSKS), one of the first Experimental Karst Systems in southern Italy, were recorded and previously discussed. Based on shared background in flood karst hydraulic modeling, this paper describes the conceptual premises and rationale of a general‐purpose hydraulic model that is suitable both for the MBSKS and for other Mediterranean, multi‐recharge, mature, conduit‐dominated karst systems. To test the reliability of the model, simulations of time–space behavior and response are performed using natural and artificial flood pulses “as tracers”, considering a “pulse” as a significant variation in water quantity and/or quality. The results of the model explain the interactions between allogenic, autogenic, and anthropogenic recharges from differentiated sources and phreatic conduit systems. These results also clarify the overall response of karst springs at typical time scales of flood pulses. Table acronym name     

The Effect of Hydraulic Gradient and Pattern of Conduit Systems on Tracing Tests: Bench-Scale Modeling

Tracer breakthrough curves provide valuable information about the traced media, especially in inherently heterogeneous karst aquifers. In order to study the effect of variations in hydraulic gradient and conduit systems on breakthrough curves, a bench scale karst model was constructed. The bench scale karst model contains both matrix and a conduit. Eight tracing tests were conducted under a wide range of hydraulic gradients from 1 to greater than 5 for branchwork and network-conduit systems. Sampling points at varying distances from the injection point were utilized. Results demonstrate that mean tracer velocities, tracer mass recovery and linear rising slope of the breakthrough curves were directly controlled by hydraulic gradient. As hydraulic gradient increased, both one half the time for peak concentration and one fifth the time for peak concentration decreased. The results demonstrate the variations in one half the time for peak concentration and one fifth the time for peak concentration of the descending limb for different sampling points under differing hydraulic gradients are mainly controlled by the interactions of advection with dispersion. The results are discussed from three perspectives: different conduit systems, different hydraulic-gradient conditions, and different sampling points. The research confirmed the undeniable role of hydrogeological setting (i.e., hydraulic gradient and conduit system) on the shape of the breakthrough curve. The extracted parameters (mobile-fluid velocity, tracer-mass recovery, linear rising limb, one half the time for peak concentration, and one fifth the time for peak concentration) allow for differentiating hydrogeological settings and enhance interpretations the tracing tests in karst aquifers.     

基于Widrow-Hoff学习算法的液压协调加载控制策略研究

针对多点动态加载系统中多路液压伺服系统特性不一致造成的响应不同步问题,提出一种基于W idrow-Hoff学习算法的液压伺服系统协调加载控制策略,通过迅速地调整伺服系统输入正弦信号的幅值和相位,使多路系统的响应在短时间内与设定信号相一致并协调动作。将此算法应用于实际加载系统,试验证明能够有效地控制多路液压伺服系统的协调动作,从而达到多点协调加载的目的。     

Analysis of karst aquifer spring flows with a gray system decomposition model

There are approximately 470,000 km(2) of karst aquifers that feed many large springs in North China. Turbulent flow often exists in these karst aquifers, which means that the classical ground water model based on Darcy's law cannot be applied here. Ground water data are rare for these aquifers. As a consequence, it is difficult to quantitatively investigate ground water flow in these karst systems. The purpose of this study is to develop a parsimonious model that predicts karst spring discharge using gray system theory. In this theory, a white color denotes a system that is completely characterized and a black color represents a system that is totally unknown. A gray system thus describes a complex system whose characteristics are only partially known or known with uncertainty. Using this theory, we investigated the karst spring discharge time series over different time scales. First, we identified three specific components of spring discharge: the long-term trend, periodic variation, and random fluctuation. We then used the gray system model to simulate the long-term trend and obtain periodic variation and random fluctuation components. Subsequently, we developed a predictive model for karst spring discharge. Application of the model to Liulin Springs, a representative example of karst springs in northern China, shows that the model performs well. The predicted results suggest that the Liulin Springs discharge will likely decrease over time, with small fluctuations.     

Karst spring responses examined by process-based modeling

Ground water in karst terrains is highly vulnerable to contamination due to the rapid transport of contaminants through the highly conductive conduit system. For contamination risk assessment purposes, information about hydraulic and geometric characteristics of the conduits and their hydraulic interaction with the fissured porous rock is an important prerequisite. The relationship between aquifer characteristics and short-term responses to recharge events of both spring discharge and physicochemical parameters of the discharged water was examined using a process-based flow and transport model. In the respective software, a pipe-network model, representing fast conduit flow, is coupled to MODFLOW, which simulates flow in the fissured porous rock. This hybrid flow model was extended to include modules simulating heat and reactive solute transport in conduits. The application of this modeling tool demonstrates that variations of physicochemical parameters, such as solute concentration and water temperature, depend to a large extent on the intensity and duration of recharge events and provide information about the structure and geometry of the conduit system as well as about the interaction between conduits and fissured porous rock. Moreover, the responses of solute concentration and temperature of spring discharge appear to reflect different processes, thus complementing each other in the aquifer characterization.     

Catchment‐scale conceptual modelling of water and solute transport in the dual flow system of the karst critical zone

Hydrological and hydrochemical processes in the critical zone of karst environments are controlled by the fracture‐conduit network. Modelling hydrological and hydrochemical dynamics in such heterogeneous hydrogeological settings remains a research challenge. In this study, water and solute transport in the dual flow system of the karst critical zone were investigated in a 73.5‐km² catchment in southwest China. We developed a dual reservoir conceptual run‐off model combined with an autoregressive and moving average model with algorithms to assess dissolution rates in the “fast flow” and “slow flow” systems. This model was applied to 3 catchments with typical karst critical zone architectures, to show how flow exchange between fracture and conduit networks changes in relation to catchment storage dynamics. The flux of bidirectional water and solute exchange between the fissure and conduit system increases from the headwaters to the outfall due to the large area of the developed conduits and low hydraulic gradient in the lower catchment. Rainfall amounts have a significant influence on partitioning the relative proportions of flow and solutes derived from different sources reaching the underground outlet. The effect of rainfall on catchment function is modulated by the structure of the karst critical zone (e.g., epikarst and sinkholes). Thin epikarst and well‐developed sinkholes in the headwaters divert more surface water (younger water) into the underground channel network, leading to a higher fraction of rainfall recharge into the fast flow system and total outflow. Also, the contribution of carbonate weathering to mass export is also higher in the headwaters due to the infiltration of younger water with low solute concentrations through sinkholes.     

Comparison of flowpaths to a well and spring in a karst aquifer

The permeability of some karst aquifers consists of networks of poorly integrated conduits and dissolution-widened fractures. The flow includes conduit flow, especially during storm recharge, but lacks the focused recharge into single master conduits that occurs in more highly developed karst systems. The proportions of conduit and dispersed flow are difficult to quantify in such systems. This study examines the flowpaths in a small karst watershed, based on comparing the physical and chemical response to storm flow at both a spring and a well. By conducting continuous monitoring at both locations, a better understanding of the flowpaths in a poorly integrated network was obtained. A more permeable flowpath to the spring leads to faster storm response and lower ion concentrations. The flowpath to and from the well is more complicated. The higher ion content and slower storm response suggest slower, more dispersed flowpaths. However, the well has greater variation in ion chemistry. Periodic recharge may dilute well concentrations due to faster (conduit or fracture) flowpaths. Although karst systems such as this are difficult to characterize, applying a variety of geochemical and physical monitoring techniques at multiple locations illustrates that the flowpaths can vary in both space and time.     

Estimating Preferential Flow in Karstic Aquifers Using Statistical Mixed Models

Karst aquifers are highly productive groundwater systems often associated with conduit flow. These systems can be highly vulnerable to contamination, resulting in a high potential for contaminant exposure to humans and ecosystems. This work develops statistical models to spatially characterize flow and transport patterns in karstified limestone and determines the effect of aquifer flow rates on these patterns. A laboratory‐scale Geo‐HydroBed model is used to simulate flow and transport processes in a karstic limestone unit. The model consists of stainless steel tanks containing a karstified limestone block collected from a karst aquifer formation in northern Puerto Rico. Experimental work involves making a series of flow and tracer injections, while monitoring hydraulic and tracer response spatially and temporally. Statistical mixed models (SMMs) are applied to hydraulic data to determine likely pathways of preferential flow in the limestone units. The models indicate a highly heterogeneous system with dominant, flow‐dependent preferential flow regions. Results indicate that regions of preferential flow tend to expand at higher groundwater flow rates, suggesting a greater volume of the system being flushed by flowing water at higher rates. Spatial and temporal distribution of tracer concentrations indicates the presence of conduit‐like and diffuse flow transport in the system, supporting the notion of both combined transport mechanisms in the limestone unit. The temporal response of tracer concentrations at different locations in the model coincide with, and confirms the preferential flow distribution generated with the SMMs used in the study.     

Numerical modeling of geothermal groundwater flow in karst aquifer system in eastern Weibei,Shaanxi Province,China

The quantitative assessment of geothermal water resources is important to the exploitation and utilization of geothermal resources. In the geothermal water systems the density of groundwater changes with the temperature, therefore the variations in hydraulic heads and temperatures are very complicated. A three-dimensional density-dependent model coupling the groundwater flow and heat transport is established and used to simulate the geothermal water flow in the karst aquifers in eastern Weibei, Shaanxi Province, China. The multilayered karst aquifer system in the study area is cut by some major faults which control the regional groundwater flow. In order to calibrate and simulate the effect of the major faults, each fault is discretized as a belt of elements with special hydrological parameters in the numerical model. The groundwater dating data are used to be integrated with the groundwater flow pattern and calibrate the model. Simulation results show that the calculated hydraulic heads and temperature fit with the observed data well.

     

Numerical modeling of geothermal groundwater flow in karst aquifer system in eastern Weibei,Shaanxi Province,China

The quantitative assessment of geothermal water resources is important to the exploitation and utilization of geothermal resources. In the geothermal water systems the density of groundwater changes with the temperature, therefore the variations in hydraulic heads and temperatures are very complicated. A three-dimensional density-dependent model coupling the groundwater flow and heat transport is established and used to simulate the geothermal water flow in the karst aquifers in eastern Weibei, Shaanxi Province, China. The multilayered karst aquifer system in the study area is cut by some major faults which control the regional groundwater flow. In order to calibrate and simulate the effect of the major faults, each fault is discretized as a belt of elements with special hydrological parameters in the numerical model. The groundwater dating data are used to be integrated with the groundwater flow pattern and calibrate the model. Simulation results show that the calculated hydraulic heads and temperature fit with the observed data well.     

Numerical modeling of geothermal groundwater flow in karst aquifer system in eastern Weibei, Shaanxi Province, China

The quantitative assessment of geothermal water resources is important to the exploitation and utilization of geothermal resources. In the geothermal water systems the density of groundwater changes with the temperature, therefore the variations in hydraulic heads and temperatures are very complicated. A three-dimensional density-dependent model coupling the groundwater flow and heat transport is established and used to simulate the geothermal water flow in the karst aquifers in eastern Weibei, Shaanxi Province, China. The multilayered karst aquifer system in the study area is cut by some major faults which control the regional groundwater flow. In order to calibrate and simulate the effect of the major faults, each fault is discretized as a belt of elements with special hydrological parameters in the numerical model. The groundwater dating data are used to be integrated with the groundwater flow pattern and calibrate the model. Simulation results show that the calculated hydraulic heads and temperature fit with the observed data well.     

A high‐altitude temporary spring in a compartmentalized carbonate aquifer: the role of low‐permeability faults and karst conduits

The aim of this research was to refine the actual conceptual model related to the activation of high‐altitude temporary springs within the carbonate Apennines in southern Italy. The research was carried out through geophysical, hydrogeological, hydrochemical and isotopic investigations at the Acqua dei Faggi experimental site during five hydrologic years. The research demonstrated that, in carbonate aquifers where low‐permeability faults cause the aquifer system to be compartmentalized, high‐altitude temporary springs may be recharged by groundwater. In such settings, neither surface water infiltration in karst systems nor perched temporary aquifers play a role of utmost importance. The rare (once or a few time a year) activation of such springs is due to the fact that groundwater unusually reach the threshold head that allows the spring to flow. The activation of the studied high‐altitude temporary spring also depended on relationships between a low‐permeability fault core and a karst system that locally interrupts the low‐permeability barrier. In fact, when the hydraulic head did not reach the karst system, the concentrated head loss within the fault core did not allow the spring to flow, because the groundwater entirely flowed through the fault towards the downgradient compartment. Copyright © 2009 John Wiley & Sons, Ltd.     

Flow and entrapment of dense nonaqueous phase liquids in physically and chemically heterogeneous aquifer formations

The migration and entrapment of dense nonaqueous phase liquids (DNAPLs) in aquifer formations is typically believed to be controlled by physical heterogeneities. This belief is based upon the assumption that permeability and capillary properties are determined by the soil texture. Capillarity and relative permeability, however, will also depend on porous medium wettability characteristics. This wettability may vary spatially in a formation due to variations in aqueous phase chemistry, contaminant aging, and/or variations in mineralogy and organic matter distributions. In this work, a two-dimensional multiphase flow simulator is modified to simulate coupled physical and chemical formation heterogeneity. To model physical heterogeneity, a spatially correlated permeability field is generated, and then related to the capillary pressure-saturation function according to Leverett scaling. Spatial variability of porous medium wettability is assumed to be correlated with the natural logarithm of the intrinsic permeability. The influence of wettability on the hysteretic hydraulic property relations is also modeled. The simulator is then employed to investigate the potential influence of coupled physical and chemical heterogeneity on DNAPL flow and entrapment. For reasonable ranges of wettability characteristics, simulations demonstrate that spatial variations in wettability can have a dramatic impact on DNAPL distributions. Higher organic saturations, increased lateral spreading, and decreased depth of infiltration were predicted when the contact angle was varied spatially. When chemical heterogeneity was defined by spatial variation of organic-wet solid fractions (fractional wettability porous media), however, the resultant organic saturation distributions were more similar to those for perfectly water-wet media, due to saturation dependent wettability effects on the hydraulic property relations.     

Assessing the Nonlinearity of Karst Response Function under Variable Boundary Conditions

The hydraulic and transfer response of karst aquifers is complex and often highly nonlinear: due to their high transmissivity and connection with the surface, such systems are very sensitive to modifications of their boundary conditions. The aim of this study was to assess the variation of the response depending on both upstream and downstream parameters, and propose a methodology to simulate the response of the karst system depending on those parameters. The impact of the variations of multiple environmental parameters on the response of a karstic system submitted to tidal variations (Normandy, France) was investigated after a campaign of artificial tracer tests acquired in very different hydrologic conditions (rainfall events, low tide, high tide, low/high piezometric level, and low/high waters). Principal components analysis and hierarchical clustering were applied on both environmental variables and karstic system response variables (parameters of the residence time distribution [RTD] curves). Equations between the RTD parameters and the most relevant variables were established using a symbolic regression algorithm. It appeared that the variations of the RTD parameters depend mainly on the cumulated rainfall preceding the injection, the piezometric level of the aquifer, and on the tide parameters. The hydraulic conditions downstream of the aquifer have a strong influence on the hydraulic and transfer response of the aquifer. The response of the aquifer in various and extreme conditions has been simulated using the equations resulting from the symbolic regression algorithm. Such relationships can be useful for management of water resources in karst media, and support decision making.     

Assessing “Urban Karst” Effects from Groundwater–Storm Sewer System Interaction in a Till Aquitard

Storm sewer systems and their associated utility trenches may strongly influence the effects of urbanization on a groundwater system. This study was undertaken to identify the causes of district-wide basement infiltration in an aquitard system. It comprised widespread continuous monitoring of utility trench wells and dye tracing from storm sewer system exfiltration tests. The results indicate that a major effect of urbanization on shallow groundwater is related to storm sewer system exfiltration, which is marked by a characteristic pattern of head variations in the aquitard unrelated to distributed surface infiltration. The aquitard constrains flow from storm sewer system exfiltration to the utility trench, creating an urban flow path for groundwater discharge. Temporary buildup of water levels in the utility trench drives relatively high-velocity flow through the permeable sewer bedding material of the utility trench to a separate foundation drainage collector system, ultimately causing a severe “urban karst” effect that produces system surcharging and widespread basement water infiltration. The main conditions causing the “urban karst” are the large hydraulic conductivity ratio between the utility trench material and the aquitard, and the shallow depth and low gradient of the storm sewer system imposed by a very flat drainage basin.     

Study of a semi‐active stiffness damper under various earthquake inputs

Semi‐active stiffness damper (SASD) is one of many semi‐active control systems with the capability to mitigate the dynamic response using only a small amount of external power. The system consists of a hydraulic damper connected to the bracing frame in a selected story unit. In this paper, study of a SASD in two building models of five‐stories under four benchmark earthquake records is reported. The purpose of this study is to evaluate the effectiveness of the control system against structure type and varying earthquake inputs. Various control laws are chosen to work with SASD, such as: resetting control, switching control, linear quadratic regulator (LQR) and modified LQR, and the results are compared with no control and passive control cases. Numerical results show that the use of a SASD is effective in reducing seismic responses. Control effectiveness is dependent on the type of structure and earthquake excitation. Passive control is less effective than other control cases as expected. Resetting control, switching control and LQR generally perform similarly in response reduction. While modified LQR is more efficient and robust compared with other control algorithms. Copyright © 2002 John Wiley & Sons, Ltd.     

Dual compensation strategy for real‐time hybrid testing

Real‐time hybrid testing is an experimental technique for evaluating the dynamic responses of structural systems under seismic loading. Servo‐hydraulic actuators, by nature, induce inevitable time delay between the command and the achieved displacements. This delay would lead to incorrect test results and even cause instability of the system; therefore, delay compensation is critical for stability and accuracy of hybrid simulations of structural dynamic response. In this paper, a dual delay compensation strategy is proposed by a combination of a phase lead compensator and a restoring force compensator. An outer‐loop feed‐forward phase lead compensator is derived by introducing the inverse model in the z domain. The adaptive law based on the gradient algorithm is used to estimate the system delay in the format of parametric model during the test. It is shown mathematically that the parameter in the delay estimator is guaranteed to converge. The restoring force compensator is adopted to improve the accuracy of experimental results especially when the structure is subjected to high frequency excitations. Finally, analytical simulations of an inelastic SDOF structure are conducted to investigate the feasibility of the proposed strategy. The accuracy of the dual compensation strategy is demonstrated through several shaking table tests. Copyright © 2012 John Wiley & Sons, Ltd.     

From rainfall to spring discharge: Coupling conduit flow,subsurface matrix flow and surface flow in karst systems using a discrete–continuum model

Physics-based distributed models for simulating flow in karst systems are generally based on the discrete–continuum approach in which the flow in the three-dimensional fractured limestone matrix continuum is coupled with the flow in discrete one-dimensional conduits. In this study we present a newly designed discrete–continuum model for simulating flow in karst systems. We use a flexible spatial discretization such that complicated conduit networks can be incorporated. Turbulent conduit flow and turbulent surface flow are described by the diffusion wave equation whereas laminar variably saturated flow in the matrix is described by the Richards equation. Transients between free-surface and pressurized conduit flow are handled by changing the capacity term of the conduit flow equation. This new approach has the advantage that the transients in mixed conduit flow regimes can be handled without the Preissmann slot approach. Conduit–matrix coupling is based on the Peaceman’s well-index such that simulated exchange fluxes across the conduit–matrix interface are less sensitive to the spatial discretization. Coupling with the surface flow domain is based on numerical techniques commonly used in surface–subsurface models and storm water drainage models. Robust algorithms are used to simulate the non-linear flow processes in a coupled fashion. The model is verified and illustrated with simulation examples.