This paper reports the interaction between clay and acidic wastewater. However, this work investigates the structural and textural evolution after the leachate permeability test of clay soils from three potentials sites for acid effluents storage in the south of Tunisia (soil 1, soil 2, and soil 3). We can notice that the coefficient of permeability decreases according to the time in the case of soil 1 and soil 2 and increase from 6.8 × 10–10 to 1.1 × 10–8 m/s for soil 3. The textural changes for the three varieties of clay soils obtained after the leachate permeability test were studied through nitrogen gas adsorption at liquid nitrogen temperature; we determined the specific surface areas (SBET) and total pore and micropore volume. The textural study data have indicated that soil 1 had the lowest textural properties with a pore volume in the 0.06–0.09 cm3 g–1 ranges and with a surface area (SBET) varying between 35.4 and 47.4 m2 g–1. A detailed structural and morphologic modification were undertaken by scanning electron microscopy (SEM) equipped with energy-dispersive spectroscopy (EDS); their results show that soil 1 and soil 2 are able to uptake the noxious elements. By comparison, the selectivity of the elimination of these elements is in the order F > P > S for soil 1. The quantitative analysis of anions shows that the sorption capacity of fluoride for soil 1 is about 60 mg/g and is much higher compared to others anions.