GATE Civil Engineering Transportation Engineering Syllabus

Define negative cant and where it occurs.

Negative cant occurs on a branch (turnout) curve of a contrary flexure where the outer rail of the main line is the inner rail of the branch curve. The cant provided for the main line acts as negative (adverse) cant for the branch line, so the branch line speed must be restricted accordingly.

What is the basic runway length and the standard atmospheric reference conditions for airport design?

Basic runway length is the length required under standard conditions: mean sea level elevation, standard temperature $15^{\circ}\text{C}$, zero effective runway gradient, no wind, and a standard atmosphere. Corrections are then applied for actual elevation, temperature, and gradient at the site.

State the elevation correction applied to basic runway length.

Runway length is increased by $7\%$ for every $300\,\text{m}$ rise in elevation above mean sea level: $$\text{Correction} = \frac{7}{100}\times\frac{E}{300}\times L$$ where $E$ is elevation in metres and $L$ is the basic runway length.

State the temperature correction for runway length and the airport reference temperature.

Airport reference temperature $= T_a + \frac{T_m - T_a}{3}$, where $T_a$ is monthly mean of daily average temperatures and $T_m$ the monthly mean of daily maximums of the hottest month. Length is increased by $1\%$ for every $1^{\circ}\text{C}$ by which the reference temperature exceeds the standard temperature at that elevation (standard temp $= 15 - 0.0065E$).

State the gradient (slope) correction for runway length and the ICAO check on total correction.

For ICAO, length is increased by $20\%$ for every $1\%$ of effective runway gradient (applied after elevation and temperature corrections). Check: the combined correction for elevation plus temperature should not exceed $35\%$; if it does, a specific site study is required.

What is a taxiway and what governs the geometric design of an exit taxiway?

A taxiway connects the runway with terminal/apron/hangar areas. Exit (turn-off) taxiways allow aircraft to leave the runway quickly to increase runway capacity. High-speed exit taxiways are angled at about $30^{\circ}$ to the runway and use large turning radii (e.g., $R \approx 30\,\text{m}$+) so aircraft can exit at higher speed; geometry is governed by exit speed, turning radius, and deceleration distance.

State the formula for the turning radius of an exit taxiway given exit speed.

$$R = \frac{V^{2}}{127(e + f)}$$ where $V$ is the turn-off speed in $\text{km/h}$, $e$ the superelevation (taken low, near zero on taxiways), and $f$ the coefficient of friction (taken about $0.13$ for taxiway design). This gives the minimum radius for the design turn-off speed.

What are the desirable properties of road aggregates and the tests used to measure them?

Desirable properties and their tests: strength → Aggregate Crushing Value & Aggregate Impact Value; hardness → Los Angeles Abrasion test; toughness → Impact test; durability → Soundness test; shape → Flakiness & Elongation Index; adhesion with bitumen → Stripping value test; and particle size/grading via sieve analysis.

Give the typical IRC limiting values for Aggregate Impact Value and Los Angeles Abrasion Value for surface course aggregates.

For bituminous surface courses, Aggregate Impact Value (AIV) should be $\leq 30\%$ (preferably $< 24\%$ for wearing courses), and Los Angeles Abrasion Value should be $\leq 30\%$ for surface courses (up to $40\%$ for bases). Aggregate Crushing Value should be $\leq 30\%$ for wearing courses.

List the main tests used to characterize bitumen (binder).

Bitumen is tested for: Penetration test (consistency/grade), Ductility test (extensibility), Softening point (Ring & Ball, temperature susceptibility), Viscosity test, Flash and Fire point (safety), Specific gravity, and Solubility/Loss on heating (purity & durability).

What does the penetration test measure and how is penetration grade expressed?

The penetration test measures the consistency (hardness) of bitumen as the distance in tenths of a millimetre that a standard needle penetrates vertically under a load of $100\,\text{g}$ for $5\,\text{s}$ at $25^{\circ}\text{C}$. A grade such as $80/100$ means penetration lies between $80$ and $100$ ($1\,\text{unit} = 0.1\,\text{mm}$); higher penetration = softer bitumen.

What is the softening point and its significance for bitumen?

Softening point is the temperature (in $^{\circ}\text{C}$) at which bitumen attains a particular degree of softening, determined by the Ring and Ball apparatus (temperature at which the bitumen lets a steel ball fall $25\,\text{mm}$). It indicates temperature susceptibility; bitumen with higher softening point is preferred for warm climates to resist deformation.

What are the desirable properties of a good bituminous paving mix?

A good bituminous mix should have: (1) stability — resistance to deformation under traffic, (2) durability — resistance to weathering/ageing, (3) flexibility — to accommodate movement without cracking, (4) sufficient air voids — to prevent bleeding while avoiding excess permeability, (5) workability — for ease of laying and compaction, and (6) adequate skid resistance.

What is the Marshall stability test and the two main parameters it reports?

The Marshall test evaluates bituminous mix design by loading a compacted cylindrical specimen ($101.6\,\text{mm}$ dia, $63.5\,\text{mm}$ high) at $50.8\,\text{mm/min}$ at $60^{\circ}\text{C}$. The two key parameters are: Marshall Stability (maximum load in $\text{kN}$ the specimen carries) and Flow value (deformation in $\text{mm}$, units of $0.25\,\text{mm}$, at failure).

Define VMA, VFB, and air voids ($V_v$) in a bituminous mix.

$V_v$ (air voids) = percentage of air voids in the total mix volume. VMA (Voids in Mineral Aggregate) = volume of voids between aggregate particles, i.e., air voids plus volume of effective bitumen. VFB (Voids Filled with Bitumen) = percentage of VMA filled with bitumen, $\text{VFB} = \frac{\text{VMA} - V_v}{\text{VMA}}\times 100$.

What are the key design factors for flexible and rigid pavements?

Common design factors: design wheel load (and tyre pressure), subgrade strength (CBR / $k$-value), climatic factors (temperature, rainfall), traffic volume and growth, pavement material properties, and design life. Flexible pavements use load via grain-to-grain transfer relying on CBR; rigid pavements use slab flexural strength and the modulus of subgrade reaction $k$.

Compare load transfer mechanisms of flexible vs rigid pavements.

Flexible pavements transmit wheel load to the subgrade through grain-to-grain contact, spreading load over a wide area in a layered (Boussinesq-type) manner; they have low flexural strength and reflect subgrade deformations. Rigid (concrete) pavements have high flexural rigidity and act as a slab/beam, distributing load over a large area through bending (slab action), largely independent of minor subgrade variations.

What is the Equivalent Single Wheel Load (ESWL) and how does it vary with depth?

ESWL is the single wheel load that produces the same stress/deflection at a given depth as a set of multiple (dual) wheels. At shallow depths ESWL equals one wheel load; at large depths it approaches the total load of all wheels. It is found by the equal-stress concept, plotting load vs depth on a log-log scale between $d/2$ and $2S$ (where $d$ = clear distance, $S$ = centre-to-centre spacing).

State the Group Index method's Group Index formula for subgrade evaluation.

$$\text{GI} = 0.2a + 0.005ac + 0.01bd$$ where $a$ = percent passing $0.075\,\text{mm}$ sieve minus $35$ ($0$–$40$), $b$ = percent passing $0.075\,\text{mm}$ minus $15$ ($0$–$40$), $c$ = liquid limit minus $40$ ($0$–$20$), and $d$ = plasticity index minus $10$ ($0$–$20$). A higher GI indicates a poorer subgrade soil.

State the IRC method for flexible pavement design and the parameter it is based on.

IRC:37 designs flexible pavements based on cumulative standard axle load repetitions in terms of millions of standard axles (msa) and the subgrade CBR. The cumulative number of standard axles is $$N = \frac{365\,A\,[(1+r)^{n} - 1]\,D\,F}{r}$$ where $A$ = initial traffic (cvpd), $r$ = growth rate, $n$ = design life, $D$ = lane distribution factor, $F$ = vehicle damage factor.

What is the Vehicle Damage Factor (VDF) and the fourth-power law used in pavement design?

VDF is the number of standard axles ($80\,\text{kN}$) equivalent to one commercial vehicle, used to convert mixed traffic to standard axles. It is based on the fourth-power law: $$\text{Equivalency factor} = \left(\frac{\text{axle load}}{\text{standard axle (80 kN)}}\right)^{4}$$ so axle damage rises with the fourth power of the load.

State Westergaard's modulus of subgrade reaction $k$ and how it is obtained.

The modulus of subgrade reaction $k = \frac{p}{\Delta}$ is the pressure $p$ sustained per unit deflection $\Delta$, obtained from a plate load test using a $75\,\text{cm}$ diameter plate at a standard deflection of $\Delta = 0.125\,\text{cm}$. Units are $\text{kg/cm}^3$ or $\text{MPa/m}$; it represents the subgrade support for rigid pavement design.

State the formula for the radius of relative stiffness in rigid pavement design.

$$l = \left[\frac{E h^{3}}{12 k (1-\mu^{2})}\right]^{1/4}$$ where $E$ = modulus of elasticity of concrete, $h$ = slab thickness, $\mu$ = Poisson's ratio of concrete, and $k$ = modulus of subgrade reaction. It characterizes the stiffness of the slab relative to the subgrade.

State Westergaard's equation for critical wheel load stress at the interior of a rigid pavement slab.

$$\sigma_{i} = \frac{0.316 P}{h^{2}}\left[4\log_{10}\!\left(\frac{l}{b}\right) + 1.069\right]$$ where $P$ = wheel load, $h$ = slab thickness, $l$ = radius of relative stiffness, and $b$ = equivalent radius of resisting section (a function of contact radius $a$ and $h$).

How are warping (temperature) stresses at the edge and interior of a rigid slab calculated?

Using Bradbury's coefficients: interior warping stress $\sigma_{ti} = \frac{E\,e\,t}{2}\left(\frac{C_x + \mu C_y}{1-\mu^{2}}\right)$ and edge warping stress $\sigma_{te} = \frac{C E e t}{2}$, where $E$ = elastic modulus, $e$ = coefficient of thermal expansion, $t$ = temperature differential, $C, C_x, C_y$ = Bradbury coefficients depending on $L/l$ and $W/l$.

Why are joints provided in rigid (cement concrete) pavements, and what are the main types?

Joints relieve stresses from temperature/moisture changes and aid construction. Main types: (1) Expansion joints — allow slab expansion, prevent buckling; (2) Contraction joints — allow slab contraction, control shrinkage cracking; (3) Warping (hinge) joints — relieve warping stresses; (4) Construction joints — where paving stops. Dowel bars transfer load across; tie bars hold longitudinal joints together.

Distinguish between time mean speed and space mean speed.

Time mean speed $\bar{v}_t = \frac{1}{n}\sum v_i$ is the arithmetic mean of spot speeds at a point. Space mean speed $\bar{v}_s = \frac{n}{\sum \frac{1}{v_i}}$ is the harmonic mean over a length of road. Always $\bar{v}_t \geq \bar{v}_s$, related by $\bar{v}_t = \bar{v}_s + \frac{\sigma_s^{2}}{\bar{v}_s}$.

State the fundamental relation of traffic flow and the Greenshields model.

Fundamental relation: $$q = k\,v_s$$ where $q$ = flow (vehicles/hour), $k$ = density (vehicles/km), $v_s$ = space mean speed. Greenshields assumes a linear speed-density relation $v = v_f\left(1 - \frac{k}{k_j}\right)$, giving maximum flow $q_{max} = \frac{v_f\,k_j}{4}$ at $v = \frac{v_f}{2}$ and $k = \frac{k_j}{2}$, where $v_f$ = free speed, $k_j$ = jam density.

Define Peak Hour Factor (PHF) and give its formula for 15-minute counts.

PHF measures the variation of traffic flow within an hour (uniformity of demand). $$\text{PHF} = \frac{\text{Peak hour volume}}{4 \times \text{peak 15-minute volume}}$$ Values range from about $0.25$ to $1.0$; a PHF near $1.0$ indicates uniform flow, while lower values indicate greater short-term surges. The maximum flow rate $= \frac{V}{\text{PHF}}$.

What is the design service volume and the role of the Passenger Car Unit (PCU) in traffic studies?

PCU converts a mixed traffic stream into an equivalent stream of passenger cars (car = $1.0$ PCU; truck/bus $\approx 3.0$; two-wheeler $\approx 0.5$; cycle $\approx 0.5$) to express flow and capacity uniformly. Design service volume is the maximum hourly volume a facility can carry at the chosen Level of Service, obtained as capacity adjusted by the volume-to-capacity ratio and PHF.