BE Civil Engineering (IOE, TU) Transportation Engineering I (IOE, CE 652) Question Paper 2080 Nepal

Principles of highway planning surveys

Highway planning surveys collect the basic data required to plan a rational, economical road network. The four classic surveys are:

1. Economic studies – population distribution, per-capita income, trends of production and consumption, existing modes of transport.
2. Financial studies – sources of revenue (taxes, tolls, fuel levies), funds available, road-user benefits.
3. Traffic (road-use) studies – traffic volume, origin–destination, traffic flow patterns, axle-load and growth rate.
4. Engineering studies – topography, soil and material surveys, drainage, special problems (slides, river crossings).

Role of the master plan

The master plan is the final road network proposed for the area for a target horizon (usually 20 years). It fixes the alignment, classification and priority of every road. Because funds are limited, the plan is implemented in phases (typically three 5–7 year phases); the saturation system or maximum-utility approach is used to fix the order of construction so that the road giving the maximum utility per unit length is built first.

Saturation system computation

Utility unit basis:

• Population: 1 unit per 1000 persons served
• Productivity: 1 unit per 10 tonnes/day

Total utility of a route = population units + productivity units. Utility per unit length = total utility / length.

Route AB:

$$U_{AB}=\frac{60}{1}+\frac{120}{10}=60+12=72\text{ units},\qquad \frac{U}{L}=\frac{72}{18}=4.00$$

Route BC:

$$U_{BC}=45+\frac{90}{10}=45+9=54\text{ units},\qquad \frac{U}{L}=\frac{54}{24}=2.25$$

Route CD:

$$U_{CD}=30+\frac{60}{10}=30+6=36\text{ units},\qquad \frac{U}{L}=\frac{36}{30}=1.20$$

Recommendation

Construct in the order AB → BC → CD, since AB gives the highest utility per unit length (4.00), followed by BC (2.25) and CD (1.20).

Definitions

Stopping sight distance (SSD): the minimum distance visible to a driver, ahead of the vehicle, that is just sufficient to stop the vehicle safely without colliding with an obstruction on the carriageway. It is the sum of the lag distance (during perception–reaction) and the braking distance.

Overtaking sight distance (OSD): the minimum distance open to the vision of the driver of a vehicle intending to overtake a slower vehicle ahead, with safety against on-coming traffic.

(a) Stopping sight distance

$$V=65\,\text{km/h}=\frac{65}{3.6}=18.06\,\text{m/s}$$

Lag distance $=v\,t=18.06\times2.5=45.14\,\text{m}$

Braking distance $=\dfrac{v^2}{2gf}=\dfrac{18.06^2}{2\times9.81\times0.36}=\dfrac{326.2}{7.063}=46.18\,\text{m}$

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

(b) Overtaking sight distance

Speeds: design (overtaking) $v=65/3.6=18.06\,\text{m/s}$; overtaken $v_b=50/3.6=13.89\,\text{m/s}$; acceleration $a=2.5\,\text{km/h/s}=2.5/3.6=0.694\,\text{m/s}^2$.

OSD $= d_1+d_2+d_3$

$d_1$ (distance during reaction at speed $v_b$):

$$d_1=v_b\,t=13.89\times2.0=27.78\,\text{m}$$

Minimum spacing $s=0.2\,v_b+6=0.2\times13.89+6=8.78\,\text{m}$

Overtaking time $T=\sqrt{\dfrac{4s}{a}}=\sqrt{\dfrac{4\times8.78}{0.694}}=\sqrt{50.6}=7.11\,\text{s}$

$d_2$ (distance travelled by overtaking vehicle during the manoeuvre):

$$d_2=v_b\,T+2s=13.89\times7.11+2\times8.78=98.76+17.56=116.32\,\text{m}$$

$d_3$ (distance travelled by on-coming vehicle in time $T$):

$$d_3=v\,T=18.06\times7.11=128.39\,\text{m}$$ $$\boxed{OSD=27.78+116.32+128.39\approx 272.5\,\text{m}}$$

Overtaking zone

The minimum length of an overtaking zone $=3\times OSD=3\times272.5\approx \mathbf{817.5\,m}$ (desirable $=5\times OSD$). Sign posts SP1/SP2 mark the zone.

(a) Design superelevation (IRC method)

Step 1 – superelevation for 75% of design speed, neglecting friction:

$$0.75V=0.75\times60=45\,\text{km/h}$$ $$e=\frac{(0.75V)^2}{127R}=\frac{45^2}{127\times130}=\frac{2025}{16510}=0.1227$$

This exceeds $e_{max}=0.07$, so superelevation is limited.

Step 2 – set $e=e_{max}=0.07$ and check friction at full design speed:

$$f=\frac{V^2}{127R}-e=\frac{60^2}{127\times130}-0.07=\frac{3600}{16510}-0.07=0.218-0.07=0.148$$

Since $f=0.148<0.15$ (allowable), the design is safe.

$$\boxed{e_{design}=0.07\ (7\%)}$$

(b) Extra widening

Number of lanes $n=2$, wheelbase $l=6.0\,\text{m}$, $R=130\,\text{m}$, $V=60\,\text{km/h}$.

Mechanical widening:

$$W_m=\frac{n\,l^2}{2R}=\frac{2\times6.0^2}{2\times130}=\frac{72}{260}=0.277\,\text{m}$$

Psychological widening:

$$W_{ps}=\frac{V}{9.5\sqrt{R}}=\frac{60}{9.5\times\sqrt{130}}=\frac{60}{9.5\times11.40}=\frac{60}{108.3}=0.554\,\text{m}$$ $$\boxed{W_e=W_m+W_{ps}=0.277+0.554\approx 0.83\,\text{m}}$$

(c) Length of transition curve

$v=60/3.6=16.67\,\text{m/s}$.

(i) Rate of change of centrifugal acceleration:

$$C=\frac{80}{75+V}=\frac{80}{75+60}=\frac{80}{135}=0.593\,\text{m/s}^3\quad(\text{within }0.5\text{–}0.8)$$ $$L_s=\frac{v^3}{C\,R}=\frac{16.67^3}{0.593\times130}=\frac{4630.6}{77.09}=60.1\,\text{m}$$

(ii) Empirical IRC (plain/rolling) formula:

$$L_s=\frac{2.7V^2}{R}=\frac{2.7\times60^2}{130}=\frac{9720}{130}=74.8\,\text{m}$$

Adopted value: the larger of the two governs, so adopt $L_s\approx \mathbf{75\,m}$ (round to a convenient figure).

Data

Deviation angle (algebraic difference of grades):

$$N=g_1-g_2=(+0.04)-(-0.03)=0.07$$

SSD $S=180\,\text{m}$, eye height $H=1.2\,\text{m}$, object height $h=0.15\,\text{m}$.

Assume $L>S$

For a summit curve when the length is greater than the sight distance:

$$L=\frac{N\,S^2}{2\left(\sqrt{H}+\sqrt{h}\right)^2}$$

Compute the denominator term:

$$\sqrt{H}+\sqrt{h}=\sqrt{1.2}+\sqrt{0.15}=1.0954+0.3873=1.4827$$ $$\left(\sqrt{H}+\sqrt{h}\right)^2=2.198,\qquad 2\times2.198=4.397$$

Therefore:

$$L=\frac{0.07\times180^2}{4.397}=\frac{0.07\times32400}{4.397}=\frac{2268}{4.397}=515.8\,\text{m}$$

Verify assumption

Since $L=515.8\,\text{m}>S=180\,\text{m}$, the assumption $L>S$ is valid.

$$\boxed{L\approx 516\,\text{m}}$$

The summit curve length required for safe stopping sight distance is about 516 m.

Importance of traffic volume studies

Traffic volume studies measure the number and class of vehicles passing a point per unit time. They are used to:

• fix the number of lanes and geometric/structural design of roads;
• establish relative importance of routes and justify improvements;
• plan signal timings, regulation and one-way schemes;
• compute capacity, congestion and accident exposure.

Concept of PCU

Because mixed traffic contains vehicles of widely differing size, speed and manoeuvrability, each class is converted to an equivalent number of standard passenger cars using a Passenger Car Unit (PCU) factor. This gives a single homogeneous measure of demand for capacity analysis.

(a) Equivalent PCU per hour

$$\boxed{\text{Demand}=2010\,\text{PCU/h}}$$

(b) Number of lanes and level of service

Lane capacity $=1500\,\text{PCU/h}$.

$$\text{Lanes required}=\frac{2010}{1500}=1.34\Rightarrow \textbf{2 lanes (rounded up)}$$

With 2 lanes the supplied capacity $=2\times1500=3000\,\text{PCU/h}$.

Volume-to-capacity (v/c) ratio:

$$\frac{v}{c}=\frac{2010}{3000}=0.67$$

A v/c ratio of about 0.67 indicates stable flow (roughly Level of Service C): operations are acceptable with moderate restriction on speed and manoeuvring, but a single lane (v/c = 1.34) would be heavily over-saturated and unacceptable.

Aggregate tests and their significance

Summary

For a bituminous surface course the aggregate must be strong (low crushing/impact value), hard (low abrasion value), durable (low soundness loss), cubical (low flakiness/elongation) and hydrophobic/well-bonding (good stripping resistance). Aggregates meeting all these limits give a stable, long-lasting wearing surface.

(a) Air voids $V_a$

$$V_a=\left(1-\frac{G_{mb}}{G_{mm}}\right)\times100=\left(1-\frac{2.38}{2.50}\right)\times100=(1-0.952)\times100=4.8\%$$

(b) Voids in mineral aggregate (VMA)

Percentage of aggregate by weight of total mix: $P_s=100-5.2=94.8\%$.

$$VMA=100-\frac{G_{mb}\,P_s}{G_{sb}}=100-\frac{2.38\times94.8}{2.65}=100-\frac{225.6}{2.65}=100-85.14=14.86\%$$

(c) Voids filled with bitumen (VFB)

$$VFB=\frac{VMA-V_a}{VMA}\times100=\frac{14.86-4.8}{14.86}\times100=\frac{10.06}{14.86}\times100=67.7\%$$

Comment on Marshall limits

All three volumetric parameters lie within typical Marshall design ranges, so the mix is satisfactory for a dense bituminous surface course.

Results: $V_a\approx\mathbf{4.8\%}$, $VMA\approx\mathbf{14.86\%}$, $VFB\approx\mathbf{67.7\%}$.

Data

Deviation angle:

$$N=|g_1-g_2|=|(-0.03)-(+0.04)|=0.07$$

Headlight height $h_1=0.75\,\text{m}$, beam angle $\alpha=1^\circ$, $S=180\,\text{m}$.

Length for $L>S$ (headlight sight distance)

$$L=\frac{N\,S^2}{2h_1+2S\tan\alpha}$$

Using $h_1=0.75\,\text{m}$ and $\tan1^\circ=0.01746$ (so $2\tan\alpha=0.0349\approx0.035$):

$$L=\frac{N\,S^2}{1.5+0.035\,S}=\frac{0.07\times180^2}{1.5+0.035\times180}$$ $$=\frac{0.07\times32400}{1.5+6.30}=\frac{2268}{7.80}=290.8\,\text{m}$$

Check assumption

Since $L=290.8\,\text{m}>S=180\,\text{m}$, the assumption $L>S$ is valid.

$$\boxed{L\approx 291\,\text{m}}$$

The valley curve must be at least about 291 m long so that the headlight beam illuminates the full stopping sight distance at night. (Comfort and drainage criteria should additionally be checked, and the larger value adopted.)

Requirements of an ideal alignment

An ideal highway alignment should be:

1. Short – the shortest route between two terminal points (consistent with other constraints).
2. Easy – easy to construct, maintain and operate, with easy gradients and curves.
3. Safe – safe geometric design (sight distance, stable slopes, good drainage).
4. Economical – minimum total cost (construction + maintenance + vehicle operating cost).

Factors controlling alignment in hilly terrain (Nepal)

• Stability of slopes – avoid unstable/landslide-prone hill faces and weak strata.
• Hydrology and drainage – control of hill streams, cross-drainage, avoiding water-logged reaches.
• Gradient and resisting length – gradients limited (ruling ~5–6%); use of hairpin bends to gain height.
• Geometric standards – minimum radius, sight distance and curve standards for the design speed.
• Geology and soil – avoid faults, springs, expansive soils; founding on sound rock where possible.
• Obligatory points – mountain passes, bridge sites, intermediate towns to be served/avoided.

Stages of engineering surveys

1. Map / desk study – study of topographic maps and aerial photos to choose alternative corridors.
2. Reconnaissance survey – rapid field examination of the corridors to eliminate unsuitable ones.
3. Preliminary survey – topographic, soil and traffic surveys of selected routes; compare alternatives technically and economically.
4. Final location and detailed survey – pegging the centre line on the ground and collecting data for detailed design and drawings.

Sorted data

Arranged in ascending order:

$$42,\ 46,\ 47,\ 48,\ 50,\ 51,\ 53,\ 55,\ 58,\ 60$$

(a) Mean spot speed

$$\sum v = 42+48+55+51+60+47+53+58+50+46 = 510$$ $$\bar v=\frac{510}{10}=51.0\,\text{km/h}$$

(b) Median speed

For $n=10$, the median is the average of the 5th and 6th sorted values:

$$\text{Median}=\frac{50+51}{2}=50.5\,\text{km/h}$$

The central tendency of the sample is therefore about 50–51 km/h.

(c) 85th percentile speed (rank method)

Rank position $=0.85\times(n+1)=0.85\times11=9.35$. Interpolating between the 9th value (58) and the 10th value (60):

$$V_{85}=58+0.35\times(60-58)=58+0.70=58.7\,\text{km/h}$$ $$\boxed{\bar v=51.0,\quad \text{median}=50.5,\quad V_{85}\approx58.7\,\text{km/h}}$$

Use of the 85th percentile speed

The 85th percentile speed (the speed at or below which 85% of vehicles travel) is adopted as the design/safe speed for fixing speed limits and many geometric design elements, because designing for it satisfies the great majority of drivers while restraining the small fast minority.

(a) Classification of roads in Nepal (Nepal Road Standard)

• National highways (NH): the main long-distance arterial roads connecting major regions, capitals and international borders (e.g., the East–West Highway). Highest geometric standards.
• Feeder roads (FR): roads that link important towns, district headquarters and economic centres to the national highway network.
• District roads (DR): roads serving traffic within a district, connecting villages and production areas to feeder roads/highways.
• Urban (municipal) roads: roads inside municipalities/urban areas serving local city traffic.

(Functionally roads are also grouped by mobility/access into arterial, collector and local roads.)

(b) Cross-section terms

• Carriageway: the part of the road actually used by moving vehicles — the paved traffic lanes. Width = number of lanes × lane width.
• Roadway (formation width): the carriageway plus the shoulders (and any separators) — i.e., the full top width of the road formation between the inner edges of side drains.
• Right of way (ROW / land width): the total width of land acquired for the road, including the roadway, side drains, slopes, and reserve land for future widening, utilities and landscaping. It is the widest of the three.

Relationship: Carriageway $\subset$ Roadway $\subset$ Right of way.