Review of the mix design basics Calculation exercise 1

Teachers:

Exercise 1 We require a mix with a 28 day compressive strength of 35 MPa and a slump of 90 mm, made with ordinary Portland cement with cement strength of 49,5 MPa. Grading of the aggregate is presented in the handed out forms. Moisture contents of the aggregate are: Sand2,5 % Gravel 2,0 % Coarse gravel (somero)0,0 % The estimated amount of absorbing water in the aggregate is estimated at 0,4 %

The steps of mix design Calculate the proportioning strength (suhteituslujuus) K s K s = 1,2*K*42,5/N N is the test strength of the cement Specify the # < 0,125 mm & # 4 mm passing values from the mix design form, when K s and the maximum grain size are known. Generate groups of equations (3) in order to solve the %-values of the aggregates. Calculate the amounts of aggregate and the granulometric value of H (rakeisuusluku H) of the combined aggregate Use the mix design form to specify the amounts of water, cement and aggregate Export the material data to the “Concrete composition” form, i.e. BETONIN KOOSTUMUS Remember to take into account the effective amount of water ( = total water – absorbed water) when calculating the final mix.

Exercise 1 solution Proportioning strength K s : 1,2 * 35 * 42,5/49,5 N/mm 2 = 36 MPa The maximum grain size (maksimiraekoko) is 95 % of the combined OR 90 % of the coarsest grading

Proportioning strength Passing values [%] for the < 0,125mm # and < 4mm # aggregates

ABCABC Generate 3 groups of equations in order to solve the %-values for the aggregates.

# 0,125 mm: A * 12B * 3C * 0= 4,0 # 4 mm: A * 100B * 30C * 5= 37 A+B+C= 1 A= 27 % B= 25 % C= 48 %

48

Amount of water and air: 187 l/m 3 = 167 (water)+ 20 (air) Amount of aggregate: 1925 kg/m 3 Amount of cement: 287 kg/m 3

2,5 2,0 0 0,4 = total - absorbed 2,1 1,6 -0,4 48

17 = =531 = 167 – 17 =150 48

Problem 2 How does the mix design change when the coarse gravel (somero) is changed to crushed stone/rubble (sepeli)?

vrs. Concrete containing rubble, i.e. crushed stone, is stiffer than concrete containing natural aggregates of the same size. Rubble-percentage is the share of rubble from total aggregate amount. More fine material is needed in the mix design. The correction is done by hand: Correction in the # 4 mm: 1…3 % more depending on the amount of crushed stone # 0,125 mm: + 0,1…0,4 % Correction in the cement amount is done automatically in the concrete mix design -form Crushed stone as aggregate

If crushed stone is used: The # 4 mm value is corrected by (depending on the amount of crushed stone) 1 – 3 % up The # 0,125 mm value is raised by 0,1 – 0,4 % In another words more fine material is needed in the mix ! a = 20 %b = 60 %c = 20 % → new value for H Excercise 2: Coarse gravel subsituted by crushed stone # 0,125 mm: A * 12B * 3C * 0= 4,2 (was 4,0) # 4 mm: A * 100B * 30C * 5= 39 (was 37) A+B+C= 1

Problem 3 Frost-resistant concrete, 6 % air. → air-entrainment The design strength stays the same at K35 However, the strength of the solid part of the conrete needs to be increased since there is more air in the same unit volume.

This is done by keepin the water-air-cement –ratio the same as in the original mix design The correction is done by the form

Air-entrained concrete: The air bubbles act as fine material: 1,5 % addition of air REDUCES the # 4 mm value by 1 % The # 0,125 mm value is % of the # 4 mm value. If the concrete contains also crushed material: 10 % crushed stone increases the # 4 mm value by 1 % The # 0,125 mm value is % of the # 4 mm value.

The amount of additional air is 6 % – 2 % = 4 % # 4 mm: 4 / 1,5 = 2,6 % 37 – 2,6 = 34 % # 0,125 mm:6 – 7 % of # 4 mm value 0,07*34 = 2,4 % # 0,125 mm: A * 12B * 3C * 0= 2,4 # 4 mm: A * 100B * 30C * 5= 34 A+B+C= 1 No analytical answer -> solution through trial and error A = 20 %B = 40 %C = 40 %

To recap: Nykänen´s method is only one of many mix design methods – All concrete proportioning methods are only a preliminary starting point Using crushed aggregate requires more fine material in the mix design In air-entrained concrete the air bubbles act as fine material