Flexible design: four-lane, AADT 12,000

Assumptions

Design method: AASHTO-93 structural number with layer coefficients from the given moduli. Not stated in the problem, so assumed: design life 20 years (new alignment, no construction period), 50:50 directional split, design-lane factor 0.8 for two lanes in one direction, reliability 90 % ($Z_R=-1.282$), $S_0=0.45$, $\Delta PSI=4.2-2.5=1.7$, drainage coefficients 1.0. Standard axle 80 kN, fourth power law for ESAL.

Step 1 - ESAL per day (first year, both directions)

Step 2 - Design ESAL

$$W_{18}=196.7\times0.5\times0.8\times365\times\frac{(1.04)^{20}-1}{0.04}=196.7\times0.4\times365\times29.778=855345$$

Step 3 - Layer coefficients (E in psi) and required SN

• Subgrade $M_R=10\times6.5=65$ MPa $=9427$ psi.
• $a_1=0.323\log_{10}(2400\times145)-1.42=0.370$, $a_2=0.249\log_{10}(500\times145)-0.977=0.233$, $a_3=0.227\log_{10}(275\times145)-0.839=0.205$.
• Required $SN$ over base (protecting $M_R$ = 500 MPa): $SN_1=1.38$; over sub-base (275 MPa): $SN_2=1.77$; over subgrade: $SN_3=3.10$.

Step 4 - Thicknesses

• AC is specified as 7.5 cm (2.95 in): $SN_{AC}=0.370\times2.953=1.09$. A layer-wise check over the base would ask for $SN_1=1.38$ (about 95 mm of AC). However, the base modulus is 500 MPa = 72 500 psi, and AASHTO-93 states that this layered check should not be used above a base or sub-base with a modulus above 40 000 psi; the AC over such a stiff base is fixed by cost and minimum-thickness considerations instead. For 0.5-2 million ESAL the AASHTO minimum AC thickness is 3.0 in (about 75 mm), so the specified 7.5 cm is acceptable. (The sub-base, 275 MPa = 39 900 psi, is below the limit, so the check above the sub-base is valid.)
• Base: $D_2\ge(SN_2-SN_{AC})/a_2=(1.77-1.09)/0.233=2.92$ in $=74$ mm; this is below the AASHTO minimum base thickness (6 in for 0.5-2 million ESAL), so provide 15 cm (5.91 in): $a_2D_2=1.38$.
• Sub-base: $D_3\ge(SN_3-SN_{AC}-a_2D_2)/a_3=(3.10-1.09-1.38)/0.205=3.08$ in $=78$ mm; provide the minimum practical 15 cm: $a_3D_3=1.21$.
• Check: SN above the sub-base $=1.09+1.38=2.47\ge1.77$, and total $SN=1.09+1.38+1.21=3.68\ge3.10$ - safe. The base and sub-base are governed by minimum thicknesses because the design traffic is light.

  +--------------------------+
  | Asphalt concrete  7.5 cm |
  | Base (500 MPa)   15.0 cm |
  | Sub-base (275)   15.0 cm |
  | Subgrade CBR 6.5 %       |
  +--------------------------+

Answer: AC 7.5 cm, base 15 cm, sub-base 15 cm (total 37.5 cm), for a design traffic of about 0.86 million ESAL. The passenger cars and light trucks cause very little damage; the 3-axle trucks produce most of the ESAL.