$1.$ The $170-$ft long bottom of a trench excavation must be level and $6-$ft wide. The cut is uniformly $12-$ft deep. The stiff clay must be sloped for Type A soil $($USCS $=$ CL$).$ Both the sides and ends of the excavation are sloped. The soil is $116-$pcf in situ and $93-$pcf loose.

A$.$ What is the bank volume of the trench soil, in BCY$?$

B$.$ What is the volume of the soil after excavation, in LCY$?$

$2.$ A hydraulic backhoe with a $0\mathrm{.}95-$CY bucket shall cut the sloped trench of problem #$1.$ Job efficiency is a $40$ min$/$hr$.$ The machine$$s maximum $8-$ft level cutting depth is $13\mathrm{.}15-$ft$.$ A $60-$degree average swing angle is achievable. Think about it: Because of the trapezoidal cross$-$section, the average depth of cut for the excavation is NOT at $12-$ft $-$: $2=6\mathrm{.}0-$ft depth, although for a more steeply sloped trench the average depth is practically the same. On the other hand, shallow OSHA side slopes would move the average depth of cut higher. Mathematically, we seek an average depth where the ditch cross$-$sectional area above the depth equals the cross$-$sectional area below the average depth of cut.

A$.$ Estimate the hourly production in LCY$/$hr$.$

B$.$ Rounded up to the nearest hour, how many hours should be planned for the excavation?

$3.$ A hydraulic backhoe cuts a building basement that is uniformly $18-$ft deep. The bottom of the basement is $80-$ft x $110-$ft$,$ and the soil is OSHA Type B$,$ common earth. Its heaped bucket capacity is $3\mathrm{.}7-$LCY$.$ Job efficiency is a $50-$min$/$hr$.$ The machine$$s maximum $8-$ft level cutting depth is $24-$ft$.$ You note that hauler access to position effectively is limited$,$ so on average the site will require an average swing angle of $90-$degrees between excavator cut and hauler bed.

A$.$ Determine the production rate in LCY$/$hr$.$

B$.$ Determine the duration in hours of the basement excavation activity