Transportation Engineering

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

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'.

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

SSD = Braking distance + lag distance
where,
Braking distance = Braking distance required to come to stop
Lag distance = distance travelled during the perception reaction time.

For, Road 'A':
\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}

For Road 'B':
\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}}}