blending of aggregates warning: if your mind hasn’t yet blended with “gradation of aggregates”...

BLENDING OF BLENDING OF AGGREGATESAGGREGATES

Warning: If your mind hasn’t yetWarning: If your mind hasn’t yet blended with “blended with “Gradation of Gradation of AggregatesAggregates” (posted on the ” (posted on the

instructor’s website) then you’ll instructor’s website) then you’ll probably struggle with this probably struggle with this

presentation. You should also have presentation. You should also have ““Assignment 1 ExampleAssignment 1 Example” at the ready.” at the ready.

BLENDING OF BLENDING OF AGGREGATESAGGREGATESBLENDING OF BLENDING OF AGGREGATESAGGREGATESBLENDING OF BLENDING OF AGGREGATESAGGREGATES

What is asphalt What is asphalt concrete?concrete?

Basically, its just aggregate…Basically, its just aggregate…

……coated with asphalt coated with asphalt cement…cement…

……and then compacted.and then compacted.

There are 3 basic elements to There are 3 basic elements to the compacted mix…the compacted mix…

1. Aggregate Particles1. Aggregate Particles

2. Asphalt Cement2. Asphalt Cement3. Air Voids3. Air Voids

Not all the asphalt Not all the asphalt cement ends up coating cement ends up coating the aggregate the aggregate particles…particles………some is absorbed some is absorbed into the water-into the water-permeable voids within permeable voids within the aggregate the aggregate particles.particles.

VMAVMA

Are you a Are you a member?member?

Of what…the “Virile Men’s Association”?Of what…the “Virile Men’s Association”?… “… “Voluptuous Mama’s of America”?Voluptuous Mama’s of America”?

Voids in the Mineral Voids in the Mineral AggregateAggregate

… “… “Volatile Mercenaries of Alberta”?Volatile Mercenaries of Alberta”?… … so what’s it mean?so what’s it mean?Any help?Any help?Well, VMA is one of the most important Well, VMA is one of the most important properties of an asphalt paving mix.properties of an asphalt paving mix.Firstly, here’s a representation of a Firstly, here’s a representation of a

compacted paving mix.compacted paving mix.There’s stone, and sand particles all There’s stone, and sand particles all

coated with asphalt cement and there’s a coated with asphalt cement and there’s a few air voids (the white spaces).few air voids (the white spaces).

If we removed all the asphalt cement but If we removed all the asphalt cement but the aggregate stayed put it would look like the aggregate stayed put it would look like

this:this:

The space occupied by the asphalt cement The space occupied by the asphalt cement and air voids (not including the asphalt and air voids (not including the asphalt

cement absorbed) is cement absorbed) is voids in the mineral voids in the mineral aggregateaggregate..

This diagram shows the mix without the This diagram shows the mix without the aggregate…there’s just the aggregate…there’s just the asphalt asphalt

cementcement and and air voidsair voids..

Vmb is the Bulk Volume of the Mix

In mathematical terms…In mathematical terms…

Vvma = Va + Vbe

100%V

VVMA

mb

vma

Vvma is the Volume of Voids in the Mineral Aggregate

Va is the Volume of Air Voids in the Mix

Vbe is the Effective Volume of Asphalt Cement in the Mix

VMA and Dense Graded VMA and Dense Graded AggregateAggregate

Once the mix has been compacted to its Once the mix has been compacted to its densest state then there’s nowhere for densest state then there’s nowhere for

particles to go when subjected to traffic.particles to go when subjected to traffic.

Densely graded mixes are going to offer Densely graded mixes are going to offer the greatest resistance to loads because the greatest resistance to loads because

they minimize the void space and therefore they minimize the void space and therefore the movement paths within the mix.the movement paths within the mix.

100%Dd

p ii

where pwhere pii = total % passing sieve size i = total % passing sieve size i

ddii = width of opening of sieve size i = width of opening of sieve size i

D = largest size (sieve opening) inD = largest size (sieve opening) in

gradationgradation

Mathematically, Fuller Grading Curves offer Mathematically, Fuller Grading Curves offer the maximum density and minimum voids:the maximum density and minimum voids:


When plotted they look like this:When plotted they look like this:

Fuller Grading Curves

#200

0.149 0.297 0.59 1.19 2.38 4.76 9.52 12.7 19.1 25 37.5 50 630%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10 100

Sieve Opening (mm)

% P

assi

ng

0.074

#100 #50 #30 #16 #8 #4 ⅜" ½ ¾" 1" 1½" 2" 2½"

These can be used to set grading limits (“specs”) These can be used to set grading limits (“specs”) as with the as with the redred and and greengreen dashed curves. dashed curves.

Notice that the High Spec is above the ⅜” Fuller Notice that the High Spec is above the ⅜” Fuller Curve below the #8 sieveCurve below the #8 sieve

This allows for a reduction in the number of finer This allows for a reduction in the number of finer sizes which will in turn allow an increase in voids sizes which will in turn allow an increase in voids

But why would we want to But why would we want to increaseincrease the voids? the voids?The goal is to blend the stock aggregates to The goal is to blend the stock aggregates to produce a blend that falls between the two limitsproduce a blend that falls between the two limits


This is a compromise between stability This is a compromise between stability (lower with higher voids) and durability.(lower with higher voids) and durability.

Experience has shown that asphalt mixes Experience has shown that asphalt mixes need to have between 3% and 5% air voidsneed to have between 3% and 5% air voids

If the voids are too low, then asphalt If the voids are too low, then asphalt cement can bleed to the surface in hot cement can bleed to the surface in hot

weather.weather.

Its analogous to Portland Cement Concrete Its analogous to Portland Cement Concrete and air entraining to match exposure to the and air entraining to match exposure to the

environment.environment.So minimum VMA values are specified for So minimum VMA values are specified for different Nominal Maximum Particle Sizesdifferent Nominal Maximum Particle Sizes

Blending Stock AggregatesBlending Stock AggregatesNormally, aggregate stocks come from Normally, aggregate stocks come from different sources:different sources:

1. stone comes from crushed bedrock,1. stone comes from crushed bedrock,

2. sand comes from natural deposits,2. sand comes from natural deposits,

3. mineral filler comes from the bottom of 3. mineral filler comes from the bottom of the crusher (dust)the crusher (dust)

There are two basic approaches:There are two basic approaches:1.1. Simultaneous equations Simultaneous equations (used on (used on

Assignment 1)Assignment 1)

2.2. Trial and Error (spreadsheet, used for Trial and Error (spreadsheet, used for lab)lab)

Assignment 1 Assignment 1 ExampleExample

Two questions using simultaneous Two questions using simultaneous equations.equations.1. Produce a blend of the given aggregates that results in 28.0%

passing the 0.6 mm sieve.

MATERIALMATERIAL % % UsedUsed 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075

Cyclone A Cyclone A CrushedCrushed

100.0100.0%%

100.0%100.0% 100.0%100.0% 90.0%90.0% 59.0%59.0% 16.0%16.0% 3.2%3.2% 2.0%2.0% 0.5%0.5% 0.0%0.0% 0.0%0.0% 0.0%0.0%

NewmarkeNewmarket Sandt Sand

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 96.0%96.0% 82.0%82.0% 73.0%73.0% 51.0%51.0% 36.0%36.0% 21.0%21.0% 9.2%9.2%

DFC DUSTDFC DUST 2.0%2.0% 100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0%

The proportion of dust is set at 2 %.The proportion of dust is set at 2 %.

The condition given is for the 0.6 mm sieve.The condition given is for the 0.6 mm sieve.Let Let CC be the fraction of be the fraction of Cyclone A CrushedCyclone A Crushed and and NN be the be the fraction of fraction of Newmarket SandNewmarket Sand..

When we apply the proportions to find the percent When we apply the proportions to find the percent passing the 0.6 mm sieve for the blend, we get:passing the 0.6 mm sieve for the blend, we get:

0.0050.005CC + 0.51 + 0.51NN + 1.00(.02) = 0.28 + 1.00(.02) = 0.2811

The second condition is that all the proportions must sum The second condition is that all the proportions must sum to 1:to 1:

oorr

0.0050.005CC + 0.51 + 0.51NN = 0.26 = 0.26

CC + + NN = 0.98 = 0.9822

Multiply equation 2 by 0.005 then subtract 2 from 1Multiply equation 2 by 0.005 then subtract 2 from 1

0.0050.005CC + 0.005 + 0.005NN = 0.0049 = 0.0049

(0.51 - 0.005)(0.51 - 0.005)NN = 0.26 - 0.0049 = 0.26 - 0.0049(0.505)(0.505)NN = 0.2551 = 0.2551NN = 0.505149 ≈ 50.51% = 0.505149 ≈ 50.51%

50.5150.51%%

Therefore, Therefore, CC = 100% - 50.51% - 2% = = 100% - 50.51% - 2% = 47.49%47.49%

47.49%47.49%

CC + + NN + 0.02 = 1.0 + 0.02 = 1.0

Assignment 1 Example: Assignment 1 Example: Q 1 Q 1 Cont’dCont’d

Now for the blended gradationNow for the blended gradation

Before we start to crank off the blend, let’s check Before we start to crank off the blend, let’s check the proportions by finding Pthe proportions by finding P0.60.6

This is the percent passing the 0.6 mm sieve This is the percent passing the 0.6 mm sieve given for condition 1.given for condition 1.Now we do the same for all the other sizes…Now we do the same for all the other sizes…

PP0.60.6 = 0.4749x0.5% + 0.5051x51.0% + 0.02x100.0% = = 0.4749x0.5% + 0.5051x51.0% + 0.02x100.0% = 27.9976%27.9976%

PP0.60.6 ≈ 28.0% ≈ 28.0%

SIEVE SIZE (mm):SIEVE SIZE (mm): 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075

BLEND:BLEND:

SPECIFICATIONSPECIFICATIONLow:Low: 100.0%100.0% 100.0%100.0% 100.0%100.0% 80.0%80.0% 70.0%70.0% 50.0%50.0% 35.0%35.0% 25.0%25.0%

18.018.0%%

13.013.0%% 8.0%8.0% 4.0%4.0%

High:High: 100.0%100.0% 100.0%100.0% 100.0%100.0%100.0100.0

%% 90.0%90.0% 70.0%70.0% 50.0%50.0% 40.0%40.0%29.029.0

%%23.023.0

%% 16.0%16.0% 10.0%10.0%

TARGET:TARGET: 100.0%100.0% 100.0%100.0% 100.0%100.0% 90.0%90.0% 80.0%80.0% 60.0%60.0% 42.5%42.5% 32.5%32.5%23.523.5

%%18.018.0

%% 12.0%12.0% 7.0%7.0%



47.4947.49%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 90.0%90.0% 59.0%59.0% 16.0%16.0% 3.2%3.2% 2.0%2.0% 0.5%0.5% 0.0%0.0% 0.0%0.0% 0.0%0.0%


50.5150.51%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 96.0%96.0% 82.0%82.0% 73.0%73.0% 51.0%51.0% 36.0%36.0% 21.0%21.0% 9.2%9.2%

DFC DUSTDFC DUST 2.0%2.0% 100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0%

100.0%100.0% 100.0%100.0% 100.0%100.0% 95.3%95.3% 80.5%80.5% 58.1%58.1% 44.9%44.9% 39.8%39.8% 28.0%28.0% 20.2%20.2% 6.6%6.6%

PP25.425.4 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0%100.0%

PP19.019.0 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0%100.0%

PP16.016.0 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0%100.0%

PP12.712.7 = 0.4749x90.0%+0.5051x100.0%+0.02x100.0% = = 0.4749x90.0%+0.5051x100.0%+0.02x100.0% = 95.251%95.251%

PP12.712.7 ≈ 95.3% ≈ 95.3%

PP9.59.5 = 0.4749x59.0% + 0.5051x100.0% + 0.02x100.0% = = 0.4749x59.0% + 0.5051x100.0% + 0.02x100.0% = 80.529%80.529%

PP9.59.5 ≈ 80.5% ≈ 80.5%

PP4.754.75 = 0.4749x16.0% + 0.5051x96.0% + 0.02x100.0% = = 0.4749x16.0% + 0.5051x96.0% + 0.02x100.0% = 58.088%58.088%

PP4.754.75 ≈ 58.1% ≈ 58.1%

PP2.362.36 = 0.4749x3.2% + 0.5051x82.0% + 0.02x100.0% = = 0.4749x3.2% + 0.5051x82.0% + 0.02x100.0% = 44.938%44.938%

PP2.362.36 ≈ 44.9% ≈ 44.9%

PP1.181.18 = 0.4749x2.0% + 0.5051x73.0% + 0.02x100.0% = = 0.4749x2.0% + 0.5051x73.0% + 0.02x100.0% = 39.822%39.822%

PP1.181.18 ≈ 39.8% ≈ 39.8%

PP0.30.3 = 0.4749x0.0% + 0.5051x36.0% + 0.02x100.0% = = 0.4749x0.0% + 0.5051x36.0% + 0.02x100.0% = 20.184%20.184%

PP0.30.3 ≈ 20.2% ≈ 20.2%

PP0.0750.075 = 0.4749x0.0% + 0.5051x9.2% + 0.02x100.0% = = 0.4749x0.0% + 0.5051x9.2% + 0.02x100.0% = 6.647%6.647%

PP0.0750.075 ≈ 6.6% ≈ 6.6%

That’s the one all right! So we’re good to go.That’s the one all right! So we’re good to go.

12.612.6

PP0.1500.150 = 0.4749x0.0% + 0.5051x21.0% + 0.02x100.0% = = 0.4749x0.0% + 0.5051x21.0% + 0.02x100.0% = 12.607%12.607%

PP0.1500.150 ≈ 12.6% ≈ 12.6%

Assignment 1 Example: Assignment 1 Example: Q1 Q1 FinaleFinaleMATERIALMATERIAL % %

UsedUsed 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075


47.4947.49%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 90.0%90.0% 59.0%59.0% 16.0%16.0% 3.2%3.2% 2.0%2.0% 0.5%0.5% 0.0%0.0% 0.0%0.0% 0.0%0.0%


50.5150.51%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 96.0%96.0% 82.0%82.0% 73.0%73.0% 51.0%51.0% 36.0%36.0% 21.0%21.0% 9.2%9.2%

DFC DUSTDFC DUST 2.0%2.0% 100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0%

The table above is used to weigh out and The table above is used to weigh out and blend the sieved stock for individual 1210 g blend the sieved stock for individual 1210 g

specimens.specimens.

Any sizes with 100% passing will retain Any sizes with 100% passing will retain none of the material. Hence 0 g are none of the material. Hence 0 g are

recorded for all these sizes.recorded for all these sizes.

These values represent the cumulative mass These values represent the cumulative mass (the scale reading) after adding the required (the scale reading) after adding the required

mass of each stock sieve sizemass of each stock sieve size

First, how much Cyclone A will be used?First, how much Cyclone A will be used?

For a specimen with 1210 g of aggregate we need For a specimen with 1210 g of aggregate we need 47.49% of 1210 g of all Cyclone A sizes = 574.63 g47.49% of 1210 g of all Cyclone A sizes = 574.63 g

CUMULATIVE WEIGHT CUMULATIVE WEIGHT 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36PassinPassin

g g 2.36 2.36

Cyclone A CrushedCyclone A Crushed 47.49%47.49%(% (% USED)USED)

Newmarket SandNewmarket Sand 50.51%50.51%(% (% USED)USED)

DFC DUSTDFC DUST 2.0 2.0 (% (% USED)USED)

Total Specimen Mass (g):Total Specimen Mass (g): 12101210

% AC% ACWeightWeight

(g)(g)

4.3%4.3%

4.8%4.8%

5.3%5.3%

5.8%5.8%

6.3%6.3%

6.8%6.8%

574.6574.633611.1611.17724.224.2

00 00

00 00 00 00

00 00 00 00 00 00

57.557.5 235.6235.6 482.7482.7 556.2556.2

Now, how much Newmarket Sand will be Now, how much Newmarket Sand will be used?used?

For a specimen with 1210 g of aggregate we need For a specimen with 1210 g of aggregate we need 50.51% of 1210 g of all Newmarket Sand sizes = 611.17 g50.51% of 1210 g of all Newmarket Sand sizes = 611.17 g

And, how much DFC Dust will be used?And, how much DFC Dust will be used?

For a specimen with 1210 g of aggregate we need 2% of For a specimen with 1210 g of aggregate we need 2% of 1210 g for DFC Dust = 24.2 g1210 g for DFC Dust = 24.2 g

24.424.4 110.0110.0

507.1507.1 666.2666.2 12101210

54.454.4

61.061.0

67.767.7

74.574.5

81.481.4

88.388.3

Now for the other Cyclone A masses:Now for the other Cyclone A masses:

The 12.7 mm sieve will retain 100 – 90 or 10% of the The 12.7 mm sieve will retain 100 – 90 or 10% of the mass of Cyclone A used: 0.10 x 574.63 = 57.5 gmass of Cyclone A used: 0.10 x 574.63 = 57.5 g

The 9.5 mm sieve will retain 100 – 59 or 41% of the mass The 9.5 mm sieve will retain 100 – 59 or 41% of the mass of Cyclone A used: 0.41 x 574.63 = 235.6 gof Cyclone A used: 0.41 x 574.63 = 235.6 g

The 4.75 mm sieve will retain 100 – 16 or 84% of the The 4.75 mm sieve will retain 100 – 16 or 84% of the mass of Cyclone A used: 0.84 x 574.63 = 482.7 gmass of Cyclone A used: 0.84 x 574.63 = 482.7 g

The 2.36 mm sieve will retain 100 – 3.2 or 96.8% of the The 2.36 mm sieve will retain 100 – 3.2 or 96.8% of the mass of Cyclone A used: 0.968 x 574.63 = 556.2 gmass of Cyclone A used: 0.968 x 574.63 = 556.2 g

Now for the other Newmarket Sand masses:Now for the other Newmarket Sand masses:

The 4.75 mm sieve will retain 100 – 96 or 4% of the mass The 4.75 mm sieve will retain 100 – 96 or 4% of the mass of Newmarket Sand used: 0.04 x 611.17 = 24.4 gof Newmarket Sand used: 0.04 x 611.17 = 24.4 g

The 2.36 mm sieve will retain 100 – 82 or 18% of the The 2.36 mm sieve will retain 100 – 82 or 18% of the mass of Newmarket Sand used: 0.18 x 611.17 = 110.0 gmass of Newmarket Sand used: 0.18 x 611.17 = 110.0 g

We can check these numbers by summing We can check these numbers by summing over each size and calculating the % passing over each size and calculating the % passing which should agree with the blend gradationwhich should agree with the blend gradation

57.557.5 235.6235.6

PP12.712.7 = 100%x(1.00 – 57.5/1210) = 95.25% = 100%x(1.00 – 57.5/1210) = 95.25% (95.3%)(95.3%)PP9.59.5 = 100%x(1.00 – 235.6/1210) = 80.5% = 100%x(1.00 – 235.6/1210) = 80.5% (80.5%)(80.5%)PP4.754.75 = 100%x(1.00 – 507.1/1210) = 58.1% = 100%x(1.00 – 507.1/1210) = 58.1% (58.1%)(58.1%)PP2.362.36 = 100%x(1.00 – 666.2/1210) = 44.9% = 100%x(1.00 – 666.2/1210) = 44.9% (44.9%)(44.9%)The last column should (and does) sum to The last column should (and does) sum to the total specimen mass (1210 g)the total specimen mass (1210 g)

The final step(s) is to determine the mass of The final step(s) is to determine the mass of asphalt cement required for the 6 asphalt asphalt cement required for the 6 asphalt

contents listed.contents listed.

Since we’re using % of total mix, we have to Since we’re using % of total mix, we have to use a bit of algebra. (I won’t tell anyone if use a bit of algebra. (I won’t tell anyone if

you don’t.)you don’t.)

Let the Mass of AC required = MLet the Mass of AC required = Mb b and Pand Pbb = = %AC%AC100%

M1210M

pb

bb

bbb MM1210

100%p

)(

100%p

1M100%

p(1210) b

bb

b

bb p-100%

p(1210)M

Applying this formula to each %AC:Applying this formula to each %AC:

54.4449321)(1210)(0.04.3-100

4.3(1210)Mb

61.0504202)(1210)(0.0

4.8-1004.8

(1210)Mb

67.7559662)(1210)(0.0

5.3-1005.3

(1210)Mb

74.5615711)(1210)(0.0

5.8-1005.8

(1210)Mb

81.46723586)(1210)(0.0

6.3-1006.3

(1210)Mb

88.3729614)(1210)(0.0

6.8-1006.8

(1210)Mb

00 00

PP16.016.0 = 100%x(1.00 – 0/1210) = 100.0% = 100%x(1.00 – 0/1210) = 100.0% (100.0%)(100.0%)PP19.019.0 = 100%x(1.00 – 0/1210) = 100.0% = 100%x(1.00 – 0/1210) = 100.0% (100.0%)(100.0%)

Assignment 1 Example : Assignment 1 Example : Q 2Q 22. Produce a blend of the given aggregates that results in 74.0% passing the 9.5 mm sieve and 61.0% passing the 2.36 mm sieve.MATERIALMATERIAL % %

UsedUsed 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075

Gumshoe Gumshoe GoldGold

100.0100.0%%

100.0100.0%%

98.0%98.0% 79.0%79.0% 34.0%34.0% 9.0%9.0% 2.0%2.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%

Saltwater Saltwater SludgeSludge

100.0100.0%%

100.0100.0%%

100.0%100.0% 98.0%98.0% 89.0%89.0% 67.0%67.0% 48.0%48.0% 21.0%21.0% 8.0%8.0% 1.5%1.5% 1.0%1.0% 0.0%0.0%

H's Donut H's Donut CrumbsCrumbs

100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0100.0%%

100.0%100.0% 53.0%53.0% 26.0%26.0% 5.0%5.0% 2.0%2.0%

The conditions given are for the 9.5 mm & 2.36 mm The conditions given are for the 9.5 mm & 2.36 mm sieves.sieves.

Let Let GG be the fraction of be the fraction of Gumshoe GoldGumshoe Gold, , SS be the fraction be the fraction of of Saltwater SludgeSaltwater Sludge and and HH be the fraction of be the fraction of Homer’s Homer’s

Donut CrumbsDonut Crumbs..

Applying the first condition for PApplying the first condition for P9.59.5::

11

The third condition is that all the proportions must sum to The third condition is that all the proportions must sum to 1:1:

0.340.34GG + 0.89 + 0.89SS + + HH = = 0.740.7422

GG + + SS + + HH = = 1.001.00

GG = 0.392098555 ≈ 39.21% = 0.392098555 ≈ 39.21%

1.101.10%%

and and HH = 0.596856414% ≈ 59.69% = 0.596856414% ≈ 59.69%

39.2139.21%%

59.6959.69%%

0.020.02GG + 0.48 + 0.48SS + + HH = = 0.610.6133

SS = 0.011045029 ≈ = 0.011045029 ≈ 1.10%1.10%

The second condition for PThe second condition for P2.362.36::

Using the Sharp EL546W Calculator, Mode 21:Using the Sharp EL546W Calculator, Mode 21:for instructions, visit for instructions, visit http://math.mohawkcollege.ca/calc.asphttp://math.mohawkcollege.ca/calc.asp

Assignment 1 Example: Assignment 1 Example: Q 2 Q 2 Cont’dCont’d

Now for the blended gradationNow for the blended gradation

Before we start to crank off the blend, let’s check Before we start to crank off the blend, let’s check the proportions by finding Pthe proportions by finding P9.59.5 and P and P2.362.36

Now we do the same for all the other sizes…Now we do the same for all the other sizes…

PP0.60.6 = 0.3921x0.0% + 0.0110x8.0% + 0.5969x53.0% = 31.7237% = 0.3921x0.0% + 0.0110x8.0% + 0.5969x53.0% = 31.7237%

PP0.60.6 ≈ 31.7% ≈ 31.7%

SIEVE SIZE (mm):SIEVE SIZE (mm): 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075

BLEND:BLEND:

SPECIFICATIONSPECIFICATIONLow:Low: 100.0%100.0% 100.0%100.0% 90.0%90.0% 75.0%75.0% 65.0%65.0% 55.0%55.0% 40.0%40.0% 28.0%28.0%

15.015.0%% 5.0%5.0% 2.0%2.0% 0.0%0.0%

High:High: 100.0%100.0% 100.0%100.0% 100.0%100.0% 95.0%95.0% 85.0%85.0% 75.0%75.0% 70.0%70.0% 60.0%60.0%35.035.0

%%23.023.0

%% 12.0%12.0% 5.0%5.0%

TARGET:TARGET: 100.0%100.0% 100.0%100.0% 95.0%95.0% 85.0%85.0% 75.0%75.0% 65.0%65.0% 55.0%55.0% 44.0%44.0%25.025.0

%%14.014.0

%% 7.0%7.0% 2.5%2.5%



39.2139.21%%

100.0100.0%%

100.0100.0%%

98.0%98.0% 79.0%79.0% 34.0%34.0% 9.0%9.0% 2.0%2.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%


1.101.10%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 98.0%98.0% 89.0%89.0% 67.0%67.0% 48.0%48.0% 21.0%21.0% 8.0%8.0% 1.5%1.5% 1.0%1.0% 0.0%0.0%


59.6959.69%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 53.0%53.0% 26.0%26.0% 5.0%5.0% 2.0%2.0%

100.0%100.0% 100.0%100.0% 99.2%99.2% 91.7%91.7% 74.0%74.0% 64.0%64.0% 61.0%61.0% 59.9%59.9% 31.7%31.7% 15.5%15.5% 1.2%1.2%

PP25.425.4 = 0.3921x100% + 0.0110x100.0% + 0.5969x100% = 100% = 0.3921x100% + 0.0110x100.0% + 0.5969x100% = 100%PP19.019.0 = 0.3921x100% + 0.0110x100% + 0.5969x100% = 100% = 0.3921x100% + 0.0110x100% + 0.5969x100% = 100%PP16.016.0 = 0.3921x98.0% + 0.0110x100% + 0.57969x100% = 99.2158% = 0.3921x98.0% + 0.0110x100% + 0.57969x100% = 99.2158%

PP16.016.0 ≈ 99.2% ≈ 99.2%

PP12.712.7 = 0.3921x79.0% + 0.0110x98.0% + 0.5969x100 = 91.7439% = 0.3921x79.0% + 0.0110x98.0% + 0.5969x100 = 91.7439%

PP12.712.7 ≈ 91.7% ≈ 91.7%

PP9.59.5 = 0.3921x34.0% + 0.0110x89.0% + 0.5969x100.0% = 74.0004% = 0.3921x34.0% + 0.0110x89.0% + 0.5969x100.0% = 74.0004%

PP9.59.5 ≈ 74.0% ≈ 74.0%

PP4.754.75 = 0.3921x9.0% + 0.0110x67.0% + 0.5969x100.0% = 63.9559% = 0.3921x9.0% + 0.0110x67.0% + 0.5969x100.0% = 63.9559%

PP4.754.75 ≈ 64.0% ≈ 64.0%

PP2.362.36 = 0.3921x2.0% + 0.0110x48.0% + 0.5969x100.0% = 61.0022% = 0.3921x2.0% + 0.0110x48.0% + 0.5969x100.0% = 61.0022%

PP2.362.36 ≈ 61.0% ≈ 61.0%

PP1.181.18 = 0.3921x0.0% + 0.0110x21.0% + 0.5969x100% = 59.921% = 0.3921x0.0% + 0.0110x21.0% + 0.5969x100% = 59.921%

PP1.181.18 ≈ 59.9% ≈ 59.9%

PP0.30.3 = 0.3921x0.0% + 0.0110x1.5% + 0.5969x26.0% = 15.5359% = 0.3921x0.0% + 0.0110x1.5% + 0.5969x26.0% = 15.5359%

PP0.30.3 ≈ 15.5% ≈ 15.5%

PP0.0750.075 = 0.3921x0.0% + 0.0110x0.0% + 0.5969x2.0% = 1.1938% = 0.3921x0.0% + 0.0110x0.0% + 0.5969x2.0% = 1.1938%

PP0.0750.075 ≈ 1.2% ≈ 1.2%

Got ‘em both! So we’re good to go.Got ‘em both! So we’re good to go.

3.03.0

PP0.1500.150 = 0.3921x0.0% + 0.0110x1.0% + 0.5969x5.0% = 2.9955% = 0.3921x0.0% + 0.0110x1.0% + 0.5969x5.0% = 2.9955%

PP0.1500.150 ≈ 3.0% ≈ 3.0%

Assignment 1 Example: Assignment 1 Example: Q2 Q2 FinaleFinaleMATERIALMATERIAL % %

UsedUsed 25.425.4 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36 1.181.18 0.6000.600 0.3000.300 0.1500.150 0.0750.075


39.2139.21%%

100.0100.0%%

100.0100.0%%

98.0%98.0% 79.0%79.0% 34.0%34.0% 9.0%9.0% 2.0%2.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0% 0.0%0.0%


1.101.10%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 98.0%98.0% 89.0%89.0% 67.0%67.0% 48.0%48.0% 21.0%21.0% 8.0%8.0% 1.5%1.5% 1.0%1.0% 0.0%0.0%


59.6959.69%%

100.0100.0%%

100.0100.0%%

100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 100.0%100.0% 53.0%53.0% 26.0%26.0% 5.0%5.0% 2.0%2.0%

The table above is used to weigh out and The table above is used to weigh out and blend the sieved stock for individual 1200 g blend the sieved stock for individual 1200 g

specimens.specimens.

Any sizes with 100% passing will retain Any sizes with 100% passing will retain none of the material. Hence 0 g are none of the material. Hence 0 g are

recorded for all these sizes.recorded for all these sizes.

These values represent the cumulative mass These values represent the cumulative mass (the scale reading) after adding the required (the scale reading) after adding the required

mass of each stock sieve sizemass of each stock sieve size

First, how much Gumshoe Gold will be used?First, how much Gumshoe Gold will be used?

For a specimen with 1200 g of aggregate we need For a specimen with 1200 g of aggregate we need 39.21% of 1200 g of all Gumshoe Gold sizes = 470.5 g39.21% of 1200 g of all Gumshoe Gold sizes = 470.5 g

CUMULATIVE WEIGHT CUMULATIVE WEIGHT 19.019.0 16.016.0 12.712.7 9.59.5 4.754.75 2.362.36PassinPassin

g g 2.36 2.36

Gumshoe GoldGumshoe Gold 39.2139.21

%%(% (% USED)USED)

Saltwater SludgeSaltwater Sludge1.101.10

%%(% (% USED)USED)

Homer's Donut Homer's Donut CrumbsCrumbs

59.6959.69%%

(% (% USED)USED)

Total Specimen Mass (g):Total Specimen Mass (g): 12001200

% AC% ACWeightWeight

(g)(g)

5.0%5.0%

5.5%5.5%

6.0%6.0%

6.5%6.5%

7.0%7.0%

7.5%7.5%

470.5470.5

13.213.2

716.3716.3

00 9.49.4

00 00 0.30.3 1.51.5

00 00 00 00 00 00

98.898.8 310.5310.5 428.2428.2 461.1461.1

Now, how much Saltwater Sludge will be Now, how much Saltwater Sludge will be used?used?

For a specimen with 1200 g of aggregate we need For a specimen with 1200 g of aggregate we need 1.10% of 1200 g of all Saltwater Sludge sizes = 13.2 g1.10% of 1200 g of all Saltwater Sludge sizes = 13.2 g

4.44.4 6.96.963.263.2

69.869.8

76.676.6

83.483.4

90.390.3

97.397.3

Now for the other Gumshoe Gold masses:Now for the other Gumshoe Gold masses:

The 12.7 mm sieve will retain 100 – 79 or 21% of the The 12.7 mm sieve will retain 100 – 79 or 21% of the mass of Gumshoe Gold used: 0.21 x 470.5 = 98.8 gmass of Gumshoe Gold used: 0.21 x 470.5 = 98.8 g

The 9.5 mm sieve will retain 100 – 34 or 66% of the mass The 9.5 mm sieve will retain 100 – 34 or 66% of the mass of Gumshoe Gold used: 0.66 x 470.5 = 310.5 gof Gumshoe Gold used: 0.66 x 470.5 = 310.5 g


The 2.36 mm sieve will retain 100 – 2.0 or 98.0% of the The 2.36 mm sieve will retain 100 – 2.0 or 98.0% of the mass of Gumshoe Gold used: 0.98 x 470.5 = 461.1 gmass of Gumshoe Gold used: 0.98 x 470.5 = 461.1 g

Now for the other Saltwater Sludge masses:Now for the other Saltwater Sludge masses:

The 4.75 mm sieve will retain 100 – 67 or 33% of the The 4.75 mm sieve will retain 100 – 67 or 33% of the mass of Saltwater Sludge used: 0.33 x 13.2 = 4.4 gmass of Saltwater Sludge used: 0.33 x 13.2 = 4.4 gThe 2.36 mm sieve will retain 100 – 48 or 52% of the The 2.36 mm sieve will retain 100 – 48 or 52% of the mass of Saltwater Sludge used: 0.52 x 13.2 = 6.9 gmass of Saltwater Sludge used: 0.52 x 13.2 = 6.9 g

We can check these numbers by summing We can check these numbers by summing over each size and calculating the % passing over each size and calculating the % passing which should agree with the blend gradationwhich should agree with the blend gradation

PP12.712.7 = 100%x(1.00 – 98.8/1200) = 91.8% = 100%x(1.00 – 98.8/1200) = 91.8% (91.8%)(91.8%)PP9.59.5 = 100%x(1.00 – 312.0/1200) = 74.0% = 100%x(1.00 – 312.0/1200) = 74.0% (74.0%)(74.0%)PP4.754.75 = 100%x(1.00 – 432.6/1200) = 64.0% = 100%x(1.00 – 432.6/1200) = 64.0% (64.0%)(64.0%)PP2.362.36 = 100%x(1.00 – 468.0/1200) = 61.0% = 100%x(1.00 – 468.0/1200) = 61.0% (61.0%)(61.0%)The last column should (and does) sum to The last column should (and does) sum to the total specimen mass (1200 g)the total specimen mass (1200 g)

The final step(s) is to determine the mass of The final step(s) is to determine the mass of asphalt cement required for the 6 asphalt asphalt cement required for the 6 asphalt

contents listed.contents listed.

Since we’re using % of total mix, we have to Since we’re using % of total mix, we have to use a bit of algebra. (I won’t tell anyone if use a bit of algebra. (I won’t tell anyone if

you don’t.)you don’t.)

Let the Mass of AC required = MLet the Mass of AC required = Mb b and Pand Pbb = = %AC%AC

100%M1200

Mp

b

bb

bbb MM1200

100%

p )(

100%

p1M

100%

p(1200) b

bb

b

bb p-100%

p(1200)M

Applying this formula to each %AC:Applying this formula to each %AC:

63.2526316)(1200)(0.05.0-100

5.0(1200)Mb

69.8582011)(1200)(0.0

5.5-1005.5

(1200)Mb

76.6638298)(1200)(0.0

6.0-1006.0

(1200)Mb

83.4695187)(1200)(0.0

6.5-1006.5

(1200)Mb

90.3752688)(1200)(0.0

7.0-1007.0

(1200)Mb

97.3810811)(1200)(0.0

7.5-1007.5

(1200)Mb

00 9.49.4 98. 898. 8 312.0312.0 432.6432.6 468.0468.0 12001200

How much Homer’s Donut Crumbs will be How much Homer’s Donut Crumbs will be used?used?

PP16.016.0 = 100%x(1.00 – 9.4/1200) = 99.2% = 100%x(1.00 – 9.4/1200) = 99.2% (99.2%)(99.2%)PP19.019.0 = 100%x(1.00 – 0.0/1200) = 100.0% = 100%x(1.00 – 0.0/1200) = 100.0% (100.0%)(100.0%)For a specimen with 1200 g of aggregate we need For a specimen with 1200 g of aggregate we need 59.69% of 1200 g of all Homer’s Donut Crumb sizes = 59.69% of 1200 g of all Homer’s Donut Crumb sizes =

716.3 g716.3 g

The 9.5 mm sieve will retain 100 – 89 or 11% of the mass The 9.5 mm sieve will retain 100 – 89 or 11% of the mass of Saltwater Sludge used: 0.11 x 13.2 = 1.5 gof Saltwater Sludge used: 0.11 x 13.2 = 1.5 g


The 12.7 mm sieve will retain 100 – 98 or 2% of the mass The 12.7 mm sieve will retain 100 – 98 or 2% of the mass of Saltwater Sludge used: 0.02 x 13.2 = 0.3 gof Saltwater Sludge used: 0.02 x 13.2 = 0.3 g

Trial and ErrorTrial and Error Before the third lab, each group must Before the third lab, each group must perform its blending calculations.perform its blending calculations. The The first priorityfirst priority is making sure your sieve is making sure your sieve results are reasonable.results are reasonable. If you’ve mixed up any sizes, even if you If you’ve mixed up any sizes, even if you have a sieving error of 0%, you’ll still be have a sieving error of 0%, you’ll still be using garbage for data.using garbage for data.

The instructor will provide you with a set The instructor will provide you with a set that is free of calculation errors, based that is free of calculation errors, based on the data you submitted after you on the data you submitted after you submit the report for the first lab.submit the report for the first lab.

Trial and ErrorTrial and ErrorOnce you have a decent set of data, start Once you have a decent set of data, start an Excel spreadsheet using the following an Excel spreadsheet using the following format:format:

Sieve SizeSieve Size Spec LimitsSpec Limits

Size Size DesignatioDesignatio

nn

OpeninOpening g

(mm)(mm)

Lower Lower LimitLimit

Upper Upper LimitLimit

3/4"3/4" 19.119.1 100%100% 100%100%

1/2"1/2" 12.712.7 98%98% 100%100%

3/8"3/8" 9.529.52 75%75% 90%90%

#4#4 4.764.76 50%50% 60%60%

#8#8 2.382.38 36%36% 60%60%

#16#16 1.191.19 25%25% 58%58%

#30#30 0.590.59 16%16% 45%45%

#50#50 0.2970.297 7%7% 26%26%

#100#100 0.1490.149 3%3% 10%10%

#200#200 0.0740.074 0%0% 5%5%

Sieve Analysis ResultsSieve Analysis Results

CACA FAFA MFMF

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

86.0%86.0% 100.0100.0%%

100.0100.0%%

7.8%7.8% 96.3%96.3% 100.0100.0%%

1.1%1.1% 88.9%88.9% 100.0100.0%%

0.8%0.8% 80.7%80.7% 99.9%99.9%

0.5%0.5% 61.1%61.1% 99.6%99.6%

0.4%0.4% 30.4%30.4% 98.3%98.3%

0.4%0.4% 11.4%11.4% 88.2%88.2%

0.4%0.4% 5.4%5.4% 57.5%57.5%

Stock ProportionsStock Proportions

Blended Blended AggregateAggregate

52.0 52.0 46.0 46.0 2.0 2.0

CACA FAFA MFMF

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

44.7%44.7% 46.0%46.0% 2.0%2.0% 92.7%92.7% 2.70%2.70%

4.1%4.1% 44.3%44.3% 2.0%2.0% 50.4%50.4% 0.00%0.00%

0.6%0.6% 40.9%40.9% 2.0%2.0% 43.5%43.5% 0.00%0.00%

0.4%0.4% 37.1%37.1% 2.0%2.0% 39.5%39.5% 0.00%0.00%

0.3%0.3% 28.1%28.1% 2.0%2.0% 30.4%30.4% 0.00%0.00%

0.2%0.2% 14.0%14.0% 2.0%2.0% 16.2%16.2% 0.00%0.00%

0.2%0.2% 5.2%5.2% 1.8%1.8% 7.2%7.2% 0.00%0.00%

0.2%0.2% 2.5%2.5% 1.2%1.2% 3.8%3.8% 0.00%0.00%

Percent PassingPercent Passing

This section is for your sieve analysis This section is for your sieve analysis results.results.

The numbers shown are for illustration only (they The numbers shown are for illustration only (they weren’t that great)weren’t that great)This section is for the sieve sizes and specs.This section is for the sieve sizes and specs.These are the trial proportions for CA (PThese are the trial proportions for CA (PCACA)) & FA & FA

(P(PFAFA).).The stock proportions are found by multiplying The stock proportions are found by multiplying

each sieve result by the trial proportion.each sieve result by the trial proportion.

Eg.: 4.1% = 7.8% x 0.520Eg.: 4.1% = 7.8% x 0.520Eg.: 44.3% = 96.3% x 0.460Eg.: 44.3% = 96.3% x 0.460Eg.: 2.0% = 100% x 0.020Eg.: 2.0% = 100% x 0.020

The gradation of the blended aggregate is found by The gradation of the blended aggregate is found by adding the proportions of the materials:adding the proportions of the materials:

Eg.: 50.4% = 4.1% + 44.3% + Eg.: 50.4% = 4.1% + 44.3% + 2.0%2.0%

The last column shows the percent error if the The last column shows the percent error if the blend percent passing is outside the spec rangeblend percent passing is outside the spec range

Where does the 2.7% come from?Where does the 2.7% come from?The error in PThe error in P3/8”3/8” is 92.7% - 90% = 2.7% is 92.7% - 90% = 2.7%

% Out % Out of Specof Spec

TotalTotal

2.7%2.7%

The PThe PMFMF is calculated (100 – P is calculated (100 – PCACA – P – PFAFA))

Trial and ErrorTrial and ErrorOf course a grading plot makes the Of course a grading plot makes the numbers easier to understand:numbers easier to understand:



nn

OpeninOpening g

(mm)(mm)



3/4"3/4" 19.119.1 100%100% 100%100%

1/2"1/2" 12.712.7 98%98% 100%100%

3/8"3/8" 9.529.52 75%75% 90%90%

#4#4 4.764.76 50%50% 60%60%

#8#8 2.382.38 36%36% 60%60%

#16#16 1.191.19 25%25% 58%58%

#30#30 0.590.59 16%16% 45%45%

#50#50 0.2970.297 7%7% 26%26%

#100#100 0.1490.149 3%3% 10%10%

#200#200 0.0740.074 0%0% 5%5%


CACA FAFA MFMF

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

86.0%86.0% 100.0100.0%%

100.0100.0%%

7.8%7.8% 96.3%96.3% 100.0100.0%%

1.1%1.1% 88.9%88.9% 100.0100.0%%

0.8%0.8% 80.7%80.7% 99.9%99.9%

0.5%0.5% 61.1%61.1% 99.6%99.6%

0.4%0.4% 30.4%30.4% 98.3%98.3%

0.4%0.4% 11.4%11.4% 88.2%88.2%

0.4%0.4% 5.4%5.4% 57.5%57.5%



52.0 52.0 46.0 46.0 2.0 2.0

CACA FAFA MFMF

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

44.7%44.7% 46.0%46.0% 2.0%2.0% 92.7%92.7% 2.70%2.70%

4.1%4.1% 44.3%44.3% 2.0%2.0% 50.4%50.4% 0.00%0.00%

0.6%0.6% 40.9%40.9% 2.0%2.0% 43.5%43.5% 0.00%0.00%

0.4%0.4% 37.1%37.1% 2.0%2.0% 39.5%39.5% 0.00%0.00%

0.3%0.3% 28.1%28.1% 2.0%2.0% 30.4%30.4% 0.00%0.00%

0.2%0.2% 14.0%14.0% 2.0%2.0% 16.2%16.2% 0.00%0.00%

0.2%0.2% 5.2%5.2% 1.8%1.8% 7.2%7.2% 0.00%0.00%

0.2%0.2% 2.5%2.5% 1.2%1.2% 3.8%3.8% 0.00%0.00%


What would it look like before specifying What would it look like before specifying PPCACA and P and PFAFA??


TotalTotal

2.7%2.7%

Blended Aggregates

#200

0.149 0.297 0.59 1.19 2.38 4.76 9.52 12.7 19.10%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10 100

Sieve Opening (mm)

% Passin

g

High Spec Low Spec Blended Aggregate

0.074

#100 #50 #30 #16 #8 #4 3/ 8" 1/ 2" 3/ 4"

Trial and ErrorTrial and Error



nn

OpeninOpening g

(mm)(mm)



3/4"3/4" 19.119.1 100%100% 100%100%

1/2"1/2" 12.712.7 98%98% 100%100%

3/8"3/8" 9.529.52 75%75% 90%90%

#4#4 4.764.76 50%50% 60%60%

#8#8 2.382.38 36%36% 60%60%

#16#16 1.191.19 25%25% 58%58%

#30#30 0.590.59 16%16% 45%45%

#50#50 0.2970.297 7%7% 26%26%

#100#100 0.1490.149 3%3% 10%10%

#200#200 0.0740.074 0%0% 5%5%


CACA FAFA MFMF

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

86.0%86.0% 100.0100.0%%

100.0100.0%%

7.8%7.8% 96.3%96.3% 100.0100.0%%

1.1%1.1% 88.9%88.9% 100.0100.0%%

0.8%0.8% 80.7%80.7% 99.9%99.9%

0.5%0.5% 61.1%61.1% 99.6%99.6%

0.4%0.4% 30.4%30.4% 98.3%98.3%

0.4%0.4% 11.4%11.4% 88.2%88.2%

0.4%0.4% 5.4%5.4% 57.5%57.5%


What would it look like before specifying What would it look like before specifying PPCACA and P and PFAFA??



100.0 100.0

CACA FAFA MFMF

0.0%0.0% 0.0%0.0% 100.0%100.0% 100.0%100.0% 0.0%0.0%

0.0%0.0% 0.0%0.0% 100.0%100.0% 100.0%100.0% 0.0%0.0%

0.0%0.0% 0.0%0.0% 100.0%100.0% 100.0%100.0% 10.0%10.0%

0.0%0.0% 0.0%0.0% 100.0%100.0% 100.0%100.0% 40.0%40.0%

0.0%0.0% 0.0%0.0% 100.0%100.0% 100.0%100.0% 40.0%40.0%

0.0%0.0% 0.0%0.0% 99.9%99.9% 99.9%99.9% 41.9%41.9%

0.0%0.0% 0.0%0.0% 99.6%99.6% 99.6%99.6% 54.6%54.6%

0.0%0.0% 0.0%0.0% 98.3%98.3% 98.3%98.3% 72.3%72.3%

0.0%0.0% 0.0%0.0% 88.2%88.2% 88.2%88.2% 78.2%78.2%

0.0%0.0% 0.0%0.0% 57.5%57.5% 57.5%57.5% 52.5%52.5%

Now you’re looking at the grading curve Now you’re looking at the grading curve for the mineral filler (Pfor the mineral filler (PMFMF = 100%) = 100%)

If you specified 100% CA you’d see the CA grading curve, If you specified 100% CA you’d see the CA grading curve, or 100% FA would get you the FA grading curveor 100% FA would get you the FA grading curveTypically you’d set the PTypically you’d set the PMFMF to a reasonable to a reasonable number (say number (say 4%4%) and set P) and set PCACA = P = PFA FA (= say (= say 48%48%))


TotalTotal

390%390%

Blended Aggregates

#200

0.149 0.297 0.59 1.19 2.38 4.76 9.52 12.7 19.10%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10 100

Sieve Opening (mm)

% Passin

g


0.074

#100 #50 #30 #16 #8 #4 3/ 8" 1/ 2" 3/ 4"




nn

OpeninOpening g

(mm)(mm)



3/4"3/4" 19.119.1 100%100% 100%100%

1/2"1/2" 12.712.7 98%98% 100%100%

3/8"3/8" 9.529.52 75%75% 90%90%

#4#4 4.764.76 50%50% 60%60%

#8#8 2.382.38 36%36% 60%60%

#16#16 1.191.19 25%25% 58%58%

#30#30 0.590.59 16%16% 45%45%

#50#50 0.2970.297 7%7% 26%26%

#100#100 0.1490.149 3%3% 10%10%

#200#200 0.0740.074 0%0% 5%5%


CACA FAFA MFMF

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

86.0%86.0% 100.0100.0%%

100.0100.0%%

7.8%7.8% 96.3%96.3% 100.0100.0%%

1.1%1.1% 88.9%88.9% 100.0100.0%%

0.8%0.8% 80.7%80.7% 99.9%99.9%

0.5%0.5% 61.1%61.1% 99.6%99.6%

0.4%0.4% 30.4%30.4% 98.3%98.3%

0.4%0.4% 11.4%11.4% 88.2%88.2%

0.4%0.4% 5.4%5.4% 57.5%57.5%


Typically you’d set the PTypically you’d set the PMFMF to a reasonable to a reasonable number (say number (say 4%4%) and set P) and set PCACA = P = PFA FA (= say (= say 48%48%))



48.0 48.0 48.0 48.0 4.0 4.0

CACA FAFA MFMF

48.0%48.0% 48.0%48.0% 4.0%4.0% 100.0%100.0% 0.0%0.0%

48.0%48.0% 48.0%48.0% 4.0%4.0% 100.0%100.0% 0.0%0.0%

41.3%41.3% 48.0%48.0% 4.0%4.0% 93.3%93.3% 3.3%3.3%

3.7%3.7% 46.2%46.2% 4.0%4.0% 54.0%54.0% 0.0%0.0%

0.5%0.5% 42.7%42.7% 4.0%4.0% 47.2%47.2% 0.0%0.0%

0.4%0.4% 38.7%38.7% 4.0%4.0% 43.1%43.1% 0.0%0.0%

0.2%0.2% 29.3%29.3% 4.0%4.0% 33.6%33.6% 0.0%0.0%

0.2%0.2% 14.6%14.6% 3.9%3.9% 18.7%18.7% 0.0%0.0%

0.2%0.2% 5.5%5.5% 3.5%3.5% 9.2%9.2% 0.0%0.0%

0.2%0.2% 2.6%2.6% 2.3%2.3% 5.1%5.1% 0.1%0.1%

This curve is a bit too far to the fine end indicating that This curve is a bit too far to the fine end indicating that more coarse is needed and less fine: try 4% more CA and more coarse is needed and less fine: try 4% more CA and 2% less FA to drop the No 200 to about midrange2% less FA to drop the No 200 to about midrange


TotalTotal

3.4%3.4%

Blended Aggregates

#200

0.149 0.297 0.59 1.19 2.38 4.76 9.52 12.7 19.10%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10 100

Sieve Opening (mm)

% Passin

g


0.074

#100 #50 #30 #16 #8 #4 3/ 8" 1/ 2" 3/ 4"




nn

OpeninOpening g

(mm)(mm)



3/4"3/4" 19.119.1 100%100% 100%100%

1/2"1/2" 12.712.7 98%98% 100%100%

3/8"3/8" 9.529.52 75%75% 90%90%

#4#4 4.764.76 50%50% 60%60%

#8#8 2.382.38 36%36% 60%60%

#16#16 1.191.19 25%25% 58%58%

#30#30 0.590.59 16%16% 45%45%

#50#50 0.2970.297 7%7% 26%26%

#100#100 0.1490.149 3%3% 10%10%

#200#200 0.0740.074 0%0% 5%5%


CACA FAFA MFMF

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

100.0100.0%%

86.0%86.0% 100.0100.0%%

100.0100.0%%

7.8%7.8% 96.3%96.3% 100.0100.0%%

1.1%1.1% 88.9%88.9% 100.0100.0%%

0.8%0.8% 80.7%80.7% 99.9%99.9%

0.5%0.5% 61.1%61.1% 99.6%99.6%

0.4%0.4% 30.4%30.4% 98.3%98.3%

0.4%0.4% 11.4%11.4% 88.2%88.2%

0.4%0.4% 5.4%5.4% 57.5%57.5%



52.0 52.0 46.0 46.0 2.0 2.0

CACA FAFA MFMF

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

52.0%52.0% 46.0%46.0% 2.0%2.0% 100.0%100.0% 0.00%0.00%

44.7%44.7% 46.0%46.0% 2.0%2.0% 92.7%92.7% 2.70%2.70%

4.1%4.1% 44.3%44.3% 2.0%2.0% 50.4%50.4% 0.00%0.00%

0.6%0.6% 40.9%40.9% 2.0%2.0% 43.5%43.5% 0.00%0.00%

0.4%0.4% 37.1%37.1% 2.0%2.0% 39.5%39.5% 0.00%0.00%

0.3%0.3% 28.1%28.1% 2.0%2.0% 30.4%30.4% 0.00%0.00%

0.2%0.2% 14.0%14.0% 2.0%2.0% 16.2%16.2% 0.00%0.00%

0.2%0.2% 5.2%5.2% 1.8%1.8% 7.2%7.2% 0.00%0.00%

0.2%0.2% 2.5%2.5% 1.2%1.2% 3.8%3.8% 0.00%0.00%


Adding more coarse would drop the curve below the Adding more coarse would drop the curve below the lower spec for the No. 4 sieve but more coarse would be lower spec for the No. 4 sieve but more coarse would be needed to get the curve below the high limit for the 3/8” needed to get the curve below the high limit for the 3/8” sievesieve

In this instance the CA PIn this instance the CA P3/8”3/8” is too close to the upper spec is too close to the upper speca coarser CA (1/2”) would be required to meet the speca coarser CA (1/2”) would be required to meet the spec

After a bit more tinkering the error on the After a bit more tinkering the error on the 3/8” sieve3/8” sieve could not be reduced below could not be reduced below 2.7%2.7%. This was the best I . This was the best I could do.could do.

……and the final gradation curve...and the final gradation curve...


TotalTotal

2.7%2.7%

Blended Aggregates

#200

0.149 0.297 0.59 1.19 2.38 4.76 9.52 12.7 19.10%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.01 0.1 1 10 100

Sieve Opening (mm)

% Passin

g


0.074

#100 #50 #30 #16 #8 #4 3/ 8" 1/ 2" 3/ 4"


It takes a lot of work to get the It takes a lot of work to get the gradation plot to look like the ones gradation plot to look like the ones shown in this presentationshown in this presentationA step-by-step example of how A step-by-step example of how this is done can be found in the this is done can be found in the ““Graphing StandardsGraphing Standards” posted on ” posted on my website home pagemy website home page

blending of aggregates warning: if your mind hasn’t yet blended with “gradation of aggregates”...

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