Terzaghi’s Effective Stress Principle and Hydrological Deformation of Karst Aquifers Detected by GNSS Measurements

Analyses of GNSS (Global Navigation Satellite Systems) data acquired by stations located in karst areas of the Apennine chain (Italy) have revealed a strong correlation between changes in water table levels occurring in the saturated zone of karst aquifers and horizontal ground displacements. Many previous studies have explained this phenomenon by the widening and closing of sub-vertical water-filled fractures of the rock mass due to the hydraulic head rising and lowering, respectively, neglecting the role of the water pressure in the overall stress field acting in the saturated rock mass. In this study, the Skempton generalization of Terzaghi’s effective stress principle and the laws of linear elasticity were combined to explain the detected hydrological deformation of karst mountains, providing new analytical solutions. The water pressure variation associated with the water table rising and lowering is the main driver of the observed hydrological deformation, controlled by the elastic properties of the rock mass and the coefficient of earth pressure at rest, K0. The phenomenon of the hydrological deformation could be assimilated to the thermal expansion of solids, whose magnitude depends on the physical and geometric characteristics of the material and the temperature increase. Similarly, the hydrologically induced ground displacements measured by GNSS stations depend on the deformation of a specific aquifer portion caused by variations in the groundwater pressure.