Civil Engineering Reference
In-Depth Information
The stress-dilatancy criterion equation is given by
τ
σ
=
φ
c
+
ψ
tan(
)
(10.19)
φ
p
, and
B
are material parameters
and they depend only on the nature of the soil grains. The voids ratio or water
content is included in the critical stress
φ
c
,
5.
In Eqs. (10.6) and (10.14) the parameters
σ
c
. In Eq. (10.19) the angle of dilation
ψ
depends on the initial state.
6. The peak state of a soil is related to the state parameter.
Worked examples
Example 10.1: Determination of peak state parameters
Table 10.1 shows data obta-
ined at the peak state from a series of shear tests on the same soil as that in the examples
in Chapter 9 (Note that the samples reached their peak state at one of only two different
voids ratios.) The peak states are plotted in Fig. 10.19. The points fall close to two
straight lines given by
c
pe
=
15
◦
in both cases.
The test results can be normalized with respect to the equivalent stress
60 kPa and
c
pe
=
φ
p
=
130 kPa with
σ
c
given by
Eq. (9.8). The soil parameters are
C
c
2.17. The normalized stresses
are given in Table 10.1 and these are plotted in Fig. 10.20. The data now all fall close
to a single straight line given by
c
p
=
=
0.46 and
e
=
φ
p
=
15
◦
.
0.2 and
Table 10.1
Peak states of a soil - Example 10.1
τ
p
(kPa)
σ
p
(kPa)
σ
c
(kPa)
τ
p
/
σ
c
σ
p
/
σ
c
Sample
e
p
A
138
300
1.03
300
0.46
1.00
C
123
240
1.03
300
0.41
0.80
E
108
180
1.03
300
0.36
0.60
G
93
120
1.03
300
0.31
0.40
B
264
540
0.89
606
0.44
0.90
D
228
420
0.89
606
0.38
0.70
F
198
300
0.89
606
0.33
0.50
Figure 10.19
Peak states of a soil - Example 10.1.
