# Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study and Available Data

^{3}). A stilling basin, designed to dissipate the energy of the discharged flow, is located immediately downstream of the dam. The stilling basin bottom consists of concrete slabs, and dissipating blocks are located above them. The deposits below the dam and the stilling basin are surrounded by a cut-off wall (20–25 m deep) with the aim of obtaining an isolated “box” (Figure 1 and Figure 2). The box is designed to limit the interactions between the water in the reservoir and the aquifer underneath the dam and the basin; in particular, the objective of the wall is to prevent excessive uplift forces on the entire structure. The uplift force consists of an upward pressure at the interface between the structure and its permeable foundation [26], due to the increased hydraulic heads in the aquifer caused by the raising water levels in the lake. Because, on gravity dams, the uplift forces decrease the effective weight of the structure, they must be controlled and reduced to avoid stability problems. For this reason, in addition to the cut-off wall, the groundwater heads inside the box are also conditioned by a 110 m long drainage trench located upstream of the dam, about 3 m below its bottom (Figure 2).

#### 2.2. Inverse Approach

#### 2.3. Flow Model and Calibration

^{2}. The cells are on a regular grid in the plane (4 m × 4 m) and are 2 m thick except for the top and bottom layers where they follow the structure and the clayey layer, respectively. The 13 layers are useful to reproduce, with accuracy of 2 m, the length of the cut-off wall (variable from 16 to 24 m from ground level) and to better describe the aquifer heterogeneity. The groundwater flow model extends for a small portion inside the reservoir, upstream of the cut-off wall, to take into account the interactions between the water in the lake and the aquifer below (Figure 3). According to the modeled area, the active cells are 8181. To adequately reproduce the conceptual model of the study domain (Figure 1), several types of boundary conditions (BCs) were considered. The lake, upstream of the dam, was represented by means of a specified head BC (layer 1), the drainage trench under the structure was modeled using the drain package of MODFLOW (layer 1), and the horizontal flow barrier (HFB) package (layers 1–12) was used to simulate the cut-off wall that delimits the box below the dam. The HFB package was developed [39] to simulate barriers to flow such as slurry and cut-off walls by reducing the conductance between pairs of adjacent cells in the finite difference grid. As an additional parameter, the HFB package requires a hydraulic characteristic that is the ratio between the hydraulic conductivity of the barrier and the thickness of the barrier. Considering that the cut-off wall consists of concrete 1 m thick, we assumed $5\times {10}^{-10}{\mathrm{s}}^{-1}$ as hydraulic characteristic value; for more details on how to compute heads close to hydraulic barrier, see also references [40,41]. The lateral and downstream boundary conditions were no flow except for the locations where the cut-off wall does not reach the clayey layer; this region was described by means of a general head BC (layers 9–13). Figure 3 shows the computational grid and summarizes the location of the boundary conditions. The top and bottom of the model were also considered impervious.

## 3. Results

^{−5}m/s; in natural logarithmic scale the mean is −11.7 and the variance is 2.1.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Top view of the study area: Location of the monitoring wells and of the cross-section AA’ of Figure 2. The cyan star denotes the position of the borehole Bh.

**Figure 2.**Sketch view of the vertical cross section (AA’) of the investigated area with the indication of the aquifer of interest. Figure not to scale. Monitoring wells no. 9 and no. 3 with the indication of the observation depth: Shallow (S), medium (M) and deep (D). The plan view is shown in Figure 1.

**Figure 3.**Model grid and types of boundary conditions. The black line is the external boundary of the dam and the stilling basin; the gray lines represent the computational grid used to model the study area.

**Figure 4.**Lake stage above datum (a.d.) during the analyzed 145 days (

**a**,

**b**), observed hydraulic heads in two monitoring wells: no. 9 (

**a**) and no. 6 (

**b**), both at medium depth. The circles identify the hydraulic heads used in the inversion process. The location of the monitoring points is reported in Figure 1.

**Figure 5.**Three-dimensional view of the estimated hydraulic conductivity field: The results are reported in terms of natural logarithm of the parameters (ln HK) with units m/s in the physical space.

**Figure 6.**Estimated hydraulic conductivity field for layer 10: The results are reported in terms of natural logarithm of the parameters (ln HK) with units m/s in the physical space.

**Figure 8.**Observed versus computed hydraulic heads (350 data), best linear fit (solid line, with equation) and its coefficient of determination R

^{2}and performance metrics: Mean error ME, mean absolute error MAE, root mean square error RMSE and normalized one nRMSE. The 45-degrees line (dashed line) is reported for comparison.

**Figure 9.**Observed and computed hydraulic heads above datum (a.d.) during the analyzed 145 days in two monitoring wells: (

**a**) no. 9 (

**b**) no. 6, both at medium depth. The location of the monitoring points is reported in Figure 2.

**Figure 10.**Three-dimensional view of the standard deviation (SD) of the estimated hydraulic conductivity field. The results are reported in terms of natural logarithm of the parameters (ln HK) with units m/s in the physical space.

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**MDPI and ACS Style**

D’Oria, M.; Zanini, A.
Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy. *Water* **2019**, *11*, 176.
https://doi.org/10.3390/w11010176

**AMA Style**

D’Oria M, Zanini A.
Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy. *Water*. 2019; 11(1):176.
https://doi.org/10.3390/w11010176

**Chicago/Turabian Style**

D’Oria, Marco, and Andrea Zanini.
2019. "Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy" *Water* 11, no. 1: 176.
https://doi.org/10.3390/w11010176