--- title: "Flexible pavement life with 140 cvpd traffic" subject: "Transportation Engineering II" chapter: 2 key: "semester_7/transportation_engineering_ii:flexible-design-life-years-140-cvpd" source: https://www.bctengineer.com/q/semester_7/transportation_engineering_ii/flexible-design-life-years-140-cvpd site: BCT Engineering --- # Flexible pavement life with 140 cvpd traffic Transportation Engineering II · Chapter 2: Highway Pavement - Asked in: 2076 Chaitra, 8 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/flexible-design-life-years-140-cvpd - Whole chapter: https://www.bctengineer.com/md/semester_7/transportation_engineering_ii/chapter-2 ## Question A proposed flexible pavement design of single lane carriageway consists of 75mm of Asphalt concrete, 120 mm of emulsified stabilized base course and 145mm of granular subbase. The expected commercial traffic volume is 140 cvpd. The expected traffic composition is 30% truck, 30% of mini truck and 40% of bus, whose truck factors are 5.6, 0.6 and 0.1 respectively. The expected annual traffic growth rate is 8% for all vehicles, and 18month required for construction to be completed. The CBR test conducted at 7 locations strating from Ch.0+100 at the interval of 200m distance gave the value of 11,9,7,10,8,6,4. E_sub base=275 MPa, E_base=500MPa and E_surface=2400 MPa. How many years can this pavement last? ## Short answer Using AASHTO, subgrade CBR 5 % (90th percentile) and structural number 3.37 give a capacity of 0.79 million ESAL. With vehicle damage factor 1.90, opening traffic 157 cvpd (8 % growth, 1.5-year construction), solving the traffic equation yields a pavement life of 5.9 years. ## Answer #### Approach The structure is given, so its capacity (ESAL) is found with the layer-coefficient (structural number) method of AASHTO, then divided by the yearly traffic to get the life. Assumed: reliability 90 % ($Z_R=-1.282$), $S_0=0.5$, $\Delta PSI=2.0$, drainage coefficients $m=1$, single lane so the design lane takes 100 percent of traffic. #### Step 1 - Subgrade CBR values at 7 locations: 11, 9, 7, 10, 8, 6, 4. The 90th percentile value (90 percent equal or greater) lies between 4 % (100 percent) and 6 % (85.7 percent) and is about 5.4 %; adopt **CBR = 5 %**, $M_R=10\times5=50$ MPa $=7252$ psi. #### Step 2 - Layer coefficients (E in psi) $$ \begin{aligned} a_1&=0.323\log_{10}(2400\times145.04)-1.42=0.370\\ a_2&=0.249\log_{10}(500\times145.04)-0.977=0.233\\ a_3&=0.227\log_{10}(275\times145.04)-0.839=0.205 \end{aligned} $$ #### Step 3 - Structural number of the section $$ SN=0.370\times\frac{75}{25.4}+0.233\times\frac{120}{25.4}+0.205\times\frac{145}{25.4}=1.092+1.102+1.172=3.37 $$ #### Step 4 - ESALs the pavement can carry With $SN=3.37$ and $M_R=7252$ psi in the AASHTO-93 equation: $\log_{10}W_{18}=5.896$, so $W_{18}=786452$ ESAL ($\approx0.79$ million). #### Step 5 - Traffic per year VDF from truck factors: $0.30\times5.6+0.30\times0.6+0.40\times0.1=1.90$. Traffic at opening (18 months of construction): $A=140(1.08)^{1.5}=157.1$ CVPD. $$ W_{18}=365\,A\,F\,\frac{(1.08)^n-1}{0.08}\ \Rightarrow\ \frac{(1.08)^n-1}{0.08}=\frac{786452}{365\times157.1\times1.90}=7.22 $$ $$ (1.08)^n=1+0.08\times7.22=1.577\ \Rightarrow\ n=\frac{\ln1.577}{\ln1.08}=5.92\ \text{years} $$ **Answer:** the pavement will last about **5.9 years** after opening (CBR 5 %, SN = 3.37, capacity 0.79 million ESAL). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the life of the given pavement found? A. Compute the ESALs the section can carry (via SN), then divide by yearly traffic growth to find years B. Read the life directly from the CBR C. Use the thickness only D. Take the design life as 20 years Answer: A. Capacity W18 from SN and M_R is equated to cumulative traffic, then solved for n. (Key point: Approach) 2. Design CBR is taken as 5 %. What subgrade modulus is used? A. M_R = 10 x 5 = 50 MPa (7252 psi) B. M_R = 5 MPa C. M_R = 500 MPa D. M_R = 275 MPa Answer: A. M_R = 10 x CBR in MPa, and 50 MPa = 7252 psi. (Key point: Design CBR and MR) 3. How is SN of the section computed? A. Sum of coefficient x thickness in inches for each layer B. Sum of the moduli C. Thickness in mm times the coefficient D. Only the surface layer coefficient Answer: A. SN = a1D1 + a2D2 + a3D3 with thicknesses converted to inches, giving 3.37. (Key point: Structural number) 4. With 30 % at 5.6, 30 % at 0.6 and 40 % at 0.1, what is the VDF? A. 2.1 B. 1.90 C. 6.3 D. 0.63 Answer: B. 0.30x5.6 + 0.30x0.6 + 0.40x0.1 = 1.68 + 0.18 + 0.04 = 1.90. (Key point: Weighted truck factor) 5. After finding [(1.08)^n - 1]/0.08 = 7.22, how is n obtained? A. n = 7.22 B. (1.08)^n = 1 + 0.08 x 7.22, so n = ln(1.577)/ln(1.08), about 5.9 years C. n = 7.22 x 0.08 D. n = 786452/365 Answer: B. Rearranging the growth-sum formula gives (1.08)^n = 1.577 and n of about 5.9 years. 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