Guidelines for Seismic Design of Road Bridges

IRC SP 114: Scope Overview

The Scope of IRC SP 114 generally defines the applicability of guidelines for structural design and analysis of specific highway components or materials.

Key Points from Clause 9.1.2 & Related Clauses:

• Material Strength Factor (ß) for Concrete:

• N1(60)cs Calculation:

[ N1(60)_{cs} = a + B \times N1(60) ]

• Factor f based on Degree of Reaction (Dr):

• Kg Factor:

[ K_g = \frac{Ovo}{p} (f - 1) ]

• MSF (Modulus Strength Factor):

[ MSF = \frac{102.24}{M^{2.56}} ]

• CRR (Critical Rupture Ratio):

[ CRR = CRR_{7.5} \times MSF \times K_o \times K_a ]

• Factor of Safety (FOS):

[ FOS = \frac{CRR}{CSR} ]

Summary:

• The Scope defines the limits of material properties and design parameters.
• Use ß for adjusting concrete strength effects.
• Calculate N1(60)cs for specific soil or material characteristics.
• Adjust factors f, Kg, MSF, CRR, and FOS based on test data and conditions.

flowchart LR
    A[Concrete Strength FC] --> B[Determine ß]
    B --> C[N1(60)cs Calculation]
    C --> D[Calculate f based on Dr]
    D --> E[Compute Kg]
    E --> F[

IRC SP 114 - General Design Provisions (Clause 6.4 and related)

Key Design Parameters & Symbols

Basic Design Formula for Seismic Force (Equivalent Static Method)

[ F_h = A_n \times W ]

Where:

• ( A_n = I \times Z \times S \times C ) (Design seismic coefficient)
• ( W ) = Effective seismic weight of the structure

Fundamental Natural Period Estimation (for bridges)

[ T = C_t \times h^x ]

• ( h ) = Height of structure (m)
• ( C_t, x ) = Constants depending on bridge type (refer clause 6.4 or relevant tables)

Design Shear and Moment

• Design Shear, ( V_a ): Calculated from seismic forces and load combinations
• Design Moment, ( M_c ): Based on shear and axial forces at critical sections

Important Tables (Summary)

Ductile Detailing & Capacity Design (Refer Chapters 7 & 9)

• Design for ductility and capacity to

IRC SP 114: Structural Ductility & Energy Dissipation Key Points

1. Ductility & Energy Dissipation Principles

• Seismic design ensures adequate strength and ductility of substructure (Clause 3.6).
• Energy dissipation occurs mainly through inelastic behavior at plastic hinge regions.
• Plastic hinge locations must be predetermined using capacity-based design.

2. Design Specifications

• RCC/PSC Substructure:
  • Design as under-reinforced to ensure ductile failure.
  • Provide closely spaced transverse stirrups in plastic hinge zones for confinement and to prevent buckling.
• Steel Substructure:
  • Detail compression zones to avoid premature buckling.
  • Ensure ductile detailing at joints for overall ductility.

3. Seismic Design Considerations (Clause 6.3.1)

• Account for:
  • Bridge flexibility, damping, energy dissipation, and seismic isolation devices.
• Ensure:
  • Uniform horizontal strength & stiffness along bridge length.
  • Pre-identification of plastic hinge locations.
  • Ductility provisions in plastic hinge regions unless seismic isolation devices are used.
• Capacity protected regions can be designed elastically without ductility provisions.

4. Typical Capacity-Based Design Formula for Plastic Hinge Flexural Strength

[ M_p \geq M_u = \gamma_{Rd} \times M_{design} ]

Where:

• (M_p) = Plastic moment capacity at hinge
• (M_u) = Ultimate moment demand
• (\gamma_{Rd}) = Partial safety factor for resistance

5. Plastic Hinge Detailing Summary

flowchart LR
    A[Seismic Load] --> B[Sub

IRC SP 114: Seismic Analysis Methods (Clause 5.5 Requirements)

Though specific clauses are not detailed, typical seismic analysis methods per IRC and related codes include:

Key Seismic Analysis Methods:

• Equivalent Static Method: Simplified lateral force method.
• Response Spectrum Method: Uses design response spectra for dynamic analysis.
• Time History Analysis: Detailed dynamic analysis using ground motion records.

Requirements for Seismic Analysis Methods (General):

• Modeling: Accurate representation of mass, stiffness, and damping.
• Modal Analysis: Consider sufficient modes to capture 90-95% mass participation.
• Damping: Usually 5% critical damping for typical structures.
• Load Combinations: Include seismic loads combined with dead/live loads.
• Response Spectrum: Use design spectrum per IRC or IS 1893.

Typical Formula for Base Shear (Equivalent Static Method):

[ V_b = A_h \times W ]

Where:

Design Horizontal Seismic Coefficient (A_h):

[ A_h = \frac{Z I S_a}{2 R g} ]

• (Z) = Zone factor
• (I) = Importance factor
• (S_a/g) = Spectral acceleration coefficient
• (R) = Response reduction factor
• (g) = Acceleration due to gravity

flowchart LR
    A[Seismic Analysis Methods] --> B[Equivalent Static Method]
    A --> C[Response Spectrum Method]
    A --> D[Time History Analysis]
    B --> E[Calculate Base Shear]
    C --> F[Modal Analysis]
    D --> G[Dynamic Response]

Summary: Use Equivalent Static for low-rise, simple structures; Response Spectrum for medium complexity; Time History for critical, complex designs. Ensure method meets IRC SP 114 Clause 5.5 requirements on modeling, damping, and load combinations.

IRC SP 114 - Clause 5.5: Requirements of Method of Seismic Analysis

This clause outlines the essential criteria for seismic analysis methods used for bridges and structures:

Key Requirements:

• Accuracy: The method must realistically simulate the dynamic behavior of the structure under seismic loads.
• Modeling: Structural components and soil-structure interaction should be adequately represented.
• Load Combinations: Seismic loads combined with gravity and other loads as per code.
• Damping: Appropriate damping ratios (typically 5% for most structures).
• Response Spectrum: Use of site-specific or code-provided response spectra.
• Modal Analysis: For multi-degree freedom systems, modal superposition methods are recommended.
• Time History Analysis: For critical structures, nonlinear time history analysis is preferred.

Commonly Used Formulas:

• Seismic Base Shear, Vb:

[ V_b = A_h \times W ]

Where:

• ( A_h ) = Design horizontal seismic coefficient (from code or response spectrum)

• ( W ) = Seismic weight of the structure

• Fundamental Natural Period, T:

[ T = 0.075 \times h^{0.75} ]

Where:

• ( h ) = Height of the structure (m)

Typical Damping Values:

flowchart LR
    A[Start: Define Structure] --> B[Select Seismic Analysis Method]
    B --> C{Linear or Nonlinear?}
    C -->|Linear| D[Modal Response Spectrum Analysis]
    C -->|Nonlinear| E[Time History Analysis]
    D --> F[Calculate Base Shear and Responses]
    E --> F
    F --> G[Check Against Design Criteria]
    G --> H[Design or Modify Structure]

Summary: Use modal response spectrum for typical bridges; nonlinear time history for critical cases. Ensure proper modeling, damping, and load combinations as per IRC SP 114 Clause 5.5.

IRC SP 114 - Design Provisions (Clause 6.4 & Related Sections)

Key Design Parameters & Symbols

• I: Importance Factor (accounts for bridge importance)
• Z: Seismic Zone Factor (based on location)
• S: Soil Profile Factor (soil type influence)
• C: Bridge Flexibility Factor
• T1: Fundamental Natural Period (sec)
• W: Seismic Weight (total mass considered)
• Fh: Horizontal Seismic Force = An × W
• An: Design Seismic Horizontal Coefficient = Z × I × S × C

Basic Seismic Force Formula

[ F_h = A_n \times W = Z \times I \times S \times C \times W ]

Capacity Design Concepts (Chapter 7)

• Design components for ductility and over-strength.
• Calculate design moment (M_{Ed}), shear (V_{Ed}), axial force (N_{Ed}) at plastic hinge locations.
• Use over-strength factor (Y_o) for moment magnification.

Typical Design Checks

Ductile Detailing (Chapter 9)

• Follow specific reinforcement detailing for RC and steel.
• Ensure confinement, avoid brittle failure.

Seismic Isolation (Chapter 10)

• Effective time period (T_{eff}), damping (J_{eff}).
• Design displacement (d_{ad}) and stiffness parameters (K_{gi}), (K_{ti}).

Summary Table: Design Coefficients

Seismic Design Method - IRC SP 114 (Chapter 7 Overview)

Key Methods:

• Force Based Design (7.2):
  Calculate seismic forces using design base shear formula:
  [ V = A \times W ] where:

  • (V) = design base shear
  • (A) = design horizontal seismic coefficient (from seismic zone map & spectrum)
  • (W) = effective seismic weight of the structure

• Capacity Design (7.3):
  Ensures ductile failure by designing members to yield in a preferred sequence, typically:

  • Plastic hinges form in beams before columns
  • Design moments and shear forces are amplified to ensure overstrength

Structural Components (7.4 & 7.5):

• Design critical sections with ductile detailing (adequate confinement, stirrup spacing, anchorage length) per IS code guidelines.

Second Order Effects (7.6):

• Consider P-Δ effects for slender piers and columns.

Design of Joints (7.7):

• Ensure joints can transfer forces without brittle failure.

Important Tables & Maps:

• Seismic Zone Map: Defines seismic zones (II, III, IV, V) with corresponding design coefficients.
• Design Seismic Spectrum: Provides spectral acceleration values for different periods.
• Capacity Design Factors: Amplification factors for moments and shear in critical members.

Summary Diagram:

flowchart TD
    A[Seismic Zone Map] --> B[Determine Seismic Coefficient A]
    B --> C[Calculate Base Shear V = A × W]
    C --> D[Force Based Design]
    D --> E[Capacity Design: Amplify Moments & Shear]
    E --> F[Ductile Detailing of Sections]
    F --> G[Check Second Order Effects]
    G --> H[Design Joints]

For detailed formulas, spectral data, and ductile detailing rules, refer to IRC SP 114 Chapters 6-10 and Appendices A-1 to A-5.

Design of Substructure and Superstructure per IRC SP 114 (2018):

Substructure Design (Clauses 8.3.1 & 8.3.6)

• Seismic Forces: Calculated using seismic analysis methods in Chapter 6.
• Time Period Calculation: Must consider geometry of superstructure, substructure, foundation, and their connections.
• Load Combinations: Horizontal and vertical seismic components considered per Chapter 5.
• Verification:
  • Strength and stability checked under Ultimate Limit State (ULS) seismic load combinations.
  • Serviceability Limit State (SLS) checks not required for seismic loads.
  • Partial safety factors per IRC:6 Annex B (Tables B.1 & B.2).
• Non-collapse and Damage Minimization: Ensured by strength criteria and ductile detailing.

Superstructure Design (Clause 8.2)

• Follow seismic design provisions in Chapter 6.
• Ensure compatibility with substructure seismic response.
• Use ductile detailing as per Chapter 9.

Key Formula for Seismic Design Force (Simplified):

[ F = \alpha \times W ] Where:

• ( F ) = Design seismic force on substructure/superstructure
• ( \alpha ) = Seismic coefficient from seismic analysis (depends on zone, soil, damping)
• ( W ) = Weight of the structure component

Load Combinations (Example):

Reference Tables:

• IRC:6 Annex B Tables B.1 & B.2: Partial safety factors for different load combinations.
• Seismic Zone Map & Spectrum: Chapter 4 for seismic coefficients.

flowchart TD
    A[Seismic Analysis (Chapter 6)] --> B[Calculate Seismic Forces]
    B --> C[Design Substructure (Clause 8.3)]
    B --> D[Design Superstructure (Clause 8.2)]
    C --> E[Check Strength & Stability (ULS)]
    D --> F[Ductile Detailing (Chapter 9)]
    E & F --> G[Ensure Non-collapse & Damage Minimization]

Summary: Use

IRC SP 114 - Ductile Detailing of Structures (Chapter 9)

9.1 Ductile Detailing of Reinforced Concrete Structures

Key points for ductile detailing (IRC SP 114):

• Confinement of Concrete: Use closely spaced transverse ties or hoops in potential plastic hinge zones to enhance ductility.
• Minimum Reinforcement: Ensure minimum longitudinal and transverse reinforcement as per IS 13920 for ductile detailing.
• Development Length: Provide adequate development length for bars to develop yield strength.
• Lap Splices: Locate lap splices away from plastic hinge zones or provide mechanical anchorage.
• Shear Reinforcement: Use closely spaced stirrups in plastic hinge zones to prevent shear failure.

Typical Specifications (per IS 13920):

Key Formula: Development Length (Ld)

[ L_d = \frac{{\phi \times \sigma_{bd}}}{{4 \times \tau_{bd}}} ]

Where:

• (\phi) = bar diameter
• (\sigma_{bd}) = design stress in the bar
• (\tau_{bd}) = design bond stress (from IS 456 Table 21)

flowchart LR
    A[Plastic Hinge Zone] --> B[Close Spaced Ties]
    B --> C[Improved Confinement]
    C --> D[Enhanced Ductility]
    A --> E[Proper Lap Splices]
    E --> D
    A --> F[Sufficient Development Length]
    F --> D

Summary: IRC SP 114 refers to IS 13920 for ductile detailing of RC structures, emphasizing confinement, lap splices, development length, and shear reinforcement to ensure ductility under seismic or cyclic loading.

Key Specifications & Formulas for Seismic Isolation Devices (IRC SP 114, Chapter 10):

1. Types & Properties of Isolation Devices:

• Low-damping elastomeric bearing: Viscous damping ratio, ζ ≤ 0.06
• High-damping elastomeric bearing: ζ = 0.10 to 0.20
• Lead-rubber bearing: Composite damping ratio & parameters
• Fluid Viscous Dampers: Viscous force-displacement relation, viscous resistance, max displacement, velocity
• Friction Sliding Dampers: Dynamic sliding friction, max displacement

2. Design Considerations:

• Applicable for structures with fundamental period T ≤ 1.0 sec (without isolation).
• Avoid use in Type III soft soil.
• Isolation reduces seismic response by:
  • Period elongation (↓ forces, ↑ displacements)
  • Increased damping (↓ displacements & forces)
  • Combination of both (preferred).

3. Functions of Isolation Devices:

• Vertical load capacity + lateral flexibility + vertical rigidity
• Energy dissipation (hysteretic, viscous, frictional)
• Lateral restoring force
• Horizontal restraint under service loads

4. Damping Force Model (Typical for Fluid Viscous Dampers):

[ F = C_d \cdot v^\alpha ] Where:

• (F) = damping force
• (C_d) = damping coefficient
• (v) = velocity
• (\alpha) = velocity exponent (usually ~1)

5. Design Verification:

• Test-based verification mandatory except for simple elastomeric low damping bearings & flat sliding bearings.

Summary Table: Viscous Damping Ratios for Bearings

flowchart TD
    A[Seismic Isolation Devices] --> B[Period Elongation]
    A --> C[Increased Damping]
   

Liquefaction of Soil - Key Formulas & Specifications (IRC SP 114: Appendix A-5)

1. Definition (Clause 8.4.4)

• Liquefaction: Loss of shear strength/stiffness due to increased pore water pressure in saturated cohesionless soil during earthquake shaking.
• Evaluated for loose sands beneath water table, typically up to 20 m depth.

2. Key Parameters

3. Stress Reduction Coefficient (rd)

[ r_d = \begin{cases} 1.0 - 0.00765z, & z \leq 9.15 \text{ m} \ 1.174 - 0.0267z, & 9.15 < z \leq 20 \text{ m} \end{cases} ]

where z = depth below ground surface (m).

4. Overburden Pressures

[ \sigma_0 = \gamma_{sat} \times z ] [ \sigma' = \gamma_{sub} \times z ]

5. Cyclic Stress Ratio (CSR)

[ CSR = 0.65 \times \frac{a_{max}}{g} \times \frac{\sigma_0}{\sigma'} \times r_d ]

• (a_{max}/g) = peak ground acceleration ratio
• (r_d) = stress reduction coefficient

6. Factor of Safety Against Liquefaction (FOS)

[ FOS = \frac{CRR}{CSR} ]

• CRR: Cyclic Resistance

IRC SP 114: Worked Examples & Illustrations - Key Points

Elastic Seismic Acceleration Method (Clause 5.2.1 & Appendix A-3)

• Purpose: Compute seismic forces using simplified formulas and structural modeling.
• Model includes: Superstructure, substructure, bearings, foundation, soil springs.
• Span Cases:

Key Formulas & Parameters:

• Contributory Mass (M): Sum of span masses affecting seismic load.
• Seismic Force (F):
  [ F = m \times a ]
  where ( m ) = contributory mass, ( a ) = seismic acceleration.
• Time Period (T): Simplified formulas available depending on span and substructure height.
• Ductile Detailing: Refer Chapter 9 for reinforcement and capacity design.
• Capacity Design: Clause 7.3 & 7.4 explain design of components to ensure ductility.

Useful Tables:

• Span condition parameters (height, bearing, foundation) for seismic modeling.
• Load combinations and mass contributions per span.
• Soil spring stiffness for pile/well foundations.

Reference Appendices for Worked Examples:

• A-1: Elastic Seismic Acceleration Method (detailed stepwise calculations).
• A-2: Elastic Response Spectrum Method.
• A-4: Hydrodynamic pressure on piers.
• A-5: Soil liquefaction illustration.

Diagram: Simplified Model for Case 1 (Simply Supported Span)

graph LR
    Superstructure -->|Mass M1, M2| Bearing[Elastomeric Bearing]
    Bearing --> Substructure[Substructure (10m Height)]
    Substructure --> Foundation[Open Foundation (Fixed Base)]

**For detailed stepwise calculations, refer Appendix A-1 of