1. BLENDING OF AGGREGATES Warning: If your mind hasn’t yet blended with “Gradation of Aggregates” (posted on the instructor’s website) then you’ll probably struggle with this presentation. You should also have “Assignment 1 Example” at the ready.

2. What is asphalt concrete? Basically, its just aggregate… …coated with asphalt cement… …and then compacted. There are 3 basic elements to the compacted mix… 1. Aggregate Particles 2. Asphalt Cement 3. Air Voids Not all the asphalt cement ends up coating the aggregate particles… …some is absorbed into the water-permeable voids within the aggregate particles.

3. VMA Are you a member?Of what…the “Virile Men’s Association”?… “Voluptuous Mama’s of America”? Voids in the Mineral Aggregate … “Volatile Mercenaries of Alberta”?… so what’s it mean?Any help?Well, VMA is one of the most important properties of an asphalt paving mix. Firstly, here’s a representation of a compacted paving mix. There’s stone, and sand particles all coated with asphalt cement and there’s a few air voids (the white spaces). If we removed all the asphalt cement but the aggregate stayed put it would look like this: The space occupied by the asphalt cement and air voids (not including the asphalt cement absorbed) is voids in the mineral aggregate. This diagram shows the mix without the aggregate…there’s just the asphalt cement and air voids. V mb is the Bulk Volume of the Mix In mathematical terms… V vma = V a + V be V vma is the Volume of Voids in the Mineral Aggregate V a is the Volume of Air Voids in the Mix V be is the Effective Volume of Asphalt Cement in the Mix

4. VMA and Dense Graded Aggregate Once the mix has been compacted to its densest state then there’s nowhere for particles to go when subjected to traffic. Densely graded mixes are going to offer the greatest resistance to loads because they minimize the void space and therefore the movement paths within the mix. where pi = total % passing sieve size i di = width of opening of sieve size i D = largest size (sieve opening) in gradation Mathematically, Fuller Grading Curves offer the maximum density and minimum voids:

5. When plotted they look like this: These can be used to set grading limits (“specs”) as with the red and green dashed curves. Notice that the High Spec is above the ⅜” Fuller Curve below the #8 sieve This allows for a reduction in the number of finer sizes which will in turn allow an increase in voids But why would we want to increase the voids?The goal is to blend the stock aggregates to produce a blend that falls between the two limits

6. This is a compromise between stability (lower with higher voids) and durability. Experience has shown that asphalt mixes need to have between 3% and 5% air voids If the voids are too low, then asphalt cement can bleed to the surface in hot weather. Its analogous to Portland Cement Concrete and air entraining to match exposure to the environment. So minimum VMA values are specified for different Nominal Maximum Particle Sizes

7. Blending Stock Aggregates Normally, aggregate stocks come from different sources: 1. stone comes from crushed bedrock, 2. sand comes from natural deposits, 3. mineral filler comes from the bottom of the crusher (dust) There are two basic approaches: 1.S imultaneous equations (used on Assignment 1) 2.T rial and Error (spreadsheet, used for lab)

8. Assignment 1 Example Two questions using simultaneous equations. 1. Produce a blend of the given aggregates that results in 28.0% passing the 0.6 mm sieve. MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Cyclone A Crushed 100.0%100.0%100.0%90.0%59.0%16.0%3.2%2.0%0.5%0.0%0.0%0.0% Newmarket Sand 100.0%100.0%100.0%100.0%100.0%96.0%82.0%73.0%51.0%36.0%21.0%9.2% DFC DUST 2.0%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 condition given is for the 0.6 mm sieve. Let C be the fraction of Cyclone A Crushed and N be the fraction of Newmarket Sand. When we apply the proportions to find the percent passing the 0.6 mm sieve for the blend, we get: 0.005C + 0.51N + 1.00(.02) = 0.28 1 The second condition is that all the proportions must sum to 1: or 0.005C + 0.51N = 0.26 C + N = 0.98 2 Multiply equation 2 by 0.005 then subtract 2 from 1 0.005C + 0.005N = 0.0049 (0.51 - 0.005)N = 0.26 - 0.0049(0.505)N = 0.2551N = 0.505149 ≈ 50.51%50.51%Therefore, C = 100% - 50.51% - 2% = 47.49%47.49%C + N + 0.02 = 1.0

9. Assignment 1 Example: Q 1 Cont’d Now for the blended gradation Before we start to crank off the blend, let’s check the proportions by finding P0.6 This is the percent passing the 0.6 mm sieve given for condition 1. Now we do the same for all the other sizes… P0.6 = 0.4749x0.5% + 0.5051x51.0% + 0.02x100.0% = 27.9976% P0.6 ≈ 28.0% SIEVE SIZE (mm): 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 BLEND: SPECIFICATION Low:100.0%100.0%100.0%80.0%70.0%50.0%35.0%25.0%18.0%13.0%8.0%4.0% High:100.0%100.0%100.0%100.0%90.0%70.0%50.0%40.0%29.0%23.0%16.0%10.0% TARGET:100.0%100.0%100.0%90.0%80.0%60.0%42.5%32.5%23.5%18.0%12.0%7.0% MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Cyclone A Crushed 47.49%100.0%100.0%100.0%90.0%59.0%16.0%3.2%2.0%0.5%0.0%0.0%0.0% Newmarket Sand 50.51%100.0%100.0%100.0%100.0%100.0%96.0%82.0%73.0%51.0%36.0%21.0%9.2% DFC DUST 2.0%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% 80.5% 58.1% 44.9% 39.8% 28.0%20.2% 6.6%P25.4 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0%P19.0 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0% P16.0 = 0.4749x100.0%+0.5051x100.0%+0.02x100.0% = 100.0%P12.7 = 0.4749x90.0%+0.5051x100.0%+0.02x100.0% = 95.251% P12.7 ≈ 95.3% P9.5 = 0.4749x59.0% + 0.5051x100.0% + 0.02x100.0% = 80.529% P9.5 ≈ 80.5% P4.75 = 0.4749x16.0% + 0.5051x96.0% + 0.02x100.0% = 58.088% P4.75 ≈ 58.1% P2.36 = 0.4749x3.2% + 0.5051x82.0% + 0.02x100.0% = 44.938% P2.36 ≈ 44.9% P1.18 = 0.4749x2.0% + 0.5051x73.0% + 0.02x100.0% = 39.822% P1.18 ≈ 39.8% P0.3 = 0.4749x0.0% + 0.5051x36.0% + 0.02x100.0% = 20.184% P0.3 ≈ 20.2% P0.075 = 0.4749x0.0% + 0.5051x9.2% + 0.02x100.0% = 6.647% P0.075 ≈ 6.6% That’s the one all right! So we’re good to go.12.6P0.150 = 0.4749x0.0% + 0.5051x21.0% + 0.02x100.0% = 12.607% P0.150 ≈ 12.6%

10. Assignment 1 Example: Q1 Finale MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Cyclone A Crushed 47.49%100.0%100.0%100.0%90.0%59.0%16.0%3.2%2.0%0.5%0.0%0.0%0.0% Newmarket Sand 50.51%100.0%100.0%100.0%100.0%100.0%96.0%82.0%73.0%51.0%36.0%21.0%9.2% DFC DUST 2.0%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 blend the sieved stock for individual 1210 g specimens. Any sizes with 100% passing will retain none of the material. Hence 0 g are recorded for all these sizes. These values represent the cumulative mass (the scale reading) after adding the required mass of each stock sieve size First, how much Cyclone A will be used? For a specimen with 1210 g of aggregate we need 47.49% of 1210 g of all Cyclone A sizes = 574.63 g CUMULATIVE WEIGHT CUMULATIVE WEIGHT 19.016.012.79.54.752.36 Passing 2.36 Passing 2.36 Cyclone A Crushed Cyclone A Crushed 47.49% (% USED) Newmarket Sand Newmarket Sand 50.51% (% USED) DFC DUST DFC DUST 2.0 (% USED) Total Specimen Mass (g): 1210 % AC Weight (g) (g)4.3% 4.8% 5.3% 5.8% 6.3% 6.8% 574.63 611.17 24.2 0 0 00 0 0 00 0 0 0 0 57.5235.6482.7 556.2Now, how much Newmarket Sand will be used? For a specimen with 1210 g of aggregate we need 50.51% of 1210 g of all Newmarket Sand sizes = 611.17 g And, how much DFC Dust will be used? For a specimen with 1210 g of aggregate we need 2% of 1210 g for DFC Dust = 24.2 g24.4 110.0 507.1 666.21210 54.4 61.0 67.7 74.5 81.4 88.3Now for the other Cyclone A masses: 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 g 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 g 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 g 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 g Now for the other Newmarket Sand masses: 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 g 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 g We can check these numbers by summing over each size and calculating the % passing which should agree with the blend gradation57.5235.6P12.7 = 100%x(1.00 – 57.5/1210) = 95.25% (95.3%)P9.5 = 100%x(1.00 – 235.6/1210) = 80.5% (80.5%)P4.75 = 100%x(1.00 – 507.1/1210) = 58.1% (58.1%)P2.36 = 100%x(1.00 – 666.2/1210) = 44.9% (44.9%)The last column should (and does) sum to the total specimen mass (1210 g) The final step(s) is to determine the mass of asphalt cement required for the 6 asphalt contents listed. Since we’re using % of total mix, we have to use a bit of algebra. (I won’t tell anyone if you don’t.) Let the Mass of AC required = Mb and Pb = %AC Applying this formula to each %AC:0 0P16.0 = 100%x(1.00 – 0/1210) = 100.0% (100.0%)P19.0 = 100%x(1.00 – 0/1210) = 100.0% (100.0%)

11. Assignment 1 Example : Q 2 2. 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. MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Gumshoe Gold 100.0%100.0%98.0%79.0%34.0%9.0%2.0%0.0%0.0%0.0%0.0%0.0% Saltwater Sludge 100.0%100.0%100.0%98.0%89.0%67.0%48.0%21.0%8.0%1.5%1.0%0.0% H's Donut Crumbs 100.0%100.0%100.0%100.0%100.0%100.0%100.0%100.0%53.0%26.0%5.0%2.0% The conditions given are for the 9.5 mm & 2.36 mm sieves. Let G be the fraction of Gumshoe Gold, S be the fraction of Saltwater Sludge and H be the fraction of Homer’s Donut Crumbs. Applying the first condition for P9.5: 1 The third condition is that all the proportions must sum to 1: 0.34G + 0.89S + H = 0.74 2 G + S + H = 1.00 G = 0.392098555 ≈ 39.21%1.10%and H = 0.596856414% ≈ 59.69%39.21% 59.69%0.02G + 0.48S + H = 0.61 3 S = 0.011045029 ≈ 1.10% The second condition for P2.36: Using the Sharp EL546W Calculator, Mode 21: for instructions, visit http://math.mohawkcollege.ca/calc.asp

12. Assignment 1 Example: Q 2 Cont’d Now for the blended gradation Before we start to crank off the blend, let’s check the proportions by finding P9.5 and P2.36 Now we do the same for all the other sizes… P0.6 = 0.3921x0.0% + 0.0110x8.0% + 0.5969x53.0% = 31.7237% P0.6 ≈ 31.7% SIEVE SIZE (mm): 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 BLEND: SPECIFICATION Low:100.0%100.0%90.0%75.0%65.0%55.0%40.0%28.0%15.0%5.0%2.0%0.0% High:100.0%100.0%100.0%95.0%85.0%75.0%70.0%60.0%35.0%23.0%12.0%5.0% TARGET:100.0%100.0%95.0%85.0%75.0%65.0%55.0%44.0%25.0%14.0%7.0%2.5% MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Gumshoe Gold 39.21%100.0%100.0%98.0%79.0%34.0%9.0%2.0%0.0%0.0%0.0%0.0%0.0% Saltwater Sludge 1.10%100.0%100.0%100.0%98.0%89.0%67.0%48.0%21.0%8.0%1.5%1.0%0.0% H's Donut Crumbs 59.69%100.0%100.0%100.0%100.0%100.0%100.0%100.0%100.0%53.0%26.0%5.0%2.0% 100.0%100.0%99.2%91.7% 74.0% 64.0% 61.0% 59.9% 31.7%15.5% 1.2%P25.4 = 0.3921x100% + 0.0110x100.0% + 0.5969x100% = 100%P19.0 = 0.3921x100% + 0.0110x100% + 0.5969x100% = 100% P16.0 = 0.3921x98.0% + 0.0110x100% + 0.57969x100% = 99.2158% P16.0 ≈ 99.2% P12.7 = 0.3921x79.0% + 0.0110x98.0% + 0.5969x100 = 91.7439% P12.7 ≈ 91.7% P9.5 = 0.3921x34.0% + 0.0110x89.0% + 0.5969x100.0% = 74.0004% P9.5 ≈ 74.0% P4.75 = 0.3921x9.0% + 0.0110x67.0% + 0.5969x100.0% = 63.9559% P4.75 ≈ 64.0% P2.36 = 0.3921x2.0% + 0.0110x48.0% + 0.5969x100.0% = 61.0022% P2.36 ≈ 61.0% P1.18 = 0.3921x0.0% + 0.0110x21.0% + 0.5969x100% = 59.921% P1.18 ≈ 59.9% P0.3 = 0.3921x0.0% + 0.0110x1.5% + 0.5969x26.0% = 15.5359% P0.3 ≈ 15.5% P0.075 = 0.3921x0.0% + 0.0110x0.0% + 0.5969x2.0% = 1.1938% P0.075 ≈ 1.2% Got ‘em both! So we’re good to go.3.0P0.150 = 0.3921x0.0% + 0.0110x1.0% + 0.5969x5.0% = 2.9955% P0.150 ≈ 3.0%

13. Assignment 1 Example: Q2 Finale MATERIAL % Used 25.419.016.012.79.54.752.361.180.6000.3000.1500.075 Gumshoe Gold 39.21%100.0%100.0%98.0%79.0%34.0%9.0%2.0%0.0%0.0%0.0%0.0%0.0% Saltwater Sludge 1.10%100.0%100.0%100.0%98.0%89.0%67.0%48.0%21.0%8.0%1.5%1.0%0.0% H's Donut Crumbs 59.69%100.0%100.0%100.0%100.0%100.0%100.0%100.0%100.0%53.0%26.0%5.0%2.0% The table above is used to weigh out and blend the sieved stock for individual 1200 g specimens. Any sizes with 100% passing will retain none of the material. Hence 0 g are recorded for all these sizes. These values represent the cumulative mass (the scale reading) after adding the required mass of each stock sieve size First, how much Gumshoe Gold will be used? For a specimen with 1200 g of aggregate we need 39.21% of 1200 g of all Gumshoe Gold sizes = 470.5 g CUMULATIVE WEIGHT CUMULATIVE WEIGHT 19.016.012.79.54.752.36 Passing 2.36 Passing 2.36 Gumshoe Gold Gumshoe Gold 39.21% (% USED) Saltwater Sludge 1.10% (% USED) Homer's Donut Crumbs Homer's Donut Crumbs 59.69% (% USED) Total Specimen Mass (g): 1200 % AC Weight (g) (g)5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 470.5 13.2 716.3 09.4 0 0 0.3 1.5 0 0 0 00 0 98.8310.5428.2461.1Now, how much Saltwater Sludge will be used? For a specimen with 1200 g of aggregate we need 1.10% of 1200 g of all Saltwater Sludge sizes = 13.2 g4.46.9 63.2 69.8 76.6 83.4 90.3 97.3Now for the other Gumshoe Gold masses: 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 g 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 g The 4.75 mm sieve will retain 100 – 9 or 91% of the mass of Gumshoe Gold used: 0.91 x 470.5 = 428.2 g 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 g Now for the other Saltwater Sludge masses: 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 g 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 g We can check these numbers by summing over each size and calculating the % passing which should agree with the blend gradation P12.7 = 100%x(1.00 – 98.8/1200) = 91.8% (91.8%)P9.5 = 100%x(1.00 – 312.0/1200) = 74.0% (74.0%)P4.75 = 100%x(1.00 – 432.6/1200) = 64.0% (64.0%)P2.36 = 100%x(1.00 – 468.0/1200) = 61.0% (61.0%)The last column should (and does) sum to the total specimen mass (1200 g) The final step(s) is to determine the mass of asphalt cement required for the 6 asphalt contents listed. Since we’re using % of total mix, we have to use a bit of algebra. (I won’t tell anyone if you don’t.) Let the Mass of AC required = Mb and Pb = %AC Applying this formula to each %AC:09.4 98. 8 312.0432.6468.01200How much Homer’s Donut Crumbs will be used? P16.0 = 100%x(1.00 – 9.4/1200) = 99.2% (99.2%)P19.0 = 100%x(1.00 – 0.0/1200) = 100.0% (100.0%)For a specimen with 1200 g of aggregate we need 59.69% of 1200 g of all Homer’s Donut Crumb sizes = 716.3 g 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 g The 16.0 mm sieve will retain 100 – 98 or 2% of the mass of Gumshoe Gold used: 0.02 x 470.5 = 9.4 g 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 g

14. Trial and Error  B B B Before the third lab, each group must perform its blending calculations.  T T T The first priority is making sure your sieve results are reasonable.  I I I If you’ve mixed up any sizes, even if you have a sieving error of 0%, you’ll still be using garbage for data. TTTThe instructor will provide you with a set that is free of calculation errors, based on the data you submitted after you submit the report for the first lab.

15. OOOOnce you have a decent set of data, start an Excel spreadsheet using the following format: Sieve Size Spec Limits Size Designation Opening (mm) Lower Limit Upper Limit 3/4"19.1100%100% 1/2"12.798%100% 3/8"9.5275%90% #44.7650%60% #82.3836%60% #161.1925%58% #300.5916%45% #500.2977%26% #1000.1493%10% #2000.0740%5% Sieve Analysis Results CAFAMF 100.0%100.0%100.0% 100.0%100.0%100.0% 86.0%100.0%100.0% 7.8%96.3%100.0% 1.1%88.9%100.0% 0.8%80.7%99.9% 0.5%61.1%99.6% 0.4%30.4%98.3% 0.4%11.4%88.2% 0.4%5.4%57.5% Stock Proportions Blended Aggregate 52.046.02.0 CAFAMF 52.0%46.0%2.0%100.0%0.00% 52.0%46.0%2.0%100.0%0.00% 44.7%46.0%2.0%92.7%2.70% 4.1%44.3%2.0%50.4%0.00% 0.6%40.9%2.0%43.5%0.00% 0.4%37.1%2.0%39.5%0.00% 0.3%28.1%2.0%30.4%0.00% 0.2%14.0%2.0%16.2%0.00% 0.2%5.2%1.8%7.2%0.00% 0.2%2.5%1.2%3.8%0.00% Percent Passing This section is for your sieve analysis results. The numbers shown are for illustration only (they weren’t that great) This section is for the sieve sizes and specs. These are the trial proportions for CA (PCA) & && & FA (PFA). The stock proportions are found by multiplying each sieve result by the trial proportion. Eg.: 4.1% = 7.8% x 0.520Eg.: 44.3% = 96.3% x 0.460Eg.: 2.0% = 100% x 0.020 The gradation of the blended aggregate is found by adding the proportions of the materials: Eg.: 50.4% = 4.1% + 44.3% + 2.0% The last column shows the percent error if the blend percent passing is outside the spec range Where does the 2.7% come from? The error in P3/8” is 92.7% - 90% = 2.7% % Out of Spec Total 2.7% The PMF is calculated (100 – PCA – PFA)

16. Trial and Error OOOOf course a grading plot makes the numbers easier to understand: Sieve Size Spec Limits Size Designation Opening (mm) Lower Limit Upper Limit 3/4"19.1100%100% 1/2"12.798%100% 3/8"9.5275%90% #44.7650%60% #82.3836%60% #161.1925%58% #300.5916%45% #500.2977%26% #1000.1493%10% #2000.0740%5% Sieve Analysis Results CAFAMF 100.0%100.0%100.0% 100.0%100.0%100.0% 86.0%100.0%100.0% 7.8%96.3%100.0% 1.1%88.9%100.0% 0.8%80.7%99.9% 0.5%61.1%99.6% 0.4%30.4%98.3% 0.4%11.4%88.2% 0.4%5.4%57.5% Stock Proportions Blended Aggregate 52.046.02.0 CAFAMF 52.0%46.0%2.0%100.0%0.00% 52.0%46.0%2.0%100.0%0.00% 44.7%46.0%2.0%92.7%2.70% 4.1%44.3%2.0%50.4%0.00% 0.6%40.9%2.0%43.5%0.00% 0.4%37.1%2.0%39.5%0.00% 0.3%28.1%2.0%30.4%0.00% 0.2%14.0%2.0%16.2%0.00% 0.2%5.2%1.8%7.2%0.00% 0.2%2.5%1.2%3.8%0.00% Percent Passing WWWWhat would it look like before specifying PCA and PFA? % Out of Spec Total 2.7%

17. Trial and Error Sieve Size Spec Limits Size Designation Opening (mm) Lower Limit Upper Limit 3/4"19.1100%100% 1/2"12.798%100% 3/8"9.5275%90% #44.7650%60% #82.3836%60% #161.1925%58% #300.5916%45% #500.2977%26% #1000.1493%10% #2000.0740%5% Sieve Analysis Results CAFAMF 100.0%100.0%100.0% 100.0%100.0%100.0% 86.0%100.0%100.0% 7.8%96.3%100.0% 1.1%88.9%100.0% 0.8%80.7%99.9% 0.5%61.1%99.6% 0.4%30.4%98.3% 0.4%11.4%88.2% 0.4%5.4%57.5% Percent Passing WWWWhat would it look like before specifying PCA and PFA? Stock Proportions Blended Aggregate 100.0 CAFAMF 0.0%0.0%100.0%100.0%0.0% 0.0%0.0%100.0%100.0%0.0% 0.0%0.0%100.0%100.0%10.0% 0.0%0.0%100.0%100.0%40.0% 0.0%0.0%100.0%100.0%40.0% 0.0%0.0%99.9%99.9%41.9% 0.0%0.0%99.6%99.6%54.6% 0.0%0.0%98.3%98.3%72.3% 0.0%0.0%88.2%88.2%78.2% 0.0%0.0%57.5%57.5%52.5% NNNNow you’re looking at the grading curve for the mineral filler (PMF = 100%) IIIIf you specified 100% CA you’d see the CA grading curve, or 100% FA would get you the FA grading curve TTTTypically you’d set the PMF to a reasonable number (say 4%) and set PCA = PFA (= say 48%) % Out of Spec Total 390%

18. Trial and Error Sieve Size Spec Limits Size Designation Opening (mm) Lower Limit Upper Limit 3/4"19.1100%100% 1/2"12.798%100% 3/8"9.5275%90% #44.7650%60% #82.3836%60% #161.1925%58% #300.5916%45% #500.2977%26% #1000.1493%10% #2000.0740%5% Sieve Analysis Results CAFAMF 100.0%100.0%100.0% 100.0%100.0%100.0% 86.0%100.0%100.0% 7.8%96.3%100.0% 1.1%88.9%100.0% 0.8%80.7%99.9% 0.5%61.1%99.6% 0.4%30.4%98.3% 0.4%11.4%88.2% 0.4%5.4%57.5% Percent Passing TTTTypically you’d set the PMF to a reasonable number (say 4%) and set PCA = PFA (= say 48%) Stock Proportions Blended Aggregate 48.048.04.0 CAFAMF 48.0%48.0%4.0%100.0%0.0% 48.0%48.0%4.0%100.0%0.0% 41.3%48.0%4.0%93.3%3.3% 3.7%46.2%4.0%54.0%0.0% 0.5%42.7%4.0%47.2%0.0% 0.4%38.7%4.0%43.1%0.0% 0.2%29.3%4.0%33.6%0.0% 0.2%14.6%3.9%18.7%0.0% 0.2%5.5%3.5%9.2%0.0% 0.2%2.6%2.3%5.1%0.1% TTT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 2% less FA to drop the No 200 to about midrange % Out of Spec Total 3.4%

19. Trial and Error Sieve Size Spec Limits Size Designation Opening (mm) Lower Limit Upper Limit 3/4"19.1100%100% 1/2"12.798%100% 3/8"9.5275%90% #44.7650%60% #82.3836%60% #161.1925%58% #300.5916%45% #500.2977%26% #1000.1493%10% #2000.0740%5% Sieve Analysis Results CAFAMF 100.0%100.0%100.0% 100.0%100.0%100.0% 86.0%100.0%100.0% 7.8%96.3%100.0% 1.1%88.9%100.0% 0.8%80.7%99.9% 0.5%61.1%99.6% 0.4%30.4%98.3% 0.4%11.4%88.2% 0.4%5.4%57.5% Stock Proportions Blended Aggregate 52.046.02.0 CAFAMF 52.0%46.0%2.0%100.0%0.00% 52.0%46.0%2.0%100.0%0.00% 44.7%46.0%2.0%92.7%2.70% 4.1%44.3%2.0%50.4%0.00% 0.6%40.9%2.0%43.5%0.00% 0.4%37.1%2.0%39.5%0.00% 0.3%28.1%2.0%30.4%0.00% 0.2%14.0%2.0%16.2%0.00% 0.2%5.2%1.8%7.2%0.00% 0.2%2.5%1.2%3.8%0.00% Percent Passing AAAAdding more coarse would drop the curve below the 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” sieve IIIIn this instance the CA P3/8” is too close to the upper spec aaaa coarser CA (1/2”) would be required to meet the spec AAAAfter a bit more tinkering the error on the 3/8” sieve could not be reduced below 2.7%. This was the best I could do. …………and the final gradation curve... % Out of Spec Total 2.7%

20. Trial and Error  I I I It takes a lot of work to get the gradation plot to look like the ones shown in this presentation AAAA step-by-step example of how this is done can be found in the “Graphing Standards” posted on my website home page