# Transportation Engineering

 Question 1
Consider the Marshall method of mix design for bituminous mix. With the increase in bitumen content, which of the following statements is/are TRUE?
 A the Stability decreases initially and then increases B the Flow increases monotonically C the air voids (VA) increases initially and then decreases D the voids filled with bitumen (VFB) increases monotonically
GATE CE 2023 SET-2      Highway Materials
Question 1 Explanation:
For marshall mix design, following graphical results are obtained.
$\Rightarrow$ Stability increases initially and then decreases
Hence option (A) is INCORRECT $\Rightarrow$ Flow increases monotonically
Hence option (B) is CORRECT $\Rightarrow$ Air voids decreases continously
Hence option (C) is INCORRECT $\Rightarrow$ VFB increases monotonically
Hence option (D) is CORRECT Question 2
The figure presents the time-space diagram for when the traffic on a highway is suddenly stopped for a certain time and then released. Which of the following statements are true? A Speed is higher in Region $\mathrm{R}$ than in Region $\mathrm{P}$ B Volume is lower in Region $Q$ than in Region $P$ C Volume is higher in Region $\mathrm{R}$ than in Region $\mathrm{P}$ D Density is higher in Region $\mathrm{Q}$ than in Region $\mathrm{R}$
GATE CE 2023 SET-2      Traffic Engineering
Question 2 Explanation:
Any vertical line drawn in the graph which cuts arrow lines give positions of vehicles in different regions at a particular time.
Slope of a line in a region represents speed of vehicles in that particular region.

From the Plot :
1. Distance between position of vehicles in region ' $P$ ' is greater than that in region $R \Rightarrow$ Density in region ' $P$ ' is greater than that in region ' $R$ '.
2. Slope of lines in region ' $Q$ ' $=0 \Rightarrow$ Speed of vehicles in region ' $\mathrm{Q}$ ' is zero.
3. Slope of lines in region ' $P$ ' is greater than in region ' $R$ ' $\Rightarrow$ speed of vehicles in region ' $P$ ' is greater than in region ' $R$ '.
4. Since vehicles in region ' $Q$ ' are stationary, flow or volume in region ' $Q$ ' is zero and hence lower than in region $\mathrm{P}$ or region $\mathrm{R}$. And density in region ' $\mathrm{Q}$ ' is higher than in region $\mathrm{P}$ or region $\mathrm{R}$.
5. Boundary between region ' $P$ and ' $R$ ' represents 'forward moving slope wave' means slope is positive.
i.e. $\quad$ slope $=\frac{q_{R}-q_{P}}{K_{R}-K_{P}} \gt 0$
q - Flow
$\mathrm{K}$ - Density.
Since $\mathrm{K}_{\mathrm{R}} \gt \mathrm{K}_{\mathrm{P}}$
$\Rightarrow \mathrm{q}_{\mathrm{R}}$ should be greater than $\mathrm{q}_{\mathrm{P}}$.
$\Rightarrow$ Volume/flow in region ' $R$ ' is higher than in Region 'P'.

 Question 3
As per the Indian Roads Congress guidelines (IRC 86: 2018), extra widening depends on which of the following parameters?
 A Horizontal curve radius B Superelevation C Number of lanes D Longitudinal gradient
GATE CE 2023 SET-2      Geometric Design of Highway and Planning
Question 3 Explanation:
As per IRC $86: 2018$ Clause 8.6 Widening of Carriageway on Curves:
At sharp horizontal curves, it is necessary to widen the carriageway to provide for safe passage of vehicles. The widening required has two components: (i) mechanical widening to components for the extra width occupied by a vehicle on the curve due to tracking of the rare wheels, and (ii) psychological widening to permit easy crossing of vehicles since vehicles in a lane tend to wander more on a curve than on a straight reach.
On two-lane or wider roads, it is necessary that both the above components should be fully catered for so that the lateral clearance between vehicles of curves is maintained equal to the clearance available on straight. Position of single-lane roads however is somewhat different.
Since during crossing maneuvers outer wheels of vehicles have in any case to use the shoulder whether on the straight or on the curve. It is, therefore sufficient on single lane roads if only the mechanical component of widening is taken into account.
Based on the above considerations, the extra width of carriageway to be provided at horizontal curves on single and two-lane roads is given in Table For multi-lane roads, the pavement widening may be calculated by adding half the widening for two-lane roads to each lane.
Table : Extra width of Pavement at Horizontal Curves Question 4
Which of the following is equal to the stopping sight distance?
 A (braking distance required to come to stop) + (distance travelled during the perception- reaction time) B (braking distance required to come to stop) - (distance travelled during the perception- reaction time) C (braking distance required to come to stop) D (distance travelled during the perception- reaction time)
GATE CE 2023 SET-2      Geometric Design of Highway and Planning
Question 4 Explanation:
SSD $=$ Braking distance + lag distance
where,
Braking distance $=$ Braking distance required to come to stop
Lag distance $=$ distance travelled during the perception reaction time.
 Question 5
A plot of speed-density relationship (linear) of two roads (Road $A$ and Road $B$ ) is shown in the figure. If the capacity of Road $A$ is $C_{A}$ and the capacity of Road $B$ is $C_{B}$, what is $\frac{C_{A}}{C_{B}}$ ?
 A $\frac{k_A}{k_B}$ B $\frac{u_A}{u_B}$ C $\frac{k_Au_A}{k_Bu_B}$ D $\frac{k_Au_B}{k_Bu_A}$
GATE CE 2023 SET-1      Traffic Engineering
Question 5 Explanation:
\begin{aligned} \mathrm{v}_{\mathrm{f}} & =\mathrm{u}_{\mathrm{A}}, \quad \mathrm{k}_{\mathrm{j}}=\mathrm{k}_{\mathrm{A}} \\ \mathrm{c}_{\mathrm{A}} & =\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{4} \\ \mathrm{c}_{\mathrm{A}} & =\text { Capacity of road, } \end{aligned}
\begin{aligned} & v_{f}=\text { Free flow speed }=u_{B} \\ & k_{j}=\text { Jam density }=k_{B} \end{aligned}
Capacity of Road 'B' $\left(c_{B}\right)=\frac{u_{B} k_{B}}{4}$
$\therefore \quad \frac{\mathrm{C}_{\mathrm{A}}}{\mathrm{c}_{\mathrm{B}}}=\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{4\left(\frac{\mathrm{u}_{\mathrm{B}} \mathrm{k}_{\mathrm{B}}}{4}\right)}=\frac{\mathrm{u}_{\mathrm{A}} \mathrm{k}_{\mathrm{A}}}{\mathrm{u}_{\mathrm{B}} \mathrm{k}_{\mathrm{B}}}$