The sounding from a Cone Penetration Test performed at a bridge site in British

Columbia, Canada is shown below $($Niazi et al$.,2010).$ The sounding shows cone tip

resistance $(qt),$ sleeve friction $(f_s)$ and pore water pressure $(u_2)$ whereas $u_0$ indicates

the projected hydrostatic pressure from the groundwater table which is located $3\mathrm{.}0$

meters below the ground surface. Unit weight of the soils are estimated as $m=18\mathrm{.}0$

$k\frac{N}{m^3}$ between $0\mathrm{.}0-3\mathrm{.}0m,{}_{\text{s}\text{a}\text{t}}=18\mathrm{.}5k\frac{N}{m^3}$ between $3\mathrm{.}0-38\mathrm{.}0m$ and ${}_{\text{s}\text{a}\text{t}}=17\mathrm{.}5k\frac{N}{m^3}$

below $38\mathrm{.}0m$ depth $(125$ points$).$

You are tasked with utilizing this CPT sounding for site characterization and evaluation of

relevant geotechnical properties for foundation design.

Figure $1.$ CPT sounding from the Golden Ears Bridge site in British Columbia, CanadaIn practice, you would need to analyze the entire soil profile. For the sake of this homework

two points have been selected within the soil profile for your evaluation; at $30$ and $50-$meter

depths below the ground surface.

a$)$ Evaluate normalized CPT parameters and $B_q)$ using equations $4\mathrm{.}15-4\mathrm{.}17$ for

these two elevations within the soil profile. In these calculations pick a value for the

stress exponent $n$ between $0\mathrm{.}5-1\mathrm{.}0.$ Please note that a value of $n=0\mathrm{.}5$ is more suitable

for sandy soils and $1\mathrm{.}0$ for clayey soils whereas $n=0\mathrm{.}7$ is used for intermediate soils

$($sandy clay, silty sand etc.$).$ The issue here is$,$ you do not know the appropriate $n$ value

without knowing the type of the soil. Therefore, you need to start with an assumed

value of $n.$

b$)$ Evaluate the soil behavior type index, Ic for both elevations using the normalized CPT

parameters with equation $4\mathrm{.}18.$

c$)$ Calculate the stress exponent $n,$ using equation $4\mathrm{.}19.$ How does this value compare with

your initially assumed value of $n?$ If there is a difference of more than $10\%$ between

assumed and calculated $n$ values, repeat steps $a,b$ and $c$ using the calculated value of $n$ and

report the recalculated $n$ value and $I_c.$

d$)$ Comment on the type of soils at these two elevations using the table and the chart

presented in figure $4\mathrm{.}23.$

e$)$ Calculate the drained constrained modulus $M$ of the soil layers at these elevations.

You can use equations $4\mathrm{.}57-4\mathrm{.}60$ for this. Please note that $Q_{t1}$ in equations $4\mathrm{.}58$ and $4\mathrm{.}59$

for fine grained soils refer to the normalized cone resistance $(Q_{tn})$ with $n=1\mathrm{.}0$ in

equation $4\mathrm{.}15($i$.$e$.$ fine grained soil$).$

f$)$ Calculate the relative density $D_r$ and internal friction angle ${}^{\text{'}}$ if the soil is

cohesionless $($i$.$e$.,$ coarse grained$).$ You can use equation $4\mathrm{.}39$ and figure $4\mathrm{.}31$ for these

calculations.

g$)$ Calculate the undrained shear strength su and undrained elastic modulus $E$ if the soil is

cohesive $($i$.$e$.,$ fine grained$).$ You can use equations $4\mathrm{.}40$ and $4\mathrm{.}47$ for these calculations.

Assume a PI $=30$ for the clayey soil which is normally consolidated.