**3.1.3.2 Transformation of the hydrogeological system - vertical schematization**

The topography of the surface terrain was processed into digital format from maps with the scale of 1: 10 000. For purposes of modelling, the above described hydrogeological system was transformed into a three-layers system, which consists of an upper covering soil layer (1st layer), of a medium to soft sand layer (2nd layer) and of a sandy gravel to rough sands with a gravel layer (3rd layer) (Fig. 5). These type of layers were selected for modelling as follows: 1st layer: unconfined, 2nd layer: confined/unconfined (transmissivity = const.), 3rd layer: confined/unconfined (transmissivity = const.). Thicknesses of particular layers were defined from geological and hydrogeological data from the survey. The surface of the tertiary base is considered impermeable.

simulated by the use of a finite difference block-central method. The solution of systems of

Northern to western boundaries of the modelled area are chosen regarding to the demarcation of hydrogeological groundwater body of the Čenkov plain from the northern side by the higher old-Würm terrace step. The Danube River creates the southern to eastern

simultaneous linear equations is possible to obtain by various methods.

**3.1.3 Conceptual groundwater modelling 3.1.3.1 Definition of model's boundaries** 

Fig. 5. The aquifer of the Čenkov plain

tertiary base is considered impermeable.

**3.1.3.2 Transformation of the hydrogeological system - vertical schematization** 

The topography of the surface terrain was processed into digital format from maps with the scale of 1: 10 000. For purposes of modelling, the above described hydrogeological system was transformed into a three-layers system, which consists of an upper covering soil layer (1st layer), of a medium to soft sand layer (2nd layer) and of a sandy gravel to rough sands with a gravel layer (3rd layer) (Fig. 5). These type of layers were selected for modelling as follows: 1st layer: unconfined, 2nd layer: confined/unconfined (transmissivity = const.), 3rd layer: confined/unconfined (transmissivity = const.). Thicknesses of particular layers were defined from geological and hydrogeological data from the survey. The surface of the

border (Fig. 2).

Hydrogeological systems are divided into a mesh of blocks called cells, the locations of which are described in terms of rows, columns, and layers. Footprint dimensions are picked so that the whole area of the Čenkov plain is covered with a smooth overlay. Dimensions of cells are: Δ*x* = Δ*y* = 50 m. Geometry of the model is: 22.5 km x 6.5 km, (130 rows and 450 columns); 3 layers. Grid orientation was picked in the direction of the general groundwater flow and coordinate axis *x*, *y*, *z* are approximately parallel to the main hydraulic conductivity axis. Groundwater flow has always had a certain measure of unsteady flow. This results from natural conditions of recharge and drainage of groundwater. However, if the recharge and drainage groundwater conditions are changing in the time slightly, the flow is quasi-steady and practically represents certain boundary status. From the modelling target point of view a steady status of groundwater flow was considered to the date 29 September 1954.

#### **3.1.3.4 Filtration parameters of the aquifer**

Following filtration parameters were necessary for the modelling of this case: horizontal hydraulic conductivity, transmissivity, vertical hydraulic conductivity, effective porosity and coefficient of vertical leakage. *Horizontal hydraulic conductivity* of the groundwater body was obtained from the results of the hydropedological and hydrogeological survey in the study area. Data from pumping tests in probes and boreholes were globally processed by the means of interpolation method of kriging. Values vary from 7.48E-07 m s-1 to 3.99E-03 m s-1. *Transmissivity* of the layers was calculated as a multiple of horizontal hydraulic conductivity and thickness of the layer. *Vertical hydraulic conductivity*: by the modelling applications the usual ratio of the horizontal to vertical hydraulic conductivity is from 1 to 10 (Anderson & Woessner, 1992). For the first and second layer ratio 1.0 was selected in compliance with results of the field research and for the third layer the ratio 2.0. *Effective porosity* is the feature of an aquifer to receive and to send out fluid in order to build hydrostatic pressure in the layer and through to the groundwater level. Quantitatively it is expressed by the coefficient of flexible storage and coefficient of free water level storage. The value of the coefficient of the free water level storage depends on hydraulic conductivity and also on grain size distribution of sediments and varies around 0.05 up to 0.15 for loamy sands, 0.15 for soft granulated to dusty sands, 0.19 for soft granulated sands, 0.22 for medium granulated sands and 0.24 for rough granulated sands, gravels etc. Estimated values of flexible storage for unit volume of the groundwater body are stated in the work of Mucha & Šestakov (1987). *Vertical leakage* is required in the case of multiple layers groundwater body and represents the resistance to the water leakage at adjacent layers.

### **3.1.4 Calibration and verification of the model**

Calibration is a process, when the initial input model parameters are adjusted until output (dependent) model parameters at most approach the values measured in the terrain. Calibration of the model is an inverse-model process, i.e. the problem of parameter estimation is an inverse problem. Calibration of the model or the inverse model process could be performed either repetitively, either on a manual basis by way of trial and error, or by using a special computer program. The calibration was executed by the means of the special computer program PEST with manual tuning of some zones. Calibration results for

Change of Groundwater Flow Characteristics After Construction of the

Waterworks System Protective Measures on the Danube River – A Case Study in Slovakia 63

Fig. 7. Simulated steady head distribution and flowlines in the second model layer

Fig. 8. 3-D visualization of filtration velocity vectors - view from south

the status up to date 29 September 1954 are shown in Fig. 6. The difference between measured groundwater stages in probes from the Hydrometeorological Institute's observing network have calculated groundwater stages have a maximum value of 0.17 m and the regression coefficient has a value near to one, which refers to high correspondence of calculated results with measured results. The calibrated model of steady groundwater flow was verified at the low water stage in the Danube up to date 7 Aug. 2002 and at high water stage in the Danube up to date 7 May 2000. For both cases a very good accordance of measured and calculated groundwater levels was reached.

#### Comparison of Calculated and Observed Heads

Fig. 6. Plot of calculated versus observed heads

#### **3.1.5 Simulated steady head distribution and flow lines**

Data about groundwater fluctuation has shown that the basic factors which are influencing groundwater level changes are atmospheric precipitation, bank filtration from the Danube river and underground inflow from the upper terrace direction north-west and on the northern edge of the area, then evapotranspiration, and underground outflow to the Danube (draining effect of the Danube) and outflow through the drainage canals.

On Fig. 7 we can see that the drainage effect of the Danube is from RK 1745 to RK 1733 and from RK 1727 to RK 1722, and this presents altogether 17 km of bank filtration drainage systems in the river. Bank filtration recharge is from RK 1733 to RK 1727 and that is 6 km bank length of the Danube. The line of direct drainage influence of the Danube goes from the Moča village along the edge of the terrace step to the Búč village, where it turns to the south approximately to the Mária farmstead whence it continues in a southern-easterly

the status up to date 29 September 1954 are shown in Fig. 6. The difference between measured groundwater stages in probes from the Hydrometeorological Institute's observing network have calculated groundwater stages have a maximum value of 0.17 m and the regression coefficient has a value near to one, which refers to high correspondence of calculated results with measured results. The calibrated model of steady groundwater flow was verified at the low water stage in the Danube up to date 7 Aug. 2002 and at high water stage in the Danube up to date 7 May 2000. For both cases a very good accordance of

Comparison of Calculated and Observed Heads

104.0 104.5 105.0 105.5 106.0 106.5

Data about groundwater fluctuation has shown that the basic factors which are influencing groundwater level changes are atmospheric precipitation, bank filtration from the Danube river and underground inflow from the upper terrace direction north-west and on the northern edge of the area, then evapotranspiration, and underground outflow to the

On Fig. 7 we can see that the drainage effect of the Danube is from RK 1745 to RK 1733 and from RK 1727 to RK 1722, and this presents altogether 17 km of bank filtration drainage systems in the river. Bank filtration recharge is from RK 1733 to RK 1727 and that is 6 km bank length of the Danube. The line of direct drainage influence of the Danube goes from the Moča village along the edge of the terrace step to the Búč village, where it turns to the south approximately to the Mária farmstead whence it continues in a southern-easterly

7426

520

519

6024

Observed Values

Danube (draining effect of the Danube) and outflow through the drainage canals.

6062 7422

7432 7432

514

7438

**3.1.5 Simulated steady head distribution and flow lines** 

measured and calculated groundwater levels was reached.

106.5

106.0

105.5

Calculated Values

105.0

104.5

104.0

Fig. 6. Plot of calculated versus observed heads

Fig. 7. Simulated steady head distribution and flowlines in the second model layer

Fig. 8. 3-D visualization of filtration velocity vectors - view from south

Change of Groundwater Flow Characteristics After Construction of the

by the outflow river regime - its level fluctuation.

other hydrogeological units.

hydrogeological region Q 057 in both cases.

volumetric budget and hydrogeological profiles.

Waterworks System Protective Measures on the Danube River – A Case Study in Slovakia 65


It is clear the boundary between narrower and wider riverine zone, similarly as between wider and external riverine zone is conventional to the certain degree. It must be understood to the intent that its determination pursuant to the stated principles is based upon a certain length of observation time, during which all somehow extreme situations need not to occur. The most distant demarcation of the external riverine zone shall be the edge of the terraced step of the bottom land or other its demarcation at the contact with

If the natural conditions are anthropogenically influenced and create a limited possibility of a hydrodynamic link between the level of the surface stream and groundwater, as it is in the case of the constructed underground non-permeable seating wall (the "NSW") between the Danube River and hydrogeological collector with omitted sections in the NSW, so called "windows", the demarcation of the boundaries between the zones is more difficult. The coefficients of determination for the individual boreholes are considered, while they are very important for the assessment of the degree of dependence between the level of the Danube River and the groundwater level. The boundary between narrower and wider riverine zone shall be determined using two-dimensional models of groundwater flow, displaying the isolines of piezometric groundwater heads and the vectors of filtration speed. The boundary is changed in dependence upon the level condition in the watercourse. The average width of narrower riverine zone of the Danube River at the left side of the lower Váh River in the proximity of an "window" is approximately 2500 m and it is approximately 2300 m on the Čenkov plain. Wider riverine zone is earmarked by the boundary of

**5. Analyses and comparison of representative groundwater regime of the** 

The processing of the observed data and creation of numerical models enables the clarification of the laws of the groundwater regime, in particular to determine its fundamental characteristics, which are: the level heights and main directions of the groundwater flow, depth of the groundwater level under the terrain, the fluctuation of the underground level, the lines of development of changes of the groundwater level in time,

*The height of levels and main directions of groundwater flow* shall be determined using the isolines of the piezometric heights of groundwater level (piezometric contours; for a free level ground water table contours) as the basic document. Firstly they are constructed for the characteristic conditions of the factors that may affect the groundwater regime, according to the knowledge of the hydrogeological and geomorphological conditions of the territory and the preliminary assessment of the observed data. They are the extreme cases of the occurrence of the meteorological factors, such as the periods after extraordinary heavy

**territory before, and after construction of protective measures** 

direction to the river in the Čenkov locality. The second drainage area is bounded from the south from the Obid canal river mouth to the Danube up to the Štúrovo town and from the north by the "Pod kopanicami" drainage canal. The feeding effect of the river is decreased by the drainage of lower parts of the Mužliansky creek and the Obid canal. The remaining part of the study area is drained by the local system (the Obid, Krížny and Búčsky canal). On Fig. 8 there is a 3D visualization of the whole groundwater body, with velocity vectors in the second layer of the groundwater body where there are the highest filtration velocities along the Obid canal and Mužliansky creek and at their river mouths, and also along the bank of the Danube (drainage) around RK 1742. Similarly in the third layer, there are the highest filtration velocities along open streams and along the Danube bank from RK 1744 to RK 1742 and around RK 1729. The range of filtration velocity values in the whole groundwater body varies from 1E-10 m.s-1 to 1.19E-03 m.s-1. Particle tracking is used for the tracing of the groundwater flow directions, which means creating flow lines by carrying out the tracing of infinitely small imaginary elements movement situated in the flow field. In the reach from the Moča village to the Čenkov settlement groundwater flow into the Danube except the northern part in which groundwater flows to the drainage canals. From the Obid canal mouth to the Danube River (RK 1727) up to the Štúrovo town groundwater flow direction is again into the Danube. The volume water budget for the whole model at the end of the simulation is calculated in order to control the results. It indicates acceptation of the numerical solution. Continuity has to be preserved also for the total model inflow and outflow or sub region of the layer. The difference in the water budget of the study area is 0.01 % the difference should be in ideal case smaller than 0.1%, what is fulfilled. In general an error up to 1% is accepted (Konikow & Bredehoeft, 1978).
