Land subsidence due to groundwater withdrawal from the semi-confined aquifers of southwestern Flanders

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1 Land Subsidence (Proceedings of the Fifth International Symposium on Land Subsidence, The Hague, October 1995). IAHS Publ. no. 234, Land subsidence due to groundwater withdrawal from the semi-confined aquifers of southwestern Flanders L. LEBBE Laboratory for Applied Geology and Hydrogeology, University of Gent, Krijgslaan 281 S8, B-9000 Gent, Belgium Abstract Due to the heavy water withdrawal from the confined aquifers of southwestern Flanders, a subsidence cone has developed. This subsidence cone was mapped by comparing the levels of the first order of the National Geographical Institute (Belgium) between the levels of and In the centre of the subsidence cone, the drawdowns in the semi-confined aquifers have reached their maximum values. By means of an axi-symmetric hybrid finite-difference finiteelement numerical model, the evolution of the drawdown around a pumped well can be calculated. In this axi-symmetric model the groundwater reservoir can be discretized in a large number of layers, which are supposed to be laterally homogeneous. So the evolution of the drawdown can be simulated at different levels of thick semi-pervious layers. In this way, the evolution of the subsidence, which is mainly due to the compaction of the semi-pervious layers, can be simulated. Here, the evolution of the subsidence is calculated for two cases: for a pumping in the lower semi-confined aquifer and a pumping in the upper semi-confined aquifer with the same discharge rate. The hydraulic parameters of the pumped aquifers were derived from pumping test analyses. However, the hydraulic parameters of the thick semi-pervious layers had to be estimated. Thus, their specific elastic storages were estimated by means of the Van der Gun relation. These values were verified by the comparison of the calculated and the observed subsidence in the area of maximum drawdowns. The subsidence due to pumping in the lower semi-confined aquifer has proved to be very different from the subsidence caused by a pumping in the upper semi-confined aquifer. This is the case both for the radial extension and for the evolution of the subsidence. INTRODUCTION Comparison of the eighteen hundred first order level marks of the National Geographical Institute (Belgium) between the levels of and , made it possible to draw a recent ground level movement map (Pissart & Lambot, 1989). These movements are all derived with respect to the reference point at Ukkel. The absolute movement of this reference point is, however, not known. On this map, one can distinguish two large areas of ground lowering. One of this areas is located in the southwestern part of Flanders (Fig. 1). There, an almost circular area of subsidence occurs. In the centre of this area, the subsidence reaches maximum values which range between 80 and 100 mm.

2 48 L. Lebbe Fig. 1 Height changes of the first order level marks of the National Geographical Institute (Belgium) between the levelling of and (Pissart & Lambot, 1989). This subsidence area coincides with the area of minimum hydraulic heads in the two underlying semi-confined aquifers (Fig. 2). The groundwater reservoir consists of two semi-confined aquifers, which are separated by a semi-pervious layer. They are covered with a relatively thick semipervious layer (Fig. 3). At the top of the groundwater reservoir, a thin phreatic aquifer occurs. In the centre of the subsidence cone, the consolidated rocks of the Cambro- Silurian Brabant Massif occur at about 140 m below the ground surface. The upper part of this massif is fractured and forms the lower semi-confined aquifer. The massif is covered by Cretaceous and Tertiary unconsolidated rocks. The approximately 10 m thick Cretaceous deposits in the centre of the subsidence cone consist mainly of chalk and are semi-pervious. The overlying Tertiary deposits, which are principally composed of silt and clay, can also be considered to be semi-pervious. Between a depth of 86 and 100 m, silty fine sands occur that form the upper semi-confined aquifer. This aquifer is covered by Tertiary clayey and silty deposits. This semi-pervious layer has a very large areal extension and a considerable thickness under nearly the whole of the Belgian provinces West- and East-Flanders. This clay and silt layer has the same geological age as the London Clay. The superficial Quaternary sediments (sand, silt and clay) are generally thin, mostly between 2 and 13 m. In the river valleys, these sediments can be thicker. They form the phreatic aquifer. From both semi-confined aquifers, large groundwater quantities are withdrawn which cause large depression cones in the hydraulic head of both aquifers. In the centre of the cones, the drawdown since the start of the pumpings is estimated at 140 m in the lower semi-confined aquifer and about 85 m in the upper semi-confined aquifer (Lebbe et al., 1988) (Fig. 2). DRAWDOWN CALCULATED BY A NUMERICAL MODEL The applied numerical model is two-dimensional and axi-symmetric. In this model, the groundwater reservoir is discretized in a number of homogeneous layers which are

3 Land subsidence due to groundwater withdrawal in southwestern Flanders 49 Fig. 2 Hydraulic head contour lines of the lower (a) and the upper (b) semi-confined aquifers in the southwestern part of Flanders (Lebbe et al., 1988). numbered from bottom to top. Each layer is subdivided in a number of concentric rings. The lowest layer, layer 1, is bounded below by an impervious boundary. The water table always equals the top of the uppermost layer. The horizontal flow and the storage change in each layer are characterized, respectively, by one value of the horizontal conductivity and one value of the specific elastic storage. The vertical flow between two layers is governed by one value of the hydraulic resistance between those layers. The hydraulic resistance is the thickness of the layer divided by its vertical conductivity. The amount of water delivered by a unit decline of the water table is given by one value of the specific yield. In the block centred nodal circles of each ring, the drawdowns are calculated with a hybrid finite-difference finite-element model. The input parameters that define the space-time grid are the number of layers, the number of rings per layer, the

4 50 L. Lebbe aopth (m) Chronostratigraphy Llthostratigraphy sand, silt, cfay Hydrostratlgraphy ^ watortablo ==> pervious layer Layers in numerical model Drawdown versus depth clayey fine sands pervious layer sift, clay and clayey line sands / semi-pervious ' / / layer. chalk phyilites and shists Fig. 3 Chrono- and lithostratigraphical data and hydrogeological schematization of the groundwater reservoir in the centre of the subsidence area of southwestern Flanders. The vertical discretization of the groundwater reservoir in the numerical model along with the maximum drawdown vs. the depth. number of time steps, the initial radius, Rl, the initial time, 77, and the factor A. The initial radius is the inner radius of the smallest ring in the numerical model. The factor A determines the ratio of the outer and inner radii of all the rings and the ratio between the final and the starting time of the considered time steps. It is assumed that between two successive nodal circles of one layer the drawdown changes linearly with the logarithm of the distance from the pumped well. A detailed description of the numerical model is given in Lebbe (1988). In this work, the validation of this numerical model was shown by the simulation of the classical models of Theis, Jacob, Hantush & Jacob, Hantush and Boulton. SUBSIDENCE DUE TO DRAWDOWN OF THE HYDRAULIC HEAD In this paper, the real three-dimensional deformation of the groundwater reservoir is simplified to a one dimensional compression in the vertical direction. It is further assumed that the solids are incompressible and consequently, that the change in thickness of a layer is fully accounted by the change in void ratio. According to these, one can derive from Domenico & Schwartz (1990) that the thickness of a layer/, D(J), reduces with a value AD (J): AD{J) = D(J)(S S (J) - p w gn{j)p w )As (1) where AD (J) is the thickness reduction of layer J, D(J) is the thickness of layer J, S S (J) is the specific elastic storage of layer /, p w g is the specific weight of the water, n(j) is the porosity of layer /, j3 w is the water compressibility and As is the drawdown increase.

5 Land subsidence due to groundwater withdrawal in southwestern Flanders 51 Applying this formula, it is assumed that the specific elastic storage at every level is constant during the compaction and also independent of the drawdown. The thickness reduction of every layer can be found by calculating the drawdown for every layer with the numerical model. The subsidence undergone by the middle of a layer is now the sum of the thickness reductions of all the underlying layers increased with half the thickness reduction of the considered layer. For the uppermost layer of the numerical model, the calculated subsidence corresponds with the subsidence at the top of this layer. DISCRETIZATION IN THE NUMERICAL MODEL In the numerical model, the groundwater reservoir is discretized in eighteen layers (Fig. 3). The lowermost layer corresponds with the fractured top zone of the Brabant Massif. The Cretaceous deposits are discretized in two layers of respectively 4 and 5 m thick. The lower part of the Tertiary deposits, which form a semi-pervious layer, is discretized in five layers of respectively 6,7,8, and 7 m thick. The Tertiary fine sands between the depths of 86 and 100 m, are discretized in two layers of the same thickness. The thick upper part of the Tertiary deposits, which consists primarily of clay and silt, forms a semi-pervious layer. These deposits are discretized in eight layers with thicknesses between 7 and 11m. The uppermost layer of the numerical model coincides with the phreatic aquifer and has a thickness of 12 m. HYDRAULIC PARAMETERS Only the horizontal conductivities and the specific elastic storages of the pervious layers are well known. They were measured by means of pumping tests in the Brabant Massif (Lebbe et al, 1991) and in the Tertiary deposits (Lebbe et al., 1989; De Ceuckelaire et al., 1991). The other hydraulic parameters are estimated. This is particularly true for the horizontal conductivities of the semi-pervious layers and the vertical conductivities of the semi-pervious and pervious layers. The horizontal conductivity of layer 1 is equal to 0.8 m day" 1. According to the assumed thickness of the layer (50 m), the transmissivity of the pervious layer is equal to 40 m 2 day" 1. This is about the average transmissivity found in five pumping tests executed in the Brabant Massif (Lebbe et al., 1991). The average specific elastic storage found in these tests is 5.0 X 10~ 7 m" 1. This very small specific elastic storage is probably only due to the elasticity of the water. If the consolidated rocks are completely inelastic, they must have a porosity of about 11%. The horizontal conductivity of the Tertiary fine sands, which form the upper semi-confined aquifer, is equal to 0.16 m day" 1. The specific elastic storage of this layer is 9.8 x 10" 6 m" 1. This is the average value found by two pumping tests in these fine sands. Because the semi-pervious layers are horizontally stratified, they are considered as anisotropic with respect to the hydraulic conductivity. The horizontal conductivities of these layers are assumed to be two times larger than the vertical conductivity. The vertical conductivity of the Cretaceous deposits is estimated at a value of to 4.0 X 10" 4 m day" 1. The lower part of the Tertiary deposits has a vertical conductivity of 2.0 X 10" 4 m day" 1. The upper part of the Tertiary deposits, which consists

6 52 L. Lebbe principally of silt and clay, has the smallest vertical conductivity, about 8.0 x lo^mday" 1. ESTIMATION OF THE SPECIFIC ELASTIC STORAGES The specific elastic storages of the semi-pervious layers were not directly deduced from the pumping test analyses. These values are first derived with the help of the relation between the specific elastic storage and the depth of the sediments proposed by Van der Gun (1979). Based on the work of Van der Knaap (1959), Van der Gun (1979) proposes a relation between the specific elastic storages of sandy aquifers, S s, and the depth, d: S s = 1.8 xl(t Xl(r 4 <r 0-7 (2) The values derived from the specific elastic storages were verified by the comparison of the calculated and the observed subsidence in the area of maximum subsidence. The subsidence was calculated according to the method proposed by Domenico & Schwartz (1990). For this calculation the groundwater reservoir is discretized in the same way as in the numerical model. The specific elastic storages of each layer are calculated with the Van der Gun relation given above, according to the depths of the middle of the layer. The thickness reduction of every layer is then calculated by means of equation (1) with the drawdowns that occur now in the centre of the subsidence cone around Waregem. The estimated drawdowns in the pervious layers are equal to the differences between the observed hydraulic heads in these layers (Fig. 2) and the calculated head for the unpumped state of the groundwater reservoir (Lebbe et al., 1988). In the centre of the subsidence cone, the drawdowns have reached their maximum values. In the lower semiconfined aquifer they have a value of 140 m, in the upper semi-confined aquifer they reach a value of 85 m. The drawdown of the uppermost layer, which correspond with the phreatic aquifer, is put equal to 0.5 m. The drawdowns in the semi-pervious layers are calculated by linear interpolation between the drawdowns of the aquifers (Fig. 3). So, a steady state flow through the semi-pervious layer is assumed. In the calculation, a constant porosity of 0.4 was considered. The resulting subsidence is then equal to 106 mm. This value is a little higher than the observed change of the level marks between the levels of and It should be mentioned that there was already a very small subsidence before 1947 and that the subsidence had not reached his maximum value in The used drawdowns values were observed in Because the values for the specific elastic storage, estimated with the Van der Gun relation, result in calculated subsidence which is in accordance with the observed changes, these values can be used for a first attempt to simulate the subsidence due to pumping in one of the aquifers. SUBSIDENCE CALCULATED WITH THE NUMERICAL MODEL The evolution of the subsidence is calculated for a pumping in the lower semi-confined aquifer formed by the Palaeozoic Brabant Massif and secondly for a pumping in the upper semi-confined aquifer. In both calculations, a discharge rate of 192 m 3 day" 1 is chosen. This is the maximum possible withdrawal for a pumping well in the upper semi-confined aquifer. For a pumping well in the lower aquifer, however, it is a rather

7 Land subsidence due to groundwater withdrawal in southwestern Flanders 53 small discharge rate. The parameters that define the space-time grid are also the same in both calculations. The initial radius was 0.16 m, the factor which defines the ratio of the inner and the outer diameter was and fifty-eight rings were considered. This means that the outer boundary of the numerical model is situated at 100 km from the axis of the pumped well. The initial time of the calculation is equal to one minute and the drawdowns and the subsidence are calculated till 10 7 minutes, or about 19 years, after starting the pumping. The calculated subsidence are represented in subsidence-time and subsidencedistance graphs for both tests (Fig. 4). All axes of the graphs are logarithmic. In the subsidence-time graphs the evolution of the subsidence is represented for different times after the start of the pumping test. In the subsidence-distance graphs, the lateral variation of the subsidence is represented for different times after the start of the pumping. Comparing the graphs of both tests, one can draw the following conclusions. In the case of pumping in the upper semi-confined aquifer, the subsidence reaches its maximum value after about two years of pumping and for distances smaller than 500 m from the pumped well. At larger distances, the subsidence continues to increase after a longer pumping time. If the lower semi-confined layer is pumped, the subsidence has not reached his maximum value, even after a period of about 20 years of pumping and this for all distances from the pumped well. At relative large distance from the pumped SUBSIOENCEIM) SUBS1DEKCEOH ' 10* 10' 10 TJHE<MIN> 10< 10* I0 3 10* DISTANCE (HI Fig. 4 Subsidence-time and subsidence-distance graphs for the pumping test in the lower (a) and the upper (b) semi-confined aquifer both with a same discharge rate of 192 m 3 day" 1.

8 54 L. Lebbe well and after a long period of pumping, the subsidence due to pumping in the lower semi-confined aquifer is about equal to the subsidence caused by pumping in the upper semi-confined aquifer. For distances smaller than 2 km, the change of the subsidence versus the distance from the pumped well is much smaller in the case that the lower semi-confined aquifer is pumped then in the other case. CONCLUSION The subsidence due to pumpings in two different semi-confined aquifers in southwestern Flanders was studied by means of a numerical model. The evolution of the drawdowns was calculated at a large number of different levels in the thick semi-pervious layer. With these drawdowns, the evolution of the subsidence due to pumping can be calculated. First, the subsidence due to a pumping in the lower semi-confined aquifer of southwestern Flanders is calculated. The subsidence caused by pumping in the upper semi-confined aquifer is considered in the second simulation. The evolution and the lateral extension of the subsidence of both pumpings are very different. At relatively small distances from the pumped well, the subsidence is many times smaller in the first case than in the second case. At such distances, the subsidence reaches equilibrium later in the first case than in the second case. At relatively large distances the subsidence continues to increase after relatively large pumping times. At large distances from the pumped well, the subsidence of both pumpings does not differ much. This study must be considered as a first attempt to treat numerically the subsidence due to groundwater withdrawal from the semi-confined aquifers of southwestern Flanders. In a following step this subsidence should be treated taking the stress-dependence of the hydraulic parameters into account. Acknowledgements The author would like to thank the National Fund for Scientific Research (Belgium) under whose auspices the study was carried out. He wishes also to express his gratitude to Prof. W. De Breuck, Head of the Laboratory of Applied Geology and Hydrogeology, for the support given for the preparation of this paper. REFERENCES De Ceuckelaire, M., Lebbe, L., Bolle, I. & De Breuck, W. (1991) Results of the Pumping Test of the Dairy Factory INCO at Langemark (in Dutch). ReportTGO 90/53, State Univ. Gent, Lab. Appl. Geol. and Hydrogeology. Domenico, P. A. & Schwartz, F. W. (1990) Physical and Chemical Hydrogeology. John Wiley & Sons, New York. Lebbe, L. (1988) Execution of pumping tests and interpretation by means of an inverse model (in Dutch). Thesis Geagg. HogerOnderw. Geologisch Instituut, Univ. Gent, Gent. Lebbe, L., Van Camp, M., VanBurm, P., De Ceuckelaire, M., Watdez, R. & De Breuck, W. (1988) The groundwater in the Palaeozoic Basement Complex and in the Landenian aquifer in West- and East-Flanders (in Dutch). Water 41, Lebbe, L., MahaudenM. &De Breuck, W. (1989) Results ofthe pump and recovery test in the Benedictine sister's convent at Poperinge (in Dutch). Report TGO 89/53. State Univ. Gent, Lab. Appl. Geol. and Hydrogeol. Lebbe, L., MahaudenM. & De Breuck, W. (1991) Interpretation of pumping tests in the anisotropic Brabant Massif by means of a numerical inverse model. Ann. Soc. Géol. Belgique 114(1), Pissart, A. & Lambot, P. (1989) Les mouvements actuelsdu sol en Belgique; comparaison de deux nivellements IGN ( et ). Ann. Soc. Géol. Belgique 112(2), Van der Gun, J. A. M. (1979) Estimation of the elastic storage coefficient of sandy aquifers (in Dutch). 77V0 Dienst Grondwaterverkenning, Jaarverslag 1979, Van derknaap, W. (1959) Non-linear behaviour of elastic porous media. Trans AIME, 216.