Improvements of Methods of Long Term Prediction of Variations in Groundwater Resources and Regimes Due to Human Activity (Proceedings of the Exeter Symposium, July 1982). IAHS Publ. no. 136.

Artificial groundwater recharge in Quaternary gravel aquifers in the foreland of the Alps

B, HERRLING Institute of Hydromechanics, University of Karlsruhe, West Germany ABSTRACT The possibility of recharging groundwater with the high-water of streams in valleys of the glacial period which are filled with permeable sediments is numerically investigated. Due to the great distance between the water table and the surface in some of these regions, the use of gravel-pits as storage and seepage basins has been proposed and the consequences downstream in the valley are explored. A time dependent, two- dimensional horizontal finite element model has been employed. In addition, moving boundaries as a result of the sloping lateral edges of the aquifer have been considered within the model. Preliminary results are presented for a case study.

INTRODUCTION

Numerous glacial valleys in the foreland of the Alps in West Germany consist primarily of Quaternary sand and gravel sediments. In these basin and channel systems the impermeable base not only has very steep slopes at the lateral periphery but often has a slope of more than 1% in the aquifer thalweg. The groundwater flow is mainly charged by the relative high precipitation in these areas and by the inflow from transverse valley aquifers. In some regions the distance between the water table and the surface reaches up to 20 m, whereas at other places the streams are recharged by groundwater seepage. The latter is important in increasing the low water discharge during dry periods. Periods of high precipitation and the sloping land surface often make it necessary to build retarding basins as flood control reservoirs. The subject of this paper is to investigate the consequences when the high-water of the streams is used for artificial groundwater recharge thus eliminating the need for expensive retarding basins. It is proposed that existing or newly constructed gravel-pits could be built in areas where the water table is located deep beneath the surface.

REGION OF INVESTIGATION

For this investigation the Eschach, and streams near Leutkirch, West Germany, were chosen as a case study (Figs 1, 2). These streams flow into the River which empties into the . In particular, the Eschach stream is known to be very susceptible to severe high-water conditions after intense rainfalls 33 34 B.Herrling or during spring thaws, which endanger the town of Leutkirch. The average streamflow in the Eschach stream is 2 m3s-1 (1957-1978), reaching maximum values of 52 m3s-1 upstream of Urlau (Fig.2) during peak periods. The drainage area amounts to nearly 120 km at Leutkirch. Retarding areas which have been used in the past will soon be no longer available and the construction of a new retarding basin in this geographical area poses considerable complications. It is, however, well known that the aquifer in the valley of the Eschach

FIC.1 General plan of the area of interest.

stream is very conductive (K < 0.02 m s"" in connection with a saturated thickness of sometimes more than 20 m). Furthermore the distance between the water table and the surface can locally be more than 20 m. Consideration has therefore been given to artificial groundwater recharge in order to raise the groundwater levels (Werner et al., 1974; Wrobel & Werner, 1979) and thus alleviate the demand for retarding basins. The fundamental idea consists in using newly constructed or existing gravel-pits as recharge basins and filling these with the high-waters of the Eschach stream. As these pits have a very permeable bottom as opposed to the relatively dense stream bed, the water would quickly seep into the ground thus removing the danger of downstream flooding. In non-peak periods the recharged water could be stored, and could possible contribute to higher discharges in the Aitrach stream and the River II1er during dry periods. This would in fact very likely be the case since the water table comes up to the surface near the Wurzacher Ach stream. The future amount of drinking water available to nearby regions with a high density of population could also be significantly increased by drawing as much water as possible from the Eschach stream, leaving behind only a minimum streamflow. This high quality water could be tapped from a. suitable location downstream of the recharge basin. A preliminary investigation was carried out by the State Artificial groundwater recharge 35

FIG.2 Site plan of the area of investigation.

Government of Baden-Wiirttemberg to create a network of hydrological and groundwater data points. Also, numerous boreholes were drilled in order to yield information about groundwater levels and the geology of the area. In a second step, a small test pit 7 m deep was constructed which spreads over an area of 100 m2 at the bottom and of 1400 m at the surface. In 1982 artificial groundwater recharge is planned using the water of the Eschach stream. The simultaneous measurement of more than 40 parameters in the neighbourhood of the pit will yield information about the water flux and the seepage process. The latter is of particular interest because of the stratified sediments with changing hydraulic conductivities which underlie the pit. The author's intentions are to simulate these seepage processes with a numerical model. Further research is to be directed towards the downstream consequences of the artificial groundwater recharge. Here the possibility of waterlogging will be examined and if necessary further preventive measures. Additionally, the effect of the runoff in the Aitrach stream, which is considerably influenced by effluent groundwater, is to be studied. For these reasons a numerical model has been set up to simulate the groundwater flow. In a first step the model was calibrated in its steady state form (Brandstetter, 1979) using an average hydrological situation and corresponding measured groundwater levels. In a further step the model has been run for time-dependent conditions as described in the next section. 36 B.Herrling

COMPUTATION OF THE TIME-DEPENDENT, HORIZONTAL GROUNDWATER FLOW

Basic theory The basic equations describing the time-dependent, two-dimensional horizontal groundwater flow in an unconfined aquifer are the continuity equation

Sy h,t + qiri = q* (1) and Darcy's equation of motion

9i = ~Tij h'j (2) summing over i,j = 1, 2. These equations result from a vertical integration using the Dupuit assumption. The unknown parameters are the groundwater level h (height of water table) and the horizontal flux per unit length q. defined in a Cartesian coordinate system x.. The symbols (),.; and (),t denote partial differentiations with respect to the coordinates Xj_ and the time t. An inflow in the area of computation is specified by q*. In addition there is the specific yield S,, for the free surface flow and the transmissivity tensor T. •. y -* 2.J When equation (2) is set into the continuity equation (1) it results in

Sy h't~ (Tij h'-j>'i = ^ (3) computed in a second step when h is known. In this case the method of weighted residuals is the basis of the application of the finite element analysis. In time, the equations are solved in a stepwise manner as usual, starting with a given initial condition. The domain of computation is subdivided into finite elements for the integration of the weighted basic equation (3).

SJ, oh Sw h,. dt dA - Ij,f. ôh (T.. h;i),. dt dA =

IS ôh q dt dA + /g/t ôh q dt dS + ft 6hK QK dt (4)

There are chosen elements in space (triangles) and time with linear shape functions respectively. The weighting functions ôh are also functions in space and time. In space they are identical with the shape functions (Galerkin method), and in time, constant weighting functions are chosen which give the same factors as the Crank-Nicolson time integration. The previous inflow q* is replaced by an areal distributed groundwater increment q, e.g. as a consequence of the precipitation, by a line source of mass inflow q defined on element boundaries S and by a point source of mass inflow QK at node K of the element system. Equation (4) is transformed by partial integration. Using Gauss' integral theorem and employing again equation (2) this results in: Artificial groundwater recharge 37

fj, ôh S„ h,. dt dA + f.f- ôh, . T. . h, . dt dA + AC y !• A "C 1 1J J /rX- ôh q, n. dt dS = /,/, ôh q dt dA + /„/. ôh q dt dS + bull A L. ù "C

;t ShK QK dt (5) Boundary conditions are the hydrographs of groundwater level or of the flux across the boundaries.

h - h = 0 (6)

qini + i = ° <7> h signifies a prescribed water level and q a flux normal to the outer boundaries. On closed boundaries q is equal to zero. While equation (6) is considered in the final set of equations, the condition (7) is inserted directly into equation (5) and can be combined with the second term on the right side of the sign of equality. In horizontal models it is very important to consider the water exchange with the streams. Therefore a line source term (leakage term) is formulated

q' = X • B • (hs - h) (8) with the leakage parameter X, which signifies the quotient from the permeability and the thickness of the bottom layer of a stream, together with the width B and the water level h^ of a stream. The leakage term (8) is treated as the other line source term. Equation (5) then becomes

/A/t ôh S h,t dt dA + fAft &h,± T± h,j dt dA = f^ft ôh q dt dA +

/ /t ôh q dt dS + / /t ôh X B (hs - h) dt dS + J"t ôhRQK dt (9)

The integration of the weighted equation (9) is carried out in time steps of At and over the whole area A of computation and the boundaries S respectively. In practice, the finite element technique reduces the integration in space to an element area Ae which leads to three element equations with three unknown parameters. For the integration over the entire area A these equations must be added and give a large set of equations. After the boundary condition (6) is inserted, the equation system can then be solved applying Cholesky's method. As the transmissivity is a function of the groundwater level h, the problem is nonlinear. Therefore at each particular time step an iteration is used. This means obtaining a solution several times with an updated coefficient matrix.

Moving boundaries Moving boundaries are necessary in the model when the impermeable base of an aquifer has large gradients, for example at the lateral edges of a glacial valley filled with sediments. For the case in question, artificial recharge might form flood waves much greater 38 B.Hexrling tiian during times of high precipitation. This can enlarge the lateral extension of the flooded aquifer and produce a different hydraulic situation. In fact, the boundaries of the aquifer could not become dry since there always exists a small subterranean inflow from the slope. However, to obtain a stable solution in the computation many iterations are necessary because the problem becomes highly nonlinear with a thickness of the saturated aquifer of only a few centimetres. Furthermore, the basic assumptions for a horizontal model are violated in these sloping areas. To save computer time and to offer a solution which is consistent with the accuracy of the rest of the model, the following procedure is suggested: - the discretization in space remains constant - elements with at least one dry node at the beginning or the end of a time step are removed from the area of computation (Fig.3) - in the partly flooded elements only the remaining volume of water is considered and is fixed as a function of the groundwater levels in the flooded nodes.

= constant outward boundary actual water boundary

== actual boundary of computation d dry element p partly flooded element f flooded element

FIG.3 Principles of the area of moving boundaries.

A dry node is established when the respective groundwater level lies beneath the impermeable bottom in an iteration step using an average transmissivity within an element. The water balance in the partly flooded elements is not corrected before the next time step in order to reduce the iteration steps. The prescribed inflow in the dry and partly flooded elements is directly forwarded to flooded nodes using the slope direction. An element is again flooded when a horizontal extrapolation from flooded nodes predicts that formerly dry ones have become wet. A similar procedure has been used by the author to reproduce intertidal flats in front of a coastline to model tidal waves (Herrling, 1976) .

NUMERICAL RESULTS

The Leutkirch model encompasses an area of 18 km x 3 km (see Fig.21. In the model the total vertical difference in altitude amounts to 112m for the impermeable base, 104m for the surface and 82m for the water table. Fig.4 shows the network of elements (929 elements, 535 nodes), and Fig.5 the contour lines of the base of the aquifer as represented in the model. The presented island within the area Artificial groundwater recharge 39

FIG.4 Network of elements. of computation corresponds to the region in which the impermeable base rises to the surface. The element network is constructed in such a way that the streams (Fig.2) run along element sides (seepage on a line and leakage), and wells and groundwater gauges lie on nodes. The measured lysimeter data are integrally incorporated in the model as an areal distributed inflow. The nodes with prescribed water levels (boundary conditions) are marked in Fig.4 as indicated. Calibration of the model was made using field data (boundary and inflow conditions). The presented computations cover a period of 8^ months from 5 November 1979 to 21 July 1980. This period includes several incidents of high-water condition in the Eschach stream with daily average stream flows up to 16 m s (maximum 22 m s ). Although the model calibration has not yet been completed the hydraulic conductivities determined range from 0.022 to 0.0005 m s-1, and the-specific yield applied is O.2. Using the p 2TSVÎOUS C3.-L culated modelling constants, several modifications were then made in order to investigate the influence of an artificial groundwater recharge. Altogether three runs have been carried out. The first was without any additional recharge; the second with a recharge regulated to prevent the total discharge in the Eschach stream from exceeding 10 m s during high-water 40 B.Herrlinc

FIG.5 Contour lines of the aquifer bottom. conditions. The third run investigated the case of recharging almost the entire stream discharge into the aquifer, leaving in the stream only a minimum flow of 2 m3s-1. The latter is carried out on the assumption that the required recharge basin could be physically realized. Results of the three runs of the model are presented for eight nodes (triangular marked nodes in Fig.4) of the system in Fig.6. As expected, the consequences of the second run simulating only the high-water recharge are very small. The increase of the groundwater level at Leutkirch (node 218) is only 0.1-0.15 m and at node 98 only

Nos. of nodes

100 150 Time !d) FIG.6 Consequences of artificial groundwater recharge. Artificial groundwater recharge 41 about a centimetre. Thus no difference between the uninfluenced first and the second run cannot be determined in Fig.6 downstream of node 301. The consequences of the more powerful recharge of the third run (the top line of each node in Fig.6) is more significant. Here the difference in groundwater levels between the first and third run amounts to about 2 m at Leutkirch (node 218) and nearly 4 m in the aquifers west and east of Urlau (node 319 and 341) . At nodes 166 and 98 this increase is less than 0.3 m and 0.1 m respectively. Furthermore, no waterlogging can be noticed south of the Wurzacher Ach stream. On the other hand, the computation shows that the recharged water leaves as seepage especially along the Wurzacher Ach stream and thus increases the runoff of the downstream rivers in a uniform way as demanded. Though the computed situation does not reproduce the most unfavourable case, these first results show that the numerical model is a useful tool for this investigation. Further it may be remarked that the proposed artificial groundwater recharge can be a practicable alternative, providing a solution to several of the needs of the surrounding communities.

ACKNOWLEDGEMENTS The author wishes to thank Dipl.-Ing. D.Willibald, State Board for Environmental Protection, and Dipl.-Geol. F.Kupsch, Geological State Board both of Baden-wiirttemberg, West Germany, for their hydrological and geological advice.

REFERENCES

Brandstetter, B. (1979) Berechnung der Grundwasserstromung im Bereich der Leutkircher Heide unter Verwendung eines Finite- Elemente-Programms fur horizontal ebene und stationare Stromungen. Diplom Thesis, University of Karlsruhe. Herrling, B. (1976) A finite element model for estuaries with intertidal flats. In: Proc. 15th Coast. Eng. Conf. (Honolulu), 3396-3415. Wrobel, J.-P. & Werner, J. (1979) Der Raum zwischen Donau und Alpen, Hydrogeologie und freies Grundwasser. In: Hydrologischer Atlas der Bundesrepublik Deutschland (ed. by R.Keller), Textband, 235-240. H.Boldt Publishers, Boppard (West Germany). Werner, J., Strayle, G. & Walser, M. (1974) Moglichkeiten der Grundwassererschliegung und -anreicherung im Gebiet der Leutkircher Heide (Obserschwaben). Das Gas- und Wasserfach 115(12), 525-568.