Geotechnical Engineering

DHARM

562 GEOTECHNICAL ENGINEERING

a rapidly increasing settlement and the relation between stress and settlement is approxi-

mately as indicated by dashed curve C 2 in Fig. 14.9. The criterion that the slope of the settle-

ment curve should increase steeply for failure of soil is satisfied even before the failure spreads

to the surface. Hence, this type of failure will be called ‘local shear failure’. This is applicable

for very loose or very compressible soils.

C 1

C 2

c

d

O qult qult

Pressure

Settlement

C : dense soil

C : loose soil

1

2

Fig. 14.9 Relation between pressure and settlement
for dense (C 1 ) and loose (C 2 ) soil
The curve C 2 may be idealised as Ocd, a broken line, which represents are stress-strain
relation of an ideal plastic material whose shear parameters c′ and φ′ are smaller then values
c and φ for curve C 1. Based on available data on stress-strain relations, Terzaghi suggests the
following values for c′ and φ′.

c′ = (2/3)c ...(Eq. 14.78)
and tan φ′ = (2/3) tan φ ...(Eq. 14.79)
The corresponding values of the bearing capacity factors are designated N′c, Nq′ and Nγ′,
which are less than the corresponding values for general shear failure. Also c′ and φ′ must be
used wherever c and φ occur in the computation for bearing capacity.

Hence, for local shear failure,

q′ult = (2/3) cNc′ + γDf Nq′ +

1

2

γ bNγ′ ...(Eq. 14.80)

40

30

20

10

Values of in degrees

f

70 60 50 40 30 20 10 0 20 40 60 80 100

Nq Nc¢ Ng¢

Ng

Nc

Values of N and Ncq Values of Ng

f= 44° N = 260g

f= 48° N = 780g

Nq¢

Fig. 14.10 Terzaghi’s bearing capacity factors (Terzaghi, 1943)

(Full lines for general shear and dashed lines for local shear)