Question

Q5) Prepare a mix design (Use ACI Method of Mix Design) which will be used for a pier located at the South Carolina. South Carolina is hot and humid with daytime temperatures averaging between 30–34 °C in most of the state and overnight lows averaging 21–23 °C on the coast and from 19–23 °C inland. Winter temperatures are much less uniform in South Carolina. Coastal areas of the state have very mild winters with high temperatures approaching an average of 16 °C and overnight lows in the 5-8 °C. Inland, the average January overnight low is around 2 °C in Columbia and just below freezing in the Upstate. While precipitation is abundant the entire year in almost the entire state, the coast tends to have a slightly wetter summer, while inland March tends to be the wettest month. Pier will be constructed during winter season. The specified strength is 29 MPa at 28 days and it is required that no more than 2 test result in 400 will fall below the specified strength. The sieve analysis result of used aggregate is given in Table.

BS Sieve   Mass Retained (gr)
10.0 mm   0
5.00 mm   8
2.36 mm   27
1.18 mm   43
600 μm   51
300 μm   90
150 μm   39
< 150 μm   10

For the other properties of fine aggregate, a specified amount of sand particles were taken from stockpile to determine the physical properties. 490 gr of saturated surface dry aggregate was prepared for this test. Mass of container was filled with water and weighted as 1437 gr. Then sand particles were added to the container which were initially filled by water and weighted as 1605 gr and after 24 hours the samples were taken from oven and weighted as 480 gr.

For Coarse aggregate: SSD bulk specific gravity: 2.75, absorption capacity = 1.5 %, total moisture: 2.5 %, Dry-rodded unit weight: 1500 kg/m3.
Cement: Type V, Sp.Gravity:3.1. For 0.34 m3 of concrete the cement content should not be exceeded 110 kg.

Answer 1

Ans) Let the total volume of trial mix be 1 m3 . The nominal aggregate size suitable for construction of concrete pier is 19 mm. Slump recommended is 50 - 100 mm. According to ACI 211.1-91, table 6.3.3, for 75 mm slump and nominal aggregate size of 19 mm , amount of water required per cubic meter of concrete is 193 kg

=> Amount of water = 193 kg per m3 concrete

Since, concrete exposed to cold environment we can expect freeze thaw cycles, so class of exposure is moderate , so air content for 19 mm aggregate size is 5 %

Now, required compressive strength as per ACI,

fcr = f'c + 8.3

=> fcr = 29 + 8.3 = 37.3 MPa

Now according to Table 6.3.4 (a) , for compressive strength of 37.3 MPa, water cement ratio is 0.385

Minimum Cement content per cubic meter concrete = 110 / 0.34 = 323.53 kg

Hence, amount of cement = Amount of water / w-c ratio = 193/ 0.385 = 501.3 kg > 323.53 kg (Hence OK)

Now, calculate fineness modulus according to given sieve analysis :

Sieve (mm)	Retained (gm)	Cumulative retained (gm)	Cumulative retained percent
10.00	0	0	0
5.00	8	8	2.98
2.36	27	35	13.05
1.18	43	78	29.10
600m	51	129	48.13
300 m	90	219	81.7
150 m	39	258	96.3

We know, fineness modulus (FM) = Sum of cumulative retained / 100

=> FM = (2.98 + 13.05 + 29.1 + 48.3 + 81.7 + 86.3) / 100

=> FM = 2.61

  Now, according to table 6.3.6 for nominal aggregate size of 19 mm and fineness modulus of 2.60 , volume of coarse aggregate is 0.64 m3

=> Amount of coarse aggregate = dry rodded density x volume = 1500 x 0.64 = 960 kg

Volume of fine aggregate = Total volume of concrete - Volume of all water, cement, coarse aggregate and air

=> Fine aggregate volume = 1 - [(193/1000) + (501.3 / 3.1 x 1000) + (960/ 2.75 x 1000) + 0.05]

=> Fine aggregate volume = 1 - 0.7538 = 0.2462 m3

=> Amount of fine aggregate = volume x specific gravity x water density

Specific gravity of fine aggregates can be calculated using given data :

Mass of sample (M1) = 490 gm

Mass of contained + water (M2) = 1437 gm

Mass of container + water + soil (M3) = 1605 gm

Specific gravity = M1 / (M3 - M2) = 490 / (1605 - 1437) = 2.91

=> Colume of fine aggregate =  0.2462 x 2.91 x 1000 = 716.4 kg

Also, moisture in fine aggregate = (490 - 480) x100 / 480 = 2.08 %

Now, since both aggregates has moisture and has absorption capacity , amount of mixing water needs to be corrected as shown :

Net Water absorbed by coarse aggregate = (0.015 - 0.025) x 960 = -9.6 kg

Net Water absorbed by fine aggregate = (0 - 0.0208) x 716.4 = - 14.9 kg

=> Actual amount of water to be added = 193 - 9.6 - 14.9 = 168.5 kg

Hence, batch weight for trial mix of 1 cubic meter is as follows :

Ingredient	Amount (kg)
Cement	501.3
Water	168.5
Coarse aggregate	960
Fine aggregate	716.4