Geotechnical Engineering

DHARM

288 GEOTECHNICAL ENGINEERING

critical value will tend to decrease in volume during shearing, while sands with initial void

ratio less than the critical with tend to increase in volume.

The critical void ratio is dependent upon the cell pressure (in the case of triaxial com-

pression tests) or effective normal pressure (in the case of direct shear tests), besides a few

other particle characteristics. It bears a reciprocal relationship with pressure. The value of

critical void ratio under a given set of conditions may be determined by plotting the volume

changes versus void ratio. The value for which the volume change is zero is the critical one.

8.11.3 Shearing Strength of Sands

The shearing strength of cohesionless soils has been established to depend primarily upon the

angle of internal friction which itself is dependent upon a number of factors including the

normal pressure on the failure plane. The nature of the results of the shear tests will be influ-

enced by the type of test—direct shear or triaxial compression, by the fact whether the sand is

saturated or dry and also by the nature of stresses considered—total or effective.

Each direct shear test is usually conducted under a certain normal stress. Each stress-

strain diagram therefore reflects the beahaviour of a specimen under a particular normal

stress. A number of specimens are tested under different normal stresses. It is to be noted that

only the effective normal stress is capable of mobilising shear strength. The results when

plotted appear as shown in Fig. 8.30.

Shearing strain

Shearing stress

tf3

tf2 t

f1

ss= 3

ss= 2

ss= 1

sss 321 >>

Normal stress

Shearing strength

s =

sftan

(a) Idealized stress-strain diagrams (b) Idealized shear strength envelope

f

Fig. 8.30 Shear characteristics of sands from direct shear tests
It may be observed from Fig. 8.30 (a) that the greater the effective normal pressure
during shear, the greater is the shearing stress at failure or shearing strength. The shear
strength plotted against effective normal pressure gives the Coulomb strength envelope as a
straight line, passing through the origin and inclined at the angle of internal friction to the
normal stress axis. It is shown in Fig. 8.30 (b). The failure envelope obtained from ultimate
shear strength values is assumed to pass through the origin for dry cohesionless soils. The
same is true even for saturated sands if the plot is made in terms of effective stresses. In the
case of dense sands, the values of φ obtained by plotting peak strength values will be some-
what greater than those from ultimate strength values.
Ultimate values of φ may range from 29 to 35° and peak values from 32 to 45° for sands.
The values of φ selected for use in practical problems should be related to soil strains expected.
If soil deformation is limited, using the peak value for φ would be justified. If the deformation
is relatively large, ultimate value of φ should be used.