I developed a new model named POLARIS describing the complex conductivity of (pyrite-free) shaly poorly sorted sands. This model is based on the solution given by the effective medium theory for grains coated by an electrical double layer and immersed in a background electrolyte. The electrical double layer comprises the Stern layer and the diffuse layer. Both layers play very distinct roles in the in-phase and quadrature conductivities. The polarization of the shaly sands is mainly controlled by the polarization of the Stern layer (except at very high salinities) with a very small mobility of the counterions contained in this layer. The in-phase component of the conductivity is controlled by the conductivity of the pore water with a contribution associated with the diffuse layer (the contribution of the Stern layer seems negligible). The fraction of counterions in the Stern layer is computed from a simple sorption isotherm and is used to infer the quadrature conductivity. The quadrature conductivity is assumed to be frequency independent, which is a reasonable approximation in clayey sands and sandstones, in agreement with observations. The polarization model is also based on the assumption that the Stern layer is discontinuous between grains, an assumption that is consistent with recent models of ionic transport in clayey sands. POLARIS explains the dependence of the quadrature conductivity on the salinity, cation exchange capacity, specific surface area (or specific surface per unit pore volume), and temperature. It can be used to predict the saturation and the permeability (inside 1 order of magnitude).