Void Ratio Calculator

On the three-phase soil diagram, void ratio is void volume divided by solid volume, e = Vv / Vs. Referring voids to solids is deliberate: solid grains are effectively incompressible, so Vs stays constant and every change in e is a change in void volume alone. Porosity divides voids by total volume, so its denominator shrinks during compression, making rate-of-change relationships awkward. The two convert through e = n / (1 - n) and n = e / (1 + e), so 40 percent porosity is a void ratio of 0.667. When volumes are not measured directly, e follows from dry density and specific gravity as e = Gs gamma-w / gamma-d minus 1, with Gs near 2.65 for quartz sands and 2.70 to 2.75 for clays. Typical values run from 0.2 to 0.4 in dense gravel, 0.4 to 0.9 in sands and 0.8 to 1.5 in normally consolidated clays; the lacustrine clay beneath Mexico City reaches void ratios above 6, which is why that ground has settled metres in a century. For granular soils relative density, Dr = (emax - e) / (emax - emin), matters more than e itself, since the same e can be dense in one gradation and loose in another. In consolidation testing the slope of e against log effective stress gives the compression index Cc used in settlement calculations. Caveats: Gs should be measured per ASTM D854, since assuming 2.65 for a clay introduces several percent error, and the total volume of a soft sample is hard to measure without disturbance.

Void ratio became a working engineering variable with the birth of soil mechanics as a discipline. Karl Terzaghi, then teaching at Robert College in Istanbul, published his theory of one-dimensional consolidation in 1923 and his book Erdbaumechanik auf bodenphysikalischer Grundlage in 1925, which set out the phase relationships between solids, water and air and the effective stress principle that governs how void space changes under load. Terzaghi chose the solids volume as the reference precisely because it does not change during consolidation, and the convention has been standard ever since. Arthur Casagrande, who worked with Terzaghi after both moved to the United States and later held a chair at Harvard, extended the concept in two directions during the 1930s. He developed the graphical construction for estimating preconsolidation pressure from the void ratio versus log effective stress curve, a procedure presented in 1936 at the first International Conference on Soil Mechanics and Foundation Engineering at Harvard and still taught today. At the same conference he introduced the critical void ratio, the density at which a sand shears without volume change, which distinguishes contractive soils prone to liquefaction from dilatant ones and became the foundation of later critical state theory developed at Cambridge by Kenneth Roscoe and colleagues from the late 1950s. Standardised laboratory procedures followed, including ASTM D854 for specific gravity of solids and ASTM D2435 for one-dimensional consolidation, which report their results in terms of void ratio.