Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.

Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 82

82
smaller) than that obtained using the full geometrical width an eccentric vertical load with "negative" eccentricity. The
of the foundation. The ramifications of these findings are resultant moment, which is negative in case of loading eccen-
relevant to design practices in which the loading details are not tricity along footing width b3 (a) and positive in case of loading
known at the time of the design. This issue was touched upon eccentricity along footing length b2 (b)(refer to Figure 69 for
in Section 3.1.7 and will be further discussed in Chapter 4. sign conventions), then acts in the opposite direction to the
The change in variability between the two cases as well as the horizontal load. The induced rotations counteract the dis-
mean bias are greatly affected by a few outliers and will be placements forced by the horizontal load, leading to a higher
further discussed in Chapter 4. The effects of the moment resistance of the footing compared with the inclined-centric
direction (or load eccentricity) with respect to the horizontal load case and, thus, to higher failure loads. In contrast, the
load, noted in Tables 35 and 36 as positive and negative footing in the lower part of Figure 69 is loaded by an eccentric
moments for tests conducted by Perau (1995), are discussed vertical load with "positive" eccentricity. This leads to a pos-
in the following sections. itive moment in the case of loading eccentricity along footing
width b3 (a), and a negative moment in the case of loading
eccentricity along footing length b2 (b), which acts in the same
3.7 Loading Direction Effect
direction as the horizontal load. The induced rotations enforce
for Inclined-Eccentric Loading
the horizontal displacements; hence, the footing resistance is
The loading direction in the case of inclined-eccentric load- smaller than in the case of inclined-centric loading, leading to
ing affects the failure loads. Figure 69 presents the definitions smaller failure loads.
established for the loading direction along the footing width In a different approach, when the moment is in the "opposite"
(a) and along the footing length (b) (see also Butterfield et al., direction, it induces higher contact stresses between the foun-
1996) depending on the eccentricity direction in relation to the dation and the soil in the "front" of the foundation where the
direction of the applied lateral load. The footing in the upper lateral load is applied. As the foundation-soil friction is pro-
part of Figure 69 (a) and (b) is loaded by a horizontal load and gressive, the higher contact stress results in a higher friction
resistance and, hence, the overall layer capacity. In contrast,
when the moment acts in the "same" direction, the contact
e3
M2 stress at the "front" of the footing decreases, thereby reducing
the friction and resulting in a decrease in the total foundation
F1 F1 resistance (bearing capacity). The effect of the loading direction
F3 F3
expressed in Tables 35 and 36 is demonstrated in a graphical
b3 b3 format in Figures 70 and 71. Figures 70 and 71 present a his-
Moment acting in direction opposite to the lateral loading negative eccentricity togram and PDF of the bias as well as the relationship between
e3
M2
measured and calculated bearing capacity for inclined-eccentric
loading under positive and negative moments, respectively. A
F1 F1 comparison of Figures 70 and 71 shows an increase of the bias
F3 F3
for the negative moment cases.
b3 b3 The effect of loading direction is further demonstrated by the
Moment acting in the same direction as the lateral loading positive eccentricity results of two tests carried out by Gottardi (1992) and shown
e3
M2 in Figure 72. The failure loads in the case of loading in the
same direction (positive loading eccentricity) are significantly
F1 F1 smaller than the failure loads in the case of opposite loading
F3 F3
direction (negative loading direction). The influence on the
b3 b3 bias is substantial--0.37 versus 0.64 for the two-slope criterion
Moment acting in direction opposite to the lateral loading negative eccentricity and 0.37 versus 0.66 for the minimum slope criterion. Hence,
e3
M2
it appears that this difference cannot be neglected and needs
to be considered.
F1 F1 Figure 73 shows the load-displacement curves for two
F3 F3
double tests (positive and negative loading eccentricity) con-
b3 b3 ducted by Perau (1995) and one double test by Montrasio
Moment acting in the same direction as the lateral loading positive eccentricity (1994), applying different loading directions at the same level
Figure 69. Loading directions for the case of of vertical loading. The results of Perau's and Montrasio's tests
inclined-eccentric loadings: (a) along footing show a similar trend. Montrasio's test leads to a bias of 1.86
width and (b) along footing length. versus 1.97 (positive versus negative loading eccentricity),

OCR for page 82

83
10
0.4
Inclined-eccentric loading
using Minimum Slope criterion (Vesic, 1963)
3
Positive eccentricity
n=8
Interpreted bearing capacity, qu,meas
mean = 2.16
COV = 1.092
0.3
Number of observations
2
Frequency
(ksf)
1
0.2
lognormal
distribution
1 normal Inclined-eccentric loading
distribution Positive eccentricity
0.1
Data (n = 8)
Data best fit line
No bias line
0.1
0 0
0.1 1 10
0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 Calculated bearing capacity, qu,calc
Bias, = qu,meas / qu,calc (Vesic, 1975 and modified AASHTO)
(a) (ksf)
(b)
Figure 70. (a) Histogram and probability density function of the bias and (b) relationship between measured
and calculated bearing capacity for all inclined, eccentrically loaded shallow foundations under positive moment.
10
0.5
Inclined-eccentric loading
using Minimum Slope criterion (Vesic, 1963)
Negative eccentricity
3 n=7
Interpreted bearing capacity, qu,meas
mean = 3.43 0.4
COV = 0.523
Number of observations
0.3
Frequency
(ksf)
2
1
0.2
lognormal
distribution Inclined-eccentric loading
1 normal Negative eccentricity
distribution Data (n = 7)
0.1
Data best fit line
No bias line
0.1
0 0
0.1 1 10
1.2 1.8 2.4 3 3.6 4.2 4.8 5.4 6 6.6 7.2 Calculated bearing capacity, qu,calc
Bias, = qu,meas / qu,calc (Vesic, 1975 and modified AASHTO)
(a) (ksf)
(b)
Figure 71. (a) Histogram and probability density function of the bias and (b) relationship between measured
and calculated bearing capacity for all inclined, eccentrically loaded shallow foundations under negative moment.

OCR for page 82

84
F3 [kN] [kip]
1.6
0.3
1.2
0.2
0.8
0.1
0.4
u3 [in] 0.2 0.15 0.1 0.05 0 1 2 3 F1 [kip]
0 0
u3 [mm] 6 4 2 0 4 8 12 F1 [kN]
2
0.1
GoE6.1, e=-0.0167
GoE6.2, e=+0.0167
4
0.2
6
0.3
8
u1 [mm] [in]
Figure 72. Loaddisplacement curves for inclined-eccentric loading with different loading
directions utilizing data from Gottardi (1992).
indicating a minor effect of the loading direction. However, this adopted in order to differentiate the failure load of vertical-
effect is more significant in Perau's tests, where the evaluation centric loading from the vertical component F1 of the inclined
of the failure loads leads to a mean bias of 1.79 (COV 0.206) failure loads (refer to Figure 65 and Section 3.6.2). In this
for a horizontal load and moment acting in the same direc- context, small load inclinations coincide with relatively high
tion (positive loading eccentricity) and 2.76 (COV 0.152) for vertical load levels. Figure 74 shows an evaluation of the bear-
a moment in an opposite loading direction (negative loading ing capacity in the F2/F10 - M3/(F10 · b2) plane performed by
eccentricity). Lesny (2001) using Perau's (1995) test results. In reference to
In general, it can be stated that the effect of the loading Figure 64, F2 is the horizontal component of the inclined load
direction is less pronounced if the vertical load (F1) is relatively and b2 is the footing length in the same direction. Different
high (i.e., the load inclination is relatively small) because this loading directions and different load levels have been ana-
effect is predominantly determined by the load inclination lyzed in Figure 74, resulting in distorted trend lines due to the
and not by the load eccentricity. The level of the vertical load existence of a higher capacity if horizontal load and moment
(F1) can properly be expressed by relating it to the failure load act in the opposite direction (i.e., both load components are
for centric vertical loading (F10). The notation F10 has been positive and the loading eccentricity is negative). However,