Practical reliability analysis and design by Monte Carlo Simulation in spreadsheet - Risk and Reliability in Geotechnical Engineering - page 316

space, that is, w 1 , w 2 , and w 3 in Cells B12-D12 of the uncertainty model worksheet shown
in Figure 7.7. The “PDF of X , P ( X )” input field records the respective cell references of the
PDF values of the random variables (e.g., Cells B13-D13 in the uncertainty model worksheet
for w 1 , w 2 , and w 3 ). The “Driving variable, Y ” input field contains the cell reference (i.e.,
Cell B18 in the deterministic model worksheet shown in Figure 7.6 ) of the driving variable
BD/FS . The “Variable(s) to record, Y ” input field contains the cell references of Cells A2-E2
in a worksheet named “Mid-Record,” which are used to record 1/ FS uls , 1/ FS sls , BD / FS min , ϕ′,
B , and D during the simulation. After the input fields are set up, Subset Simulation is per-
formed by clicking the “Run” button.
After the simulation, an output worksheet is created by the Subset Simulation Add-In
to record the results, including the random samples generated in simulation and their cor-
responding values of 1/ FS uls , 1/ FS sls , and BD / FS min . The simulation results are used as input
of the RBD Add-In (see Figure 7.4b ) to calculate the respective failure probability p f ULS and
p f SLS of ULS and SLS failures for given B and D combinations, as shown in Figure 7.8a and b .

(a)

1

Subsim B = 0.9 m
Subsim B = 1.2 m
Subsim B = 1.5 m
Direct MCS B = 0.9 m
Direct MCS B = 1.2 m
Direct MCS B = 1.5 m

0.1

0.01

0.001

3.0 m 4.6 m

β T ULS = 3.2 or
p T ULS = 0.00069

2.0 m

0.0001

0.00001 0

2 4 6 8 10

Depth of drilled shaft, D (m)

(b)

1

Subsim B = 0.9 m
Subsim B = 1.2 m
Subsim B = 1.5 m
Direct MCS B=0.9 m
Direct MCS B=1.2 m
Direct MCS B=1.5 m

0.1

0.01

3.2 m 4.4 m

β T SLS = 2.6 or
p T SLS =0.0047

6.4 m

0.001

0.0001

0.00001

0 2 4 6 8 10

Depth of drilled shaft, D (m)

Figure 7.8 Conditional probability of failure from Subset Simulation and Direct MCS. (a) Ultimate limit state
(ULS) failure. (b) Serviceability limit state (SLS) failure.