Terzaghi’s effective stress principle and hydrological deformation of karst massifs detected by GNSS and InSAR

Abstract

Previous studies have shown that carbonate massifs of the Apennine chain (Italy) undergo deformation in response to groundwater level variations occurring in the saturated zone of karst aquifers. This study focuses on the Matese massif, hosting one of the main karst aquifers of the central-southern Apennine. Our analyses revealed a hydrological component in the time series of the horizontal and vertical ground displacements measured by GNSS (Global Navigation Satellite Systems) and InSAR (Interferometric Synthetic Aperture Radar). In particular, contraction and dilatation phases of the karst massif appear associated with the lowering and rising of the groundwater levels, respectively. Various authors have explained this phenomenon by the widening and closing of sub-vertical waterfilled fractures dissecting the rock mass due to varying hydraulic heads, neglecting the role of the effective stress state acting in the aquifer saturated zone. We present new equations explaining the observed deformational phenomenon in its generality, which are based on Terzaghi’s effective stress principle (Skempton’s generalization) and linear elasticity. The study shows that hydrological deformation of karst massifs is similar to the thermal expansion of solids. In the first case, the deformation is primarily due to pore water pressure variations occurring in the aquifer saturated zone, which are associated with water table oscillations, and is controlled by the elastic properties of the rock mass and the coefficient of earth pressure at rest, K0.