Calculation of Linear Waterway, Span Lengths, Scour Depth and Foundation Level for Bridges
Designing a bridge over a watercourse involves a series of interrelated calculations. The size of the waterway, the needed span(s), the expected scour depth, and the final foundation level all influence each other. This page summarises the most commonlyused procedures, the governing equations and the design checks recommended in most codes (AASHTO LRFD, Eurocode 2, Indian Bridge Design Code, etc.).
1. Determining the Linear Waterway (Effective Flow Width)
1.1 Definition
The linear waterway, usually denoted as B, is the horizontal distance across the water surface that conveys the design flow Q. It is not merely the channel banktobank width; it incorporates any overbank flow that will occur at the design flood stage.
1.2 Steps
- Obtain design discharge (Qdes) typically the 100year or 200year flood, derived from hydrologic analysis.
- Choose an appropriate hydraulic roughness coefficient (Mannings *n* or DarcyWeisbach *f*).
- Assume a trial water depth (y) based on previous floodplain studies or empirical formulas (e.g., y = 0.6Hmax).
- Use the continuity equation and the hydraulic radius to solve for the width:
Q = (1/n)AR^(2/3)S^(1/2)
where A = By, R = A/P, S = slope.
Rearranging for B:
B = Qn / [y(yB)^(2/3)S^(1/2)]
Iterate until the calculated B stabilises. The final value is the linear waterway that will be used for span layout.
2. Span Length Determination
2.1 Constraints
- Clearance over the linear waterway usually a minimum of 1.2B to allow for future widening and debris.
- Maximum practical span for the selected superstructure type (e.g., 30m for slabbeam, 60m for prestressed girder).
- Vertical clearance under the bridge (navigation, floodlevel clearance).
2.2 Simple Span Selection
For a singlespan bridge:
Lspan = max(1.2B, Lmin)
where Lmin is the minimum span required by the chosen structural system. If Lspan exceeds the practical limit, the bridge must be split into multiple spans with piers located in the streambed. The location of intermediate piers is usually taken at equal intervals, but hydraulic impacts (velocity, scour) must be examined.
3. Scour Depth Estimation
3.1 Why Scour Matters
Scour is the removal of soil around bridge foundations caused by flowing water. It is the leading cause of bridge failure worldwide, so an accurate estimate of the maximum probable scour depth (Scmax) is essential.
3.2 Common Methods
3.2.1 HEC18 (US) Empirical Formula
For a cylindrical pier:
Sc = K1K2K3K4(a)(V1/g)
where
- K1 = flow coefficient (1.0)
- K2 = pier shape factor
- K3 = soil condition factor
- K4 = angle of attack factor
- a = pier diameter (m)
- V1 = approach velocity at design flood (m/s)
- g = 9.81m/s
3.2.2 Eurocode 2 Simplified Approach
Sc = (V2 / (2g))
= 1.5 for cohesive soils, 2.0 for granular. V2 is the velocity at the pier upstream.
3.3 Determining Velocity
Velocity is obtained from the hydraulic analysis used for the linear waterway. For a rectangular channel:
V = Q / (By)
Replace Q with the design discharge and (B,y) with the values obtained in Section1.
4. Foundation Level Selection
4.1 Required Embedment Depth
The foundation must be placed below the predicted scour depth plus an additional safety margin (commonly 0.5m to 1.0m). Thus:
Dembed = Scmax + Msafety
4.2 Typical Foundation Types
- Spread footings Used when competent rock lies shallow; depth typically 0.81.2m below scour.
- Driven piles Common for soft alluvial soils; length chosen to reach a refusal layer or to achieve the required embedment depth.
- Drilled shafts (caissons) Employed for very large loads or where vibration must be avoided.
4.3 Example Calculation
| Parameter | Value |
|---|---|
| Design discharge, Qdes | 150m/s |
| Manning n | 0.035 |
| Channel slope, S | 0.0015 |
| Assumed depth, y | 3.0m |
| Calculated linear waterway, B | 45m |
| Chosen span length, Lspan | 55m (1.2B) |
| Approach velocity, V1 | 1.11m/s |
| Pier diameter, a | 1.2m |
| K factors (HEC18) | KKKK = 1.00.50.31.0 = 0.15 |
| Scour depth, Sc | 0.151.2(1.11)/9.81 0.22m |
| Safety margin | 0.8m |
| Required embedment depth | ~1.0m below anticipated river bed |
Because the calculated scour is modest, a shallow spread footing can be used, provided the bearing stratum has a bearing capacity > 200kN/m. If a deeper scour is anticipated (e.g., in sandy rivers with higher velocities), a pile group with a nominal length of 12m might be selected.
5. Design Verification Checklist
- Linear waterway width satisfies hydraulic capacity for the selected design flood.
- Span length meets clearance requirements and stays within the structural system limits.
- Scour depth is computed using at least two accepted methods; the larger value governs.
- Foundation level is placed below Scmax+margin, and soil investigations confirm sufficient bearing capacity.
- Hydraulic impacts of any intermediate piers (flow constriction, added scour) are reanalysed.
6. References (selected)
- AASHTO LRFD Bridge Design Specifications, 9th Edition, 2022.
- US Department of Transportation, Hydraulic Design of Bridges (HEC18), 2017.
- Eurocode 2: Design of Concrete Structures, EN 199211, 2004.
- Indian Road Congress (IRC) 371999 Design Loads for Code.
**Calculation Of Linear Waterway, Span Lengths, Scour Depth And Foundation Level For Bridg...
