Degree of Saturation Calculator

Degree of saturation S is the fraction of the void volume occupied by water, and it follows from the three-phase soil identity S * e = w * Gs. Here w is gravimetric water content measured by oven drying at 110 plus or minus 5 degrees C under ASTM D2216, Gs is the specific gravity of the solids from a pycnometer test under ASTM D854, and e is the void ratio, the volume of voids divided by the volume of solids. The identity is exact rather than empirical: it simply restates that the mass of water equals its volume times the density of water. Once e is known the calculator also returns porosity n = e / (1 + e), dry unit weight Gs * gamma_w / (1 + e), and saturated unit weight (Gs + e) * gamma_w / (1 + e), with gamma_w taken as 9.81 kN per cubic meter. Typical values give useful context. Quartz sands have Gs near 2.65, most clays 2.70 to 2.80, and organic soils can drop below 2.4. Void ratio runs about 0.4 to 0.9 in sands, 0.6 to 1.5 in soft clays, and above 3 in peats. Soil compacted at optimum moisture content in a Proctor test usually sits at S near 80 to 90 percent, while material in the capillary fringe just above the water table can be effectively saturated at zero or negative pore pressure. The main caveat is error propagation: S is a product and quotient of three measured quantities, so a two percent error in each can push a computed S several points past 100 percent, which is physically impossible and signals a bad Gs assumption, water loss during sampling, or a volume measurement problem rather than genuine supersaturation.

The three-phase description of soil, and with it the definitions of void ratio, porosity, water content, and degree of saturation, was consolidated by Karl Terzaghi in Erdbaumechanik auf bodenphysikalischer Grundlage, published in Vienna in 1925. Terzaghi needed a consistent volumetric bookkeeping scheme to state his effective stress principle, and the phase diagram supplied it. Arthur Casagrande, working with Terzaghi at MIT and later Harvard through the late 1920s and 1930s, standardized the laboratory procedures that supply the inputs, including the water content determination and the classification tests that became the Unified Soil Classification System. For decades saturation was treated mainly as a bookkeeping index, since classical soil mechanics assumed soils were either fully saturated or fully dry. That changed as engineers confronted compacted fills, arid-region soils, and rainfall-triggered slope failures where partial saturation controls behavior. Alan Bishop proposed an effective stress equation for unsaturated soil in 1959 using a parameter chi tied to the degree of saturation. Delwyn Fredlund and Norbert Morgenstern argued in 1977 that two independent stress state variables, net normal stress and matric suction, describe unsaturated soil more reliably than a single chi-weighted stress. Their framework, together with the soil-water characteristic curve that links suction to saturation, turned S from a descriptive index into a governing variable in modern unsaturated soil mechanics and in slope stability analyses of infiltration-driven landslides.