Table 1 Results of numerical simulations.

From: Probabilistic analysis and simulation of crack propagation in concrete pavements and surfaces

\(q\)

#Fails/5E5

\(\mu_{{n_{f} }}\)

\(\mu_{{n_{s} }} = \mu_{{n_{f} }} - m\)

\(P_{f} = 1 - \frac{{\mu_{{n_{s} }} }}{{\mu_{{n_{f} }} }}\)

\(1 - 2q\)

0.0*

1

33

0

1.000

1.000

0.05

1

37

4

0.892

0.900

0.10

1

41

8

0.805

0.800

0.17

1

50

17

0.660

0.660

0.25

1

65

32

0.508

0.500

0.3

1

81

48

0.407

0.400

0.35

1

108

75

0.306

0.300

0.4

1

161

128

0.205

0.200

0.45

0.37

268

235

0.123

0.100

0.49

0

–

–

0.000

0.020

0.5*

0

–

–

0.000

0.000

  1. *Simulations were not run for these limiting cases.
  2. \(\mu_{{n_{f} }}\): mean of \(n_{f}\) from \(N \times M\) = 500,000 simulations
  3. \(\mu_{{n_{s} }}\): mean number of crack segments going sideways (left or right) before reaching \(m\)\(m\)