Modulus of Deformation

Synonyms

Young’s modulus

Definition

The deformation modulus is Young’s modulus (E) for a rock mass (E_rm) or a soil mass; it is the ratio of principal stress in one direction (σ_x) to corresponding strain in the elastic range in the same direction (ε_x). It is not easily measured, so estimation methods based on geophysical measurements or rock mass classification schemes tend to be used. Estimates of a dynamic Poisson’s ratio (ν_d) can be calculated from surface or downhole geophysical measurements of compression-wave (Vp) and shear-wave (Vs) velocities, and a dynamic shear modulus (G_d) can be calculated using geophysical measurement of shear-wave velocity (Vs) and estimates of mass density (ρ) for the volume of earth materials. A dynamic rock mass deformation modulus (E_rmd) can be estimated as

$$ {E}_{rmd}=2\rho {\left({V}_s\right)}^2\left[1+\left(\frac{1}{2}\frac{\left(\frac{Vp^2}{Vs^2}\right)-2}{\left(\frac{Vp^2}{Vs^2}\right)-1}\right)\right]=2{G}_d\left(1+{\nu}_d\right) $$

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