Geometric Design of Roads

CIVE3707 Integrated Design Project

Plan

Elevation

Road in 3D

Roads have horizontal and vertical alignments to allow safe driving at design velocities.

Horizontal – straights joined by curves

Vertical – constant gradients joined by vertical curves

Design:

Design is an iterative process and it is often (usually) impossible to satisfy all requirements and key requirements need to be decided.

Horizontal and vertical alignments should be in phase - i.e. the tangent points of the horizontal and vertical curves should coincide, or vertical curves should be within the horizontal.

Horizontal Curves:

To change direction a vehicle needs centripetal acceleration and hence a force acting radially inwards.

A vehicle can’t change instantly from a straight to a curve and needs to change direction gradually.

Figure 1. Circular Curve

T and U are the tangent pointsI the intersection point the deflection angle.

Circular Curve Design.

Tangent length = TI = R. tan(/2)

X = R((1/cos /2) - 1)

Stages in design:1. Measure the deflection angle from the map.2. Choose R.3. Calculate the tangent lengths and X if wanted.4. Check if the curve fits.

Figure 2

Figure 3. Composite curve.

T-T1 and T2-U Transition curve

T1-T2 Circular curve

S the shift of the curve

Transition Curves:In a transition curve the radius changes from to R. The curve is a spiral.If T1 and T2 coincide the curve is wholly transitional.

Length of the transitional curve = LT = v3/3.6cR

where c is the rate of change of radial acceleration, 0.3m/s3 desirable and 0.6m/s3 maximum

S = LT2/24R

TV = VT1

= LT/2R

IT= (R + S)tan /2 + LT/2

Design of composite curves:

1. Find the deflection angle2. Select R3. Assume c = 0.3m/s3

4. Find LT

5. Find S6. Calculate IT7. If the curve is not acceptable assume new R or c and recalculate

Design of wholly transitional curves:

1. Find the deflection angle2. Assume c 3. Find R (=[v3/3.63c]0.5)4. Check R Rmin

5. If R is not acceptable c or must be reduced and the calculations repeated.

6. If R is acceptable find LT

7. Find S

Superelevation:Superelevation is the ‘banking’ on a curve to help stop a vehicle sliding off the road.

This may be applied along the transition curve to a maximum of 7% (1 in 14.5) and not less than 2.5% (1 in 40) for drainage.

Figure 4. Vertical Curve(Crest)

Vertical Alignment:Gradients are expressed in percentages eg. 1 in 100 is 1%In calculations the algebraic difference of gradients is used, and a slope rising to the right is +ve and a slope dropping to the left is -ve.

If the gradients are m and n then the algebraic difference is:

A = m - n

If A is +ve there is a crest. If A is -ve there is a sag.

A vertical curve joins two constant gradients ensuring visibility for safe overtaking, if required, safe stopping distances and a comfortable ride. The drivers eyes are assumed to be 1.05m above ground level.

Vertical Alignment:Vertical curves are ‘flat’ and it is assumed that ‘horizontal’ lengths (chord, arc, horizontal distance are the same and that vertical and orthogonal distances from the chord to the curve are the same. Vertical curves are parabolic and the general arrangement is shown in figure 4.

x= Ay2/200Lv (x = cy2 is the equation of the parabola)

Lv min = KA (ignore the sign of A)

where K is determined by sight distances for stopping and overtaking, the latter being important on crests. Lv is the vertical curve length.

H =(m)y/100 - (A)y2/200Lv

(retain the signs of m and A) Hmax/min = Lvm2/200A

Design of vertical curves:

1. From the constant gradient lines measure m and n and find A2. Select K3. Find L v, min and then adjust Lv to fit the horizontal alignment

4. Find Hmax,min

5 Sketch the approximate curve.

Overall Road Design:1. On a plan fit in horizontal straights bearing in mind the various

constraints, contours etc.2. Design the horizontal curves.3. Take a long section along the proposed centre line estimating ground

levels from the contours.4. Plot the vertical section, using an exaggerated vertical scale. On the

plot indicate the horizontal alignment.5. Select constant gradients attempting to minimise the earthworks and

match ground level etc. where required.6. Design the vertical curves trying to get the horizontal and vertical

alignments in phase.7. Repeat as necessary

( Reference: Surveying for Engineers, Uren and Price)

Straight Curve Straight Curve Straight

EGL PGL

Ver t Curve 1 Constant gradient Ver t Curve 2 Ver t Curve 3 Constant gradient Constant gradient

Chainage