--- title: "Mixing three gravel quarries to specification" subject: "Transportation Engineering I" chapter: 6 key: "semester_6/transportation_engineering_i:n-65k-gravel-blend" source: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-65k-gravel-blend site: BCT Engineering --- # Mixing three gravel quarries to specification Transportation Engineering I · Chapter 6: Highway Materials - Asked in: 2065 Kartik (old course), 10 marks - Video: [#highways, Three Methods of Proportioning of Aggregates to get the desired grading,](https://www.youtube.com/watch?v=U_lgHXkFnvE) — Transportation Engg Talks | Satish IITR - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/transportation_engineering_i/n-65k-gravel-blend - Whole chapter: https://www.bctengineer.com/md/semester_6/transportation_engineering_i/chapter-6 ## Question The table below gives the sieve analysis results of three gravel quarries under investigation. Calculate the mixing properties to meet the given gradation specification. | Sieve size (mm) | Quarry A (% passing) | Quarry B (% passing) | Quarry C (% passing) | Specification | |---|---|---|---|---| | 25.4 | 100 | 100 | 100 | 100 | | 12.7 | 100 | 100 | 95 | 90-100 | | 4.76 | 100 | 100 | 55 | 60-75 | | 1.18 | 100 | 65 | 30 | 40-55 | | 0.30 | 100 | 25 | 23 | 20-35 | | 0.15 | 75 | 18 | 9 | 12-22 | | 0.075 | 40 | 3 | 3 | 5-10 | ## Short answer Using control sieves, a trial proportion of Quarry A 10%, Quarry B 25%, Quarry C 65% is taken. The blend yields 100, 96.8, 70.8, 45.8, 31.2, 17.9, and 6.7% passing on the specified sieves, all within specification limits. ## Answer **Aim:** find the proportions $a$, $b$, $c$ (in %) of quarries A, B and C, with $a + b + c = 100$, so that the combined % passing at every sieve falls within the specification. The mix passing at a sieve is $$ P_{mix} = \frac{a\,P_A + b\,P_B + c\,P_C}{100} $$ Assumption: the "Specification" column gives the allowable range of % passing; the target is near the middle of each range. #### Step 1: Decide the main fraction by control sieves - Quarry A is a fine material (100% passes even 0.30 mm, and 40% passes 0.075 mm). Quarry B is a sand (all of it passes 4.76 mm, with few fines). Quarry C is the coarsest (gravel). - **4.76 mm sieve:** only C has coarse material (55% passing), so $P = 100 - 45\,c/100$. The range 60-75 gives $c = 55.6$ to $88.9\%$, so C is the main component (about 65%). - **0.075 mm sieve:** $P = [40a + 3(b + c)]/100 = 3 + 0.37a$ (since $b + c = 100 - a$). For 5 to 10, $a = 5.4$ to $18.9\%$, so A is a small proportion (about 10%). - The remainder is B: $b = 100 - a - c$. #### Step 2: Trial mix A : B : C = 10 : 25 : 65 | Sieve (mm) | A x 0.10 | B x 0.25 | C x 0.65 | Mix % passing | Spec | OK | |---|---|---|---|---|---|---| | 25.4 | 10.00 | 25.00 | 65.00 | 100.0 | 100 | yes | | 12.7 | 10.00 | 25.00 | 61.75 | 96.8 | 90-100 | yes | | 4.76 | 10.00 | 25.00 | 35.75 | 70.8 | 60-75 | yes | | 1.18 | 10.00 | 16.25 | 19.50 | 45.8 | 40-55 | yes | | 0.30 | 10.00 | 6.25 | 14.95 | 31.2 | 20-35 | yes | | 0.15 | 7.50 | 4.50 | 5.85 | 17.9 | 12-22 | yes | | 0.075 | 4.00 | 0.75 | 1.95 | 6.7 | 5-10 | yes | All sieves are inside the specification. (A check of all combinations in 1% steps gives the feasible range as A 6-15%, B 0-38%, C 56-85%; the least-squares fit to the mid-points is about 8 : 25 : 67, which is also acceptable. The trial mix 10 : 25 : 65 is rounded and convenient for site batching.) **Answer: Quarry A : Quarry B : Quarry C = 10% : 25% : 65%**, giving a blend passing 100, 96.8, 70.8, 45.8, 31.2, 17.9 and 6.7% on the 25.4, 12.7, 4.76, 1.18, 0.30, 0.15 and 0.075 mm sieves. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The combined % passing at a sieve is given by A. (a PA + b PB + c PC)/100 B. PA + PB + PC C. a b c / 100 D. (PA - PB)/PC Answer: A. A weighted average of passing percentages. (Key point: Mix equation) 2. Why is C the main component? A. It has the finest particles B. At 4.76 mm only C is coarse, so c must be 55.6-88.9% to reach 60-75% passing C. It has 100% passing everywhere D. It is the cheapest Answer: B. Only quarry C controls the 4.76 mm sieve. (Key point: Main component) 3. Why is A used in small proportion? A. It has no fines B. It fails all sieves C. At 0.075 mm, 3 + 0.37a must lie in 5-10, giving a = 5.4 to 18.9% D. It is only a filler for 25.4 mm Answer: C. A is the only fine source, controlling the 0.075 mm sieve. (Key point: Role of A) 4. What is the adopted A : B : C? A. 50 : 25 : 25 B. 65 : 25 : 10 C. 30 : 30 : 40 D. 10 : 25 : 65 Answer: D. The blend passes 100, 96.8, 70.8, 45.8, 31.2, 17.9 and 6.7%. 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