Transportation Engineering

Syllabus

• Transportation infrastructure: highway alignment, geometric design (cross-section, sight distances, horizontal and vertical curves, superelevation), pavement materials and their tests (aggregate, bitumen, soil).
• Highway pavements: design of flexible pavements (CBR method, IRC:37) and rigid pavements (Westergaard, IRC:58), traffic loading (standard axle, vehicle damage factor).
• Traffic engineering: traffic studies (volume, speed, origin-destination), speed-flow-density relationships, capacity and level of service, intersection and signal design.

Key concepts and formulas

Stopping sight distance (v in m/s, reaction time t, coefficient of longitudinal friction f): SSD = vt + v²/(2gf). With speed V in km/h: SSD = 0.278Vt + V²/(254f). IRC uses t = 2.5 s.

Superelevation. e + f = V²/(127R) (V in km/h, R in m). IRC limits e to 0.07 (plain and rolling terrain) and takes f = 0.15.

Overtaking sight distance. OSD = d₁ + d₂ + d₃, the distances travelled during reaction, overtaking and by the opposing vehicle.

Curves. Extra widening, transition curve length L = v³/(CR), and the length of a summit curve for sight distance S (when L > S): L = NS²/(2(√H + √h)²), with N the algebraic difference of grades.

Traffic flow.

• Fundamental relation: q = kv (flow = density × speed).
• Greenshields' model: v = v_f(1 − k/k_j). Maximum flow q_max = v_fk_j/4, at k = k_j/2 and v = v_f/2.
• Space mean speed is the harmonic mean of spot speeds; time mean speed is their arithmetic mean, and is never smaller.

Signal design (Webster). Optimum cycle length C₀ = (1.5L + 5)/(1 − Y), with total lost time L (s) and Y = Σ y_i, the sum of the critical flow ratios (flow/saturation flow). The effective green time is shared in proportion to y_i.

Pavements. Flexible pavement thickness comes from the CBR of the subgrade and the cumulative standard axles. The fourth power law: the damage of an axle load relative to the standard axle (80 kN) is (W/80)⁴. Rigid pavements are checked for wheel load stresses at the interior, edge and corner (Westergaard), plus temperature stresses.

Worked example

Find the SSD for a design speed of 80 km/h (t = 2.5 s, f = 0.35). Then, for Greenshields' model with v_f = 80 km/h and k_j = 120 veh/km, find the capacity. Finally, design the cycle length for L = 12 s and critical flow ratios 0.30 and 0.25.

V, t, f = 80, 2.5, 0.35
ssd = 0.278 * V * t + V ** 2 / (254 * f)
print(f"SSD = {ssd:.2f} m")
vf, kj = 80, 120
print(f"q_max = {vf * kj / 4:.0f} veh/h at k = {kj / 2:.0f} veh/km and v = {vf / 2:.0f} km/h")
L, Y = 12, 0.30 + 0.25
C0 = (1.5 * L + 5) / (1 - Y)
print(f"Webster cycle = {C0:.2f} s")
print(f"damage of a 100 kN axle relative to 80 kN: {(100 / 80) ** 4:.3f}")

SSD = 127.59 m
q_max = 2400 veh/h at k = 60 veh/km and v = 40 km/h
Webster cycle = 51.11 s
damage of a 100 kN axle relative to 80 kN: 2.441

Practice questions