BEARING CAPACITY ANALYSES FOR EARTHQUAKES - Geotechnical Earthquake Engineering - page 235

And finally the factor of safety is calculated as follows:

Q ult 530 kN

___ _______

FS

Q 500 kN

1.06

In summary, the factors of the safety factor in terms of a bearing capacity failure for the
strip and spread footings are as follows:

Factor of safety

Method Strip footing Spread footing

Using Eq. (8.7 a ) 3.4 0.87

Using Fig. 8.9 4.4 1.06

No moment (i.e., values from 5.5 1.7

Sec. 8.2.3)

8.3 GRANULAR SOIL WITH EARTHQUAKE-
INDUCED PORE WATER PRESSURES

8.3.1 Introduction

Section 8.2 deals with soil that is weakened during the earthquake due to liquefaction. This
section deals with granular soil that does not liquefy; rather, there is a reduction in shear
strength due to an increase in pore water pressure. Examples include sands and gravels that
are below the groundwater table and have a factor of safety against liquefaction that is
greater than 1.0 but less than 2.0. If the factor of safety against liquefaction is greater than
2.0, the earthquake-induced excess pore water pressures will typically be small enough that
their effect can be neglected.

8.3.2 Bearing Capacity Equation

Using the Terzaghi bearing capacity equation and an effective stress analysis, and recog-
nizing that sands and gravels are cohesionless (i.e., c 0), we see that Eq. (8.3) reduces
to the following:

q ult 1 2 t BN t D f N q (8.8)

For shallow foundations, it is best to neglect the second term ( t D f N q ) in Eq. 8.8. This
is because this term represents the resistance of the soil located above the bottom of the
footing, which may not be mobilized for a punching shear failure into the underlying weak-
ened granular soil layer. Thus by neglecting the second term in Eq. (8.8):

q ult 1 2 t BN (8.9)

Assuming that the location of groundwater table is close to the bottom of the footing,
the buoyant unit weight b is used in place of the total unit weight t in Eq. (8.9). In addi-
tion, since this is an effective stress analysis, the increase in excess pore water pressures
that are generated during the design earthquake must be accounted for in Eq. (8.9). Using
Fig. 5.15 can accomplish this, which is a plot of the pore water pressure ratio r u u e / ver-
sus the factor of safety against liquefaction (Chap. 6). Using the buoyant unit weight b in