A chemical analysis of a Portland cement sample yields the following oxide mass percentages: Calcium Oxide (CaO) = 64.5% Silicon Dioxide (SiO$_2$) = 21.0% Aluminum Oxide (Al$_2$O$_3$) = 5.5% Iron Oxide (Fe$_2$O$_3$) = 3.0% Sulfur Trioxide (SO$_3$) = 2.0%

Use the standard Bogue equations to calculate the approximate percentage of Tricalcium Silicate (C$_3$S), Dicalcium Silicate (C$_2$S), Tricalcium Aluminate (C$_3$A), and Tetracalcium Aluminoferrite (C$_4$AF).

Standard Bogue Equations: C$_3$S = 4.07(CaO) - 7.60(SiO$_2$) - 6.72(Al$_2$O$_3$) - 1.43(Fe$_2$O$_3$) - 2.85(SO$_3$) C$_2$S = 2.87(SiO$_2$) - 0.754(C$_3$S) C$_3$A = 2.65(Al$_2$O$_3$) - 1.69(Fe$_2$O$_3$) C$_4$AF = 3.04(Fe$_2$O$_3$)

A concrete mix design for a heavily reinforced bridge deck calls for a total cementitious material content (Portland cement + fly ash) of 380 kg per cubic meter of concrete.

To ensure adequate workability around the dense rebar cage without adding excess water, a High-Range Water Reducer (HRWR) is specified. The manufacturer's recommended dosage rate is 650 mL per 100 kg of cementitious material.

Calculate the exact volume (in liters) of HRWR required for a single transit mixer truck carrying an 8.0 cubic meter batch of this concrete.

A massive concrete mat foundation (3 meters thick) is being poured for a high-rise building. The mix design utilizes standard Type I Portland cement. Four days after the pour, thermal sensors embedded deep within the core of the foundation register a peak temperature of 85°C. At the same time, a cold front arrives, and the surface temperature of the concrete drops rapidly to 15°C.

Evaluate the thermal gradient and the potential for catastrophic failure known as Delayed Ettringite Formation (DEF) and Thermal Cracking.