Geotechnical Engineering

DHARM

SHEARING STRENGTH OF SOILS 275

Here, tan ψ = sin φ ...(Eq. 8.41)

and d = c cos φ ...(Eq. 8.42)

Equation 8.40 indicates a linear relationship between (σ 1 + σ 3 )/2 and (σ 1 – σ 3 )/2 and may

be plotted from the results of a series of triaxial compression tests, as shown in Fig. 8.15.

y

Modified failure

envelope (K -line)

f

(ss 13 + )/2

(

)/2

ss^1

3

Fig. 8.15 Alternative procedure of evaluating shear strength parameters
(After Lambe and Whitman, 1969)
The best straight line is fitted to the data so that the averaging of the inevitable scatter
of the experimental results is automatically taken care of. Once the values, d and ψ are ob-
tained, c and φ may be computed by using Eqs. 8.41 and 8.42.
Graphical Presentation of Data from Triaxial Compression Tests
The following are the usual set of graphs plotted making use of data from triaxial com-
pression tests :
(i) Major principal stress versus % axial strain
(ii)σ 1 /σ 3 versus % axial strain
(iii) % Volumetric strain versus % axial strain
(iv) Major principal stress versus volume change
(v) Mohr’s circles at failure for each set of soil samples tested, from which the sehar
strength parameters may be evaluated.
A host of other useful information may be obtained from the data gathered from the
trixial compression test if it is properly presented.

Types of Failure of a Triaxial Compression Test Specimen
A triaxial compression test specimen may exhibit a particular pattern or shape as fail-
ure is reached, depending upon the nature of the soil and its condition, as illustrated in Fig. 8.16.

(a) Brittle failure (b) Semi-plastic failure (c) Plastic failure

Fig. 8.16 Failure patterns in triaxial compression tests