# TEST METHOD FOR COMBINING AGGREGATE GRADATIONS

When the aggregate gradations for a PCC mixture are sampled and tested individually, the results must be mathematically combined to create a theoretical combined gradation. This combined gradation is based on their relative percent volume in the mixture.

Each individual aggregate gradation shall start with the largest appropriate sieve for that material and shall include all the consecutive smaller sieve sizes through the #200 sieve. They shall include: 1/2-in., 1-in., 3/4-in., 1/2-in., 3/8-in., #4, #8, #16, #30, #50, #100, and #200 sieves. For coarse and intermediate aggregates, the #16 through #100 sieves may be determined mathematically.

The following methods outline the procedures to be used to determine the combined gradation. Method A is generally used for most aggregate combinations. Method B should be used when the specific gravity of the individual aggregates differ by more than 0.25.

###### METHOD A

Multiply relative percentage by the percent passing and sum all aggregates for each sieve size.

 P = Aa + Bb + Cc P = Combined percent passing of a given sieve A,B,C = Percent passing given sieve for aggregate A, B, and C a,b,c = Relative percent of total aggregates A, B, and C

Aggregate

Intermediate

Aggregate

Aggregate

% Passing

## Combined

% Retained

Relative Percentà

0.472

0.118

0.410

1 1/2 inch

100

100

100

100

0.0

1 inch

83

100

100

92

8.0

3/4 inch

65

100

100

83.4

8.5

1/2 inch

35

100

100

69.3

14.2

3/8 inch

14

100

100

59.4

9.9

No. 4

2.1

33

96

44.2

15.2

No. 8

0.9

2.8

82

34.4

9.8

No. 16

0.8

2.3

63

26.5

7.9

No. 30

0.7

1.8

37

15.7

10.8

No. 50

0.5

1.2

9.4

4.3

11.4

No. 100

0.4

0.7

1

0.7

3.6

No. 200

0.3

0.1

0.4

0.3

0.4

###### STEP 1:

The percent volume of each of the aggregates is determined from the volume proportions of the mixture design. The relative proportion of each aggregate of the total aggregate is determined by dividing the individual aggregate portion in the mix by the total aggregate portion in the mix.

Example:

A mixture design has the following mix proportions by volume:

Cement                                                                             0.110

Water                                                                                0.150

Air Entraining                                                                    0.070

Fine Aggregate (PCC Sand)                                             0.270

½ inch Intermediate Aggregate (Limestone Chip)            0.100

1½ inch Coarse Aggregate (Limestone PCC Stone)        0.300

Total                                                                      1.000

The total aggregate portion is: 0.270 + 0.100 + 0.300 = 0.670

The relative percent retained portion for each aggregate by volume is determined as follows:

Fine Aggregate (0.270/0.670) = 0.403

Intermediate Aggregate (0.100/0.670) = 0.149

Coarse Aggregate (0.300/0.670) = 0.448

Check the total aggregate relative portions. They should equal 1.000.

0.403 + 0.149 + 0.448 = 1.000 (OK)

###### STEP 2:

These volume proportions are then adjusted by the specific gravity of the aggregates, since gradations are based on percent weight retained on each sieve. The proportion retained by weight is determined by multiplying each aggregate’s volume proportion by its specific gravity. These weights are then summed to obtain a total weight. The proportion by weight is then determined by dividing each aggregate’s weight by the total weight.

Example:

Proportion

Volume

Specific

Gravity

Weight

Proportion

By Weight

## Fine

0.403

2.67

1.07601

(1.07601/2.64912) =  0.406

## Intermediate

0.149

2.59

0.38591

(0.38591/2.64912  =  0.146

#### Coarse

0.448

2.65

1.18720

(1.18720/2.64912) =  0.448

Total

1.000

2.64912

1.000

###### STEP 3:

Determine the theoretical combined gradation from the individual gradations. This is done by multiplying the percent retained on each sieve for the individual gradations by the relative portion of the aggregate volumes. Then total the percent retained of each product for each sieve size. This is the theoretical combined percent retained for each sieve. The total of these percents retained should equal 100.0. If the total is off due to rounding, prorate the rounding error.

Example:                                                   Coarse Aggregate

Sieve

% Retained

## Volume

% Retained

1 1/2 inch

0.0

0.448

0.0

1 inch

1.4

0.448

0.6

3/4 inch

23.7

0.448

10.6

1/2 inch

31.0

0.448

13.9

3/8 inch

24.5

0.448

11.0

No. 4

14.1

0.448

6.3

No. 16

0.7

0.448

0.3

No. 30

0.8

0.448

0.4

#### No. 100

0.4

0.448

0.2

No. 200

0.2

0.448

0.1

Minus 200

0.8

0.448

0.4

Similar calculations are done for the intermediate and fine aggregates.

###### STEP 4:

The individual adjusted gradations are summed to get the theoretical combined gradation, percent retained. The theoretical combined gradation, percent passing, may be calculated by subtracting subsequent sieves beginning with 100, as per IM 302. The following table shows the calculations:

Aggregate

Intermediate

Aggregate

Aggregate

% Retained

## Combined

% Passing

1 1/2 inch

0.0

0.0

100

1 inch

0.6

0.6

99.4

3/4 inch

10.6

0.0

10.6

88.8

1/2 inch

13.9

3.2

17.1

71.7

3/8 inch

11.0

5.4

0.0

16.4

55.3

No. 4

6.3

4.9

2.0

13.2

42.1

No. 8

0.9

0.4

4.1

5.4

36.7

No. 16

0.3

0.3

5.6

6.2

30.5

No. 30

0.4

0.1

12.9

13.4

17.1

No. 50

0.1

0.2

12.0

12.3

4.8

No. 100

0.2

0.1

3.1

3.4

1.4

No. 200

0.1

0.1

0.2

0.4

1.0

Minus 200

0.4

0.2

0.4

1.0

0.0

The theoretical combined gradations are used in graphically displaying aggregate blends of PCC mixture designs and for plotting control charts to compare target gradation with working ranges of the mixture design.