26.8. Numerical example - 1

The specic gravities and weight proportions for aggregate and bitumen are as under for the preparation of Marshall mix design. The volume and weight of one Marshall specimen was found to be 475 cc and 1100 gm. Assuming absorption of bitumen in aggregate is zero, find V , V , VMA and VFB; v b Item A 1 A 2 A 3 A 4 B Wt (gm) 825 1200 325 150 100 Sp. Gr 2.63 2.51 2.46 2.43 1.05

In this chunk, we outline the specific gravities and weight proportions of aggregates and bitumen used in the Marshall mix design. It identifies the total weights of five different components of the mix and provides their respective specific gravities. The total weight of a sample Marshall specimen is noted, along with its volume. Later, we are tasked with calculating various critical parameters (air voids, volume of bitumen, voids in mineral aggregate, and voids filled with bitumen) using the provided weights and specific gravities.

Think of preparing a cake, where each ingredient (like flour, sugar, baking powder) has a specific measurement (weight) and density (specific gravity). In this case, aggregates and bitumen are like the ingredients, and understanding how much of each is needed ensures the cake (or mix) turns out just right.

Solution G_t = (825 + 1200 + 325 + 150 + 100) / (825/2.63 + 1200/2.51 + 325/2.46 + 150/2.43 + 100/1.05) = 2600 / 1080.86 = 2.406

This chunk presents the method for calculating the theoretical specific gravity of the mix, denoted as G_t. The formula requires summing the weights of all components, while considering their specific gravities to find the total volume they represent. The process involves dividing the total weight of the components by the weighted average of their specific gravities. This gives an insight into how the mix behavior is expected under load.

Imagine you’re finding the average score of students in a class. You would add up all the scores (weights) and then divide that total by the number of students (considering how well each student performed based on their individual scores). Here, you're weighing the contributions of each ingredient based on their specific density.

G_m = W_m / W_w = 1100 / 475 = 2.316

This chunk describes how to calculate the bulk specific gravity of the mix, represented as G_m. The equation uses the weight of the mix measured in air and the weight of the mix measured in water. The bulk specific gravity reflects the actual density of the mix, which is crucial because it incorporates the volume of air voids present in the sample.

Think of measuring how much a sponge weighs in air versus when it is soaked in water. The weight difference shows how much air the sponge contains, just how we measure both air-filled voids and solid mass in our mixes.

V_v = (G_t - G_m) / G_t * 100 = (2.406 - 2.316) / 2.406 * 100 = 3.741 %

This chunk focuses on calculating the percentage of air voids in the mix, denoted as V_v. The equation compares the theoretical specific gravity with the bulk specific gravity, indicating how much volume in the mix is not filled with solids. The air voids percentage is critical in assessing the compaction quality and durability of the asphalt mixture.

Imagine a sealed bag of chips where some space is occupied by air rather than chips. The percentage of air in the bag represents the air voids. Similarly, in our mix design, air voids can affect the overall integrity and longevity of the asphalt.

V_b = (1.05 * 1100) / G_m = 20.052 %

Here, we calculate the volume of bitumen as a percentage of the total volume based on its weight and specific gravity. This chunk shows the process of determining how much of the mix’s overall volume is taken up by bitumen, an essential component that binds the aggregates together and affects its performance.

This is akin to checking the oil content in a salad dressing. If there's too much or too little oil (bitumen), it will impact the flavor and texture (performance) of the salad mix.

VMA = V_v + V_b = 23.793 % VFB = V_b / VMA * 100 = 20.052 / 23.793 * 100 = 84.277 %

In this final part of the example, we calculate two important parameters: Voids in Mineral Aggregate (VMA) and Voids Filled with Bitumen (VFB). VMA considers the overall space in the aggregate, while VFB describes the proportion of that space filled by bitumen. Both are vital for determining the durability and performance of the asphalt mix.

It's similar to evaluating how much of a cake is filled with frosting versus how much is just air. Knowing how much space is taken up helps us appreciate the cake's richness (or, in this case, the asphalt's performance).

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