Detail Quantity Estimate for Road, Bridge and Irrigation Works

5.1 Pipe culverts, slab culverts and box culverts

A culvert is a cross-drainage structure of span up to about 6 m carrying the road over a small stream. Three kinds are examined:

Items for a slab culvert

Worked estimate — an RCC slab culvert

Item 1 — Earthwork in excavation

Item 2 — PCC 1:3:6 in foundation

Item 3 — Brickwork in abutments, wing walls and parapets

The slab bearing must be deducted from the abutment masonry — that volume is occupied by the RCC slab and is measured as concrete, not as masonry. Omitting the deduction counts the same volume twice.

Item 4 — RCC 1:2:4 in the deck slab

Item 5 — Bar bending schedule

Bar bending schedule — deck slab (one-way, B < L/2)

Weight per metre is taken as w = d²/162. Some textbooks use d²/160, which gives figures about 1.2% higher — 1.600 instead of 1.580 kg/m for a 16 mm bar. Either is acceptable provided you state which you have used.

Item 6 — Formwork

Item 7 — Wearing coat

For a box culvert take the four elements as one unit: base slab, two vertical walls, top slab, plus the haunches. Its great advantage in the estimate is that no separate foundation is needed — the base slab is the foundation.

Geometry after Dawadi, RCC slab culvert; every quantity recomputed here from the dimensions.

5.2 T-beam bridge (superstructure, abutment and pier)

A T-beam bridge has a deck slab cast monolithically with longitudinal girders, so that each girder and the slab above it act as a T. It is the standard medium-span (10–25 m) RCC road bridge.

Superstructure

The single commonest error is double counting the flange. The deck slab is measured across the full width including the part over the girders, so each girder must be measured only for its web below the slab — not its full T-depth.

Worked estimate — superstructure of a T-beam bridge

Abutment and pier

Both are measured as a stack of prisms, bottom upward, each with its own dimensions:

• Foundation / footing — length × breadth × thickness.
• Stem or shaft — where the face is battered, use the mean thickness of top and bottom.
• Cap and bed block under the bearings.
• Dirt wall and wing / return walls for the abutment, measured separately.
• Backfilling behind the abutment, with filter media and weep holes.

One pier

One abutment

The abutment stem is battered from 1.50 m at the bottom to 0.60 m at the top, so its mean thickness is ½(1.50 + 0.60) = 1.05 m. Using either the top or the bottom thickness alone would be wrong by about 43%.

Dawadi, RCC T-beam, well, septic, caisson, pier; quantities computed here from the stated dimensions.

5.3 Well foundation

A well foundation is a deep foundation sunk through a river bed to a firm stratum below the scour level. It is used where an open foundation cannot be taken down — the standard foundation for bridge piers in Nepal's braided rivers.

Parts, and how each is measured

Worked estimate — one well foundation

Brickwork in well steining is one of the classic "state the unit" questions — it is measured and paid in m³ (§1.2). Sinking of the well is paid separately, per metre of depth, because the effort increases sharply with depth; it is not included in the rate for the steining.

Dawadi, RCC T-beam, well, septic, caisson, pier.

5.4 Earthwork in road construction in plain and hilly areas

Road earthwork means bringing the ground to formation level, by cutting where the ground is high and filling (banking) where it is low. The cross-section is a trapezium.

The s·D² term is the two side triangles taken together: each has base sD and height D, so the two contribute 2 × ½ × sD × D = sD². Cutting and filling normally take different side slopes, which is why s_c and s_f are kept apart.

Three methods of finding the volume between two sections

Let two cross-sections a distance L apart have depths d₁ and d₂.

Worked estimate — earthwork along a road

Earthwork in FILLING (embankment) — B = 10 m, side slope 2:1

Earthwork in CUTTING — B = 10 m, side slope 2:1

Mid-sectional and mean-sectional bracket the true volume from below and above; the prismoidal formula is Simpson's rule applied to the cross-sectional area and always lies between them. If a question asks you to "compare the methods", that bracketing is the answer — and the worked table above demonstrates it.

Hilly ground — the two-level section

In hilly country the ground itself slopes across the road, so the two side slopes are no longer of the same length and the simple trapezium no longer applies. The section is then a two-level section, and its area is

Do not use A = (B·d + s·d²) × r²/(r² − s²). That expression omits the s·b² term and under-estimates the area — by about 2% in the worked example below, and by more as the formation widens. The full form above is the one that reproduces the tabulated areas exactly, and it is the form Chakraborti derives in §8-7 as s·b² + 2b·r²·H + r²·s·H², all divided by (r² − s²).

A road on a cross slope is called a two-level section, because the ground meets the two side slopes at two different levels. Where the transverse and longitudinal slopes are uniform between two cross-sections, that reach is a two-level section and the formula above applies to it directly.

Worked example — road on a cross slope

Earthwork on a cross slope — two-level section, mean sectional area method

Cutting and filling must still be worked out separately, because earth cut on the hill side is used to build up the valley side. The estimate then shows how much material must be borrowed or wasted — which is exactly what a mass haul diagram answers.

The zero point — where cutting changes to filling

Along a hill road the formation crosses the ground surface somewhere between two chainages. That crossing is the zero point (or balance point): the section there is neither cutting nor filling. It must be located, because the cutting volume is measured up to it and the filling volume from it.

Two quantities at the zero point are found by averaging, because the section there is transitional:

Worked illustration. Cutting 0.70 m deep at chainage 30 m, filling 0.80 m high at chainage 60 m; cross slopes 1 in 12 and 1 in 10; formation 8 m in cutting and 10 m in banking:

Note that the cross slope is averaged harmonically, not arithmetically. The arithmetic mean of 12 and 10 would be 11.00; the harmonic mean is 10.909. A slope is a rate, and rates average harmonically — the same reason an average speed over equal distances is a harmonic mean.

Presentation

Road earthwork is set out chainage by chainage exactly as in the tables above — chainage, ground level, formation level, depth of cut or fill, area, mean area, length, and volume of cutting and of filling in separate columns — and the two columns are totalled separately so that the balance of earthwork is visible.

Formulas transcribed from Dawadi, estimating earth work §6.3; the worked table is computed here.

5.5 Estimation of pavement work and retaining works in roads

Pavement work

Once the formation is ready, the pavement is measured layer by layer. Each layer is an area × a compacted thickness:

Always use the compacted thickness for payment. The loose thickness is greater — 120 mm of loose ballast compacts to about 80 mm — and the difference is absorbed in the rate through the norms.

Worked estimate — one kilometre of metalled road

The √(1 + s²) factor appears again here. For a 2:1 slope it is √5 = 2.236, so each sloping face is 2.236 times the bank height, not equal to it. Using the height alone would under-measure the turfing by more than half.

Retaining and breast walls

Hill roads need a great deal of retaining work, and it is measured as a stack of prisms exactly like a bridge abutment:

• Retaining wall — holds up filled ground on the valley side.
• Breast wall — supports the cut face on the hill side.
• Toe wall — protects the toe of an embankment.
• Gabion wall — wire crates filled with boulders; measured in m³ of crate, with the wire mesh in m² or by weight.

Worked example — 50 m of stone masonry retaining wall, 0.60 m wide at the top, 1.80 m at the bottom, 4.00 m high, on a 0.30 m PCC bed:

Add, separately: weep holes (number, one per 1.5–2 m² of face), and any drainage channel behind or in front of the wall.

Road estimate after Dawadi, 1 km highway, RCC water tank and building §6.6; every quantity recomputed here.

5.6 Earthwork and lining works in irrigation canals

An irrigation canal is estimated the same way as a road — a trapezoidal section repeated along a chainage — but here the section is a channel rather than an embankment, and it usually has to be lined.

Earthwork in the canal

Cutting and filling are kept in separate columns, chainage by chainage, exactly as for a road. Where the canal runs partly in cutting and partly on a bank, the bank itself is a further filling item with its own section.

Lining

Lining reduces seepage and prevents scour. It is measured on the wetted perimeter — the surface actually covered:

Worked estimate — 500 m reach of a lined canal

The √(1 + s²) is simply the slope length of one side per unit depth — for a 1.5:1 side slope it is √(1 + 2.25) = 1.803, so each sloping face is 1.803 D long, not D. Forgetting it under-measures the lining by about half the side area.

Items to be measured

1. Clearing and grubbing of the alignment.
2. Earthwork in excavation, by class of soil; and earthwork in filling for banks, in compacted layers.
3. Dressing and trimming of the bed and side slopes — m².
4. PCC or brick lining to bed and sides — m² or m³ on the wetted perimeter.
5. Construction joints and expansion joints — running metre.
6. Structures on the canal — head regulator, cross regulator, outlets, falls, aqueducts and culverts, each estimated separately.
7. Service road on the bank, and turfing of the slopes.

Canal sections after Dawadi, estimating earth work; the hydraulic relations are the standard trapezoidal-channel geometry.

Sources consulted for this chapter

• Er. Narayan Prasad Dawadi, Estimating and Costing lecture notes (IOE, Pashchimanchal Campus) — the 1 km metalled road, the RCC slab culvert, the well foundation and the earthwork formulas
• Notes by RK Sir (course handwritten notes) — the two-level (cross slope) section formula and its worked chainage table — which corrected the formula previously printed here
• Pandey & Katwal, Complete Manual of Estimating and Costing (T.U., B.E. Civil) — the zero (balance) point, the harmonic mean cross slope and the mean formation width at that point
• M. Chakraborti, Estimating, Costing and Specification in Civil Engineering — ch. VIII — earthwork by mid-sectional, trapezoidal and prismoidal formulas, area of turfing, culverts and pavements; §8-7 independently confirms the two-level section formula

End of Chapter 5 — Detail Quantity Estimate for Road, Bridge and Irrigation Works