Guidelines for the Design of Small Bridges and Culverts

Scope of IRC SP 13: Key Specifications and Formulas

IRC SP 13 primarily deals with design and construction precautions for hydraulic structures like abutments and wing walls, focusing on geometric standards, quality control, and material specifications.

1. Weighted Mean Diameter of Particles (dm)

Used for soil particle size analysis (important for scour and foundation design):

[ d_m = \frac{\sum (\text{Average size of sieve opening} \times % \text{weight retained})}{100} ]

Example from Table B:

[ d_m = \frac{74.365}{100} = 0.74365 \approx 0.74 \text{ mm} ]

2. Typical Dimensions for Abutments & Wing Walls

• Dimensions vary with effective span (1m to 6m) and height (H).
• Tables provide parameters like b2, b4, B1, B2 for different spans and heights.
• Use these tables for preliminary design sizing.

3. Velocity Determination (Example)

Given:

• Radius ( R = 5.2,m )
• Manning’s ( n = 0.025 )
• Slope ( s = 0.0045 )

Procedure:

• Locate ( R ) on chart.
• Move vertically to intersect ( n ) curve.
• Horizontally to intersect ( s ) curve.
• Vertically down to velocity scale.

Result: Velocity ( V = 8.04, m/s )

Summary

IRC SP 13 - Site Inspection: Key Points & Specifications

1. Site Inspection Essentials (Article 2)

• Site Selection Criteria:

  • Straight stream reach, downstream of bends.
  • Away from large tributary confluences.
  • Well-defined banks.
  • Feasible straight approach roads.
  • Preferably a square crossing.

• Inspection of Existing Structures:

  • Check max flood marks, afflux, scour tendencies.
  • Assess probable max discharge.
  • Note brushwood collection risks.
  • Evaluate adequacy and defects of existing structures.
  • Record all observations carefully.

• Channel Condition Notes:

  • Estimate silt factor.
  • Estimate coefficient of rugosity (roughness).

2. Weighted Mean Diameter of Particles (dm)

[ d_m = \frac{\sum (\text{Average size} \times % \text{weight retained})}{100} ]

Example from Table B:

[ d_m = \frac{74.365}{100} = 0.74365 \approx 0.74 \text{ mm} ]

3. Standard Design Spans (Clause 5.60)

Use next higher standard span if exact match unavailable.

Summary

• Site inspection is critical for flood, scour, and hydraulic assessment.
• Use weighted mean diameter for particle size in silt/sediment analysis

IRC SP 13: Essential Design Data for Small Bridges & Culverts

1. Standard Spans for Slab Bridges (MORT&H)

• Use next higher span design if exact span not available.
• Tar paper bearings are standard for RCC slab bridges.

2. Bearing Capacity Categories for Soil

• Replace soft/loose patches with compacted granular fill (max 300 mm layers).

3. Base Slab Thickness & Depth of Key (DK)

4. Box Culvert Standard Sizes (Single Cell Examples)

• 2m×2m, 5m×3m, 5m×4m, 5m×5m, 6m×3m, 6m×4m, 7m×5m, 8m×6m, etc.
• Designed for foundation bearing capacity up to 20 t/m².
• Use next higher size if exact size not available.

5. Box Cell Designation (No./Width/Height/Earth Cushion)

| Designation | a (mm) |

Key Formulas and Specifications from IRC SP 13 for Hydraulic Design & Flood Discharge

1. Flood Discharge Estimation

• Empirical Runoff Formulae (Clause 4.1):

  • Dickens Formula: [ Q = C \times M^{3/4} ]

    • (Q) = peak runoff (m³/s)
    • (M) = catchment area (km²)
    • (C) depends on rainfall:
      • 11-14 for 60-120 cm annual rainfall
      • 14-19 for >120 cm rainfall
      • 22 for Western Ghats

  • Alternate form: [ Q = C \times M^{2/3} ]

2. Rational Method for Flood Discharge

• Required data: Cross-sectional area (A), wetted perimeter (P), bed slope (S), and regional storm intensity (I_o).
• Hydraulic mean depth: [ R = \frac{A}{P} ]
• Velocity (Manning's formula): [ V = \frac{1}{n} R^{2/3} S^{1/2} ]
  • (n) = rugosity coefficient (see Table 5.1 in IRC SP 13)
• Discharge: [ Q = A \times V ]

3. Lacey's Equations for Alluvial Streams

• Silt factor: [ K_{sf} = 1.5 \sqrt{d_{50}} ]
  • (d_{50}) = median grain size (mm)
• Used to compute regime width, depth, slope for stable alluvial channels.

4. Design Discharge Selection (Clause 6.2)

• Compare discharges from 3 methods; select highest provided it does not exceed the second highest by >50%.
• Design for floods with 50-year return period for economy.
• For small culverts, runoff formula discharge may suffice.

Summary Flow for Flood Discharge Estimation

flowchart TD
    A[Start: Collect Survey Data] --> B[Calculate A, P, S from cross-section]
    B --> C[Calculate

Key Formulas & Specifications for Streams with Rigid and Alluvial Boundaries (IRC SP 13)

1. Design Discharge (Q) Selection

• Estimate flood discharge by 3 methods (Para 4.1 to 6.1.2).
• Adopt highest Q, unless it exceeds next highest by >50%, then limit to that.
• Design for 50-year flood frequency for economy (Clause 6.2.2).

2. Lacey's Theory for Alluvial Streams (Article 7)

• Applies to streams with erodible (alluvial) boundaries that reach regime state (stable cross-section & slope).
• Silt factor (Ksf) depends on grain size.

Key Lacey’s Equations:

• ( Q ) = discharge (m³/s)
• ( P ) = wetted perimeter (m)
• ( R ) = hydraulic mean depth (m)
• ( g ) = acceleration due to gravity (9.81 m/s²)

3. Linear Waterway for Bridges (Article 8)

• For wholly alluvial streams, linear waterway = regime width ( W ) from Lacey's equation (7.2a).
• Avoid contraction below regime width to prevent deep foundations and costly training works.
• For streams with rigid banks but alluvial bed (quasi-alluvial), use actual surface width at HFL.

4. Rugosity Coefficient (n) for Natural Streams (Table 5.1 excerpt)

IRC SP 13: Normal and Maximum Scour Depth

1. Normal Scour Depth (D)

• For alluvial streams with linear waterway ≥ regime width,
  Normal scour depth ( D ) = Regime depth (from Eq. 7.2b, not provided here).

• For streams with rigid banks but erodible bed,
  Calculate as per Article 9 (details not given).

2. Maximum Scour Depth (D_max)

Calculated as multiples of the normal scour depth ( D ):

• Modify for contraction effects if necessary.
• ( D_{max} ) must not be less than the deepest scour hole found by inspection.

3. Empirical Formula (Clause 1.34)

[ \text{Scour depth} = 1.34 \times K_{sf} \times (12.4 \times D^2)^{1/3} ]

• ( K_{sf} ) = scour factor (site-specific)
• ( D ) = flow depth or characteristic dimension

4. Additional Notes

• Foundation depth should consider past precedents.
• Provide protection (curtain walls, aprons) if on bouldary strata.
• Scour varies with flow obstructions and bends.

Summary Diagram

flowchart TD
    A[Calculate Normal Scour Depth (D)] --> B{Site Condition}
    B -->|Straight reach, single span| C[Max Scour Depth = 1.27 × D]
    B -->|Curves, diagonal current, multi-span| D[Max Scour Depth = 2 × D]
    C & D --> E[Modify for contraction effects]
    E --> F[Ensure ≥ deepest observed scour hole]

Key Takeaway: Use multiples of normal scour depth based on site conditions, verify with site inspection, and apply protective measures as needed.

Foundation Design Key Points from IRC SP 13

1. Net Bearing Capacity (NBC) Categories for Soil:

2. Base Slab Thickness & Key Depth (DK):

3. Weighted Mean Diameter (dm) of Particles:

[ d_m = \frac{\sum (\text{Average size} \times % \text{weight retained})}{100} ]

Example from table: (d_m = 0.74 , mm)

4. Construction Precautions:

• Replace soft/loose bearing patches with compacted granular fill in layers ≤ 300 mm.
• Backfill density must comply with MDRT&H Clause 305.2.1.5.
• Designs provided mainly for box cell structures; embankment design is separate.

5. Typical Dimensions for Abutments & Wing Walls:

• Refer to provided tables for span vs. height (H), thickness (b2, b3), and other dimensions.
• Wing walls and abutment dimensions vary with span and effective span.

Summary Diagram of Base Slab Key Depth

graph TD
    A[Base Slab Thickness (e)] -->|≤ 900 mm| B[DK = 1200 mm]
    A -->|> 900 mm| C[DK = e + 300 mm]

Use these tables and guidelines for preliminary foundation design and soil bearing capacity checks as per IRC SP 13. For detailed structural design, refer to relevant sections and specifications.

IRC SP 13: Key Specifications for Standard Designs of Small Bridges & Culverts

1. Standard Slab Bridges (MORT&H Design)

• Design spans (c/c supports): Round figures (e.g., 6 m design span → 5.6 m clear span)
• Span details:

• Skew slab bridges: Effective spans of 4, 6, 8, 10 m with skew angles 15°, 22.5°, 30°, 35°
• Bearings: Tar paper bearings for RCC spans
• Note: Use next higher span design if exact match not available

2. H.P. Culverts

• RCC pipe culverts: 1000 mm & 1200 mm diameter (Type NP3/NP4, IS:458)
• PSC pipes: NP4 type (IS:784) also permitted

3. RCC Box Culverts & Small Bridges (MORT&H Standard Sizes)

Key Specifications & Tables for RCC Slab & Box Culverts (IRC SP 13)

1. RCC Solid Slab Superstructure (Skew) — Right Effective Span (4m, 6m, 8m, 10m)

• Steel quantity includes 5% extra for laps and wastage.
• Wearing coat: 12 mm mastic asphalt + 50 mm asphaltic concrete (Clause 10.0).

2. Box Cell Structures

• Dimensions: Single cell from 2m x 2m to 8m x 7m; double and triple cells also detailed.
• Earth Cushion: With and without earth cushion options.
• Concrete Grades:

• Minimum cement content: 310 kg/m³ (moderate), 400 kg/m³ (severe).
• Max water-cement ratio: 0.45 (moderate

Masonry Arch Bridges Design (IRC SP 13)

Key Reactions & Moments (per 1m width of arch ring)

• Unit weight of masonry, fill, road crust = 2.24 t/m³
• Positive moment sign indicates tension on the inside of arch ring.

Arch Geometry & Materials

• Rise-to-span ratio = 1/4
• Arch ring masonry: Concrete blocks (M15), dressed stones, or bricks in 1:3 cement mortar.
• Minimum crushing strength of stone/brick units = 10.5 MPa
• Permissible stresses as per IRC Bridge Code Section IV (2002).

Concrete Grades for Superstructure

• Cement content: min 310 kg/m³ (Moderate), 400 kg/m³ (Severe)
• Max water-cement ratio: 0.45 (Moderate), 0.40 (Severe)

Design Notes

• Design for vertical & horizontal reactions and moment at springing due to dead & live loads.
• Live load as per IRC Class 70R or two lanes of IRC Class A.
• Footpath load: 5 kN/m²; superstructure slab bearing width: 400 mm.
• Expansion joint: 20 mm (no allowance for abutment tilting).

flowchart LR
    A[Dead Load + Live Load] --> B[Arch Ring]
    B --> C{Reactions at Springing}
    C --> D[Vertical Reaction]
    C --> E[Horizontal Reaction]
    C --> F[Moment at Springing]
    F --> G[Tension on Inside of Arch

IRC SP 13: Material Specifications - Key Points

1. Concrete Grades & Strengths

• Use IS 8112 (Ordinary Portland Cement) or IS 269 cement.
• Concrete slump: 50-75 mm (per IS 516).
• Admixtures (superplasticizers) allowed with approval.

2. Wearing Coat for Box Cell Structures

• Mastic asphalt: 12 mm thick prime coat.
• Asphaltic concrete wearing coat: 50 mm thick (Clause 512, MoRT&H).
• Alternative: 75 mm thick cement concrete wearing coat (M30 grade, w/c ratio ≤ 0.40) with reinforcement (8 mm HYSD bars @ 200 mm c/c, reduced to 100 mm near expansion joints).

3. Weighted Mean Diameter of Particles (dm)

[ d_m = \frac{\sum (d_i \times w_i)}{100} ] Where:

• ( d_i ) = average size of sieve fraction (mm)
• ( w_i ) = % weight retained

Example from table:
[ d_m = 0.74 \text{ mm} ]

Summary Diagram: Concrete Grade Selection

flowchart TD
    A[Exposure Condition] -->|Moderate| B(M20 for Box Cell)
    A -->|Severe| C(M25 for Box Cell)
    B --> D{Element}
    C --> D
    D -->|Wing Walls| E(M20/M25)
    D -->|Curtain Wall| F(M15/M20)
    D -->|Levelling Course| G(M15)

For detailed dimensions,

IRC SP 13: Load and Stress Considerations - Key Formulas & Tables

1. Weighted Mean Diameter of Particles (dm)

Used for soil gradation in backfill: [ d_m = \frac{\sum (\text{Average size}_i \times %\text{weight retained}_i)}{100} ] Example from table:
[ d_m = 0.74 \text{ mm (weighted mean diameter)} ]

2. Net Bearing Capacity for Soil Categories

3. Base Slab Thickness Key Depth (DK)

4. RCC Solid Slab Superstructure (Skew) - Depth & Quantities

Steel quantity includes 5% extra for laps/wastage.

5. Concrete Strength Requirements

IRC SP 13: Protection Work and Maintenance - Key Points

1. Floor Protection Works (Article 20.1)

• Purpose: Prevent scour and erosion around foundations on erodible soils.
• Design Criteria:
  • Post-protection velocity ≤ 2 m/s
  • Discharge intensity ≤ 2 m³/m width
• Flooring Dimensions:
  • Extend 3 m upstream and 5 m downstream of the bridge.
  • Extend to line connecting ends of splayed wing walls if longer.
  • Top of flooring: 300 mm below lowest bed level.
• Flooring Layers:
  • 150 mm thick flat stone/bricks on edge in cement mortar (1:3).
  • Over 300 mm thick M15 concrete.
  • Over 150 mm thick M10 concrete base.
• Joints: Provide expansion joints approx. every 20 m.

2. Excavation & Foundation Preparation (20.1.2.1)

• Ensure no loose pockets or depressions.
• Soil compacted to true level.
• Concrete laid in dry bed.

3. Maintenance

• Regular inspection and repair of floor protection.
• Monitor scour and sediment deposition.

4. Weighted Mean Diameter of Particles (dm) for Soil

Used for assessing soil gradation affecting scour:

IRC SP 13: Worked Examples & Case Studies – Key Data & Tables

1. Typical Worked Examples Include:

• R.C.C. Solid Slab Superstructure (Skew) for spans 4m to 10m (with/without footpaths)
• Box Cell Structures (Single, Double, Triple cells) with/without Earth Cushion
• Protection works and maintenance for box culverts

2. Key Tables & Dimensions

a) Weighted Mean Diameter of Particles (dm)

Used for soil gradation in foundation design:

b) Abutment Dimensions (Example for Effective Span 6m)

(Refer to span-specific tables for other dimensions)

c) Wing Wall Dimensions (High End Example for 3m Span)

IRC SP 13 - References and Appendices: Key Highlights

The document includes critical references and appendices that support design and construction of small bridges and culverts:

Appendices (Pages 89-105)

• Appendix A: Heaviest Rainfall in One Hour (mm)
  • Provides rainfall intensity data essential for hydrological design and peak discharge estimation.
• Appendix B: Filling Behind Abutments, Wing, and Return Walls
  • Details on earth filling specifications and compaction behind bridge structures.

Important Tables and Articles for Reference

Key Formula (Rational Method for Peak Runoff)

[ Q = CiA ]

• Q = Peak discharge (m³/s)
• C = Runoff coefficient (dimensionless)
• i = Rainfall intensity (mm/hr) from Appendix A
• A = Catchment area (km²)

Structural Specifications

• Detailed dimensions and reinforcement quantities for RCC box culverts and slabs (Articles 12, 14, 19).
• Guidelines on scour depth and foundation depth (Articles 9, 11).

flowchart TD
    A[Rainfall Intensity Data (Appendix A)] --> B[Calculate Peak Runoff Q = CiA]
    B --> C[Design Discharge (Article 6)]
    C --> D[Determine Scour Depth (Article 9)]
    D --> E[Foundation Depth (Article 11)]
    E --> F[Structural Design (Articles 12, 14, 19)]

Use these references and appendices for detailed design inputs, hydrological data, and structural specifications per IRC SP 13.