Critical state strength of soil - The Mechanics of Soils and Foundations - page 133

of the strength and stiffness of soil and it is necessary to determine both voids ratio
or water content and normal effective stress; water content or stress alone are not
sufficient.
In Sec. 8.4 I considered the relationship between the current state and a critical line,
which is below the critical state line, and introduced the ideas of states on the wet side
of critical and on the dry side of critical, as shown in Fig. 8.7. While this qualitative
description is important it is necessary to quantify state as the distance of current state
from the critical state line.
Earlier in this Chapter I described procedures for normalizing test results for shear
and triaxial tests and these are illustrated in Figs. 9.6 and 9.9. What I am going to do
now is combine the ideas of state and normalizing to define state parameters.
Figure 9.13(a), which is like Fig. 9.6, shows a state at A with voids ratio e a and
normal effective stress σ a together with a critical state line. The vertical and horizontal

distances of the point A from the critical state line are

S v = e − e λ (9.19)

and

σ c − σ a log S s = log log (9.20)

or

S s = σ c
σ a

(9.21)

where S v and S s are alternative state parameters. From the geometry of Fig. 9.13(a)
these state parameters are related by

S v = C c log S s (9.22)

If the state A is on the critical state line S v = 0 and S s = 1. For states on the dry side

of critical S v is positive and S s > 1: for soils on the wet side of critical S v is negative

and S s < 1.

From Fig. 9.13(b) the state parameters for triaxial tests are

S v = − v λ (9.23)

and

p c
p a

S s = (9.24)

From the geometry of Fig. 9.13(b) these state parameters are related by

S v = λ ln S s (9.25)

The state parameter S v is similar to the state parameter defined by Been and Jefferies
(1985). The state parameter S s is similar to the overconsolidation ratio given by