poel-params: Parameter sensitivity to Poisson's ratio
In abarbour/poel: Tools to facilitate working with simulations from poel

Description Usage Arguments Details References Examples

Functions to investigate sensitivity of normalized-parameters

poel_lambda(nu)

poel_alpha(nu, nuu)

poel_beta(nu, nuu)

poel_chi(nu, nuu)

`nu`	numeric; Poisson's ratio
`nuu`	numeric; undrained Poisson's ratio

poel_lambda gives the Lame constant, normalized by μ, the elastic shear modulus; this has no dependence on the undrained Poisson's ratio

poel_alpha gives the effective stress coefficient, normalized by 1 / B where B is Skempton's coefficient. Hence, to obtain Biot's pore pressure coefficient (generally written as α) take this value and divide by B.

poel_beta gives the bulk compressibility, normalized by 1 / μ / B^2

poel_chi gives the Darcy conductivity, normalized by D / μ / B^2 where D is the hydraulic diffusivity, which is proportional to permeability

H.-J. Kümpel; Poroelasticity: parameters reviewed. Geophys J Int 1991; 105 (3): 783-799. doi: 10.1111/j.1365-246X.1991.tb00813.x

a1 <- poel_alpha(0.25,0.33)
a2 <- poel_alpha(0.20,0.40)
a2/a1

# try multiple values
poel_alpha(0.25,seq(0,1,by=0.1))

# Make a sensitivity matrix
# Poisson's ratios
nu <- nuu <- seq(0,0.5,by=0.01)
alpgrd <- outer(nu, nuu, "poel_alpha")
B <- 0.75 # Skempton's coefficient
biot <- alpgrd/B

fields::image.plot(nu, nuu, biot, asp=1)
contour(nu, nuu, biot, add=TRUE)