$(4)$ In a CBR test, the following data was collected and tabulated as follows. What is the CBR for this

soil?

$(5)$ A CU triaxial compression test was conducted on a saturated clay sample with a confining stress of

$220$kPa. The sample failed when the axial stress $($deviator stress$)$ applied was $160$kPa. The pore water

pressure at failure was measured to be $95$kPa. Assume the cohesion intercepts $c=c^{\text{'}}=0$kPa.

$($b$)$ Determine the effective angle of internal friction $({}^{\text{'}}).$

$($c$)$ Determine the normal effective stress $({}_{\text{'}ff}^{\text{'}})$ and shear stress $({}_{\text{'}ff}^{ff})$ on the plane of failure.

$($d$)$ The expected shear strength at failure if a direct shear test is conducted on the same sand with an

effective normal stress of $150$kPa is conducted.

Note: If Mohr circle construction is used, it must be drawn to scale using a grid note.

$(6)$

$($a$)$ Derive the angle of failure plane $({}_t)$ in triaxial tests using a Mohr$-$Coulomb failure criteria.

$($b$)$ Compare drained shear behaviors of loose sands and dense sands in typical CD triaxial testing by

drawing stress$-$strain curves and volume change$-$strain curves. Explain whether the soil dilates or

contracts during shear.

$($c$)$ Explain using a sketch why it is not possible to determine the principal stresses in a direct shear test

specimen for an applied horizontal shear stress, which is not large enough to cause failure.

$(7)$ In a direct shear test on sand, the vertical normal stress on the specimen is $300$kPa and the horizontal

shear stress at failure is $210$kPa.

$($a$)$ Derive the friction angle of the sand and the magnitude and direction of the principal stresses at

failure.

$($b$)$ During a CD triaxial test, the sand specimen failed at a principal stress difference of $130$kPa.

Determine the initial confining stress of the test.

$($c$)$ The stress conditions of the same sand behind a retaining wall are, vertical stress ${}_v=200$kPa and

horizontal stress ${}_h=80$kPa. Determine the factor of safety against failure. Is the wall safe?

$($d$)$ The horizontal stress oh in $($c$)$ reduces, as a result of the movement of the wall, while ${}_v$ remains

unchanged. Determine the ${}_h$ that will cause failure.

Note: If Mohr circle construction is used, it must be drawn to scale using a grid note.$(1)$ As the chief transportation soils engineer you are asked to characterize the subgrade soil as fill

material for constructing a new rigid pavement runway at the Chicago O'Hare Airport. Typical load$-$

deformation curves are given as obtained from a standard size plate$-$loading test conducted on this silty

subgrade. Laboratory testing efforts indicated this soil to have a resilient modulus of $9,000.$ Compute

the modulus of subgrade reaction, k$-$value, according to the definitions used by $($a$)$ Corps of Engineers,

$($b$)$ AASHTO, and $($c$)$ Portland Cement Association. What k$-$value would you recommend for the runway

design?

Plate Load Tests $-$ Chicago O'Hare Alrport

$(2)$ A well$-$graded granular material $($ max size $=1$ inch$)$ with $0\%$ passing the #$200$ sieve is tested in

triaxial compression. At a confining pressure of $15,$ the applied axial stress at failure was measured to

be $72.$ What is the angle of internal friction for this granular material?

$(3)$ A clayey subgrade soil was tested in unconfined compression test at the University of Illinois

Advanced Transportation Research and Engineering Laboratory. The following test data were recorded:

Initial diameter of the sample: $40mm$

Initial height of the sample: $75mm$

Deformation at maximum load: $5\mathrm{.}7mm$

Maximum load: $192N$

$($a$)$ Compute the unconfined compressive strength of this soil?

$($b$)$ Report the soil's strength in equivalent CBR$.$