A Marshall Mix Design test was performed on a series of asphalt concrete specimens with varying binder contents ($4.0\%$, $4.5\%$, $5.0\%$, $5.5\%$, and $6.0\%$). After plotting the test data, the following asphalt contents were found to correspond to the design criteria peaks:

• Asphalt content at Maximum Stability: $5.2\%$
• Asphalt content at Maximum Bulk Specific Gravity (Density): $5.4\%$
• Asphalt content at $4.0\%$ Air Voids (median of $3-5\%$ target range): $5.0\%$

Calculate the Optimum Asphalt Content (OAC) based on the standard Marshall method averaging procedure.

A compacted asphalt specimen has a bulk specific gravity ($G_{mb}$) of $2.350$ and contains $5.5\%$ asphalt binder by total weight of the mix ($P_b = 5.5$). The bulk specific gravity of the combined aggregate ($G_{sb}$) is $2.650$. The measured air voids ($V_a$) in the compacted mix is $4.2\%$. Calculate the Voids in Mineral Aggregate (VMA) and the Voids Filled with Asphalt (VFA).

A soil sample proposed for a highway subgrade undergoes sieve analysis and Atterberg limits testing. The results are:

• Percent passing the No. $200$ sieve ($F_{200}$): $65\%$
• Liquid Limit (LL): $45$
• Plasticity Index (PI): $20$

Calculate the Group Index (GI) of this soil to evaluate its suitability as a subgrade material.

In the early 20th century, both petroleum-based bitumen (asphalt) and coal-based tar were widely used as binders in road construction ("tarmac"). Today, tar is virtually banned in modern highway construction, entirely replaced by bitumen. Explain the chemical, physical, and environmental reasons for this shift.

Portland Cement Concrete (PCC) possesses extremely high compressive strength, making it ideal for carrying heavy truck loads without deforming. However, PCC has a very low tensile strength (typically only about $10\%$ of its compressive strength). How does highway engineering compensate for this inherent material weakness when designing concrete pavements?