variable symbol
correlation length (typical linear dimension of largest void) \(\xi\)
time \(t\)
critical (failure) time \(t_{c}\)
axial sample strain \(\epsilon\)
critical (failure) strain \(\epsilon_{c}\)
strain rate \(\dot{\epsilon}\)
differential stress \(\sigma\)
axial stress \(\sigma_{1}\)
confining pressure (radially-symmetric) \(\sigma_{3}\)
sample length \(L\)
critical (failure) stress \(\sigma_{c}\)
sample co-ordinate system \(x,y,z\)
dip \(\phi\)
strike \(\theta\)
porosity \(\varphi\)
number of segmented voids \(N\)
individual void \(i\)
volume of an individual void (pore or micro-crack) \(V_{i}\)
volume of the largest void \(V_{\max}\)
sample radius \(R\)
length of analyzed sub-volume \(l\)
volume of analyzed sub-volume \(V_{\text{subvol}}\)
corrected Akaike Information Criterion AICc
first-order moment of inertia (void centroid) \(M\)
second-order moment of inertia (covariance matrix) \(I\)
void ellipsoid radius \(r\)
mean void ellipsoid radius \(\overset{\overline{}}{r}\)
power-law exponent of void volume distribution \(\beta\)
Euclidean distance between two voids (inter-void distance) \(L_{i}\)
two-point correlation (fractal) dimension (power-law exponent of inter-void distance distribution) \(D\)
cumulative complementary (survivor) function of frequency-volume distribution \(\Phi\left(V\right)\)
completeness threshold of frequency-volume distribution \(V_{t}\)
tapering corner threshold of frequency-volume distribution \(V_{c}\)
modified Bayesian Information Criterion BIC
incremental probability distribution of inter-void lengths \({P(L}_{i})\)
exponent of incremental inter-void length distribution \(D_{\text{inc}}\)