Civil Engineering Reference
In-Depth Information
As a final check, the FS calculated from the earthquake-induced punching shear analy-
sis must be compared with the FS calculated from the static bearing capacity analysis (i.e.,
nonearthquake condition). The reason for this comparison is that FS for the earthquake
punching shear case [Eq. (8.1)] could exceed the FS calculated from the static condition.
This often occurs when the liquefied soil layer is at a significant depth below the bottom of
the footing, or in other words at high values of
T
/
B.
In any event, the lower value of FS from
either the earthquake punching shear analysis or the static bearing capacity analysis would
be considered the critical condition.
8.2.3
Terzaghi Bearing Capacity Equation
Introduction.
The most commonly used bearing capacity equation is the equation devel-
oped by Terzaghi (1943). For a uniform vertical loading of a strip footing, Terzaghi (1943)
assumed a shallow footing and general shear failure (Fig. 8.1) in order to develop the fol-
lowing bearing capacity equation:
q
ult
Q
ult
___
BL
cN
c
1
2
t
BN
t
D
f
N
q
(8.3)
where
q
ult
ultimate bearing capacity for a strip footing, kPa or lb/ft
2
Q
ult
vertical load causing a general shear failure of underlying soil (Fig. 8.1)
B
width of strip footing, m or ft
L
length of strip footing, m or ft
t
total unit weight of soil, kN/m
3
or lb/ft
3
D
f
vertical distance from ground surface to bottom of strip footing, m or ft
c
cohesion of soil underlying strip footing, kPa or lb/ft
2
c
, N
, and
N
q
dimensionless bearing capacity factors
As indicated in Eq. (8.3), three terms are added to obtain the ultimate bearing capacity
of the strip footing. These terms represent the following:
cN
c
The first term accounts for the cohesive shear strength of the soil located below
the strip footing. If the soil below the footing is cohesionless (i.e.,
c
0), then this term
is zero.
1
t
BN
The second term accounts for the frictional shear strength of the soil
located below the strip footing. The friction angle
2
is not included in this term, but is
accounted for by the bearing capacity factor
N
. Note that
t
represents the total unit
weight of the soil located below the footing.
t
D
f
N
q
This third term accounts for the soil located above the bottom of the foot-
ing. The value of
t
times
D
f
represents a surcharge pressure that helps to increase the
bearing capacity of the footing. If the footing were constructed at ground surface (i.e.,
D
f
0), then this term would equal zero. This third term indicates that the deeper the
footing, the greater the ultimate bearing capacity of the footing. In this term,
t
repre-
sents the total unit weight of the soil located above the bottom of the footing. The total
unit weights above and below the footing bottom may be different, in which case dif-
ferent values are used in the second and third terms of Eq. (8.3).
As previously mentioned, Eq. (8.3) was developed by Terzaghi (1943) for strip foot-
ings. For other types of footings and loading conditions, corrections need to be applied to
the bearing capacity equation. Many different types of corrections have been proposed
