Effective hydraulic properties of virtual stony soils: Forward 3D simulations evaluated by 1D inverse modeling

Measuring hydraulic properties of stony soils and interpretation of the measured data is a challenge in vadose zone hydrology. The reason is not only the problem of installing suitable sensors but also the systematic measurement errors when sensors are only located in the background soil. A common approach to calculate the hydraulic properties of stony soils is by scaling the properties of the background soil according to the rock fragment content. Such modeling approaches are primarily developed for saturated flow conditions and only consider the amount of rock fragments as an input parameter. However, there is still a gap in knowledge regarding the effective properties of stony soils under unsaturated flow conditions.

Recently, 3D numerical simulation has become a convenient alternative tool to study the transport properties of heterogeneous porous media. The generation of data by numerical models is fast, measurements are repeatable and the simulation of the system under different initial and boundary conditions is easily achievable. We simulated three-dimensional unsaturated water flow in laboratory columns with stony soil material using the Hydrus 2D/3D software. Geometries were generated by assuming different volume fractions of impermeable rock fragments with spherical, cylindrical, or prolate shapes embedded in sandy loam soil. Time series of mean water contents, local pressure heads, and fluxes across the upper boundary were generated in an evaporation experiment, and a multi-step unit gradient simulation was applied to obtain values of hydraulic conductivity near saturation.

The synthetic measurement data were evaluated by inverse modeling, assuming a homogeneous system, and the effective hydraulic properties of stony soils were identified. The results were used to evaluate the scaling approaches for different volumes of rock fragments. A non-linear reduction in hydraulic conductivity by the increase of rock fractions was visible. The results also highlighted the effects of the orientation and shape of rock fragments. The orientation of rock fragments towards flow has a significant effect on the flow reduction, and in the case of prolate spheroids oriented along the flow direction, the reduction in conductivity was less significant.