Transportation Engineering
Comprehensive guide to transportation systems, traffic analysis, and infrastructure design.
Traffic Flow Theory
Traffic flow theory describes the relationships between the three fundamental parameters of traffic flow:
q = k × u
Where:
- q = flow rate (vehicles/hour)
- k = density (vehicles/km)
- u = space mean speed (km/hour)
The Greenshields model assumes a linear relationship between speed and density:
u = u_f × (1 - k/k_j)
Where:
- u_f = free-flow speed (km/hour)
- k_j = jam density (vehicles/km)
The maximum flow (capacity) occurs at:
k_c = k_j/2
u_c = u_f/2
q_c = u_f × k_j/4
Highway Geometric Design
Highway geometric design involves the design of the visible elements of the highway. Key elements include:
1. Horizontal Alignment:
The minimum radius of a horizontal curve is:
R_min = V² / (127 × (e + f))
Where:
- R_min = minimum radius (m)
- V = design speed (km/h)
- e = superelevation rate
- f = side friction factor
2. Vertical Alignment:
The minimum length of a vertical curve is determined by stopping sight distance requirements:
L = A × S² / (100 × (√(2h₁) + √(2h₂))²)
Where:
- L = length of vertical curve (m)
- A = algebraic difference in grades (%)
- S = stopping sight distance (m)
- h₁ = height of driver's eye (m)
- h₂ = height of object (m)
3. Cross-Section Elements:
- Lane width
- Shoulder width
- Median width
- Cross slope
- Side slopes
- Clear zone
Pavement Design
Pavement design involves determining the thickness and materials for road pavements. The AASHTO method is commonly used for flexible pavement design:
log₁₀(W₁₈) = Z_R × S_0 + 9.36 × log₁₀(SN+1) - 0.20 + (log₁₀(ΔPSI/(4.2-1.5)))/(0.40+(1094/(SN+1)^5.19)) + 2.32 × log₁₀(M_R) - 8.07
Where:
- W₁₈ = predicted number of 18-kip equivalent single axle loads (ESALs)
- Z_R = standard normal deviate for reliability level
- S_0 = combined standard error of traffic prediction and performance prediction
- SN = structural number
- ΔPSI = difference between initial and terminal serviceability index
- M_R = resilient modulus of the subgrade (psi)
The structural number is calculated as:
SN = a₁D₁ + a₂D₂m₂ + a₃D₃m₃
Where:
- a_i = layer coefficient for layer i
- D_i = thickness of layer i (inches)
- m_i = drainage coefficient for layer i