Considerations in the provision and design of circular or pipe culverts

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General

The provision of drainage for highway is one of the most important aspect of highway design because it ensures the protection of road facilities. Basically, the highway is protected from damage from storm water and subsurface water. These facilities include bridges and culverts.

Circular or pipe culverts are among the three (3) main configurations of culverts. Others are box culvert and oval culvert. Box culverts are still very much in use while oval culverts are being phased out. Circular culverts are often used in construction because of their economy.

Pipe culverts can be made of reinforced or prestressed concrete, unreinforced concrete, steel, cast iron, plastic or stone. However, unreinforced and reinforced pipe culverts are more common in Nigeria. Unreinforced pipe culverts are usually prefabricated or precast in the lengths of 1 m while reinforced ones can be taken up to lengths of 4 – 5m. A standard pipe culvert can be of diameter, 0.5 m, 0.75 m, 1.00 m, 1.25 m, 1.5m etc.

Precast sections of pipe culverts must be bedded and haunched in concrete and surrounded with at least 150 mm concrete. This is in accordance with Nigeria General specifications for roads and bridges and this concrete grade should be preferably 15 N/mm² or higher.

Sizing of pipe culvert

The sizing of pipe culvert begins from the hydraulic design which considers the design discharge of the culvert. Thus, the determination of design discharge forms the basic problem of hydraulic design and requires hydological analysis. Note that the criterion for the hydraulic design is based on providing free surface flow conditions in the culvert at the given design discharge and allowable design velocity and allowable head loss that are specified along the culvert.

Empirical methods such as

Isochrome method and

Q_max = α A

where α = a factor that depends on the climatic and geographical conditions and A = the catchment area have often been in use to provide hydorological data which is basically the design discharge for the culvert. Table 1 provided by Kirwald (Karadi and Krizek, 1980) are often used to estimate the average maximum discharge.

Once the design discharge is known, the dimensions of the culvert can be found according to the hydraulic conditions of its operation often with the usual trend, D = q^8/3 where D = the diameter of the pipe and q = the design discharge or through trial and error method, after which the designed culverts are checked for the velocity controls both at the inlet and outlet.

Table 1; Average maximum design discharge

Catchment Area (m2)	Surface discharge (Litres/s/m2)
Low land	Hills
Bare	Wooded	Bare	Wooded
1	5000	3000	10,000	6,000
5	3700	2400	6,000	3,800
10	2900	1700	4,000	2,500
50	1500	700	2,000	1,300
100	600	400	1,000	600
200	300	160	800	400

The methods provided above for sizing of pipe culverts are empirical methods and seems outdated. In current practice, Inlet and Outlet nomographs (see Figures 3 and 4) are used to size pipe culverts. This involves trial and error to determine the appropriate size of pipe or box culverts according to the flowchart in Figure 2.

Instructions for use of INLET-CONTROL nomograph

A

a. To determine headwater (HW), connect with a straightedge the given culvert diameter or height (D) and the discharge Q, or Q/B for box culverts; mark intersection of straightedge or HW/3; scale marked. (1).

b. If HW/D scale marked (1) represents entrance type used, read HW/D on scale (1). If some other entrance type is used extend the point of intersection in (a) horizontally on scale (2) or (3) and read HW/D.

c. Compute HW by multiplying HW/D by D.

B

a. To determine culvert size, given an HW/D value, locate HW/D on scale for appropriate entrance type. If scale (2) or (3) is used extend HW/D point horizontally to scale (1).

b. Connect point on HW/D scale (1) as found in A (a) above to given discharge and read diameter, height of size of culvert required.

C

a. To determine discharge (Q), given HW and D, located HW/D on scale for appropriate entrance type. Continue as in A (a).

b. Connect point on HW/D scale (1) as found in A (a) above and the size of culvert on the left scale and read Q or Q/B on the discharge scale.

c. If Q/B is read in (b) multiply by B to find Q.

Structural design of pipe culvert

The structural design of a reinforced circular (pipe) culvert requires a determination of the probable maximum load acting on the pipe and its distribution around the pipe periphery. Once this is known, the pipe wall may be designed by means of normal reinforced concrete design procedures. Pipe culverts are usually subjected to two types of loads viz: dead load and live load and sometimes water load for larger pipes (1000 mm and above). The dead and live load are often estimated with the Marston formula. The dead load essentially consists of the backfill/surcharge load while the live load essentially consists of the vehicle wheel load.

The Marston formula states thus:

W_c = C_dwB_d²

Where, W_c = backfill load (kN/m)

C_d = load coefficient, dependent on soil type and ratio of cover depth to trench width

w = soil density (kN/m³)

B_d = trench width (m)

The load analysis for the circular culvert is similar to that used for box culvert and a classical example of this can be found at Loading and Design of Box Culvert.

There is usually no special standard or regulations for the structural design of circular culvert but such design procedures are usually found among the general specifications and standards for roads and bridges of codes but according to Reynolds and Steedman (2008), pipe culverts should be reinforced to resist longitudinal bending resulting from unequal vertical earth pressure and unequal settlement. However, due to the uncertainty associated with the magnitude and disposition of the earth pressures, an accurate analysis of the bending moments is impracticable.

A basic guide is to take the positive moments at the top and bottom of the pipe, and the negative moments at the ends of a horizontal diameter, as 0.0625qd²

Where,            q = load at the top or pressure from the ground assuming the pressure to be distributed uniformly on a horizontal plane, and

                        d = pipe diameter

For the current practice in the structural design of pipe culverts, Oyenuga (2001) opines that BS 5400 directives are still in practice while partial factor of safety and factor for materials may be based on EC 2. He, however, considers this a hybrid approach and advised readers to consult more specialist literature. He further stated that in most cases, the moment determined from equation above usually give nominal reinforcement and no fewer than Y12@200 mm C/C lateral and Y12@300 mm C/C longitudinal reinforcement at the critical faces.

References

Karadi, G.M and Krizek, R.J. (1980): Culvert Design in some European Countries

Oyenuga, V.O. (2001): Simplified Reinforced Concrete Design. 2^nd edition. Astros Ltd, Lagos, Nigeria

Reynolds, C.E. and Steedman, J.C. (2008): Reinforced Concrete Designers Handbook. 11^th edition. Taylor and Francis, USA

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