$7\mathrm{.}37$ A doubly drained specimen, $2\mathrm{.}54cm$ in height, is consolidated in the lab under an applied stress. The time for $50\%$ overall $($or average$)$ consolidation is $15$min.

a$.$ Compute the $c_v$ value for the lab specimen.

b$.$ How long will it take for the specimen to consolidate to an average consolidation of $90\%?$

c$.$ If the final consolidation settlement of the specimen is expected to be $0\mathrm{.}52cm,$ how long will it take for $0\mathrm{.}23cm$ of settlement to occur?

d$.$ After $17$ minutes, what percent consolidation has occurred at the middle of the specimen?