--- title: "Asphalt Institute design: 1.888×10³ ESAL/day, 10 years" subject: "Transportation Engineering II" chapter: 2 key: "semester_7/transportation_engineering_ii:asphalt-institute-design-1-888e3-esal" source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/asphalt-institute-design-1-888e3-esal site: BCT Engineering --- # Asphalt Institute design: 1.888×10³ ESAL/day, 10 years Transportation Engineering II · Chapter 2: Highway Pavement - Asked in: 2066 Bhadra, 10 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/asphalt-institute-design-1-888e3-esal - Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-2 ## Question An existing single lane gravel road has to be upgraded by bituminous pavement for a specified length as it is the demand for catering the increment in volume of heavy traffic. In order to estimate the base traffic, traffic survey was carried out at two points on the existing roads. The pavement design is based on the following assumptions. i) Base traffic of 82 kN equivalent single axle load (ESAL) = 1.888×10³ ESAL per day ii) Design period = 10 years iii) Construction period = 18 months iv) Growth rate = 6% v) 87.5 percentile CBR value of sub-grade soil from 7 sample locations = 5% vi) Elastic modulus of asphalt concrete for surface course Eac = 2000 MPa vii) Elastic modulus of crushed stone base Ebase = 250 MPa viii) Elastic modulus of granular sub-base Esubbase = 125 MPa You are asked to design the pavement by Asphalt Institute Method. Draw the cross section of final pavement layers considering the minimum thickness of asphalt concrete on surface course is equal to 50 mm. Chart is provided. ## Short answer Use CBR 5% giving Mr=50 MPa; design ESAL=9.913e6. Required SNs are 2.77 for base, 3.62 for subbase, 5.01 for subgrade. Layer coefficients give asphalt concrete 205 mm, crushed stone base 140 mm, granular sub-base 270 mm, total 615 mm. ## Answer #### Given data and assumptions - Single-lane gravel road upgraded to bituminous; base traffic 1.888 x 10^3 (1888) ESAL/day (the figure is already in equivalent standard axles; the 82 kN axle is taken as the standard axle of about 80 kN / 8.2 t, so the value is used directly), growth 6 %, design period 10 years, construction period 18 months (1.5 years). - 87.5th percentile CBR = 5 %; moduli: asphalt concrete 2000 MPa, crushed stone base 250 MPa, granular sub-base 125 MPa. - Single lane: design lane factor 1.0 (the survey figure is assumed to be the total on the lane). Minimum asphalt concrete 50 mm. - Method: Asphalt Institute (AI) thickness design as taught for IOE (and used in the Nepal DoR Pavement Design Guidelines); design reliability 90 percent, terminal serviceability 2.5. #### Step 1 - Subgrade strength The design (87.5th percentile) CBR of the subgrade is given as 5 %. Resilient modulus of subgrade: $M_R = 10\times CBR = 10\times 5.0 = 50$ MPa. #### Step 2 - Design traffic (ESAL) ESAL/day at opening $=1888\times(1.06)^{1.5}=2060.4$. $$ ESAL=365\times2060.4\times\frac{(1.06)^{10}-1}{0.06}=365\times2060.4\times13.181=9.913\times10^6 $$ **Design ESAL = 9.913 $\times 10^6$** #### Step 3 - Thickness required over each layer The AI charts give the thickness of asphalt concrete (full depth) needed to protect a layer of a given modulus for the design ESAL. The same requirement is expressed here as a structural number $SN$ (AASHTO-93 relation with R = 90 percent, $S_0$ = 0.45, $\Delta PSI$ = 1.7), which closely approximates the AI chart readings (if the chart is supplied in the exam, read the thickness from it and use the same layer-coefficient steps below). | Protected layer | Modulus (MPa) | Required SN | Full-depth AC equivalent at $a_1=0.44$ (mm) | |---|---|---|---| | crushed stone base | 250 | 2.77 | 160 | | granular sub-base | 125 | 3.62 | 209 | | Subgrade | 50 | 5.01 | 289 | #### Step 4 - Layer coefficients Using $a_1=0.323\log_{10}E-1.42$, $a_2=0.249\log_{10}E-0.977$, $a_3=0.227\log_{10}E-0.839$ with $E$ in psi: - Asphalt concrete (2000 MPa): $a_1 = 0.344$ - crushed stone base (250 MPa): $a_2 = 0.158$ - granular sub-base (125 MPa): $a_3 = 0.128$ #### Step 5 - Layer thicknesses - Asphalt concrete: $D_1 \ge SN_{base}/a_1 = 2.77/0.344=205$ mm, so provide **205 mm** (minimum 50 mm). $SN_1 = 2.78$. - Crushed stone base: $D_2 \ge (SN_{sub}-SN_1)/a_2 = (3.62-2.78)/0.158 = 134$ mm, so provide **140 mm**. $SN_2 = 0.87$. - Granular sub-base: $D_3 \ge (SN_{sg}-SN_1-SN_2)/a_3 = (5.01-2.78-0.87)/0.128 = 270$ mm, so provide **270 mm**. $SN_3 = 1.36$. Check: provided $SN = 2.78+0.87+1.36 = 5.01 \ge 5.01$ (required) - safe. **Answer:** asphalt concrete 205 mm, crushed stone base 140 mm, granular sub-base 270 mm; total pavement thickness = 615 mm. ```text +-------------------------------------+ | Asphalt concrete 205 mm | +-------------------------------------+ | Crushed stone base 140 mm | +-------------------------------------+ | Granular sub-base 270 mm | +-------------------------------------+ | Subgrade, CBR 5.0 % | +-------------------------------------+ ``` ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How does the answer get the resilient modulus of the subgrade from its CBR of 5 %? A. MR = 5 x CBR = 25 MPa B. MR = 10 x CBR = 50 MPa C. MR = 100 x CBR = 500 MPa D. MR = CBR / 10 = 0.5 MPa Answer: B. The answer uses MR = 10 x CBR, giving 50 MPa for CBR 5 %. (Key point: Subgrade modulus) 2. How is the design ESAL computed? A. Multiply 1888 by 365 and by 10 years with no growth B. Multiply 1888 by 365 and by 1.5 years only C. Grow the daily ESAL over the 1.5-year construction period, then multiply by 365 and the 10-year growth factor ((1.06)^10 - 1)/0.06 D. Apply the growth factor to the construction period only and ignore the design period Answer: C. Traffic at opening = 1888 x 1.06^1.5 = 2060 ESAL/day, then 365 x 2060 x 13.181 = 9.913 x 10^6. (Key point: Design ESAL) 3. How is the asphalt concrete thickness D1 found in the layered design? A. D1 >= SN required over the base / a1 = 2.77/0.344 = 205 mm B. D1 = SN of subgrade x a1 = 5.01 x 0.344 C. D1 is just the 50 mm minimum D. D1 = SN required over the base x a2 = 2.77 x 0.158 Answer: A. The surface layer must supply the SN needed to protect the base, so divide that SN by the AC coefficient a1. (Key point: Asphalt concrete thickness) 4. Which section does the answer finally adopt? A. AC 50 mm, base 140 mm, sub-base 270 mm; total 460 mm B. AC 205 mm, base 270 mm, sub-base 140 mm; total 615 mm C. AC 289 mm full depth; total 289 mm D. AC 205 mm, crushed stone base 140 mm, sub-base 270 mm; total 615 mm Answer: D. 205 + 140 + 270 = 615 mm, and the provided SN of 5.01 meets the required 5.01. 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