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From page 100... ... Similarly, the investigation of vertical loading of shallow foundations on natural soils as compared to vertical loading of shallow foundations on controlled soils, presented in Section 3.5, suggested large variations between the two groups. Earlier interpretations of the data (e.g., Paikowsky et al., 2008; Paikowsky et al., 2009b; Amatya et al., 2009) Read the entire page →
From page 101... ... The Rankine active earth pressure coefficient is given by the following: The variation of the Rankine active earth pressure coefﬁcient with the variation in the soil friction angle is presented in Table 51. The coefﬁcients of variation for earth pressure coefﬁcients in Table 51 were obtained by generating 1,000 samples of soil friction angle following lognormal distribution, with COVs of 0.10, 0.15, 0.20, and 0.25, respectively, and limiting maximum soil friction angle to 47°. Read the entire page →
From page 102... ... f = 2/3 f = 0.5 f = 0.4 f = 0.3 f = 0.2 f = 0.1 f = 0.0 Mean CO V C OV si m C OV calc COV sim COV calc COV sim COV si m C OV sim COV sim COV sim COV sim COV sim 0.10 0.09 0.10 0.10 0.09 0.20 0.17 0.15 0.14 0.12 0.11 0.1 0 0.15 0.14 0.15 0.15 0.13 0.34 0.27 0.24 0.21 0.19 0.17 0.1 5 0.20 0.19 0.21 0.22 0.17 0.64 0.45 0.38 0.33 0.28 0.25 0.2 2 0.25 0.22 0.27 0.27 0.21 1.04 0.61 0.49 0.41 0.35 0.31 0.2 7 0.10 0.12 0.13 0.13 0.11 0.36 0.27 0.23 0.20 0.17 0.15 0.1 3 0.15 0.17 0.19 0.19 0.16 0.70 0.43 0.35 0.30 0.26 0.22 0.1 9 0.20 0.23 0.27 0.26 0.21 1.05 0.63 0.50 0.42 0.35 0.30 0.2 6 0.25 0.27 0.34 0.33 0.25 1.39 0.84 0.67 0.55 0.46 0.39 0.3 3 0.10 0.15 0.16 0.16 0.14 0.58 0.37 0.30 0.25 0.22 0.18 0.1 6 0.15 0.22 0.24 0.24 0.20 0.97 0.59 0.48 0.39 0.33 0.28 0.2 4 0.20 0.28 0.33 0.30 0.25 1.13 0.73 0.59 0.49 0.42 0.35 0.3 0 0.25 0.31 0.43 0.34 0.30 1.19 0.80 0.65 0.55 0.46 0.39 0.3 4 0.10 0.16 0.17 0.17 0.15 0.67 0.42 0.34 0.28 0.24 0.20 0.1 7 0.15 0.22 0.26 0.24 0.21 0.97 0.61 0.49 0.40 0.34 0.28 0.2 4 0.20 0.27 0.36 0.29 0.27 1.07 0.69 0.56 0.47 0.39 0.34 0.2 9 0.25 0.32 0.47 0.33 0.32 1.09 0.75 0.62 0.52 0.44 0.38 0.3 3 0.10 0.17 0.19 0.17 0.16 0.68 0.42 0.34 0.28 0.24 0.20 0.1 7 0.15 0.23 0.30 0.23 0.23 0.84 0.55 0.45 0.37 0.32 0.27 0.2 3 0.20 0.28 0.41 0.27 0.29 0.91 0.63 0.52 0.44 0.37 0.32 0.2 7 0.25 0.33 0.53 0.30 0.35 0.93 0.66 0.55 0.47 0.40 0.35 0.3 0 Notes: f is limited to a max imum of 47deg rees 25 30 35 37 40 * "COV sim" of earth pressure coefficients calculated from 1000 samples of friction angles assumed to follow lognormal distribut io n Rankine active, Ka Rankine passive, Kp So il friction angle, f Coulomb passive, Kp * Read the entire page →
From page 103... ... As such, the discussion in this section is limited in its scope and addresses solely the current limited needs. With the reasonable estimates of the COVs of soil unit weight and earth pressure coefﬁcients, the lateral pressure due to, for example, active earth pressure can be calculated as (where Ea is active earth pressure and h is height of soil) Read the entire page →
From page 104... ... is mostly due to soil and surcharge, possibly compacted, the following load distribution and load factors (load factors from AASHTO, 2007, Table 3.4.1-2) have been chosen for at-rest and active earth pressures: λLFD = bias of lateral loading due to dead load = 1.00, COVLFD = 0.30 and is assumed to follow lognormal distribution with the following distribution in soil unit weight γ (assumed to follow normal distribution) Read the entire page →
From page 105... ... In NCHRP Report 343 (Barker et al., 1991) , which forms a basis for the resistance factor in the current edition of AASHTO LRFD Bridge Design Speciﬁcations, it was found that the reliability indexes obtained using "Rational Theory" varied from 1.3 to 4.5 for the bearing capacity of footings on sand and from 2.7 to 5.7 for footings on clay (Allen, 2005) Read the entire page →
From page 106... ... of the 124 bridges analyzed, the reliability index for superstructures was between 3 and 4. A target reliability level of 3.5 is taken in the current AASHTO LRFD Bridge Design Specifications (1994) Read the entire page →
From page 107... ... The source of this large variation in the 107 Figure 92. Calculated resistance factors as a function of the bias and COV of the resistance for the chosen vertical loading distributions and ratios under the range of the examined target reliabilities. Read the entire page →
From page 108... ... Figures 94 to 98 describe the bias of the calculated bearing capacity for soil friction angles between 42.5° and 46.0° (for which Equation 120 is valid) for different loading conditions. Read the entire page →
From page 109... ... compared to the bias in the bearing capacity factor N (N) versus the soil friction angle for footings under inclined-eccentric, negative moment loadings. Read the entire page →
From page 110... ... and is closely associated to the bias in the expression of Nγ as illustrated in Figures 94 to 96. The varying bias with the soil's internal friction angle suggests that the development of the resistance factors should follow this trend, unless a correction to the methodology is developed and the expression of Nγ is modiﬁed. Read the entire page →
From page 111... ... tests have been carried out to test the ﬁt of the theoretical normal and lognormal distributions to follow the bearing resistance bias for n = 90 cases, along with the datasets after the removal of some identiﬁable outliers. Table 54 lists in detail a number of trials and the corresponding χ-squared values obtained from the GOF tests. Read the entire page →
From page 112... ... Hence, only one outlier was removed from the total dataset, resulting in 172 cases used for the resistance factor calibration for verticalcentric loading. 4.6.2 The Statistics of the Bias as a Function of the Soil's Internal Friction Angle and Resulting Resistance Factors 4.6.2.1 In-Depth Examination of Subsets Based on Internal Friction Angle Tables 55 through 57 present the biases evaluated for the bearing capacity estimation according to the soil's friction angles. Read the entire page →
From page 113... ... Statistics of bearing resistance bias and the resistance factors corresponding to soil friction angles in natural soil conditions for vertical-centric loading. Bias Resistance factor ( T = 3) Read the entire page →
From page 114... ... Hence, COVλ of 0.25 and 0.35 may be taken to represent the COVs of the biases for the controlled soil and nat114 Table 57. Statistics of bearing resistance bias and the resistance factors corresponding to soil friction angles in controlled and natural soil conditions combined, for vertical-centric loading. Read the entire page →
From page 115... ... and the 95% confidence interval of the bearing resistance bias. It can be observed that the recommended resistance factors follow the trend in the bearing resistance bias with the soil friction angle. Read the entire page →
From page 116... ... Recommended resistance factor ( T = 3) Soil conditions Soil friction angle f (deg) Read the entire page →
From page 117... ... Change in bearing resistance bias with soil friction angle for tests with a load eccentricity ratio of e/B = 1/6. ratios ranging from 0.025 to 0.333 (1/40 to 1/3) Read the entire page →
From page 118... ... Statistics of bearing resistance bias and the resistance factors corresponding to soil friction angles in controlled soil conditions for vertical-eccentric loading. Bias Resistance factor ( T = 3) Read the entire page →
From page 119... ... Assuming the mean bias to remain a constant at 1.60 for all friction angles and the COV of the bias of the bearing resistance to be related to natural and controlled soil conditions, i.e., 0.35 and 0.30, respectively, the obtained resistance factors are as follows: Natural soil conditions, for all φf : φ = 0.65 (φ obtained from MCS = 0.687) Controlled soil conditions, for all φf : φ = 0.75 (φ obtained from MCS = 0.796) Read the entire page →
From page 120... ... examining Meyerhof 's aforementioned effective width rule (1953) in calculations of the bearing capacity of shallow foundations. Read the entire page →
From page 121... ... , an argument can be made that the eccentricity ratio can be increased to e/B = 1/3 for which half of the foundation is under "tension" conditions. Some performance-based design codes (e.g., DIN 1054) Read the entire page →
From page 122... ... Statistics of bearing resistance bias and the resistance factors corresponding to soil friction angles in controlled soil conditions for inclined-centric loading. Bias Resistance factor ( T = 3) Read the entire page →
From page 123... ... 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) Read the entire page →
From page 124... ... Recommended resistance factors for shallow foundations on natural deposited granular soil conditions. Loading conditions Inclined-eccentric Soil friction angle f Vertical-centric or -eccentric Inclined-centric Positive Negative 0.40 0.65 0.45 0.35 0.50 0.40 0.70 0.55 0.45 0.40 0.65 0.50 0.45 0.75 Notes: (1) Read the entire page →
From page 125... ... analysis of shallow foundations on rock as an entire set and its subsets match the lognormal distribution, and no outliers exist for the examined datasets. 4.11.2 Calibration of Resistance Factors Table 68 shows the resistance factors (φ) Read the entire page →
From page 126... ... 4.12.2 Calibration of Resistance Factors Based on the datasets, for a majority of which the GOF tests show that lognormal distributions can be assumed to model the bias distribution, the resistance factors have been calibrated using MCS using one million samples. These factors are presented in Table 69. Read the entire page →
From page 127... ... the recommended resistance factors to be used in evaluation of the bearing capacity of shallow foundations on rock. The resistance factors for both examined methods are presented along with the efﬁciency factors providing a measure for the relative efﬁciency of the methods. Read the entire page →
From page 128... ... for soil friction angles based on different tests and lateral pressure due to at-rest or active earth pressure for cast-in-place and prefabricated footings. Resistance factor for sliding friction ( ) Read the entire page →
From page 129... ... Analogous to the calibration of resistance factors for the bearing resistance, the inﬂuence of the ratio of lateral dead load to the lateral live load has been studied and presented here. Read the entire page →

From page 100...

... Similarly, the investigation of vertical loading of shallow foundations on natural soils as compared to vertical loading of shallow foundations on controlled soils, presented in Section 3.5, suggested large variations between the two groups. Earlier interpretations of the data (e.g., Paikowsky et al., 2008; Paikowsky et al., 2009b; Amatya et al., 2009)