# Encyclopedia of Engineering Geology

2018 Edition
| Editors: Peter T. Bobrowsky, Brian Marker

# Modulus of Deformation

Reference work entry
DOI: https://doi.org/10.1007/978-3-319-73568-9_204

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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## References

1. Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43:203–215
2. Hoek E, Carter TG, Diederichs MS (2013) Quantification of the geological strength index chart. In: ARMA 47th US rock mechanics/geomechanics symposium, San Francisco, pp 672–679Google Scholar
3. RocScience (2016) Rock mass modulus. Online information on the RocScience website https://www.rocscience.com/help/rocdata/webhelp/rocdata/Rock_Mass_Modulus.htm. Accessed May 2016