Measurement of field-saturated hydraulic conductivity on fractured rock outcrops near Altamura (Southern Italy) with an adjustable large ring infiltrometer

Abstract

Up to now, field studies set up to measure field-saturated hydraulic conductivity to evaluate contamination risks, have employed small cylinders that may not be representative of the scale of measurements in heterogeneous media. In this study, a large adjustable ring infiltrometer was designed to be installed on-site directly on rock to measure its field-saturated hydraulic conductivity. The proposed device is inexpensive and simple to implement, yet also very versatile, due to its large adjustable diameter that can be fixed on-site. It thus allows an improved representation of the natural system’s heterogeneity, while also taking into consideration irregularities in the soil/rock surface. The new apparatus was tested on an outcrop of karstic fractured limestone overlying the deep Murge aquifer in the South of Italy, which has recently been affected by untreated sludge disposal, derived from municipal and industrial wastewater treatment plants. The quasi-steady vertical flow into the unsaturated fractures was investigated by measuring water levels during infiltrometer tests. Simultaneously, subsurface electrical resistivity measurements were used to visualize the infiltration of water in the subsoil, due to unsaturated water flow in the fractures. The proposed experimental apparatus works well on rock outcrops, and allows the repetition of infiltration tests at many locations in order to reduce model uncertainties in heterogeneous media.

Appendix

The unsaturated water flow in a vertical section can be described by the Richards’ equation:

$$ {\frac{\partial \theta }{\partial \psi }}{\frac{\partial \psi }{\partial t}} = - {\frac{\partial }{\partial x}}\left[ {K_{\text{fr}} (\psi ){\frac{\partial \psi }{\partial x}}} \right] - {\frac{\partial }{\partial z}}\left[ {K_{\text{fr}} (\psi )\left( {{\frac{\partial \psi }{\partial z}} - 1} \right)} \right] $$

(4)

where K _fr(L/t) is the variable hydraulic conductivity as in the vertical fracture plane with variable apertures. It should be noted that, following Hestir and Long (1990), the fracture network in a vertical section xz (or yz) of a fractured rock can be assumed equivalent to a fracture lattice, as in a fracture with variable aperture. Consequently, K _fr can be defined using the following equation (Bear 1993, p. 15)

$$ K_{\text{fr}} \left( \psi \right) = k\left( \psi \right)\overline{{k_{\text{fr}} }} \left( {x,z} \right){\frac{\rho g}{\mu }} $$

(5)

where g(L/t ²) is the gravity acceleration; ρ(M/L ³) the water density; μ(N/L ², centipoises) the dynamic water viscosity; $\overline{{k_{\text{fr}} }} = \theta_{\text{s}} {\frac{{b(x, z)^{2} }}{12}}$ the saturated fracture permeability within which b(x, z) is the nodal aperture of the vertical fracture and θ_s the saturated water content; k(ψ)(–) the relative permeability coefficient and ψ(L) is the suction head. The coefficient k(ψ) is related to the water suction head (or to the water content, θ) by means of an unsaturated hydraulic conductivity function (Reitsma and Kueper 1994; Abdel-Salam and Chrysikopoulos 1996; Bockgård and Niemi 2004, p. 789) and it can be calculated using:

$$ k(\psi ) = {\frac{{k_{\text{fr}} (\psi )}}{{\overline{{k_{\text{fr}} }} }}} $$

(6)

The field-saturated hydraulic conductivity, K _fs is related to fracture hydraulic conductivity, K _fr(ψ), at saturation and to the mean aperture of vertical fracture, by means of the permeability of the rock matrix and mean spacing between fractures of the outcrop (Hestir and Long 1990).

Equation 4 was solved by applying a finite difference grid in x and z. An iterative numerical method was used to solve the above equation and an infiltrated water mass balance check was carried out at every instant of simulation. Some numerical improvements of the Crank–Nicholson implicit method (Bear 1979) allowed an automatic increase (i.e., adjustment) of the temporal discretization step during numerical iterations in order to reduce the total computational time. A computational code calibrated in a previous work (Masciopinto and Benedini 1999) was then applied to reproduce the pressure head distributions during infiltration tests at the Altamura site. As boundary conditions at the topsoil, a variable pressure head versus time was imposed to simulate the water ring infiltration. The van Genucthen parameters for the retention curves considered for test #1 were α^* = 1.11 m⁻¹, m = 0.65, θ_r = 0.01 and θ_s = 0.99, respectively. It should be noted that α^* was reassigned at the end of the simulation, when the output of the simulation fitted the real infiltrated water depth (about 1.5 m). The parameters for nodal aperture generation in the fracture plane (x, z) were mean of aperture 10^2.1 μm in x, 10^2.47 μm in z; standard deviations of Log aperture 0.34 in x and 0.49 in z, nugget 0.02 (in x and z), sill 0.10 (in x and z) and spatial correlation length 3 m in x and 2 m in z. The details describing the geo-statistical and computational methods used for fracture aperture generation in the vertical outcrop section are reported in other works (Masciopinto 2005; Pruess and Tsang 1990). Several simulations were carried out by considering different mean fracture apertures (i.e., the model parameters) in x and z. The best model solution (see Fig. 6b) was determined when the maximum simulated depth of infiltrated water was equal to 1.5 m, 80 min after the start of the infiltration into the ring. Thus, the corresponding model output, in terms of matric head distribution also enhanced the macroscopic capillary length of 0.90 m (or α^* = 1.11 m⁻¹) and the corresponding cutoff apertures $\overline{b}_{\text{c}}$(16.5 μm) defined by the Young–Laplace equation. This pressure head is clearly visible in Fig. 6b, as the contour line −0.90 m divides the zone of fracture filled only by air from that with larger apertures filled by water and air.