BE Civil Engineering (IOE, TU) Transportation Engineering I (IOE, CE 652) Question Paper 2078 Nepal

Role of Highway Planning

Highway planning is the systematic process of deciding the location, type, capacity, phasing, and financing of a road network to meet present and projected travel demand at minimum cost. For a developing, mountainous country like Nepal it is essential because:

• Resources (funds, equipment, skilled manpower) are limited, so investment must be prioritized to maximize social and economic returns.
• Difficult terrain makes construction very costly; a wrong alignment is expensive to correct.
• A planned network integrates roads with other modes (air, rope-way, future rail) and connects rural areas to markets, schools and health services, promoting balanced regional development.

Four Stages of the Master Plan Planning Process

1. Assessment of present situation (Inventory/Surveys): Collect data on existing roads, traffic, terrain, land use, population and economic activity.
2. Forecast of future requirements (Demand projection): Project traffic growth, population and economic activity over the design period to estimate future demand.
3. Formulation of plan (Network planning): Prepare alternative network proposals, fix priorities using planning ratios/economic analysis, and schedule construction in phases (short, medium, long term).
4. Implementation and monitoring (Review): Execute the phased plan, monitor performance, and periodically revise the plan as conditions change.

Planning Surveys Required

• Economic studies: population distribution and trends, per-capita income, agricultural/industrial production, existing & potential land use.
• Financial studies: sources of revenue (taxes, tolls, grants), funding capacity, vehicle taxation.
• Traffic (road-use) studies: traffic volume counts, origin-destination (O-D) survey, traffic flow patterns, mass-transport facilities, accident records, speed & delay studies.
• Engineering studies: topographic surveys, soil & geological surveys, drainage and hydrology, material availability, existing road condition.

Road Classification as per Nepal Road Standard (NRS)

NRS classifies the road network functionally as:

Highways are further grouped by terrain (Plain/Terai, Rolling, Mountainous, Steep) and by design speed and traffic volume for the choice of geometric standards.

Definitions

Stopping Sight Distance (SSD): the minimum distance visible to a driver, required to bring the vehicle to a stop before reaching a stationary object in its path, without collision. It equals the lag (reaction) distance plus the braking distance.

Overtaking Sight Distance (OSD): the minimum distance open to the vision of a driver of a vehicle intending to overtake a slower vehicle ahead safely against traffic in the opposite direction.

Given Data

• Design speed $V = 65$ km/h $= 65/3.6 = 18.06$ m/s
• Reaction time $t_r = 2.5$ s, friction $f = 0.36$, $g = 9.81$ m/s²
• Overtaken (slow) vehicle speed $V_b = 65 - 16 = 49$ km/h $= 49/3.6 = 13.61$ m/s
• Acceleration $a = 0.99$ m/s²

(a) Stopping Sight Distance

$$SSD = V t_r + \dfrac{V^2}{2gf}$$

Lag distance $= 18.06 \times 2.5 = 45.14$ m

Braking distance $= \dfrac{(18.06)^2}{2 \times 9.81 \times 0.36} = \dfrac{326.2}{7.063} = 46.18$ m

$$SSD = 45.14 + 46.18 = 91.3 \text{ m}$$

SSD ≈ 91.3 m (≈ 92 m).

(b) Overtaking Sight Distance

OSD $= d_1 + d_2 + d_3$

$d_1$ (distance travelled by overtaking vehicle during reaction time $t_r = 2.5$ s at speed $V_b$):

$$d_1 = V_b\, t_r = 13.61 \times 2.5 = 34.03 \text{ m}$$

$d_2$ (distance travelled during the actual overtaking maneuver, time $T$):

Spacing $s = 0.7 V_b + 6 = 0.7(13.61) + 6 = 15.53$ m

$$T = \sqrt{\dfrac{4 s}{a}} = \sqrt{\dfrac{4 \times 15.53}{0.99}} = \sqrt{62.75} = 7.92 \text{ s}$$ $$d_2 = V_b\,T + 2s = 13.61 \times 7.92 + 2(15.53) = 107.79 + 31.06 = 138.85 \text{ m}$$

$d_3$ (distance travelled by the opposing vehicle during time $T$, at design speed $V$):

$$d_3 = V\,T = 18.06 \times 7.92 = 143.04 \text{ m}$$

Total OSD (two-way road):

$$OSD = 34.03 + 138.85 + 143.04 = 315.9 \text{ m}$$

OSD ≈ 315.9 m (≈ 316 m).

Given Data

• Radius $R = 300$ m, speed $V = 80$ km/h, width $W = 7.0$ m, wheelbase $l = 6.0$ m
• Two lanes $\Rightarrow n = 2$
• $e_{max} = 0.07$, $f_{max} = 0.15$

(a) Superelevation

Design (IRC) practice: superelevation is designed for 75% of design speed, ignoring friction:

$$e = \dfrac{(0.75V)^2}{127\,R} = \dfrac{V^2}{225\,R}$$ $$e = \dfrac{(80)^2}{225 \times 300} = \dfrac{6400}{67500} = 0.0948$$

Since $0.0948 > e_{max} = 0.07$, limit the superelevation to $e = 0.07$.

Check friction at full design speed with $e = 0.07$:

$$e + f = \dfrac{V^2}{127\,R} = \dfrac{(80)^2}{127 \times 300} = \dfrac{6400}{38100} = 0.168$$ $$f = 0.168 - 0.07 = 0.098$$

Since $f = 0.098 < f_{max} = 0.15$, the curve is safe at the design speed with $e = 0.07$.

Provide superelevation $e = 0.07$ (7%); required $f = 0.098 < 0.15$ → OK.

(b) Extra Widening

Total extra widening $W_e = W_m + W_{ps}$ (mechanical + psychological).

Mechanical widening:

$$W_m = \dfrac{n\,l^2}{2R} = \dfrac{2 \times (6.0)^2}{2 \times 300} = \dfrac{72}{600} = 0.12 \text{ m}$$

Psychological widening:

$$W_{ps} = \dfrac{V}{9.5\sqrt{R}} = \dfrac{80}{9.5\sqrt{300}} = \dfrac{80}{9.5 \times 17.32} = \dfrac{80}{164.5} = 0.486 \text{ m}$$

Total extra widening:

$$W_e = 0.12 + 0.486 = 0.606 \text{ m}$$

Total extra widening ≈ 0.61 m.

Given Data

• Deviation angle $N = g_1 - g_2 = (+0.035) - (-0.025) = 0.060$ (i.e., 6.0%)
• $SSD\;(S) = 120$ m
• Eye height $H = 1.2$ m, object height $h = 0.15$ m

(a) Length of Summit Curve

For a summit curve designed for SSD, the standard formula uses

$$2(\sqrt{H}+\sqrt{h})^2 = 2(\sqrt{1.2}+\sqrt{0.15})^2$$

$\sqrt{1.2} = 1.0954$, $\sqrt{0.15} = 0.3873$

$$(\sqrt{H}+\sqrt{h})^2 = (1.0954 + 0.3873)^2 = (1.4827)^2 = 2.198$$ $$2(\sqrt{H}+\sqrt{h})^2 = 4.40 \text{ (the constant, in m)}$$

Case 1: assume $L > S$:

$$L = \dfrac{N\,S^2}{2(\sqrt{H}+\sqrt{h})^2} = \dfrac{N\,S^2}{4.40}$$ $$L = \dfrac{0.060 \times (120)^2}{4.40} = \dfrac{0.060 \times 14400}{4.40} = \dfrac{864}{4.40} = 196.4 \text{ m}$$

Since $L = 196.4$ m $> S = 120$ m, the assumption is valid.

Length of summit curve $L \approx 196.4$ m (say 197 m).

(b) Validity of Assumption

The computed $L = 196.4$ m is greater than the SSD $S = 120$ m, so the case $L > S$ holds and no recomputation with the $L < S$ formula is needed. The assumption $L > SSD$ is valid and the design is acceptable.

(If $L$ had come out less than $S$, we would re-solve with $L = 2S - \dfrac{2(\sqrt{H}+\sqrt{h})^2}{N}$.)

Definitions

Traffic volume (flow, $q$): the number of vehicles crossing a given section of road per unit time (veh/h or PCU/h).

Traffic density (concentration, $k$): the number of vehicles present per unit length of road at an instant (veh/km or PCU/km).

Space-mean speed ($v_s$): the average speed of vehicles based on the average time taken to traverse a known length of road; it is the harmonic mean of spot speeds and is the speed used in the flow relationship.

Fundamental relationship:

$$q = k \times v_s$$

(a) Total Flow in PCU/hour

$$q = 720 + 450 + 540 + 180 = 1890 \text{ PCU/h}$$

Total flow $q = 1890$ PCU/h.

(b) Traffic Density

$$k = \dfrac{q}{v_s} = \dfrac{1890 \text{ PCU/h}}{40 \text{ km/h}} = 47.25 \text{ PCU/km}$$

Traffic density $k \approx 47.25$ PCU/km.

Capacity Check

The flow $q = 1890$ PCU/h exceeds the lane capacity of 1500 PCU/h.

$$\text{V/C ratio} = \dfrac{1890}{1500} = 1.26 > 1.0$$

The road is OVER capacity (V/C = 1.26 > 1.0); the section is congested and operating beyond its design capacity. Capacity augmentation (additional lane / traffic management) is required.

Requirements of an Ideal Highway Alignment

An ideal alignment should be:

1. Short: the route should be as straight/short as practicable, since a shorter route reduces construction and travel cost. (A direct line is rarely possible due to obstacles.)
2. Easy: easy to construct and maintain, with easy gradients and curves for comfortable vehicle operation.
3. Safe: safe for traffic — adequate sight distance, gentle curves, stable slopes and proper drainage; safe against landslides especially in hilly terrain.
4. Economical: lowest total cost considering initial construction, maintenance and vehicle-operation cost over the design life.

Additional considerations: it should obey controls of obstructions (lakes, marshes, historic/religious places), geometric design standards, and special considerations such as drainage, hydrology and political/strategic needs.

Four Stages of Engineering Surveys

1. Map (Provincial/Reconnaissance map) study / Desk study: study of topo sheets to identify possible routes.
2. Reconnaissance survey: field inspection of the alternative routes to assess feasibility and eliminate impractical ones.
3. Preliminary survey: detailed instrument survey of selected routes to compare them technically and economically and select the best.
4. Final location & detailed survey: pegging the final centre line on the ground and collecting data for detailed design and drawings.

Objectives of a Transition Curve

1. To gradually introduce the centrifugal force between the tangent and the circular curve, avoiding a sudden jerk on the vehicle.
2. To enable the driver to turn the steering gradually for comfort and safety.
3. To enable gradual introduction/application of the superelevation and the extra widening.
4. To improve the aesthetic appearance of the road and guide the driver visually.

Length of Transition Curve (Rate of Change of Centrifugal Acceleration)

Given: $R = 250$ m, $V = 70$ km/h $= 70/3.6 = 19.44$ m/s

Allowable rate of change of centrifugal acceleration:

$$C = \dfrac{80}{75 + V} = \dfrac{80}{75 + 70} = \dfrac{80}{145} = 0.552 \text{ m/s}^3$$

(Within permissible limits 0.5–0.8 m/s³, so acceptable.)

Length of transition curve:

$$L_s = \dfrac{v^3}{C\,R} = \dfrac{(19.44)^3}{0.552 \times 250}$$

$(19.44)^3 = 19.44 \times 19.44 \times 19.44 = 7349.0$

$$L_s = \dfrac{7349.0}{138.0} = 53.25 \text{ m}$$

Length of transition curve $L_s \approx 53.3$ m (say 54 m).

Desirable Properties of Road Aggregates

• Strength: high resistance to crushing to bear traffic wheel loads.
• Hardness: resistance to abrasion/wear from traffic and weather.
• Toughness: resistance to impact from moving wheel loads.
• Durability: resistance to weathering (soundness) so aggregates do not disintegrate.
• Good shape: roughly cubical, free from flaky and elongated particles.
• Adhesion with bitumen: good affinity so that the binder coats and sticks to aggregate (hydrophobic preferred).
• Clean, non-absorbent and of proper gradation.

Four Laboratory Tests and Their Purpose

(Other tests: Flakiness & Elongation index test for shape; Stripping/Bitumen adhesion test for affinity; Specific gravity & water-absorption test.)

Bitumen and Its Role

Bitumen is a black to dark-brown viscous, semi-solid or solid hydrocarbon material obtained as a residue from the fractional distillation of crude petroleum. It is soluble in carbon disulphide and is the most widely used binder in road construction.

Role as a binder in flexible pavements: bitumen coats and binds the aggregate particles together, providing cohesion and a waterproof, flexible matrix. It holds the aggregates in position under traffic loads, resists water penetration, and distributes wheel loads while allowing the pavement to deform slightly (flexibility) without cracking.

Penetration Test

• Measures the consistency/hardness of bitumen.
• A standard needle loaded with 100 g is allowed to penetrate the bitumen sample for 5 s at 25 °C.
• The penetration is the depth (in tenths of a millimetre, 1/10 mm) the needle sinks.
• Higher penetration = softer bitumen (e.g., 80/100 grade is softer than 60/70). It is used to grade paving bitumen.

Softening Point Test (Ring and Ball)

• Determines the temperature at which bitumen attains a particular degree of softening (the temperature at which a steel ball, supported by the bitumen in a brass ring, falls through a height of 25 mm in a heated water/glycerin bath).
• Expressed in °C.
• Higher softening point = bitumen is harder / less susceptible to temperature (better for hot climates). It indicates the temperature susceptibility of bitumen.

Summary: penetration indicates relative hardness (consistency); softening point indicates temperature susceptibility — both together help select the correct bitumen grade for the site climate.

Given Data

Spot speeds: $v_i = 30, 40, 45, 50, 60$ km/h; number of vehicles $n = 5$; length $L = 0.5$ km.

Time-Mean Speed ($v_t$)

Arithmetic mean of the spot speeds:

$$v_t = \dfrac{\sum v_i}{n} = \dfrac{30 + 40 + 45 + 50 + 60}{5} = \dfrac{225}{5} = 45.0 \text{ km/h}$$

Time-mean speed $v_t = 45.0$ km/h.

Space-Mean Speed ($v_s$)

Harmonic mean of the spot speeds:

$$v_s = \dfrac{n}{\sum \dfrac{1}{v_i}}$$

Compute $\sum 1/v_i$:

$\tfrac{1}{30} = 0.033333$, $\tfrac{1}{40} = 0.025000$, $\tfrac{1}{45} = 0.022222$, $\tfrac{1}{50} = 0.020000$, $\tfrac{1}{60} = 0.016667$

$$\sum \tfrac{1}{v_i} = 0.117222$$ $$v_s = \dfrac{5}{0.117222} = 42.65 \text{ km/h}$$

Space-mean speed $v_s \approx 42.65$ km/h.

Why $v_s \le v_t$

The time-mean speed is the arithmetic mean while the space-mean speed is the harmonic mean of the same set of speeds. By the mathematical property that the harmonic mean is always less than or equal to the arithmetic mean, $v_s \le v_t$. Physically, slower vehicles spend more time within the study length and are therefore weighted more heavily in the space-mean (distance-based) average, pulling it down. Equality holds only when all vehicles travel at the same speed.

Here $42.65 < 45.0$, confirming the relationship.

(a) Classification of Traffic Signs

Traffic signs are classified into three main groups:

1. Regulatory (mandatory) signs: enforce traffic laws/regulations; disobeying is a legal offence. Usually circular. Examples: STOP, GIVE WAY, speed limit, no entry, no parking.
2. Warning (cautionary) signs: warn the driver of hazards ahead so caution can be exercised. Usually triangular with red border. Examples: sharp curve, narrow bridge, pedestrian crossing, school ahead.
3. Informatory (guide) signs: give information/guidance about destinations, distances, facilities and routes. Usually rectangular. Examples: direction signs, place identification, petrol pump, hospital.

(b) Functions of Road Markings

Road markings are lines, patterns, words or symbols on the carriageway used to guide and regulate traffic, supplementing signs. Functions:

• Channelize and guide traffic into proper lanes (centre line, lane lines).
• Indicate where overtaking is/ is not permitted (continuous vs broken lines).
• Demarcate carriageway edges, parking areas and pedestrian crossings.
• Provide regulation (stop lines, give-way lines) and warnings without distracting the driver.
• Improve safety, especially at night and in poor visibility (with reflective paint).

(c) Origin–Destination (O–D) Survey and Its Uses

An O–D survey collects data on the points of origin and destination of trips made by road users, along with trip purpose, mode and length. Methods include roadside interview, home interview, registration-number (license-plate) method, and tag-on-vehicle / postcard methods.

Uses:

• To plan new road links, bypasses and expressways to divert through traffic.
• To locate and design intersections, terminals and parking facilities.
• To plan and phase highway network development and mass-transit routes.
• To establish desire lines showing the pattern and magnitude of travel demand.

(d) Traffic Islands and Their Types

A traffic island is a raised or marked area within a carriageway used to control and direct traffic movement and to provide safety. Types:

1. Channelizing islands: guide traffic into definite paths at intersections, reducing conflict areas.
2. Divisional (median) islands: separate opposing streams of traffic on a divided highway.
3. Pedestrian (refuge) islands: provide a safe place for pedestrians to wait while crossing a wide road.
4. Rotary (central) island: the central island of a roundabout around which traffic circulates.

(Answer any three of the above for full marks.)