Environmental Engineering Reference
In-Depth Information
in which Q uls and Q sls = ULS and SLS capacity, respectively; Q side , Q tip , and W = side resis-
tance, tip resistance, and effective shaft weight, respectively; and a = 4.0 and b = 0.4 = curve-
fitted parameters for the load-displacement model. The Q side , Q tip , and W are calculated
from
QBDK KK
side
=
π
(
/
)
σ
tan
δ
(7. 2 5)
0
n
0
vm
2
Q
=
0250
.
π
B
[ .
5
B
(
γ
γ
)
N
ζ ζζ γγ ζζζ
γγγγ
+−
(
)
DN
]
(7. 2 6)
tip
w
sdr
w
q s d r
2
WB D
=
025
.
πγ
(
γ
)
(7. 27 )
con
w
in which
σ vm is the mean vertical effective stress along the shaft depth, δ is the friction
angle at the soil-shaft interface = soil effective stress friction angle ϕ′ (for a rough interface),
γ w is the unit weight of water, N γ and N q are the bearing capacity factors, and ζ γ s , ζ γ d , ζ γ r , ζ qs ,
ζ qd , and ζ γ qr are the correction factors for the respective bearing capacity factors. The bear-
ing capacity and correction factors are calculated using the basic Vesić (1975) model with
minor updates (Kulhawy, 1991). Failure occurs when F 50 exceeds Q uls or Q sls (i.e., FS uls < 1 or
FS sls < 1). The driving variable BD/FS min is also calculated in the deterministic model work-
sheet for Subset Simulation.
Figure 7.6 shows an example of the deterministic model worksheet in an Excel spreadsheet.
The worksheet is divided into three parts: an input data zone from Rows 2 to 6, a capacity
calculation zone from Rows 7 to 11, and an output zone starting from Row 12. The input
data consist of soil properties (e.g., ϕ′ in Cell B4 in degrees or Cell C4 in radians), design
parameters, design requirements, unit weight of water and concrete, mean vertical effective
stress along the shaft depth, bearing capacity factors, correction factors for the respective
bearing capacity factors, and curve-fitted parameters for the load-displacement model. In
the capacity calculation zone, Equations 7.25 through 7.27 are implemented in Cells B9-D9
to calculate the side resistance, tip resistance, and effective shaft weight, respectively. Then,
the ULS and SLS capacities are calculated in Cells B11 and C11, respectively. In the output
Figure 7.6 Deterministic model worksheet for the drilled shaft design example.
 
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