Izbash formula

The Izbash formula is a mathematical expression used to calculate the stability of armourstone in flowing water environments.

For the assessment of granular material stability in a current, the Shields formula and the Izbash formula are commonly employed. The former is more appropriate for fine-grained materials like sand and gravel, whereas the Izbash formula is tailored for larger stone sizes. The Izbash formula was devised by Sergei Vladimirovich Izbash. Its general expression is as follows:^[1]

${\displaystyle {\frac {u_{c}}{\sqrt {\Delta gd}}}=1.7}$

or alternatively

${\displaystyle \Delta d=0.7{\frac {u^{2}}{2g}}}$

Here, the variables represent:

u_c = flow velocity in proximity to the stone

Δ = relative density of the stone, calculated as (ρ_s - ρ_w)/ρ_w where ρ_s denotes the stone's density and ρ_w is the water's density

g = gravitational acceleration

d = diameter of the stone

The coefficient 1.7 is an experimental constant determined by Izbash, encapsulating effects such as friction, inertia, and the turbulence of the current. Hence, the application of this coefficient is limited to conditions where turbulence is predominantly induced by the roughness of the construction materials in water. Adjustments are necessary when these conditions do not apply.