A cylindrical rock core sample has a total volume ($V_t$) of $150 \text{ cm}^3$. After drying, the volume of the solid mineral grains ($V_s$) is determined to be $135 \text{ cm}^3$. Calculate the porosity ($n$) and the void ratio ($e$) of the rock sample.

A highly fractured sandstone aquifer has a tested porosity ($n$) of $28\%$. Calculate its void ratio ($e$) and determine the volume of solids ($V_s$) if the total volume of the sample is $1 \text{ m}^3$.

A piece of unweathered granite has a total volume ($V_t$) of $0.05 \text{ m}^3$ and weighs $1.3 \text{ kN}$ in its natural state. The porosity ($n$) is known to be $2\%$. Assuming the voids are completely dry, calculate the dry unit weight ($\gamma_d$) and the specific gravity of the solid minerals ($G_s$). The unit weight of water ($\gamma_w$) is $9.81 \text{ kN/m}^3$.

A deep highway tunnel is being excavated through a massive formation of young, extrusive basalt. Engineers must assess the rock mass properties to design the excavation method and primary support system.

A heavy bridge pier must be founded on a thick, horizontal bed of dark grey marine shale. The structural loads are significant, and strict settlement limits apply to the bridge deck.

A new railway alignment requires a deep, open cut ($30 \text{ m}$ high) through a mountain composed entirely of slate. The regional tectonic forces have steeply tilted the foliation planes of the slate.