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 |
\(D_{\text{inc}}\) |