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OCR for page 123
123
Table 63. Recommended resistance factors for 4.9 In-Depth Re-Examination
inclined-centric loading cases. of the Uncertainty in Bearing
Resistance factor ( T = 3)
Capacity of Footings in/on
Mean bias Soil conditions Granular Soils Under
Soil friction angle Natural Controlled Inclined-Eccentric Loading
f (deg) (from Eq.
5) (COV = 0.40) (COV = 0.35)
4.9.1 Extent of Database
MCS Rec* MCS Rec
38 1.41 0.522 0.45 0.605 0.45 The number of reliable data points for the inclined-eccentric
42 1.42 0.526 0.45 0.610 0.50 loading cases for which the positive and negative loading
45 1.43 0.530 0.50 0.614 0.50
46 1.44 0.533 0.50 0.618 0.55 eccentricities could be clearly distinguished are 15 in total.
Eight were tested under a positive loading eccentricity, and
*Rec = recommended.
seven were tested under a negative loading eccentricity. The
resistance factors obtained using the bias statistics for these
The COV of the bias (COV) obtained for the data is used as cases have been used here for guidance only.
a reference value; thus, a COV of 0.35 is adopted for controlled
soil conditions (even though a maximum COV of 0.376 was 4.9.2 Inclined-Eccentric, Positive Loading
obtained for f = 45°), and a COV of 0.40 is adopted for natu- Eccentricity Condition
ral soil conditions. Table 63 presents the resistance factors for
inclined-centric loading cases for f ranging from 38° to 46° Table 64 summarizes the bias statistics for the eight footing
using Equation 124 to obtain the bias for each soil friction cases under inclined-eccentric, positive (or reversible) loading
angle and COV values of 0.35 and 0.40, assumed based on the eccentricity. The resistance factor obtained based on the bias
uncertainty evaluation. statistics was 0.65, but as could be observed in all other cases of
The minimum bias for the highest resistance factor obtained loading, the recommended resistance factor may be taken as
using the equivalent factor of safety relationship in Equa- low as 0.50.
tion 122 is 0.423 (0.60/1.4167). The minimum biases of the
data are 0.37 and 0.57 (both with f = 45 ± 0.5°), which means 4.9.3 Inclined-Eccentric, Negative Loading
that the resistance factor needs to be reduced further. The Eccentricity Condition
required resistance factor for = 0.37 is approximately 0.52
(= 0.37 × 1.4167), which can be taken as 0.50. Hence, the resis- Table 65 summarizes the bias statistics for the seven footing
tance factors for both controlled soil conditions and natural cases under inclined-eccentric, negative loading eccentricity.
soil conditions are rounded off to a much lower number than The preliminary resistance factor obtained based on the bias
resistance factors obtained from the MCS. statistics was 1.00 for the available cases of soil friction angle, but
Table 64. Statistics of bearing resistance bias and the
resistance factors corresponding to soil friction angles in
controlled soil conditions for inclined-eccentric, positive
(or reversible) loading eccentricity.
Friction angle f Bias Resistance factor ( T = 3)
n
( 0.25 deg) Mean COV MCS Preliminary
45.0 5 2.52 0.505 0.687 0.65
44.5 3 1.55 0.158 1.158 1.00
all angles 8 2.16 0.506 0.587 0.55
Table 65. Statistics of bearing resistance bias and the resistance
factors corresponding to soil friction angles in controlled soil
conditions for inclined-eccentric, negative loading eccentricity.
Friction angle f Bias Resistance factor ( T = 3)
n
( 0.25 deg) Mean COV MCS Preliminary
45.0 4 3.78 0.640 2.043 1.00
44.5 3 2.96 0.187 0.703 0.70
all angles 7 3.43 0.523 0.887 0.85
