Practical reliability analysis and design by Monte Carlo Simulation in spreadsheet - Risk and Reliability in Geotechnical Engineering - page 312

γ = 20 kN/m 3
γ con = 24 kN/m 3
m ϕ ´ = 32º
K 0 = 1.0

D

(K/K 0 ) n = 1.0

F 50 = 800 kN
y a = 25 mm

B
=1.2 m

Figure 7.5 Design example of a drilled shaft. (Adapted from Phoon, K. K., Kulhawy, F. H. and Grigoriu, M.
D. 1995. Reliability-Based Design of Foundations for Transmission Line Structures, Report TR-105000 ,
Electric Power Research Institute, Palo Alto.)

in a spreadsheet environment. The drilled shaft is installed in loose sand with a total unit
weight γ = 20.0 kN/m 3 and mean effective friction angle m ′ 32 The shaft diameter B ,

concrete unit weight γ con , nominal at-rest horizontal soil stress coefficient K 0 , and nomi-
nal operative in situ horizontal stress coefficient ratio ( K/K 0 ) n are 1.2 m, 24.0 kN/m 3 , 1.0,
and 1.0, respectively. The water table is at the ground surface. The shaft is assumed to
fail in drained general shear under a design compression load F 50 = 800 kN with an allow-
able displacement y a = 25 mm. For the ULS and SLS target reliability indices β T ULS = 3.
(i.e., p T ULS = 0 000

= °.

φ

. (i.e., p T SLS = 00. 47 ) adopted for transmission line
structure foundations in North America, Phoon et al. (1995) showed that D = 4.2 m is a fea-
sible design when the coefficient of variation (COV) of ϕ′, COV ′ φ 5-0%, and B = 1.2 m.
In addition, Wang et al. (2011a) showed that the feasible designs of the example are drilled
shafts with D ≥ 4.4 m when COV ′ φ 7% and B = 1.2 m. This drilled shaft example is rede-
signed using the above-mentioned Excel spreadsheet Add-In, as discussed in the following
three sections.

. 9) and β T SLS = 26

7.6.1 Deterministic model worksheet
The deterministic model is largely identical to the traditional drilled shaft design calcula-
tion. It takes a given set of design parameters B and D , design loads, and soil properties as
input, and produces an output of the ULS and SLS factors of safety (i.e., FS uls and FS sls ) and
the driving variable (i.e., BD / FS min ) for Subset Simulation. To enable a consistent compari-
son with the previous results by Phoon et al. (1995) and Wang et al. (2011a), FS uls and FS sls
of the drilled shaft are calculated from

FS = QF / = ( QQWF + − ) /

(7. 2 3) uls uls 5 0 side tip 5 0

b

y
B

a

(7. 24)

FS = QF / = 0 625 . a QF /

sls sls 50 uls 50