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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