Site description
The study site is located at the foot of the Apennines chain, in Abruzzo Region, inside the Tirino River valley (Fig. 1), where the carbonate formations meet the marly-arenaceous foredeep deposits. In details, in this area a superposition between the Gran Sasso carbonate unit and the Morrone – Roccatagliata, through trust faults which involve the marly - arenaceous Laga Formation, can be observed. In this framework, the Tirino river valley has been created by an extensional tectonic and filled by Quaternary deposits, such as lacustrine, detrital, and strictly alluvial one.
From the hydrogeological point of view, this area hosts the most important aquifers of the Abruzzo Region, the Gran Sasso aquifer, 700km2-wide [5], and the Morrone aquifer [12]. As abovementioned, these units are mainly calcareous and then characterized by high hydraulic conductivity due to fracturing and karstification and with wide recharge areas. The Quaternary deposits’ hydraulic conductivity changes according to the grain size, consequently they allow water flow or create local aquicludes.
In the lowest areas, where the carbonate structures are in contact with the marly ones, these aquifers generate basal springs whose discharges are between 6 m3/s and 1 m3/s; thus, the Tirino is an almost exclusively spring-fed river with a length of 13 km and a streamflow of over 12 m3/s [13]. The main springs are Basso Tirino one (Q ~ 6 m3/s), the Capo d’Acqua springs group (Q ~ 3 m3/s), and Presciano (Q ~ 2 m3/s) ones (Fig. 1); furthermore, minor springs (Q ~ 1 m3/s) are also present and called Incrementi Medio Tirino [13].
According to literature data [14] the total spring discharge of the area is 13 m3/s derived from the previous springs and from riverbed increases from other sources.
Locally the geological and hydrogeological framework is quite complex because of heterogeneity of the deposits; from literature data and available boreholes’ stratigraphies [15–18], in Fig. 2 the detailed hydrogeological set-up of the study area is shown: the Gran Sasso carbonate complex is in contact with the marly – clayey one creating a no-flux hydrogeological limit.
Step-drawdown test
Usually pumping tests are not suitable for carbonate aquifer like this, where hydraulic conductivity is due to fracturing and karstification, however a step-drawdown test has been performed and the equivalent hydraulic parameters have been estimated considering the aquifer like a porous one, as well as the influence radius, when the pumping rate was maximum.
The step drawdown test was described by Jacob [19], it implies to observe the drawdown in a well while the pumping rate is increased by step [20]; in each step the discharge rate is kept constant, and it is increased when the steady state is reached.
The step-drawdown test schedule, for this study, is shown in Table 1 and organized to avoid the interruption of drinking service.
Table 1
STEP | Period (hour.min) | Pumping rate (l/s) | Working wells | Monitoring wells |
T0 | | 635 | | |
Recovery | 2.00 | 0 | – | P5 - P6 - Pz San Rocco - Pz Piazzale - Pz Cartignano |
1 | 22.45 | 453 | P1-P2-P3-P7-P8 | P5 - P6 - Pz San Rocco - Pz Piazzale - Pz Cartignano |
2a | 7.55 | 522 | P1-P2-P3-P4-P7-P8 | P5 - P6 - Pz San Rocco - Pz Piazzale - Pz Cartignano |
2b | 16.20 | 560 | P1-P3-P4-P5-P7-P8 | P5 - P6 - Pz San Rocco - Pz Piazzale - Pz Cartignano |
3 | 72.55 | 740 | P1-P2-P3-P4-P5-P6-P7-P8 | P5 - P6 - Pz San Rocco - Pz Piazzale - Pz Cartignano |
As can be seen, the water distribution has been turned off for only 2 hours for the recovery step, and to obtain the so called “initial steady state”, then for each step an increasing number of wells have been switched on, keeping fixed the monitoring wells and piezometers; each step lasted at least 24 hours.
After the step-drawdown end, the water level has been monitored for 114 days from the beginning of the third step; this has allowed the summer period monitoring when the pumping rate is the same of the third step (740 l/s). Only small adjustment in drawdown have been recorded probably due to switch-on and switch-off of the Piazzale di Bussi well field with a pumping rate of 100 l/s.
Data elaboration
Considering the available atypical data and the derived approximations, two of the simplest and consolidated methods have been chosen for data elaboration.
For the steady-state Dupuit method have been used, while for the unsteady-state, the Theis one; both approaches have allowed the hydraulic conductivity and influence radius estimation.
The Dupuit theory [21] considers a radial flow in a well pumping at constant rate (Q) and the spreading of a depression cone until a certain distance (influence radius) where the drawdown is null because of the equilibrium between pumping and aquifer response.
Some conditions must be present, such as the steady-state conditions, which means that in each point of the aquifer the velocity vector must be constant in time, aquifer has to be homogeneous and isotropic, Darcy law [22] must be valid, the flow has to be horizontal and the same velocity in a vertical section is needed.
The Dupuit equation can be applied to both phreatic and confined aquifer and in this specific case, the aquifer has been considered as phreatic (Fig. 3) and the Dupuit equation is
\(Q=1.366K\frac{{{h}_{0}}^{2}-{{h}_{w}}^{2}}{\text{ln}{r}_{0}/{r}_{w}}\) 1
where Q is the pumping rate (m3/s), r0 is the distance between the pumping well and the no drawdown point, rw is the pumping well radius, ho and hw are the saturated thickness in static condition and the saturated thickness in the pumping well, respectively.
If two observation wells are considered, Dupuit – Thiem equation [23] can be applied
\(Q=1.366K\frac{{{h}_{2}}^{2}-{{h}_{1}}^{2}}{\text{ln}{r}_{2}/{r}_{1}}\) 2
consequently, the equation for the hydraulic conductivity (K) estimation is
\(K=\left(\frac{Q}{1.366}\right){log}\frac{{r}_{2}}{{r}_{1}}/\left({{h}_{2}}^{2}-{{h}_{1}}^{2}\right)\) 3
where Q is the pumping rate (m3/s), r1 is the distance between the observation well P1 and the pumping well, r2 is the distance between the observation well P2 and the pumping well, h1 and h2 are the saturated thickness in the observation wells P1 and P2 with static conditions, respectively (Fig. 3).
The estimation of the influence radius (r0) has been carried out using two equations, the Dupuit [21] and the Sichardt [24] ones.
The Dupuit equation is
\(\text{ln}{r}_{0}=\left(\frac{\left({{h}_{0}}^{2}-{{h}_{1}}^{2}\right)}{\left({{h}_{2}}^{2}-{{h}_{1}}^{2}\right)}\left(\text{ln}\frac{{r}_{2}}{{r}_{1}}\right)\right)+\text{ln}{r}_{1}\) 4
while the Sichardt equation is
\({r}_{0}=3000\left({h}_{0}-{h}_{w}\right)\sqrt{K}\) 5
where r1 is the distance between the observation well P1 and the pumping well, such as r2, h0 is the water table depth in static condition, hw is the hydraulic head in the pumping well, and h1 and h2 are the hydraulic heads in the observation wells P1 and P2 with static conditions, respectively.
Taking into account the thickness of the aquifer, transmissivity (T) can be also estimated, using
\(T=Kb\) 6
where K is the hydraulic conductivity and b the aquifer thickness.
In this study, for data elaboration, the abovementioned Equivalent Well (EW) has been considered as pumping well, P5, P6 wells, Cartignano, Piazzale di Bussi and San Rocco piezometers, as monitoring wells.
The unsteady theory by Thies [25] is based on the principle that if pumping continues a wider portion on the aquifer is involved in it, as consequence there is not a fixed influence radius, but it becomes bigger as well as the depression cone.
Considering the big aquifer extension [5] and the low drawdown compared with the aquifer thickness, in this case the carbonate aquifer has been considered as confined and the Theis equation applied,
\({h}_{0}-h=\frac{Q}{4\pi T}\underset{0}{\overset{\infty }{\int }}\frac{{e}^{-u}du}{u}\) 7
where \(u=\frac{{r}^{2}}{4Tt}\) and \(\underset{0}{\overset{\infty }{\int }}\frac{{e}^{-u}du}{u}= W\left(u\right)\) called Well function, h0 is the hydraulic head at a distance r from the well, h il the hydraulic head after a certain time t, Q the pumping rate (m3/s), T the transmissivity and S the storage coefficient.
This method can be applied if the aquifer is homogeneous and isotropic, it is confined with constant thickness and the well goes through all the aquifer thickness with an infinitesimal diameter [26].
The Eq. (7) can be solved using the Jacob – Cooper approximation [27] and it becomes
\({h}_{0}-h={\Delta }h =\frac{0.183Q}{T}\left(\text{log}\left(\frac{2.25Tt}{{r}^{2}S}\right)\right)\) 8
where \(\frac{0.183Q}{T}=C\) and it is the angular coefficient of the line “Drawdown vs Log time”.