Question $1(25$ marks$)$

a$)$ Give any two tests which can be performed in the laboratory to determine soil strength.$[2$

marks$]$

b$)$ Define shear strength of a soil and state the Mohr$-$Coulomb shear strength equation.

Explain the terms in the equation.

$[3$ marks$]$

c$)$ Mention the type of laboratory triaxial test that would be suitable in each of following field

conditions;

$[3$ marks$]$

i$.$ The stability of a foundation footing constructed rapidly in saturated clay.

ii$.$ An embankment constructed very slowly, founded on a clay deposit.

iii. Rapid construction of an embankment on a natural slope.

d$)$ In an unconsolidated undrained triaxial test the undrained strength of clay, $c_u$ obtained was

$17\mathrm{.}5k\frac{N}{m^2}.$ Determine the cell pressure used in the test if the effective strength parameters

are $c^{\text{'}}=0,{}^{\text{'}}=26$ and the pore pressure at failure is $43k\frac{N}{m^2}.[7$ marks$]$

e$)$ The results in the following table were obtained in consolidated undrained triaxial tests

carried out on cylindrical samples of soil from a construction site. Each sample originally

$76mm$ in height and $38mm$ in diameter experienced an axial deformation, $dh=5\mathrm{.}1mm.$

Draw the shear strength envelope and determine the shear strength parameters of the soil

in terms of total stresses. $[10$ marks$]$