$(12$ pts$.)$ Water flows in an open channel whose slope is $0\mathrm{.}05\%.$ The Manning n of channel

lining is $0\mathrm{.}04$ when the flow rate is $250\frac{m^3}{s}.$ At a given section of the channel, the cross

section is trapezoidal with a bottom width $12$ m $,$ side slope of $2$:$1(H$:$V)$ and the depth of

flow is $8$ m $.$ Use the standard step method to calculate the depth of flow $100$ m upstream

from this section where cross section is trapezoidal with a bottom width of $16$ m and side

slopes of $3$:$1(H$:$V).$ You can use any program $($e$.$g$.$ Excel$)$ for iteration or do manually.

$[$Answer: $8m]$ Relevant theory of this problem will be discussed in next week.

$10\mathrm{.}5$ A direct shear test was conducted on an overconsolidated clay specimen

having a cross$-$sectional size of $60mm60mm.$ The loading was very

slow, ensuring that there is no pore water pressure development within

the specimen $($i$.$e$.,$ drained loading$).$ The following data were recorded.

Determine the shear strength parameters $c^{\text{'}}$ and ${}^{\text{'}}.$