Steady-state Groundwater Flow Research Articles

Influence of Pipe Roof Reinforcement on Face Stability of Underwater Tunnel

The effect of seepage force on tunnel face stability with pipe roof reinforcement was studied based on the kinematic method of limit analysis. This method can be employed to define the safety factor and its corresponding critical failure mechanism for a given tunnel. The studies revealed that the existence of groundwater may seriously affect the face stability. Under the steady-state groundwater flow condition, most part of the total support pressure is owing to the seepage pressure acting on the tunnel face. There was a relatively large reduction in the seepage pressure by adopting the pipe roof reinforcement technique.

Implementing Groundwater Extraction in Life Cycle Impact Assessment: Characterization Factors Based on Plant Species Richness for the Netherlands

An operational method to evaluate the environmental impacts associated with groundwater use is currently lacking in life cycle assessment (LCA). This paper outlines a method to calculate characterization factors that address the effects of groundwater extraction on the species richness of terrestrial vegetation. Characterization factors (CF) were derived for The Netherlands and consist of a fate and an effect part. The fate factor equals the change in drawdown due to a change in groundwater extraction and expresses the amount of time required for groundwater replenishment. It was obtained with a grid-specific steady-state groundwater flow model. Effect factors were obtained from groundwater level response curves of potential plant species richness, which was constructed based on the soil moisture requirements of 625 plant species. Depending on the initial groundwater level, effect factors range up to 9.2% loss of species per 10 cm of groundwater level decrease. The total Dutch CF for groundwater extraction depended on the value choices taken and ranged from 0.09 to 0.61 m(2)·yr/m(3). For tap water production, we showed that groundwater extraction can be responsible for up to 32% of the total terrestrial ecosystem damage. With the proposed approach, effects of groundwater extraction on terrestrial ecosystems can be systematically included in LCA.

Exact sensitivity matrix and influence of the number of pilot points in the geostatistical inversion of moment equations of groundwater flow

We present novel equations for the exact sensitivity matrix of the (ensemble) mean hydraulic head under steady state groundwater flow conditions. These equations are embedded in a geostatistical inverse procedure to condition approximations of stochastic moment equations of flow on measured hydraulic conductivities and heads. Our formulation allows considerable improvement of the methodology proposed by Hernandez et al. (2003, 2006) and renders the inversion of moment equations feasible for a large number of unknown hydraulic parameters. The spatial distribution of the natural logarithm, Y, of conductivity is parameterized within the pilot points framework. Whereas prior values of Y at pilot points are obtained by a variant of kriging, posterior estimates at pilot points are obtained through a maximum likelihood fit of computed to measured heads. The maximum likelihood function also includes a regularization term. By means of a synthetic example and upon adopting formal model information criteria we explore the influence of (1) the number of pilot points and (2) the order of approximation of the governing mean flow equation on our ability to properly estimate the log conductivity and head fields and identify the relative weight of the regularization term and the parameters of the underlying Y variogram. We find that none of the adopted information criteria can identify the optimum number of pilot points and the plausibility weight and variogram parameters values can be determined by the Kashyap's Bayesian measure.

A conceptual framework of groundwater flow in some crystalline aquifers in Southeastern Ghana

A conceptual groundwater flow model was developed for the crystalline aquifers in southeastern part of the Eastern region, Ghana. The objective was to determine approximate levels of groundwater recharge, estimate aquifer hydraulic parameters, and then test various scenarios of groundwater extraction under the current conditions of recharge. A steady state groundwater flow model has been calibrated against measured water levels of 19 wells in the area. The resulting recharge is estimated to range from 8.97 × 10 −5 m/d to 7.14 × 10 −4 m/d resulting in a basin wide average recharge of about 9.6% of total annual precipitation, which results in a basin wide quantitative recharge of about 2.4 million m 3/d in the area. This compares to recharge estimated from the chloride mass balance of 7.6% of precipitation determined in this study. The general groundwater flow in the area has also been determined to conform to the general northeast–southwest structural grain of the country. The implication is that the general hydrogeology is controlled by post genetic structural entities imposed on the rocks to create ingresses for sufficient groundwater storage and transport. Calibrated aquifer hydraulic conductivities range between 0.99 m/d and over 19.4 m/d. There is a significant contribution of groundwater discharge to stream flow in the study area. Increasing groundwater extraction will have an effect on stream flow. This study finds that the current groundwater extraction levels represent only 0.17% of the annual recharge from precipitation, and that groundwater can sustain future increased groundwater demands from population growth and industrialization.

Sensitivity analysis of two-dimensional steady-state aquifer flow equations. Implications for groundwater flow model calibration and validation

This paper presents the analytical properties of the sensitivity of the two-dimensional, steady-state groundwater flow equation to the flow parameters and to the boundary conditions, based on the perturbation approach. These analytical properties are used to provide guidelines for model design, model calibration and monitoring network design. The sensitivity patterns are shown to depend on the nature of both the perturbed parameter and the variable investigated. Indeed, the sensitivity of the hydraulic head to the hydraulic conductivity extends mainly in the flow direction, while the sensitivity to the recharge spreads radially. Besides, the sensitivity of the flow longitudinal velocity to the hydraulic conductivity propagates in both the longitudinal and transverse directions, whereas the sensitivity of the flow transverse velocity propagates in the diagonal directions to the flow. The analytical results are confirmed by application examples on idealized and real-world simulations. These analytical findings allow some general rules to be established for model design, model calibration and monitoring network design. In particular, the optimal location of measurement points depends on the nature of the variable of interest. Measurement network design thus proves to be problem-dependent. Moreover, adequate monitoring well network design may allow to discriminate between the possible sources of error.

Simulating Seepage into Mine Shafts and Tunnels with MODFLOW

In cases when an equivalent porous medium assumption is suitable for simulating groundwater flow in bedrock aquifers, estimation of seepage into underground mine workings (UMWs) can be achieved by specifying MODFLOW drain nodes at the contact between water bearing rock and dewatered mine openings. However, this approach results in significant numerical problems when applied to simulate seepage into an extensive network of UMWs, which often exist at the mine sites. Numerical simulations conducted for individual UMWs, such as a vertical shaft or a horizontal drift, showed that accurate prediction of seepage rates can be achieved by either applying grid spacing that is much finer than the diameter/width of the simulated openings (explicit modeling) or using coarser grid with cell sizes exceeding the characteristic width of shafts or drifts by a factor of 3. Theoretical insight into this phenomenon is presented, based on the so-called well-index theory. It is demonstrated that applying this theory allows to minimize numerical errors associated with MODFLOW simulation of seepage into UMWs on a relatively coarse Cartesian grid. Presented examples include simulated steady-state groundwater flow from homogeneous, heterogeneous, and/or anisotropic rock into a vertical shaft, a horizontal drift/cross-cut, a ramp, two parallel drifts, and a combined system of a vertical shaft connected to a horizontal drift.

Use of stream response functions to determine impacts of replacing surface-water use with groundwater withdrawals

A regional-scale numerical groundwater model is used to study the impacts of replacing surface-water use with groundwater wells to improve low-flow stream conditions for endangered species within the Bertrand and Fishtrap watersheds, southern British Columbia, Canada and Washington, USA. Stream response functions ranging from 0 to 1.0 were calculated for individual wells placed within a steady-state groundwater flow model at varying distances from the streams to determine the impact that these replacement wells, operating under sustained pumping rates, would have on summer instream flows. Lower response ratios indicate groundwater pumping will have less of an impact on streamflow than taking an equivalent amount of water directly from a surface-water source. Results show that replacing surface-water use with groundwater withdrawals may be a viable alternative for increasing summer streamflows. Assuming combined response factors should be ≤0.5 for irrigators to undergo the expense of installing new wells, ~57% of the land area within 0.8 km of Bertrand Creek would be suitable for replacement wells. Similarly, 70% of the land area within 0.8 km of Fishtrap Creek was found to be appropriate. A visual analysis tool was developed using STELLA to allow stakeholders to quickly evaluate the impact associated with moving their water right.

Groundwater flow modelling in the upper Anga’a river watershed, Yaounde, Cameroon

The Anga’a River watershed is located within the Yaounde IV district, South-east of Yaounde City, Cameroon. The groundwater flow and particle tracking modelling was carried out to determine in detail the groundwater flow and particle migration in the shallow unconfined aquifer of the Upper Anga’a river watershed. The watershed was modelled with a grid of 106 columns x 68 rows with two layers viz., unconfined and semi-confined aquifers extending up to 50 m depth. The Anga’a river traverses in the central part of the watershed and generally flows North-South. Lateral inflows and outflows were simulated with constant head. The Anga’a river heads and the Lake levels were simulated using a river package. Natural recharge due to rainfall formed the main input to the aquifer system and the output was made of abstraction from pumping wells, base flow to Anga’a River, lake, springs and Evapotranspiration. A steady state groundwater flow simulation was carried out using Visual MODFLOW software and calibrated for the February, 2008 groundwater levels at 18 observation wells. The model computation has converged after 170 iterations with a convergence criterion of 0.01 m. The computed groundwater level contours have been following the trend of observed ones. The computed groundwater balance indicated that the Anga’a river base flows come from the groundwater regime. Groundwater Flow model results indicated that the topography controls groundwater flow in the watershed and that base flow to river is an important factor moderating groundwater movement in the Anga’a river watershed.

Series solutions for flow in stratified aquifers with natural geometry

An analytical series solution method is presented for modeling regional steady-state groundwater flow in a two-dimensional stratified aquifer cross-section where the water table is well-characterized. The aquifer system may have any number of contiguous or non-contiguous layers and the geometry of each layer is restricted only by the requirement that the elevation of the stratigraphic unconformities between layers is a function of the x-coordinate alone. Various techniques may be used to handle pinching layers, faults, and other discontinuities. The solutions are obtained by minimizing head and flow continuity errors between layers and errors in the Dirichlet surface at a set of control points along these unconformities; the governing equation is met exactly. The solutions are derived and demonstrated on multiple test cases. The errors for some specific, geometrically challenging cases are assessed and discussed.

A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

Inverse modelling is a key step in groundwater-related hydrological studies. Several inversion techniques were developed during the last decades, but hardly any comparison between them was presented. We compare seven modern inverse methods for groundwater flow: the Regularised Pilot Points Method (both the estimation, RPPM-CE, and the Monte Carlo ( MC) simulation variants, RPPM-CS), the MC variant of the Representer Method ( RM), the Sequential Self-Calibration Method ( SSC), the Moment Equations Method ( MEM), the Zonation Method ( ZM) and a non-iterative Semi-Analytical Method ( SAM). These methods are applied to a two-dimensional synthetic example, depicting steady-state groundwater flow around a pumping well. Their relative performance is assessed in terms of their ability to characterise the log-transmissivity and hydraulic head fields and to predict the extent of the well catchment, both for a mildly and a strongly heterogeneous transmissivity field. The main conclusions drawn from the comparison are: (1) MC-based methods ( RPPM-CS, SSC and RM) yield very similar results, regardless the degree of heterogeneity and despite they use different parameterisation schemes and objective functions; (2) statistical moments of the target quantities provided by MEM and RPPM-CE are similar to those of MC-based methods; (3) ZM and SAM are negatively affected by strong heterogeneity; and (4) in general, observed differences between the performances of all methods are not very large. MC-based inverse methods need considerably more CPU time than the other tested approaches. An advantage of MC-based methods is that they allow computing the posterior probability distribution of the target quantities, which can be directly fed to probabilistic risk-assessment procedures.

Effect of drainage conditions on porewater pressure distributions and lining stresses in drained tunnels

This study deals with the effect of drainage conditions on porewater pressure distributions and lining stresses in drained tunnels. Firstly, simple closed-form analytical solutions for the steady-state porewater pressure are re-derived within a common theoretical framework for two different boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference by using the conformal mapping technique. The difference in porewater pressure distributions among the analytical solutions is investigated. The numerical simulation of a drained circular tunnel under the steady-state groundwater flow condition is made to investigate the effect of porewater pressure distributions on lining stresses. Secondly, the case study of the planned South Blue Line Extension subway tunnel under the steady-state groundwater flow condition is performed for four different drainage conditions (sealed, fully-drained with zero water pressure or a constant total head, and invert only-drained) along the tunnel circumference. The effects of different drainage conditions on porewater pressure distributions, flow nets, and lining stresses are investigated.

Assessment of lake–groundwater interactions and anthropogenic stresses, using numerical groundwater flow model, for a Rift lake catchment in central Ethiopia

AbstractA steady‐state groundwater flow model (MODFLOW) was used to study lake and groundwater interactions in a complex rift volcanic catchment. It also was used to assess the effects of water pumping from wells, and of variable recharge rates associated with climate and lake level changes, on the dynamics of the volcanic aquifers surrounding Lake Awassa. The model simulations were made after first developing a reasonable conceptual model, on the basis of conventional hydrogeological mapping, pumping test and hydrometeorological data analyses, and from ancillary information obtained from hydrochemical and isotope techniques. The model results indicated that the lakes and Rift aquifers are fed by large groundwater inputs that originate in the highlands. The lakes and rivers have important roles in recharging the aquifers in some locations. Lake Awassa receives a major groundwater inflow from its southern and eastern shorelines, while substantial water leakage from the lake occurs along the northern shoreline. The annual groundwater outflow from the catchment is estimated to 52.5 × 106 m3. Scenario analyses revealed that increasing the current pumping rate from wells by fourfold will substantially reduce the groundwater level substantially, although the regional flow pattern would remain the same. There appears to be no immediate danger to the Rift aquatic environment from the current water pumping rate. Drying the small Lake Shalo and associated swamps, however, will cause a large change in the water balance of the larger Lake Awassa. Slight changes in groundwater recharge can cause large differences in groundwater levels for most of the Rift caldera floor far from the lake shores. This study provides a reasonable foundation for developing detailed transient predictive models, which can then readily be used as a decision support tool for development and implementation of sustainable water resources practices.

Modelling of lake—groundwater interaction in Turkey

A regional steady state groundwater flow model was developed for the Yalvac basin located in the watershed of Lake Egirdir, the second largest freshwater lake in Turkey. Determination of lake–groundwater interaction is an important step in taking proactive measures for optimal and beneficial use of water resources from the water management perspective. The geological structure around the lake and its surrounding aquifer system makes the modelling challenging. The hydrogeologic units in the groundwater system exhibit both confined/unconfined conditions: they are not horizontal, yet some of them are nearly vertical, which does not allow use of the ‘horizontal-layer’ concept of Modflow. The model demonstrated that it is a useful tool for planning and managing the water resources in the region by determining immeasurable components of classical water budget calculations, the groundwater inflow/outflow components, which are generally required for management of lakes. The groundwater discharge to Lake Egirdir through the Yalvac basin was estimated by means of the model. Two scenarios of hypothetical drought and wet conditions were simulated and evaluated from water resources management and groundwater–lake interaction perspectives.

Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers

Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed.

Field scale characterization and modeling of contaminant release from a coal tar source zone

A coal tar contaminated site was characterized using traditional and innovative investigation methods. A careful interpretation of hydrogeological and hydrogeochemical data allowed for the conceptualization of the heterogeneous coal tar distribution in the subsurface. Past and future contaminant release from the source zone was calculated using a modeling framework consisting of a three-dimensional steady-state groundwater flow model (MODFLOW) and two hydrogeochemical models (MIN3P). Computational time of long-term simulations was reduced by simplifying the coal tar composition using 3 composite and 2 individual constituents and sequential application of a 2D centerline model (for calibration and predictions) and a 3D model (only for predictions). Predictions were carried out for a period of 1000 years. The results reveal that contaminant mass flux is governed by the geometry of zones containing residual coal tar, amount of coal tar, its composition and the physicochemical properties of the constituents. The long-term predictions made using the 2D model show that even after 1000 years, source depletion will be small with respect to phenanthrene, 89% of initial mass will be still available, and for the moderately and sparingly soluble composite constituents, 60% and 98%, respectively.

Seepage force in a drained circular tunnel: An analytical approach

This study deals with the investigation of analytical solutions for the seepage forces acting on the lining in a drained circular tunnel under the steady-state groundwater flow condition. Two different boundary conditions (one for zero water pressure and the other for a constant total head) along the tunnel circumference are mentioned. Simple closed-form analytical solutions for seepage force along the tunnel circumference are derived in a theoretically consistent way for two different boundary conditions by using the conformal mapping technique. The seepage force predictions are compared to investigate the differences among the solutions. It is shown that the seepage forces acting on the lining should be considered for a drained tunnel and that the seepage forces greatly increase for a very deep tunnel.

Groundwater availability in the shallow aquifers of the southern voltaian system: a simulation and chemical analysis

A steady state groundwater flow simulation model was developed using available well data and general hydrogeological and geological information, for the Afram Plains area, Ghana. The hydrochemistry of groundwater from wells in the area was then evaluated to determine its suitability for irrigation and domestic uses. The assessment of the irrigation quality of groundwater from this area was based on salinity (EC) and sodium adsorption ratios (SAR), residual sodium carbonate (RSC), and permeability indices (PI). The simulation model reveals that groundwater in the Afram Plains area generally flows from the midsections in the neighborhood of Tease and surrounding areas, where significant recharge takes place, to the outer regions and discharges into the Volta Lake in the southern and eastern sections of the area. Flow magnitude and piezometric maps suggest that there is probably of less potential for groundwater extraction for sustainable irrigation in the central regions of the area, when compared to the other discharge areas. This study reveals that more than 70% of the samples analyzed fall within the C2–S1 category, referring to the medium level salinity and low sodium. Medium salinity waters may be used for irrigation on coarse textured soils with good permeability. About 15% of the data fall within the C3–S2 category, referring to water of high salinity and medium sodicity. High salinity, medium sodicity irrigation water cannot be used on fine-grained soils where drainage is restricted. This is because restricted flow is likely to result in the accumulation of salts in the root zones of crops, leading to salinity and soil clogging crisis. About 3% falls within the C3–S3 (high salinity, high sodicity) category. This category requires special soil management including improved drainage, heavy leaching and the use of chemical amendments on the water. Only one point plots within the extreme salinity–sodicity range. Concentrations of fluoride, arsenic and other natural elements in the area generally fall well within the world health standards for domestic water.

An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems

We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method.

On the Interpretation of Recharge Estimates from Steady‐State Model Calibrations

Ground water recharge is often estimated through the calibration of ground water flow models. We examine the nature of calibration errors by considering some simple mathematical and numerical calculations. From these calculations, we conclude that calibrating a steady-state ground water flow model to water level extremes yields estimates of recharge that have the same value as the time-varying recharge at the time the water levels are measured. These recharge values, however, are a subdued version of the actual transient recharge signal. In addition, calibrating a steady-state ground water flow model to data collected during periods of rising water levels will produce recharge values that underestimate the actual transient recharge. Similarly, calibrating during periods of falling water levels will overestimate the actual transient recharge. We also demonstrate that average water levels can be used to estimate the actual average recharge rate provided that water level data have been collected for a sufficient amount of time.

Steady-state groundwater flow model with variable hydraulic conductivity

Classical aquifer test models assume an isotropic and homogenous medium with Darcian flow as an ideal case. Deviations from type curves indicate the heterogeneity of the aquifer. There are heterogeneities even at small scales. There are also systematic variations which are not considered by type curves. For instance, due to the groundwater movement during the well-development phase, the hydraulic conductivity tends to decrease with radial distance from the well. For practical representation of such a systematic variation, a linear hydraulic conductivity decrease is adopted and the relevant type curve expressions are derived. These expressions are checked against the classical constant hydraulic conductivity solutions in the literature. Derived type curves are employed for the identification of aquifer parameters, namely transmissivity and the radial hydraulic conductivity variation parameters. The type curve expression derived transforms into the classical Thiem expression when the aquifer hydraulic conductivity is considered as constant. It is observed that classical steady-state flow with constant hydraulic conductivity underestimates the transmissivity by 10%.