Glossary of terms relating to soil dynamics

IS 2810 - Scope Summary

• Scope: IS 2810 covers design aspects of structures considering seismic zones based on seismic coefficients (Clause 2.81). It includes classification of seismic zones for safe design.

• Units: Uses SI units for all quantities (length in meters, force in newtons, stress in pascals, etc.).

• Seismic Zoning: The country is divided into zones with assigned seismic coefficients to guide design forces.

Key Specifications

Seismic Design Concept (Zoning)

• Structures designed per seismic zone with seismic coefficient Z.
• Zoning influences lateral design forces:
  [ F = Z \times W ] where
  (F) = design lateral force,
  (Z) = seismic zone coefficient,
  (W) = seismic weight of structure.

Summary Diagram of Seismic Design Scope

graph LR
A[Country] --> B[Seismic Zones]
B --> C[Zone 1: Low Seismicity]
B --> D[Zone 2: Moderate Seismicity]
B --> E[Zone 3: High Seismicity]
B --> F[Zone 4: Very High Seismicity]
F --> G[Higher Seismic Coefficient Z]
C --> H[Lower Seismic Coefficient Z]

Note: For detailed seismic coefficients and design forces, refer to IS 1893 (Part 1) which complements IS 2810 for seismic design.

IS 2810 (1979) provides definitions and symbols for key soil dynamics terms, essential for understanding soil behavior under dynamic loads.

Key Definitions & Symbols (Summary):

Important Notes:

• Dynamic shear modulus, G_d, varies with strain amplitude and frequency.
• Damping ratio, ξ, typically ranges from 2% to 10% for soils.
• Natural frequency depends on soil stiffness and layer thickness.

Typical Formula:

[ f_n = \frac{1}{4H} \sqrt{\frac{G_d}{\rho}} ]

• H = soil layer thickness (m)
• ρ = soil density (kg/m³)

This glossary aids in standardizing terminology for soil dynamic analysis and design. For detailed tables and extended definitions, refer to the full IS 2810 document.

Acceleration Pick-Up (IS 2810) is a transducer device that measures absolute vibration acceleration, typically ground motion during seismic events.

Key Points from IS 2810:

• Acceleration Pick-Up (Clause 2.3): Measures absolute acceleration of vibrations.
• Accelerograph (Clause 2.1): Records acceleration data from the pick-up.
• Transducer (Clause 2.68): Converts mechanical acceleration into electrical signals.
• Yield Acceleration (Clause 2.80): Threshold acceleration causing material slope yielding.

Typical Specifications & Formulas:

Yield Acceleration Concept:

• Yield Acceleration (a_y): Acceleration causing slope failure.
• Used in slope stability analysis:
  [ a_y = \frac{c' + (\sigma - u) \tan \phi'}{\rho \cdot g \cdot H} ] where:
  • (c') = effective cohesion
  • (\sigma) = normal stress
  • (u) = pore water pressure
  • (\phi') = effective angle of internal friction
  • (\rho) = soil density
  • (g) = gravity
  • (H) = slope height

Diagram: Acceleration Pick-Up & Accelerograph System

flowchart LR
    Vibration -->|Mechanical Input| Acceleration_Pickup[Acceleration Pick-Up (Transducer)]
    Acceleration_Pickup -->|Electrical Signal| Amplifier[Amplifier]
    Amplifier --> Accelerograph[Accelerograph (Recorder)]
    Accelerograph --> Data_Analysis[Data Analysis]

Summary:
Acceleration Pick-Up is a sensitive transducer converting vibration acceleration into electrical signals recorded by

Damping Characteristics (IS 2810)

• Damping Coefficient (C):
  [ C = \frac{\text{Damping Force}}{\text{Velocity}} ]

• Critical Damping Coefficient (C_c):
  [ C_c = 2 \sqrt{m k} ]
  where:

  • (m) = mass of the system
  • (k) = stiffness of the system

• Damping Factor (D):
  [ D = \frac{C}{C_c} ]
  It is a dimensionless ratio indicating the level of damping relative to critical damping.

• Viscous Damping:
  Damping force (F_d) is proportional to velocity (v):
  [ F_d = C \times v ]

Typical Damping Factors for Structures (approximate values):

graph LR
A[Velocity (v)] --> B[Damping Force (F_d)]
B -->|F_d = C × v| C[Damping Coefficient (C)]
C --> D[Damping Factor (D) = C / C_c]
D --> E[Energy Dissipation]

Summary: Damping reduces motion by dissipating energy, modeled as viscous damping proportional to velocity, quantified by the damping factor (D).

IS 2810: Soil Densification Methods – Key Points

1. Blasting (Clause 2.18.1)

• Small explosive charges are detonated at predetermined depths/points.
• Purpose: Increase soil density by shock waves and rearrangement of soil particles.
• Typical charge size and spacing depend on soil type and depth.
• Safety and controlled charge placement are critical.

2. Impact (Clause 2.18.2)

• Soil densification by dropping heavy weights (e.g., pounders or tampers).
• Weight, drop height, and number of blows are designed based on soil properties.
• Common in dynamic compaction for granular soils.

3. Dynamic Compaction (Clause 2.18)

• Combination of vibration, impact, and/or blasting.
• Used to densify loose granular soils to improve bearing capacity and reduce settlement.

4. Resonant Tamping (Clause 2.51)

• Impact blows applied at natural frequency of soil-rammer system.
• Maximizes compaction efficiency by resonance.

Typical Parameters for Impact Compaction

Formula for Energy Delivered per Blow:

[ E = W \times h ]

Where:

• (E) = Energy per blow (kN·m)
• (W) = Weight of rammer (kN)
• (h) = Drop height (m)

flowchart LR
    A[Start] --> B[Select Soil Type]
    B --> C{Method Choice}
    C -->|Blasting| D[Determine Charge Size & Depth]
    C -->|Impact| E[Select Rammer Weight & Drop Height]
    C -->|Dynamic Compaction| F[Combine Impact & Vibration]
    C -->|Resonant Tamping| G[Match Frequency & Impact]
    D --> H[Execute Blasting]
    E --> I[Drop Weights at Points]
    F --> J[Apply Vibration

IS 2810 - Free Vibration: Key Formulas & Specifications

Definitions:

• Free Vibration (2.25): System vibrates after displacement from equilibrium without external force.
• Natural Frequency (2.38, 2.26.2): Frequency at which system vibrates freely.
• Undamped Natural Frequency (2.26.5): Natural frequency ignoring damping effects.
• Force Transmitted (2.70.1): Force transmitted to support due to vibration.

Key Formulas:

1. Undamped Natural Frequency (ω_n):

[ \omega_n = \sqrt{\frac{k}{m}} ]

• k = stiffness of the system (N/m)
• m = mass of the system (kg)

2. Natural Frequency (f_n):

[ f_n = \frac{\omega_n}{2\pi} = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \quad \text{(Hz)} ]

3. Force Transmitted to Support (F):

[ F = m \times \omega_n^2 \times X ]

• X = amplitude of vibration (m)

Typical Table: Natural Frequency for Single Degree of Freedom (SDOF) Systems

graph LR
A[Displacement from Equilibrium] --> B[Free Vibration]
B --> C[Natural Frequency (f_n)]
C --> D[Force Transmitted to Support (F)]

Summary:
Free vibration analysis in IS 2810 uses the classical formula for natural frequency ( f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}} ), assuming no damping. The force transmitted to supports depends on mass, natural frequency, and vibration amplitude.

IS 2810 Key Points on Liquefaction

• Definition (Clause 2.29): Liquefaction is the loss of strength in submerged cohesionless soils due to earthquake shaking.
• Phenomenon: Soil behaves like a liquid, causing flow slides (Clause 2.23) and ground failure.
• Earthquake Loading (Clause 2.19.1): Soil samples are tested under simplified cyclic loading to simulate earthquake stresses.
• Seismic Zoning (Clause 2.81): Design seismic coefficients vary by zone, influencing liquefaction potential assessment.

Common Liquefaction Evaluation Formula (from geotechnical practice):

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

• FS: Factor of Safety against liquefaction
• CRR: Cyclic Resistance Ratio (soil resistance to liquefaction)
• CSR: Cyclic Stress Ratio (earthquake-induced stress)

Typical Parameters:

Simplified CSR formula:

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

Liquefaction Mitigation:

• Soil densification
• Drainage improvement
• Deep foundations or piles

flowchart LR
    Earthquake_Shaking --> Soil_Vibration
    Soil_Vibration --> Liquefaction{Loss of Strength?}
    Liquefaction -->|Yes| Flow_Slides
    Liquefaction -->|No| Stable_Soil

Note: IS 2810 provides definitions and seismic zoning but detailed liquefaction evaluation is supplemented by IS 1893 and geotechnical standards.

Modulus of Subgrade Reaction (k or Cp) as per IS 2810:

• Defined as the ratio of pressure intensity (p) to the total settlement (s) at the foundation-soil interface:

  [ k = \frac{p}{s} ]

• Units: Typically expressed in N/mm³ or kN/m³ (pressure per unit settlement).

• It represents soil stiffness and is essential for foundation design and soil-structure interaction.

Key Points:

Typical Values (Indicative):

flowchart LR
    Pressure(p) -->|Applied on soil| Soil
    Soil -->|Settlement(s)| Foundation
    k[Modulus of Subgrade Reaction k = p/s]

Use:

• For beam on elastic foundation models
• To estimate foundation settlements and design footing size
• Input parameter for soil-structure interaction analysis

Note:

• Modulus varies with soil type, depth, and loading conditions.
• Laboratory or plate load tests typically determine k.

IS 2810: Dynamic Load Units Summary

1. Electromagnetic Dynamic Load Unit (Clause 2.40.1)

• Produces constant dynamic load, independent of frequency.
• Generates oscillations using electromagnetic principles.
• Suitable for tests where load magnitude must remain constant regardless of oscillation frequency.

2. Mechanical Dynamic Load Unit (Clause 2.40.2)

• Produces sinusoidal, unidirectional force.
• Force generated by two unbalanced rotating masses.
• Dynamic load varies with frequency (f), typically proportional to ( f^2 ) due to centrifugal effects.

Key Definitions (Clauses 2.19 & 2.20)

• Dynamic Loading: Loading caused by time-varying forces.
• Dynamic Load Factor (DLF):
  [ \text{DLF} = \frac{\text{Dynamic Response}}{\text{Static Response}} ]

Typical Mechanical Oscillator Force Formula

[ F = m \cdot e \cdot \omega^2 = m \cdot e \cdot (2\pi f)^2 ] Where:

• ( m ) = unbalanced mass (kg)
• ( e ) = eccentricity (m)
• ( \omega = 2\pi f ) = angular frequency (rad/s)
• ( f ) = frequency (Hz)

Summary Table

graph LR
A[Dynamic Load Units] --> B[Electromagnetic Unit]
A --> C[Mechanical Unit]
B --> D[Constant Load]
C --> E[Frequency Dependent Load]
E --> F[Force: F = m e (2π f)^2]

This concise overview helps in selecting and understanding dynamic load units per IS 2810.

IS 2810: Pressure Cell Key Points

• Definition (Clause 2.45):
  A Pressure Cell is a transducer converting pressure into an electrical quantity for easier measurement.

• Units (SI) Relevant to Pressure Cell:

  Quantity	Unit	Symbol	Relation
  Pressure/Stress	Pascal	Pa	1 Pa = 1 N/m² = 1 kg/(m·s²)
  Force	Newton	N	1 N = 1 kg·m/s²
  Electric Voltage	Volt	V	1 V = 1 W/A

• Coefficient of Subgrade Reaction (Clause 2.11):
  [ C_p = \frac{\text{Pressure Intensity}}{\text{Settlement}} ] Used to relate pressure measured by the cell to soil settlement.

• Strain Gauge (Clause 2.63):
  Often used with pressure cells to measure strain in elastic elements, converting mechanical strain to electrical signals.

Typical Pressure Cell Setup

flowchart LR
    Pressure -->|Applied to| ElasticElement
    ElasticElement -->|Strain causes| StrainGauge
    StrainGauge -->|Electrical Signal| Transducer
    Transducer -->|Output Voltage| MeasurementDevice

Summary:

• Pressure cells measure soil or structural pressure by converting it to electrical signals.
• Use Pascal (Pa) for pressure units.
• Use Coefficient of Subgrade Reaction (Cp) to relate pressure to settlement.
• Strain gauges are integral for sensing strain in pressure cells.

For detailed design and calibration, refer to IS 2810 clauses on instrumentation and testing procedures.

IS 2810: Response Spectrum Key Points

• Response Spectrum (Clause 2.52) represents the maximum dynamic response (displacement, velocity, acceleration) of a single-degree-of-freedom system subjected to earthquake motion.

• Spectral Quantities (Clause 2.61):

  • Spectral Acceleration (Sa): Maximum relative acceleration.
  • Spectral Velocity (Sv): Maximum relative velocity.
  • Spectral Displacement (Sd): Maximum relative displacement.

Fundamental Relationships

For a linear SDOF system with natural frequency ( f ) and damping ratio ( \zeta ):

[ S_v = \omega S_d = \frac{S_a}{\omega} ]

Where:

• ( \omega = 2 \pi f ) = circular frequency (rad/s)
• ( S_a ) = spectral acceleration
• ( S_v ) = spectral velocity
• ( S_d ) = spectral displacement

Typical Response Spectrum Shape

graph LR
A[Low Frequency] --> B[High Spectral Displacement (Sd)]
B --> C[Peak Spectral Velocity (Sv)]
C --> D[Peak Spectral Acceleration (Sa) at High Frequency]

IS 2810 Specifications

• Response spectra are typically plotted for different damping ratios.
• Use spectral acceleration for force estimation.
• Use spectral displacement for deformation checks.
• Use spectral velocity for energy-based assessments.

Summary Table:

Use these to interpret or develop response spectra for seismic design per IS 2810.

IS 2810: Spectral Response & Displacement Key Points

• Spectral Response describes maximum responses of a Single Degree of Freedom (SDOF) system subjected to seismic input:

  • Spectral Acceleration (Sa) — max relative acceleration (Clause 2.61.1)
  • Spectral Velocity (Sv) — max relative velocity (Clause 2.61.3)
  • Spectral Displacement (Sd) — max relative displacement (Clause 2.61.2)

• Spectral Displacement (Sd) relates to Spectral Velocity and Acceleration by:

  [ S_d = \frac{S_v}{2\pi f} = \frac{S_a}{(2\pi f)^2} ]

  where:

  • ( f ) = natural frequency (Hz)
  • ( 2\pi f = \omega ) (angular frequency)

• Sinusoidal Variation (Clause 2.60): The response quantities vary sinusoidally with time.

Typical Spectral Response Relationships

Summary

• Use spectral acceleration for force estimation.
• Use spectral displacement for deformation limits.
• Spectral velocity bridges acceleration and displacement.

graph LR
A[Spectral Acceleration (Sa)] -->|divide by ω| B[Spectral Velocity (Sv)]
B -->|divide by ω| C[Spectral Displacement (Sd)]
C -->|multiply by ω| B
B -->|multiply by ω| A

This concise framework helps in seismic design and response evaluation as per IS 2810.

IS 2810: Torsional Vibrations - Key Points

1. Definition (Clause 2.67)

• Torsional vibrations are oscillations about the longitudinal axis of a shaft or system, causing twisting motion.

2. Force Transmitted (Clause 2.70.1)

• The force transmitted (F) by a torsionally vibrating system to its support depends on:
  • Amplitude of vibration
  • Frequency of oscillation
  • System stiffness and damping

3. Mechanical Oscillator (Clause 2.40.2)

• Uses two unbalanced rotating masses producing sinusoidal forces.
• Dynamic load varies with frequency ( f ).
• Force magnitude:
  [ F = m \cdot e \cdot \omega^2 ] where:
  • ( m ) = mass of unbalance
  • ( e ) = eccentricity
  • ( \omega = 2\pi f ) = angular frequency

4. Pitching (Clause 2.44)

• Related rotational vibration about the shorter horizontal axis, often coupled with torsional effects.

Typical Torsional Vibration Formulas:

graph LR
A[Unbalanced Masses] --> B[Rotating at ω]
B --> C[Sinusoidal Force F = m e ω²]
C --> D[Torsional Vibration in Shaft]
D --> E[Force Transmitted to Support]

Summary:
Torsional vibrations depend on system inertia, stiffness, and excitation frequency. IS 2810 highlights force transmission by oscillators with unbalanced masses and the importance of dynamic loads in design. Use the natural frequency formula to predict resonance and avoid excessive torsional stresses.

Vibrometer (IS 2810) - Key Points

• Definition (Clause 2.74):
  Instrument measuring phase, velocity, and acceleration of vibrations.

• Force (Clause 2.70.1):
  Force transmitted by vibrating system to support.

• Mechanical Oscillator (Clause 2.40.2):
  Produces sinusoidal, unidirectional force via two unbalanced rotating masses.

  • Dynamic load depends on frequency ( f ).
  • Force magnitude ( F = m \cdot e \cdot \omega^2 )
    where:
    ( m ) = unbalanced mass,
    ( e ) = eccentricity,
    ( \omega = 2\pi f ).

• Spectral Velocity (Clause 2.61.3):
  Maximum relative velocity response of the system.

Typical Vibrometer Measurements:

Formula Summary:

[ F = m \cdot e \cdot (2\pi f)^2 ]

• Used to calculate force from mechanical oscillator for vibrometer calibration.

graph LR
A[Mechanical Oscillator] --> B[Unbalanced Rotating Masses]
B --> C[Sinusoidal Force]
C --> D[Vibrometer]
D --> E[Measures: Phase, Velocity, Acceleration]

Note: For detailed calibration and measurement procedures, refer to IS 2810 sections on vibrometer usage and mechanical oscillator specifications.

IS 2810: Wave Types and Characteristics

Key Definitions (Clauses 2.75, 2.78)

• Wave: Disturbance propagating through a medium; displacement varies with time and position.
• Reflected/Refracted Wave (2.78.3): Incident wave components reflected back or transmitted into a second medium.
• Transverse Wave (2.78.5): Particle displacement is parallel to the wave front.

Important Formula for Transverse Wave Velocity (Ut)

[ U_t = \sqrt{\frac{G}{\rho}} = \sqrt{\frac{E}{2\rho(1+v)}} ]

Where:

• ( G ) = Shear modulus
• ( \rho ) = Mass density
• ( v ) = Poisson’s ratio
• ( E ) = Young’s modulus

This velocity (U_t) represents the speed at which shear waves travel in the medium.

Summary Table: Wave Types

flowchart LR
    A[Incident Wave] --> B[Reflected Wave]
    A --> C[Refracted Wave]
    D[Transverse Wave] -->|Displacement|| Parallel to Wave Front
    E[Longitudinal Wave] -->|Displacement|| Parallel to Propagation Direction

This concise summary aligns with IS 2810 clauses and standard wave mechanics in solids.