Criteria for earthquake-resistant design of structures

IS 1893: Scope - Key Formulas, Tables & Specifications

1. Scope Summary (Clause 1.2)

• Earthquake design must ensure:
  • Factor of safety against sliding ≥ 1.2
  • Resultant of all forces (including earthquake) lies within middle 3/4 of base width
  • Bearing pressure on soil ≤ permissible limits

2. Notations & Symbols

• Refer Appendix K for all symbols and their meanings (Clause 9.1).

3. Key Tables

Table 6: Values of CT and Cv for Stacklike Structures (Clause 5.3.2)

• k = h'/re (h' = effective height, re = radius of gyration at base)

Table 3: Values of § for Soil-Foundation Systems (Clause 3.4.3)

IS 1893: Definitions and Terminology - Key Points

1. Notations & Symbols

   • Refer to Appendix K for all letter symbols and their meanings (Clause 9.1).
   • Additional notations are detailed in Clauses 4.2.1.1 and 4.2.1.2.

2. Definitions

   • Clause 2.0 provides definitions specific to seismic design.
   • For soil mechanics/dynamics terms, refer to IS 2809-1972 and IS 2810-1979.

3. Important Table for Stacklike Structures (Clause 5.3.2 & 5.3.4):

• h' = height of the structure
• re = radius of gyration of the structural shell at base

Summary Diagram: Relation of k, CT, Cv

graph LR
    A[h'/re (k)] --> B[CT Coefficient]
    A --> C[Cv Coefficient]
    B --> D[Increases linearly with k]
    C --> E[Increases, plateaus at 1.5]

This provides the foundation for interpreting seismic parameters and structural behavior in IS 1893.

IS 1893: General Principles and Design Criteria — Key Points

1. Factor of Safety & Resultant Force Location

• Sliding safety factor: Minimum 1.2 under earthquake forces (Clause 1.2).
• Resultant force: Must lie within the middle 3/4th of the base width to avoid overturning.
• Soil bearing pressure: Should not exceed permissible limits.

2. Seismic Coefficient for Soil-Foundation Systems (Clause 3.4.3, Table 4.1)

Note: For dams, use § = 1.0.

3. Seismic Force Transfer in Substructure (Clause 3.4.2.3)

• Design horizontal seismic coefficient: ( h )
• Water weight on enveloping cylinder: ( W_e )
• Reactions at supports: ( R_1, R_2 ) modified by earthquake forces ( F_e )
• Force distribution:
  [ F_1 = \begin{cases} P R_1 & \text{if } P R_1 < F'/2 \ F'/2 & \text{if } P R_1 \geq F'/2 \end{cases} \quad,\quad F_2 = F' - F_1 ]

4. Values of ( C_e ) for Submerged Pier (Table 7)

| Height of Submerged Portion ( H ) (

IS 1893: Design Loads and Load Combinations

1. Ultimate Load Design (Steel Structures)

[ \boxed{ UL = 1.4 \times (DL + LL + EL) } ]

• UL: Ultimate Load
• DL: Dead Load
• LL: Live Load (modified as per IS 1893)
• EL: Earthquake Load

2. Limit State Design (RCC & Prestressed Concrete)

• Use partial safety factors as per IS 456-1978 and IS 1343-1980.
• Live loads as per IS 1893 clauses.
• Design for ductile failure (tensile failure preferred) and avoid premature shear/bond failure (IS 456).
• Steel structures must ensure high ductility (IS 4326).

3. Design Live Loads (Clause 3.4.3, Table 4.1)

• For dams, use § = 1.0.

Summary Diagram: Load Combination Flow

flowchart LR
    DL(Dead Load)
    LL(Live Load)
    EL(Earthquake Load)
    UL(Ultimate Load)
    DL --> UL
    LL --> UL
    EL --> UL
    UL --> Design[Design Structure per IS 1893]

References:

• IS 1893: Clause 1.4, 3.3.2, 3.4.3
• IS 456-1978, IS 1343-

IS 1893: Calculation of Seismic Forces

Key Formula (Clause 6.2 & 3.4.2.3)

The lateral seismic force, F, to be resisted by a structure is:

[ F = A_h \times W ]

Where:

• (A_h =) design horizontal seismic coefficient
• (W =) seismic weight of the structure or mass considered

Horizontal Seismic Force (Clause 3.4.2.3)

[ F_n = a_h \times W_m ]

• (F_n =) horizontal seismic force
• (a_h =) design horizontal seismic coefficient (from Clause 2.14)
• (W_m =) weight of the mass considered (ignore buoyancy/uplift)

Vertical Seismic Force

[ F_y = X_v \times W ]

• (F_y =) vertical seismic force
• (X_v =) design vertical seismic coefficient (usually 0.5 × (a_h))

Seismic Coefficients & Zone Factors (Clause 2.14)

Seismic Force on Soil Mass (Clause 7.4.2)

• Use horizontal seismic coefficient (a_h) for soil layers
• Calculate lateral earth pressure including seismic increment:
  [ P = K_a \times \gamma \times h + \text{seismic increment} ]

Summary

• Determine Zone Factor (Z) from location (Clause 2.14)
• Calculate design horizontal coefficient (a_h) considering soil and structure (Clause 3.4.2.3)
• Compute seismic weight (W) of structure or soil mass
• Apply formula: (F = a_h \times W) for horizontal force
• Include vertical force (F_y = X_v \times W) if applicable

flowchart TD
    A[Determine Zone Factor (Z)] --> B[Calculate Design Horizontal Coefficient (a_h)]
    B -->

IS 1893: Earthquake Forces on Bridges and Substructures

Key Formulas

• Hydrodynamic Force on Submerged Pier:

[ F = C_e \cdot W_e ]

Where:

• ( C_e ) = coefficient from Table 7 (depends on submerged height ( H ))

• ( W_e ) = weight of water in enveloping cylinder (see 6.5.2.2)

• Horizontal Seismic Coefficient:

[ h = \text{design horizontal seismic coefficient (Clause 3.4.2.3(a))} ]

• Force Distribution at Supports:

[ \begin{cases} F_1 = P R_1 & \text{if } P R_1 < \frac{F'}{2} \ F_1 = \frac{F'}{2} & \text{if } P R_1 > \frac{F'}{2} \ F_2 = F' - F_1 \end{cases} ]

• Sliding Safety:

Factor of safety against sliding ≥ 1.2
Resultant force must lie within the middle 3/4th of base width.

Table 7: Values of ( C_e )

Design Checks

• Earthquake forces include hydrodynamic forces on submerged piers.
• Modify earth pressure on abutments as per Clauses 8.1.1 to 8.1.4.
• Ensure bearing pressure ≤ permissible soil pressure.
• Check force transfer from superstructure to substructure (Fig.7).

flowchart LR
    A[Seismic Motion] --> B[Hydrodynamic Force (F = Ce * We)]
    B --> C[Horizontal Force on Pier]
    C --> D[Force Distribution at Supports (F1, F2)]
    D --> E[Check Sliding Safety (FS ≥ 1.2)]
    E --> F[Check Bearing Pressure &

IS 1893 Key Points for Earth and Rockfill Dams and Embankments

1. Unit Weight for Saturated Earthfill (Clause 8.2.1)

• Use saturated unit weight (γ_sat) as per Clause 8.1 formulae.
• Typically,
  [ \gamma_{sat} = \gamma_{dry} + n \times \gamma_w ]
  where:
  • ( \gamma_{dry} ) = dry unit weight
  • ( n ) = porosity
  • ( \gamma_w ) = unit weight of water (≈ 9.81 kN/m³)

2. Hydrodynamic Forces on Dams (Clause 6.6.1)

• Horizontal shear per meter width:
  [ V_h = \frac{2}{3} p_y ]
• Hydrodynamic moment per meter width:
  [ M_h = \frac{4}{15} p_y a ] where:
  • ( V_h ) = hydrodynamic shear (kg/m)
  • ( M_h ) = hydrodynamic moment (kg·m/m)
  • ( p_y ) = hydrodynamic pressure
  • ( a ) = base length

3. Stability Checks (Clause 7.4.3.1)

• Upstream slope stability must consider:
  • Full reservoir water level
  • Earthquake horizontal forces acting upstream
  • Vertical earthquake forces = 0.5 × horizontal forces (acting upwards)

Summary Table:

IS 1893 – Earth Pressure on Retaining Structures

1. Lateral Earth Pressure during Earthquake (Clause 8.1)

• Cohesion is neglected for conservative design.
• Earth pressure is dynamic and depends on seismic coefficients.

2. Active Earth Pressure (Clause 8.1.1.1 & Appendix H)

• Use graphical methods (Appendix H) for determination.
• Active pressure depends on soil properties, wall inclination, and seismic acceleration.

3. Passive Earth Pressure (Clause 8.1.2)

• Formula for passive earth pressure ( P_p ) (per meter length):

[ P_p = C_p \gamma h^2 / 2 ]

Where:

• ( C_p = (1 \pm a_v) \frac{\cos^2(\phi + \delta - \beta) \cos \alpha \cos \delta \cos(\beta - \alpha + \delta)}{\cos(\delta - \beta) \cos(\phi + \delta) \cos(\beta - \alpha)} \times \frac{1}{1 - \sin(\phi + \beta) \sin(\delta + \alpha - \beta)} )

• ( a_v ) = vertical seismic acceleration coefficient

• ( \phi ) = angle of internal friction of soil

• ( \delta ) = wall friction angle

• ( \alpha, \beta ) = wall and backfill slopes

• ( \gamma ) = unit weight of soil

• ( h ) = height of backfill

• ( X = \tan^{-1}(1 \pm a_v) )

4. Graphical Methods

• Appendix H & J provide graphical procedures to determine active and passive pressures.

Summary Table: Key Parameters

IS 1893 - Notations & Symbols (Appendix K, Clause 9.1)

This section defines key symbols used in seismic design formulas:

Usage Tips:

• Refer to these symbols when applying IS 1893 seismic load calculations.
• Combine with load factors, importance factors, and seismic coefficients for design.
• Ensure factor of safety against sliding = 1.2 (Clause 1.2).

Example: Base Shear Calculation Symbol

[ V_B = C_s \times W ] where

• (V_B) = Base shear
• (C_s) = Seismic coefficient (depends on zone, soil, structure)
• (W) = Seismic weight of the structure

flowchart LR
    A[Structure Parameters]
    B[Loads: DL, LL, EL]
    C[Seismic Coefficients: Fo, αh, αv]
    D[Calculate Base Shear (VB)]
    E[Design Forces: M, V, Q]

    A --> D
    B --> D
    C --> D
    D --> E

For detailed symbol definitions, always consult Appendix K of IS 1893.

IS 1893: Response Spectrum Method - Key Points

Definition (Clauses 1.1, 2.13)

• Response Spectrum represents maximum response of idealized SDOF systems with given natural period (T) and damping (ξ) during earthquake.
• Response types:
  • Maximum absolute acceleration (Sa)
  • Maximum relative velocity (Sv)
  • Maximum relative displacement (Sd)
• Design primarily uses acceleration spectra (Sa) to calculate seismic forces:
  [ F = m \times S_a ] where m = modal mass.

Usage (Clause 3.4.2)

• Captures dynamic characteristics of structure and ground motion.
• Recommended for buildings with irregular geometry or mass/stiffness distribution (Clause 4.2.1.1).
• Modal analysis with Response Spectrum preferred for complex structures.

Typical Response Spectrum Parameters

Basic Relationships (for SDOF system)

[ S_v = S_a \times T / (2\pi) ] [ S_d = S_v \times T / (2\pi) = \frac{S_a T^2}{4 \pi^2} ]

Summary Diagram: Response Spectrum Concept

graph LR
A[Earthquake Ground Motion]
--> B[SDOF System with Period T, Damping ξ]
--> C[Maximum Response]
C -->|Acceleration| Sa
C -->|Velocity| Sv
C -->|Displacement| Sd

In practice: Use IS 1893 provided spectral acceleration values for design periods and damping to calculate seismic forces via modal response spectrum analysis.

IS 1893 - Pressure Coefficients for Dams (Clause 7.2.1.1 & Appendix G)

Key Formula for Hydrodynamic Pressure:

[ p = C_s \cdot a_h \cdot w \cdot h ]

• p = hydrodynamic pressure at depth y (kg/m²)
• C_s = pressure coefficient (varies with dam shape & depth)
• a_h = horizontal seismic coefficient
• w = unit weight of water (kg/m³)
• h = maximum reservoir depth (m)

Variation of Pressure Coefficient (C_s):

• (C_s) depends on dam shape and depth ratio (\frac{y}{h}).
• Values are given graphically in Appendix G (Figs. 14-18) for various upstream face inclinations (15°, 30°, 45°, 60°, 75°).
• For dams with vertical or constant slopes, approximate (C_s) can be calculated using: [ C_s = C_m \left{ \left(2 - 2 \frac{y}{h}\right) + N' \left(\frac{y}{h}\right)^2 \right} ]
• (C_m) = max coefficient from Fig. 10 (depends on slope angle)
• (y) = depth below water surface
• (h) = reservoir depth

Maximum Coefficient (C_m) (Fig. 10):

Pressure Distribution Coefficients (Clause 6.5.2.1, Fig. 8):

| (y/h) | (C_1) | (C_2) | (C_s) | (C_3) (Resultant) | |---------|---------|---------

Graphical Determination of Active Earth Pressure (IS 1893, Appendix H)

Key Steps (Clause H-1.1 & Fig. 19):

• Draw line BB' inclined at angle (φ - β) to horizontal, where:
  • φ = angle of internal friction of soil
  • β = backfill slope angle
• Assume rupture planes Ba, Bb, ... such that segments Aa = ab = bc = ...
• On BB', mark equal segments Ba' = a'b' = b'c' = ... equal in length to Aa, ab, bc, etc.
• From points a', b', etc., draw active pressure vectors at angle (90° - δ - φ - α) to BB', where:
  • δ = wall friction angle
  • α = wall face inclination
• The intersection locus of rupture planes and pressure vectors forms the Modified Culmann’s line.
• Determine the maximum active pressure vector X parallel to BE.

Active Earth Pressure Formula (Clause H-1.2):

[ P_a = X \times BC ] Where:

• (P_a) = active earth pressure
• (X) = maximum active pressure vector from graphical method
• (BC) = perpendicular distance from B to AA' in Fig. 19

Summary Table of Angles:

Conceptual Diagram (Simplified):

graph LR
    A((A)) -- Aa --> a((a))
    a -- ab --> b((b))
    b -- bc --> c((c))
    BB'["Line BB' (φ - β)"]
    a'((a')) -- a'b' --> b'((b'))
    b' -- b'c' --> c'((c'))
    a' -->|Active pressure vector at (90° - δ - φ - α)| rupturePlane1((Rupture Plane))
    b' -->|Active pressure vector| rupturePlane2((Rupture Plane))
    rupturePlane1 & rupturePlane2 --> modifiedCulmann["Modified Culmann's Line"]

Key Symbols & Notations from IS 1893 (Appendix K, Clause 9.1)

Notes:

• These symbols are used consistently throughout IS 1893 for seismic design.
• Refer to Appendix K for a comprehensive list.
• Design factors like Fo (Seismic Zone Factor) and I (Importance Factor) are crucial for earthquake load calculations.
• Use these notations when applying formulas for base shear, lateral forces, and moments.

Example: Base Shear Calculation Formula

[ V_B = \alpha_h \times W ]

• (V_B) = Base shear
• (\alpha_h) = Horizontal seismic coefficient
• (W) = Total seismic weight of the structure

graph TD
A[Seismic Load Parameters] --> B[Seismic Zone Factor (Fo)]
A --> C[Importance Factor (I)]
A --> D[Design Horizontal Coefficient (αh)]
D --> E