geometric design principles

GEOMETRIC DESIGN PRINCIPLES – RURAL ROADS

Training Module on Geometric Design-Rural Roads

1. Introduction. Geometric standards depend primarily on the class and functionality of the road, the operating speed of traffic, terrain & climatic conditions. Geometric design standards relating to low-volume rural roads should take cognizance of the facts that resources in developing countries and funds are limited and earthworks have to be minimized as much as possible. But under any circumstances safety should not be compromised. It is important to consider the geometric design for rural roads slightly differently from the strict conventional parameters, as standard solutions are often not desirable. Also, geometric design takes slightly different approaches for new construction and for rehabilitation. The idea is to seize available opportunities to minimise costs of construction without compromising road safety. Situations where there are people walking 10 – 12km to access basic services indicate that there is a serious problem of accessibility. In such cases accessibility takes precedence over travel time and level of comfort, and geometric design should be relaxed. For longer roads where individual journeys are likely to take longer time, there is always tendency for the operating speed of traffic to be higher than the design speed and travel time becomes more important and the conventional geometric design standards have to be followed much more strictly. For low-volume rural roads it is sufficient to achieve minimum standards of safety in geometric design and compensate that with use of low-cost traffic controls. Below are the guidelines which can be followed in order to put in place appropriate geometric design standards for the different classes of rural roads. A clear distinction should be made between unsealed and sealed roads.

Item Acceptable Conditionally Acceptable

Not Acceptable

Gradients ≤ 12% 13 – 17% (1) > 17% Radius of Curvature ≥ 100m ≥ 50m(2)

50 – 8m (3) < 5m

Stopping sight distance

≥ 80 40 – 79m(4) < 40m

Road width 6m carriageway 3 – 5.9m carriageway(5) >6m carriageway(6)

< 3m carriageway

Table 1.0: Few basic Geometric Design Parameters for Unsealed Rural Roads Design Speed 60km/h Explanatory Notes: Conditionally Acceptable

(1) The gradient limits are acceptable on condition that the section of road with steep gradient is not too long for vehicles to climb and the gravel material is well graded and of low plasticity in order to provide the much needed traction during the wet season. Protection against erosion should be given high priority in such circumstances.

(2) This curvature limit is acceptable at low operating speed, not more than 60km/h, and in areas with difficult terrain or property boundaries.

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(3) The curvature limits are applicable in highly mountainous areas where roads are cut on steep slopes on the side of hills or mountains with no room to improve the curvature. In such cases traffic control mechanisms should be used in order to compensate for reduced road safety.

(4) For low-volume roads in hilly areas conventional stopping sight distances may not be achieved because sometimes-deep cuts will have to be excavated in order to reduce the sag and crest curves. However, the relaxation in the specification should also be compensated with use of traffic control mechanisms and adequate advance warning. This is the case where possibility requirements supersede travel time and comfort.

(5) The road width is acceptable on condition that the traffic volume is not more than 100 vehicles per day.

(6) If the road width is greater than 6m then road safety is enhanced but such a road would cost more than necessary to construct and maintain. Such a road width would be acceptable on condition that there are adequate justification is given such as the need to accommodate a diverse traffic mix e.g. a mix of non-motorised and motorised traffic.

2. Low-volume sealed roads

Almost all of class C roads that is administered by the provincial councils are mostly metaled and tared. Class C & D taken together is around 15,000km. The table 2.0 gives guidance on the minimum radii of curvature for low-volume sealed roads.

2.1 Horizontal Alignment Horizontal Alignment is usually a series of straights and circular curves connected by transition curves. Even though the provision of transition curves will ensure smooth movement in reality its provision is not considered for rural roads in SL. 2.2 Movement on a curve When vehicles negotiate a curve a sideways frictional force is developed between the tyres and road surface. This friction must be less than the maximum available friction if the bend is to be traversed safely For any given curve and speed, super elevation may be introduced to enable a component of the vehicle’s weight to reduce the frictional need. The general relationship for this effect is represented by equation number 1.0. R=V2/127(e+f) eqn1.0

Where: R= Radius of Curve (m) V=Speed of vehicles (km/hr) E= cross fall of the road (m/m)

F=Coefficient of the side friction force developed between the vehicle tyres and road surface.

Example 1:For a particular road improvement work take Rmin = 250m with a maximum super elevation of 3%,f=0.15.What should be the desirable design speed to be adopted?

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The minimum curve radius relevant to a particular design speed could be derived by substituting, the maximum super elevation (e-max) and maximum side friction possible (f-max) . Thus: Rmin = V2/127 (emax + fmax) eqn2.0 Example 2:Calculate the minimum radius to be adopted for V=70kmph,emax=4% and fmax =0.15. Table 2.0 below provides the minimum radii for different super elevation values and design speeds, whereas table 3.0 provides the maximum side friction values.

Super elevation Design Speed

2.5% 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 10.0% 30 35 30 30 30 30 30 25 25 25 40 60 60 55 55 55 50 50 45 45 50 105 100 95 90 90 85 80 80 75 60 155 150 145 135 130 125 120 115 110 70 225 215 205 195 185 180 170 165 155 80 310 300 280 270 255 240 230 220 210 90 415 400 380 355 340 320 305 290 280 100 515 500 470 445 420 400 380 365 350 Table 2.0: Minimum radii to suit for various design speeds and super elevation values.

Maximum possible side-friction values Operating Speed (Kmph) Bituminous roads Gravel Roads

30 0.21 0.14 40 0.19 0.13 50 0.17 0.12 60 0.16 0.11 70 0.15 0.10 80 0.14 0.19 90 0.13 - 100 0.128 -

Table 3.0: The maximum side friction values The values given above are based on conventional designs. Relaxation of curvature standards is not advisable because the perception of the drivers on seeing a sealed road is that the all sealed roads are high standard. Such an error could result in serious accidents. When negotiating large radius curves for example a radius of 1100m for a design speed of 70kmph even we didn’t maintain a super elevation, vehicles didn’t encounter and stability problems. So we could still maintain the normal cross falls for such large curves. This situation is referred as the adaptation of adverse cross fall. Table 4.0 provides the radii for which adverse cross-falls could be adopted.

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Minimum Radii with adverse cross fallsOperating Speed Open Built-up

30 205 160 40 360 280 50 565 440 60 810 630 70 1105 860

Table: 4.0 Curves for which adverse cross falls could be adopted. a. Transition Curves These are inserted between tangents and circular curves to reduce abrupt introduction of the lateral acceleration. It has a constantly changing radius. they can be used to link straights or two circular curves. Further they will provide convenient section over which super elevation or pavement widening could be applied. For large radius curves the rate of change of lateral acceleration is small and hence transition curves are not normally required. You can use the equation No 3.0 to assess the length of the transition curves. Ls = eV/3.6n eqn 3.0 Where: Ls=Length of Transition Curves (m) E= Super elevation of the curves. V=design speed (Km/m) N=rate of pavement rotation (m/m/sec) The shift, i.e the offset of the start of the circular curve from line of the tangent should be at least 0.25m for appearance purposes. We can omit transition if the shift is <0.25m.See fig.1.0.

Fig: 1.0: the “p” represents the shift.

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c. Other Consideration

I. The successive geometric features should be consistent II. Design speed that we referred here is the speed exceed by only 15% of the

vehicles (we called it 85% percentile speed) III. For small deflection angles, use larger curves. This will improve the visibility. This

will prevent drivers to cut the corners of small curves. IV. Avoid the use of long curves of tight radii, as drivers at speed other than the

design speed will find it difficult to remain in lane. V. For potentially hazardous tight horizontal curve that cannot be re-aligned for

economic social or due to environmental reasons, then provide sufficient warning system to drivers.

VI. Avoid potentially unsafe overtaking on curves with inadequate sight distance and provide sufficient signs, and markings or physical barriers.

d. We normally encounter several types of horizontal curves.

1. Circular Curves. 2. Reverse Curves. 3. Unidirectional Curves.

e. Details of a full Circular Curve. Lc=Length of circular portion = R Lt= Tangent length = Rtan /2 E= Radial offset from Ip = R(sec /2-1) See fi.2.0. Fig; 2.0: Details of a circular curve.

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f. Super elevation Development

Fig 3.0: How super elevation is developed.

2 Vertical Alignment The vertical alignment, which is an integral part of the geometrical design, is also critical as far as possibility and safety is concerned. Care should be taken in order to avoid sag and crest curves that are too sharp or tight because that may inhibit pass ability of large trucks. Crest curves are more hazardous than sag curves and care should be taken when establishing design limitations.

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2.1) The crest curve The longitudinal section of a road consists of gradients joined by curves. These curves are known as vertical curves. Their purpose is

To smooth the passage of a vehicle from one gradient to another. To increase the sight distance across the junction of the gradients.

The convex vertical curves are known as “CRESTS” and concave vertical curves are refereed as “SAG”. The curve geometry is a simple parabola. It provides a constant rate of change of curvature. Its forms can be derived as illustrated by fig 4.0.

X

Y

A

N

K

O

R

B

M

P

QT

L/2

L

Fig 4.0:The vertical curve geometry

Let two grade lines of gradient G1 and G2 intersects each other at O. The parabolic vertical curve of length L, inserted between these two grade lines is ANB.

a. The change of gradient, G = G2 – G1

b. RB = KO – TO = G2L/2 - (- G2L/2) =L/2(G1 + G2)

c. KM/RB = 1/2 = L/4(G1 + G2)

d. MO = KO - KM = L/4(G1 – G2) e. MN = MO/2

=L/8(G1 – G2) = - L/8(G)

f) For a simple parabola, Y = aX2 + bX

At X=0,dY/dX = G1 and , X=L/2, Y = KM + MN

= L/8(3G1 + G2)

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Solving for a and b gives,

Y = (G2 – G1) X2/2L + G1X

g) The ordinate PQ,

y = G1 X - Y y = -( G2 – G1) X2/2L

h) The mid ordinate MO,

ymax = - L/8(�G) y = ymax 4 X2 / L2

i) The elevation at Q,

Eq = Ea + G1 X – y = Ea + G1 X – ymax (4X2/L2)

L=40

L/2=20A R X

Q

P

O

NBG=5%

G=-3%ma

xy

Y

datum level = 100m

Fig 5.0: An example �G= G2 – G1

= (-3–5)/100 = - 0.08 = - 8%

RB= L/2(G1 + G2) =40/2(5-3)/100 = 0.40

ymax= - L/8(�G)

= - 40/8(-8/100) = 0.40

The elevation along the curve, Eq = Ea + G1X – ymax (4X2/L2) Elevation at A, Ea = 100m Eq = 100 + 5X/100 –0.40 (4X2/402) Ex 4: Calculate and tabulate the finished levels for chain ages 0+15 to 0+40 (You can use the Table 5.0 to record the results).

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Distance from A Elevation m m 0 100.000 5 100.225 10 100.400 15 20 25 30 35 40

Table 5.0: Finished levels to be maintained. 2.2) The SAG curve During day light adequate sight distances are always available in sag curves. However at night the distance you can see is limited by the distance illuminated by headlamp beams and hence minimum sag curve length for this situation is given by equation 3.0. Lv=AS2/150+3.5S……..eqn 3.0 Where, Lv = Length of vertical curve (m) A = Algebric difference in gradient (%) S = Sight Distance F Fig.6.0: Length illuminated by headlamps. The curvature is given by the K value, which is the length of the curve in metres for a 1% change in grade. The table 6.0 provides the minimum K values adopted by three popular design approaches. Minimum K values for vertical curves Design speed (km/h)

SATTC TRL ORN6 ARRB

Crest Curves(1)

Sag Curves(2)

Crest Curves(1)

Sag Curves(3)

Crest Curves(1)

Sag Curves(3)

40 6 8 3 1.3 50 11 12 5 2.2 5 4 60 16 16 10 3.5 9 6 70 23 20 16 4.8 14 8 80 33 25 23 10 85 30 8.1 90 46 31

100 60 36 60 13.1 63 16 Table:6.0: Minimum K values for vertical curves.

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(1) Based on stopping sight distances (2) Based on headlight illumination criteria (3) Based on comfort criteria

When designing rural roads the need for comfort considerations is a secondary matter and should not be given priority because comfort criteria is mainly fulfilled through smoothening of curves, resulting in a significant increase in earthworks. That is not desirable especially in situations where resources are scarce. Where these limits are not applicable due to constraints compensatory measures such as speed reduction humps and road signage should be put in place Longitudinal gradient is very important to facilitate drainage. For kerbed pavements longitudinal grade shouldn’t be less than 0.3%.In the case of our rural roads, it is desirable to maintain a longitudinal grade even at flat grades.

3 The cross sectional geometry. Cross-section geometry will normally consist of: Carriageway Shoulder – paved/sealed (Or unpaved raised) Drain – buildup, earth Center median Reservation for services Earthwork profiles Facilities for cyclists and other Special user groups

Fig 7.0:A typical cross - section 3.1 Carriageway Width Carriageway width depends on what is achievable in relation to what is desirable, and the future development plans for each road. The desirable minimum is usually a minimum of 6m wide carriageway. This width is adequate for two large vehicles to pass each other without getting into the shoulders. However, it is not always feasible to achieve the desired minimum because terrain constrains and financial resources can be limiting factors in the provision of rural roads. The criteria for determining carriageway width differs from country to country but for rural roads it is advisable to follow the information given in Table 7.0.

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Item Carriageway width Selection criteria 5 – 6m sealed carriageway

Traffic > 100 v.p.d. Proportion of heavies > 40% There are plans for upgrading in

the foreseeable future.

3m sealed carriageway + 1.5m unsealed shoulders(*)

Traffic < 100vehicles There is lack of capital financing

problems No plans for upgrading in the

foreseeable future. There is an adequate maintenance

capacity and resources for relatively frequent shoulder repair and grading.

There is adequate justification for sealing a single lane width instead of the full carriageway.

Carriageway width

< 3m For less than 10 v.p.d. where the road is designed only on passability criteria.

Table: 7.0: Selection of a carriageway width. * This type of road is called a ‘narrow mat’ with only the central 3 metres of the carriageway sealed and 1.5m either side as gravel shoulders.

3.2 Shoulder

The desirable width of the shoulder is 3.0m The minimum width should be 2.4m The absolute minimum width should be 1.8m

3.3 Drains

For earth drains, adopt a trapezoidal section. For buildup drains, adopt a rectangular section. Design details of road side drains system is to be dealt separately.

3.4 Center median Minimum width is 1.2m.Medians are provided for 2 way 4 lane roads and

multilane. We don’t normally encounter the provision of center median in the case of rural roads of class C and D.

3.5 Facilities for cyclists and other special user groups They are most vulnerable road user groups The minimum cycle track width is 1.5m

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Fig8.0: Well defined cycle tracks (Width is 1.5m) 3.6 Earthwork Profiles For fill slopes provide 1:1.5

(1.5 Horizontal to 1 vertical) For cut slopes provide 1:4

(1 Horizontal to 4 vertical)

4. Cross-falls Road cross-sections also differ from country to country but for rural roads the guiding principle is drainage. The cross-sectional profile should be one that enhances as much drainage as possible. In high rainfall areas it is much more beneficial to widen and deepen side drains while using the material to build up the embankment and raise the road. In order to minimize the cost of construction the side drains may be used as detours during construction and in so doing no extra money is spend on separate detours. The side drains get widened in the process. The effect is that in the event of a storm water does not rise to the level of base or sub-base layer and as such a leaner and cheaper pavement can be designed. The minimum crest height i.e. the height from invert of side drain to the central crest line should be not less than 750mm. Table 8.0 and 9.0 provide the recommended carriageway and shoulder cross-falls.

Carriageway surfacing The cross-fallConcrete 2.0% Asphalt concrete 2.5% Sealed surfacing 3.0% Unsealed gravel 4.0%

Table 8.0: Carriageway cross-falls

Shoulder Cross-fall Bitumen or similar all Weather surface

3%-4%

Gravel 4% – 5% Table 9.0: shoulder cross falls 5 Gradients Maximum gradient that could be allowed will depend on the class of road, composition of vehicles, design speed, topography etc., For high-speed roads a grade as low as 3% provides very satisfactory level of service. You can go up to grades of 6% Recommended maximum grades are listed in table No 10.0.

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Class of Road A B C D E Terrain Type F R M F R M F R M F R M F R M Maximum Grade 4 6 8 5 7 9 7 9 10 9 10 10 9 10 10Table 10.0:Maximum allowable grades. You may have to appreciate gradients in excess of the recommended general maximum gradients, provided that, It is adopted for a short section and because of that cost saving is significant. Terrain conditions are so difficult. Fraction of heavy vehicles is negligible. The road is less important and hence investment couldn’t be justified.

But we have to limit the length of steep grades to maintain the quality of the road. This length is referred as the “Critical length of Gradients ”. Table 11.0 provides the critical lengths of grades. Grade (%) Critical length (m) 3 480 4 330 5 250 6 200 7 170 8 150 9 140 10 135 12 120 Table 6.0: Critical Lengths grades. 5.1 A minimum Gradient As stated earlier we need to have a minimum longitudinal gradient to facilitate drainage effectively. It has been found that the cost of maintenance of a road section having a 0% grade is more than a section that has at least some longitudinal grade. In urban areas where either side of the pavement is kerbed, adopt a longitudinal grade not less than 0.3%.For rural areas a minimum grade of 0.5% is desirable. 6) Combination of horizontal and vertical curves. It is our conventional practice to treat horizontal and vertical alignments independently. But the profile a driver sees is the combined effect of both. Poor coordination of the horizontal and vertical alignments of a road can result in visual effects, which contribute to accidents and are detrimental to the appearance of the road. It is extremely difficult and costly to correct alignment deficiencies after the highway has been constructed. Studies suggest that initial cost savings may be more than offset by the subsequent economic loss to the public in the form of accidents and delays.

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The presentation of misleading information to drivers can be avoided by making coincident all the points where horizontal and vertical curvatures changed. Where this not possible and the curves cannot be separated entirely, the vertical curves should be either contained wholly within or wholly out side the horizontal curves. It is desirable that the horizontal and vertical curves are of the same length and the chainage of their centers should coincide. We won’t be able to achieve a realistic design in practice; as such a logical design will be a compromise between the alignment which offers the most in terms of safety, capacity, ease of uniformity of operation and pleasing appearance, within the practical limits of the terrain. The fig 9.0 below illustrates several examples of undesirable combinations of horizontal and vertical curvatures.

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Fig 09: Undesirable Combinations of horizontal and vertical profiles.

geometric design principles

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