Calculating the Water-Cementitious Ratio
The water-to-cementitious materials ratio () is the single most critical
factor dictating the compressive strength and permeability of hardened
concrete, originally formulated by Duff Abrams in 1918.
Example
A concrete mix design for a reinforced retaining wall calls for the following batch weights per cubic yard:
Portland Cement = 500 lbs
Class F Fly Ash = 100 lbs
Coarse Aggregate (SSD) = 1800 lbs
Fine Aggregate (SSD) = 1200 lbs
Total Mix Water added at the plant = 270 lbs
Calculate the ratio for this mix design.
Step-by-Step Solution
0 of 4 Steps Completed1
Calculating the Absolute Volume of Concrete Components
Mix design relies on the "Absolute Volume Method" (ACI 211.1). The basic
premise is that the sum of the absolute (solid) volumes of all individual
ingredients—cement, water, coarse aggregate, fine aggregate, and entrapped
air—must exactly equal the total designed volume of the concrete batch
(typically 1 cubic meter or 1 cubic yard).
Example
An engineer is proportioning a non-air-entrained concrete mix for a 1.0 cubic meter batch. The specific gravities (SG) and required masses for the other components have already been determined as follows:
Portland Cement: 360 kg (SG = 3.15)
Water: 180 kg (SG = 1.00)
Coarse Aggregate (SSD): 1050 kg (SG = 2.65)
Entrapped Air: Assumed 1.5% of the total volume.
Calculate the required mass of Fine Aggregate (sand) in SSD condition to yield exactly 1.0 of concrete. Assume the specific gravity of the sand is 2.60 and the density of water is 1000 kg/m.
Step-by-Step Solution
0 of 6 Steps Completed1
Adjusting Batch Weights for Aggregate Moisture
The theoretical batch weights calculated above assume the aggregates are in a
perfect Saturated Surface-Dry (SSD) condition. In reality, stockpiled
aggregates in a batch plant are almost always wet from rain or completely dry
from the sun. The theoretical batch weights must be adjusted for the actual
moisture content before batching.
Example
Continuing from the previous example, the theoretical (SSD) batch weights per cubic meter are:
Cement = 360 kg
Water = 180 kg
Coarse Agg (SSD) = 1050 kg
Fine Agg (SSD) = 766 kg
Lab testing on the stockpiles that morning reveals:
The Coarse Aggregate has an absorption capacity of 0.5% and a total moisture content of 2.0%.
The Fine Aggregate has an absorption capacity of 1.2% and a total moisture content of 6.0%.
Calculate the actual batch weights of coarse aggregate, fine aggregate, and the adjusted volume of mixing water to be added at the plant.
Step-by-Step Solution
0 of 4 Steps Completed1
Case Study: Segregation and Bleeding
Segregation is the separation of the heavy coarse aggregate from the lighter
cement paste during transport or placement. Bleeding is a specific form of
segregation where the heavier solid particles settle, forcing the lighter mix
water upwards to the surface.
Example
During the construction of a 15-foot high structural retaining wall, the contractor decides to pour the concrete from the top of the forms, allowing it to free-fall the entire 15 feet.
The mix is also highly fluid (a slump of 8 inches) because the laborers added extra water to the truck on-site to make it "flow easier" around the rebar.
Analyze the severe consequences of this placement method on the hardened concrete structure.
Step-by-Step Solution
0 of 5 Steps Completed1