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OCR for page 73

73
Initial guess
a = 114.5pcf
N60(i -1) Di
i
vi a Di 1 Di v (i 1) GWT
62.4 Di 1 GWT N60i Di+1
i+1
calculate (N1)60 i using Equation 105 N60(i +1) Di+2
N1 60 i N 60 i p a vi
(i = layer number)
calculate b using Equation 106
b 0. 88( N 1 ) 60i 99
Yes
a b ? a b a
146 ?
No
No Yes
146 Final
a b a
i a
Figure 58. Flow chart showing iteration for the estimation
of soil unit weight.
3.5 Uncertainty in the Bearing ing the minimum slope failure criterion. The soil friction angles
Capacity of Footings in/on for these cases ranged from 30.5°(±0.5) to 45° (±0.5).
Granular Soils Subjected
to Vertical-Centric Loading 3.5.2 Summary of Mean Bias Statistics
3.5.1 Scope of Case Histories Of the 172 cases, 14 foundations were tested in natural soil
In 172 load test cases of the UML-GTR ShalFound07 conditions and the remaining 158 in controlled soil conditions.
database, the foundations were subjected to vertical-centric The cases for which SPT N blow count observations are
loadings, and the load test results could be interpreted employ- available have been categorized as the cases in natural soil
Bulk density, (lb/ft3)
100 105 110
48
Soil friction angle, f (deg)
44
40
36 Test results (n = 52)
Perau, 1995
Revised correlation
32
15 15.5 16 16.5 17 17.5 18
Bulk density, (kN/m3)
Figure 59. Revised correlation for angle of internal friction
and dry unit weight of Essen sand.

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74
Vertical-Centric Loading case histories. Section G.1 presents the bias calculations for
n = 173; mean bias = 1.59, COV = 0.291 footing ID (FOTID) #35 of database UML-GTR ShalFound07
related to vertical-centric loading. Figure 60 presents a flow-
Natural soil conditions Controlled soil
chart summary of the mean bias for vertical-centric load-
(f from SPT-N counts) conditions (Dr 35%) ing cases grouped by soil conditions and footing widths.
n = 14; no. of sites = 8 n = 159; no. of sites = 7 Figures 61 to 63 present the bias histograms and probability
mean = 1.00 mean = 1.64
COV = 0.329 COV = 0.267 density functions as well as measured versus calculated bear-
ing capacity relations for all the cases and the subcategoriza-
tion of natural versus controlled soil conditions. The data
B > 1.0m 0.1 < B 1.0m B 0.1m 0.1 < B 1.0m
n=6 n=8 n = 138 n = 21 in Figures 60 to 63 represent all available cases without
no. of sites = 3 no. of sites = 7 no. of sites = 5 no. of sites = 3 giving consideration to outliers, which will be addressed in
mean = 1.01 mean = 0.99 mean = 1.67 mean = 1.48
COV = 0.228 COV = 0.407 COV = 0.245 COV = 0.391
Chapter 4.
The mean bias value for the footings in natural soil conditions
Figure 60. Summary of bias (measured over calculated was found to be around 1.0, regardless of the footing sizes
bearing capacity) for vertical-centric loading cases (the largest footing tested was about 10 ft wide). In contrast,
(Database I) (0.1 m = 3.94 in, 1 m = 3.28 ft). for the footings in controlled soil conditions the mean bias
value changed from about 1.5 for larger footings to 1.7 for
smaller footings. The variation in the mean bias with the
conditions, while those tested in laboratories using soils of footing width is further discussed in Chapter 4. Compared to
known particle size and controlled compaction have been the biases for the tests in controlled soil conditions, the biases
categorized as the cases in controlled soil conditions. Each for the tests in natural soil conditions have higher variation,
of the cases was analyzed to obtain the measured failure even when the number of sites is comparable. One may con-
from the load-settlement curve and the calculated bearing clude that as the controlled soil conditions more correctly
capacity following the equations and correlations presented represent the accurate soil parameters, the higher mean bias
in Section 3.4. The relation of the two (i.e., measured failure reflects conservatism (under-prediction) in the calculation
over calculated capacity) constitutes the bias of the case. model (i.e., the bearing capacity equation). The layer variation
Appendix G presents examples for bias calculations for the in soil conditions and the integrated parameters from the SPT
100
Vertical-centric loading
using Minimum Slope criterion (Vesic, 1963)
n = 173
mean = 1.59
Interpreted bearing capacity, qu,meas
40 COV = 0.291
0.2 10
Number of observations
lognormal
30 distribution
Frequency
(ksf)
20 normal
distribution 0.1 1
Vertical-centric loading
10 Data (n = 173)
Data best fit line
No bias line
0.1
0 0
0.1 1 10 100
0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 Calculated bearing capacity, qu,calc
Bias, = qu,meas / qu,calc (Vesic, 1975 and modified AASHTO)
(a) (ksf)
(b)
Figure 61. (a) Histogram and probability density functions of the bias and (b) relationship between measured
and calculated bearing capacity for all cases of shallow foundations under vertical-centric loading.

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75
100
0.3
Controlled soil conditions
using Minimum Slope criterion (Vesic, 1963)
n = 159
mean = 1.64
Interpreted bearing capacity, qu,meas
40 COV = 0.267
10
Number of observations
lognormal 0.2
30
distribution
Frequency
(ksf)
20 normal
distribution 1
0.1
Controlled soil conditions
10 Data (n = 159)
Data best fit line
No bias line
0.1
0 0
0.1 1 10 100
0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 Calculated bearing capacity, qu,calc
Bias, = qu,meas / qu,calc (Vesic, 1975 and modified AASHTO)
(a) (ksf)
(b)
Figure 62. (a) Histogram and probability density functions of the bias and (b) relationship between measured
and calculated bearing capacity for vertical, centrically loaded shallow foundations on controlled soil conditions.
100
6
Natural soil conditions
using Minimum Slope criterion (Vesic, 1963)
0.4
n = 14
Interpreted bearing capacity, qu,meas
5 mean = 1.00
COV = 0.329
0.3
Number of observations
4 normal
distribution
Frequency
(ksf)
10
3
0.2
lognormal
distribution
2
Natural soil conditions
0.1 Data (n = 14)
1 Data best fit line
No bias line
1
0 0
1 10 100
0.2 0.6 1 1.4 1.8 2.2 2.6 3 3.4 3.8 Calculated bearing capacity, qu,calc
Bias, = qu,meas / qu,calc (Vesic, 1975 and modified AASHTO)
(a) (ksf)
(b)
Figure 63. (a) Histogram and probability density functions of the bias and (b) relationship between measured
and calculated bearing capacity for vertical, centrically loaded shallow foundations on natural soil conditions.