Shear Strength of Soils - Elements of Soil Mechanics - page 99

Fig. 4.10 Mohr circle diagram.

Now

k = c cot φ

⇒ ( σ − σ ) = 2 c cos φ + + ( σ σ ) sin φ

1 3 1 3

which is the general form of the Mohr-Coulomb theory.
The equation can be expressed in terms of either total stress (as shown) or effective stress:

′ − ′ = ′ ′ + ′ + ′ ′

( σ σ ) 2c cos φ ( σ σ ) sin φ

1 3 1 3

4.8 Determination of the shear strength parameters

The shear strength of a soil is controlled by the effective stress that acts upon it and it is therefore obvious
that a geotechnical analysis involving the operative strength of a soil should be carried out in terms of
the effective stress parameters φ ′ and c ′ . This is the general rule and, as you might expect, there is at
least one exception. The case of a fully saturated clay subjected to undrained loading is more appropriately
analysed using total stress values and c u than by an effective stress approach. As will be illustrated in later
chapters, such a situation can arise in both slope stability and bearing capacity problems.
It is seen therefore, that both the values of the undrained parameter c u , and of the drained parameters,
φ ′ and c ′ are generally required. They are obtained from the results of laboratory tests carried out on
representative samples of the soil with loading and drainage conditions approximating to those in the
field where possible. The tests in general use are the direct shear box test, the triaxial test and the uncon-
fined compression test, an adaptation of the triaxial test.

4.8.1 The direct shear box test

The apparatus consists of a brass box, split horizontally at the centre of the soil specimen. The soil is
gripped by perforated metal grilles, behind which porous discs can be placed if required to allow the
sample to drain (see Fig. 4.11) .
The usual plan size of the sample is 60 × 60 mm 2 , but for testing granular materials such as gravel or
stony clay it is necessary to use a larger box, generally 300 × 300 mm 2 , although even greater dimensions
are sometimes used.
A vertical load is applied to the top of the sample by means of weights. As the shear plane is prede-
termined in the horizontal direction the vertical load is also the normal load on the plane of failure. Having
applied the required vertical load, a shearing force is gradually exerted on the box from an electrically
driven screwjack. The shear force is measured by means of a load transducer connected to a computer.