A highway project requires excavating a $50 \text{ m}$ segment to lower the road grade. Station $1+000$ has a cut area of $45 \text{ m}^2$, and Station $1+050$ has a cut area of $60 \text{ m}^2$. The geotechnical report indicates the native soil has a known swell factor of $15\%$.

Determine the total Bank Cubic Meters (BCM) to be excavated and the resulting Loose Cubic Meters (LCM) that must be hauled away by the trucking fleet.

A site development project requires placing $5,000 \text{ m}^3$ of compacted engineered fill (Compacted Cubic Meters, CCM) to raise the elevation for a building pad. The borrow pit material available offsite has a shrinkage factor of $12\%$ (meaning it shrinks $12\%$ from its natural bank state when fully compacted).

Calculate the volume of bank material (BCM) that must be purchased and excavated from the borrow pit to satisfy the fill requirement.

A rectangular building pad measuring $20 \text{ m} \times 30 \text{ m}$ is divided into six $10 \text{ m} \times 10 \text{ m}$ square grids. A surveyor determines the depth of cut required at each of the $12$ grid intersection nodes. For one specific $10 \text{ m} \times 10 \text{ m}$ grid square, the cut depths at its four corners are $1.2 \text{ m}$, $1.5 \text{ m}$, $1.1 \text{ m}$, and $1.8 \text{ m}$.

Calculate the cut volume for this single grid cell.

An excavation yields $3,000 \text{ BCM}$ of soil with a $20\%$ swell factor. A fleet of $15 \text{ LCM}$ capacity dump trucks will haul the material offsite. Each truck cycle (load, haul, dump, return) takes exactly $30 \text{ minutes}$ ($0.5 \text{ hours}$). The rental rate for a truck and driver is \120 / \text$.

Calculate the total transportation cost to haul all the excavated soil.