Glossary of terms and symbols relating to soil engineering

IS 2809: Scope Summary & Key Points

Scope:
IS 2809-1972 is a Glossary of Terms and Symbols relating to Soil Mechanics. It standardizes terminology, symbols, and units for soil engineering to ensure clarity and uniformity in communication.

Key Specifications:

• Physical dimensions are expressed using:

  • F (Force),
  • L (Length),
  • T (Time) instead of the traditional M (Mass), L, T.

• Symbols and Units:
  Symbols follow the term name, units in parentheses (e.g., dry density, γ_d (kN/m³)).

• Synonymous Terms:
  Cross-referenced with alphabetical precedence or significance.

• Reference Standards Included:

  • ASTM D 653-67 (Soil & Rock Mechanics terms)
  • ASCE Committee reports
  • Related IS codes (e.g., IS 1498, IS 2131)

Example Table Extract: Physical Dimensions

Important Concept: Zero Air Voids Curve (Clause 2.359)

• Represents dry density vs. moisture content at 100% saturation.
• Used for soil compaction and saturation analysis.

flowchart LR
    A[Soil Mechanics Terms] --> B[Symbols & Units]
    B --> C[Physical Dimensions (F, L, T)]
    A --> D[Synonymous Terms Cross-reference]
    A --> E[Reference Standards]
    E --> F[ASTM D 653-67]
    E --> G[IS Codes (1498, 2131, etc.)]

Summary: IS 2809 provides a comprehensive glossary to unify soil mechanics terminology and symbols, facilitating consistent engineering communication and practice.

IS 2809 - Terms and Definitions (Soil Engineering)

• Source Basis: Definitions align with ASTM D 653-67 and ASCE Soil Mechanics standards to ensure international coordination.
• Symbols & Units:
  • Symbols follow the term name, units in parentheses, e.g., void ratio (e), porosity (n).
  • Multiple symbols may be given; order is not significant.
• Physical Dimensions:
  • Represented by capital letters:
    • F = Force
    • L = Length
    • T = Time
  • (Note: Earlier M (mass) replaced by F in this revision)
• Alphabetical Cross-referencing:
  • When synonymous terms exist, the definition appears with the earlier term alphabetically, unless the later term is more significant.

Example Terms (from IS 2809 context):

flowchart LR
    A[Term] --> B[Symbol]
    B --> C[Unit]
    C --> D[Physical Dimension (F, L, T)]
    D --> E[Definition]

Note: Refer IS 2809 full glossary for comprehensive terms and symbols.

IS 2809 - Absorbed Water Key Points

• Absorbed Water (Clause 2.1): Water held mechanically in soil by surface tension, physically similar to ordinary water at the same temperature and pressure.

• Related Terms:

  • Moisture Content (Clause 2.353): Ratio of water weight to dry soil weight.
  • Hygroscopic Water Content, WH(D) (Clause 2.169): Water content of air-dried soil.
  • Moisture Equivalent (Clause 2.206): Water retained by soil after centrifugation, indicating field capacity.

Key Formula for Moisture Content (Water Content)

[ \text{Moisture Content (w)} = \frac{W_w}{W_d} \times 100 ]

• (W_w) = Weight of water in soil
• (W_d) = Weight of dry soil

Typical Water Content Ranges (Indicative)

Summary

• Absorbed water is mechanically held water, crucial for soil behavior.
• Moisture content helps quantify absorbed water.
• Hygroscopic water is minimal, absorbed water is higher, and moisture equivalent reflects field capacity.

flowchart LR
    Soil -->|Air Drying| HygroscopicWater[Hygroscopic Water]
    HygroscopicWater -->|Add Water| AbsorbedWater[Absorbed Water]
    AbsorbedWater -->|Centrifuge| MoistureEquivalent[Moisture Equivalent]

This illustrates the water states in soil per IS 2809 definitions.

IS 2809: Adobe - Key Specifications and Definitions

• Adobe (Clause 2.6):
  A light-colored clay and silt deposited in shallow desert basins or lakes, typically used as a natural building material.

• Material Properties:
  Adobe is a soil-based material with variable moisture content and density. Its strength and durability depend on clay content, compaction, and moisture.

• Relevant Parameters from IS 2809:

  • Adhesion (Clause 2.5): Shearing resistance between soil and another material at zero external pressure.
    • Unit adhesion: ( C_a ) (Force/Area)
    • Total adhesion: ( C_a ) (for FL-1)
  • Zero Air Voids Curve (Clause 2.359): Represents the dry density-moisture content relationship at 100% saturation, useful for understanding adobe compaction limits.

Practical Notes for Adobe Design:

Adobe Strength Estimation (Empirical):

[ \sigma_c = k \times \rho_d \times (1 - w) ]

• ( \sigma_c ) = compressive strength
• ( k ) = empirical constant (depends on clay mineralogy, typically 0.5 to 2 MPa/(g/cm³))
• ( \rho_d ) = dry density
• ( w ) = moisture content (decimal)

flowchart LR
    A[Clay & Silt Deposits] --> B[Adobe Material]
    B --> C[Compaction & Moisture Control]
    C --> D[Dry Density & Moisture Content]
    D --> E[Strength & Durability]

Summary: IS 2809 defines adobe as a natural clay-silt soil. Key design

IS 2809: Key Points on Arching

• Definition (Clause 2.24):
  Arching is the load transfer by shear from a yielding soil zone to adjacent less-yielding or restrained zones.

• Concept:
  When part of soil settles or yields, the load is redistributed to neighboring soil, reducing pressure on the yielding zone.

Key Formulas & Concepts (from soil mechanics & arching theory):

• Arching Ratio (β):
  [ \beta = \frac{\sigma'{yielding}}{\sigma'{less-yielding}} ] where (\sigma') is effective stress.

• Load Transfer:
  Load on yielding soil decreases; adjacent soil takes extra load.

• Passive & Active Earth Pressures (Clauses 2.2 & 2.218):
  Arching affects earth pressure distribution, modifying active/passive pressures.

Relevant Table Extract (Clause 2.344 - Uplift):

Summary Diagram of Arching:

flowchart LR
  A[Yielding Soil Zone]
  B[Less-Yielding Soil Zone]
  A -- Shear Transfer --> B
  B -- Supports Load --> Foundation

Note: For detailed design, incorporate arching effects into earth pressure calculations and consider soil stiffness contrasts.

IS 2809 - Base Course: Key Specifications & Formulas

Definition (Clause 2.27)

• Base Course: A layer of selected material of planned thickness constructed on subgrade or sub-base.
• Functions:
  • Distributes traffic load
  • Provides drainage
  • Minimizes frost action

Typical Specifications for Base Course

• Material: Well-graded granular material or crushed stone.
• Thickness: Usually ranges from 150 mm to 300 mm depending on traffic and subgrade strength.
• Compaction: Achieve Standard Compaction (Clause 2.310) — typically 95% of maximum dry density by Proctor test.
• Drainage: Must be free draining to avoid water retention.

Design Considerations

• Load Distribution: Base course spreads load over subgrade.
• Frost Protection: Thickness and material selected to minimize frost heave.
• Drainage: Permeability should be high; avoid fine particles.

Example Formula: Thickness Estimation (Empirical)

[ t_b = k \times \sqrt{W} ]

Where:

Summary Table: Base Course Thickness (Typical)

flowchart TD
    Subgrade --> Sub-base --> Base Course --> Surface Course
    Base Course -->|Load Distribution| Subgrade
    Base Course -->|Drainage| Water Drainage

Note: Always refer to IS 2809 for detailed material grading and quality requirements.

IS 2809 - Capillary Rise: Key Concepts & Formula

• Capillary Rise (hc or L): Height water rises above free water level due to capillary action in soil pores.

• Capillary Head (h): Potential causing water movement by capillarity, expressed as water head.

Key Formula for Capillary Rise Height (hc):

[ h_c = \frac{2 \sigma \cos \theta}{\rho g r} ]

Where:

• ( \sigma ) = Surface tension of water (N/m)
• ( \theta ) = Contact angle between water and soil particles (degrees)
• ( \rho ) = Density of water (kg/m³)
• ( g ) = Acceleration due to gravity (9.81 m/s²)
• ( r ) = Effective radius of soil pores (m)

Typical Values:

Notes:

• Smaller pore radius → higher capillary rise.
• Capillary rise affects foundation design and moisture control.

flowchart LR
    WaterSurface -->|Capillary Action| SoilPores
    SoilPores -->|Water Rises| hc[Height of Capillary Rise]
    hc -->|Depends on| r[Pore Radius]
    hc -->|Depends on| σ[Surface Tension]
    hc -->|Depends on| θ[Contact Angle]

This summarizes IS 2809 definitions and standard engineering relations for capillary rise.

IS 2809 - Clay: Key Points and Formulas

Definitions:

• Clay (2.54): Microscopic/submicroscopic particles from rock decomposition; plastic over a range of water content.
• Clay Size (2.55): Soil particles finer than 0.002 mm.
• Bentonitic Clay (2.35): High montmorillonite content; exhibits high swelling on wetting.
• Activity (2.4):
  [ \text{Activity} = \frac{\text{Plasticity Index (PI)}}{\text{Clay Fraction (% finer than 0.002 mm)}} ]

Specifications & Use:

• Plasticity Index (PI): Indicates clay's plasticity range.
• Activity Classification:
  • Low Activity: < 0.75
  • Normal Activity: 0.75 – 1.25
  • High Activity: > 1.25

Typical Application:

• Bentonite is used for sealing due to swelling.
• Clay's plasticity and activity guide suitability for construction.

flowchart LR
    Clay["Clay (<0.002 mm)"] --> Plasticity["Plasticity Index (PI)"]
    Clay --> ClayFraction["Clay Fraction (%)"]
    Plasticity --> Activity["Activity = PI / Clay Fraction"]
    Clay --> Bentonite["Bentonitic Clay (High Montmorillonite)"]
    Bentonite --> Swelling["High Swelling on Wetting"]

For detailed design, refer to IS 2809 tables on clay classification and swelling potential.

IS 2809 Key Formulas and Specifications: Coefficient of Curvature

• Coefficient of Curvature (Cc):
  [ C_c = \frac{D_{30}^2}{D_{10} \times D_{60}} ]
  where:

  • (D_{10}), (D_{30}), (D_{60}) = particle diameters at 10%, 30%, and 60% finer by weight respectively.

• Coefficient of Uniformity (Cu):
  [ C_u = \frac{D_{60}}{D_{10}} ]

Interpretation:

• For well-graded soils,
  [ 1 < C_c < 3 \quad \text{and} \quad C_u > 4 \quad (\text{for gravels}), \quad C_u > 6 \quad (\text{for sands}) ]

Summary Table:

These coefficients help classify soil gradation and predict compaction and permeability behavior.

graph LR
A[Grain Size Distribution Curve] --> B[D10]
A --> C[D30]
A --> D[D60]
B & C & D --> E[Calculate Cc and Cu]
E --> F[Soil Classification & Engineering Properties]

IS 2809 - Cohesionless Soil Key Points

• Definition (Clause 2.69):
  Soil with little or no cohesion when submerged and minimal strength when air-dried.

• Shear Strength (Coulomb's Equation):
  [ s = c + \sigma \tan \phi ] For cohesionless soils:

  • c ≈ 0 (negligible cohesion)
  • Shear strength depends mainly on effective stress (σ) and angle of internal friction (φ).

• Apparent Cohesion (Clause 2.68.1):
  Sometimes granular soils exhibit apparent cohesion due to capillary forces in unsaturated conditions, but this disappears when submerged.

Typical Properties of Cohesionless Soils

Practical Notes:

• Design shear strength for cohesionless soils usually assumes c = 0.
• Use effective stress parameters for stability and bearing capacity calculations.
• Apparent cohesion should not be relied upon for submerged or long-term stability.

graph LR
A[Cohesionless Soil] --> B[Shear Strength: s = σ tan φ]
A --> C[Cohesion c ≈ 0]
A --> D[Apparent Cohesion (Capillary Forces)]
D --> E[Disappears when submerged]

IS 2809: Critical Slope Overview

• Critical Slope (θc): Maximum angle from horizontal where a soil bank of height H stands unsupported without failure.

• Critical Height (Hc): Maximum height for vertical/sloped bank stability under given conditions.

• Critical Circle: The slip surface yielding minimum factor of safety in slope stability analysis.

Key Formulas

For cohesionless soil (dry or submerged):

[ \tan \theta_c = \frac{c'}{\gamma H} + \tan \phi' ]

Where:

• (c') = effective cohesion (usually 0 for cohesionless soil)
• (\gamma) = unit weight of soil
• (H) = height of slope
• (\phi') = effective angle of internal friction

For purely cohesionless soil:

[ \theta_c = \phi' ]

Typical Values (for cohesionless soil)

Notes

• Critical slope depends on soil type, moisture, and compaction.
• For cohesive soils, cohesion (c') increases critical slope.
• Stability analysis often uses critical circle method to determine factor of safety.

graph LR
A[Soil Bank] --> B[Height H]
A --> C[Critical Slope θc]
C --> D[Stability depends on φ', c', γ]
B --> E[Critical Height Hc]
E --> F[Max unsupported height]

Density Index (Relative Density), ID(D) as per IS 2809 is defined by:

[ \boxed{ I_D = \frac{e_{max} - e}{e_{max} - e_{min}} } ]

Where:

• ( e_{max} ) = Void ratio in loosest state
• ( e ) = Void ratio in the field (current state)
• ( e_{min} ) = Void ratio in densest state (laboratory achievable)

Key Points:

• ID ranges from 0 (loosest) to 1 (densest).
• Used to assess the compactness of cohesionless soils.
• Important in evaluating soil strength and settlement characteristics.

Related Terms:

Summary Diagram:

flowchart LR
    A[Void Ratio in Loosest State (emax)] -->|Subtract| B[Void Ratio in Field (e)]
    B -->|Divide by| C[Difference (emax - emin)]
    C --> D[Density Index (ID)]

This formula helps quantify soil compaction critical for foundation and earthwork design.

IS 2809: Passive Earth Pressure Key Points

Definition (Clause 2.113.3)

• Passive Earth Pressure (Pp, pp): Maximum earth pressure when soil is compressed enough to fully mobilize its shear resistance along a failure surface.

Key Concepts

• Passive pressure acts against a structure moving into the soil.
• It is much higher than active earth pressure due to soil compression.

Typical Formula for Passive Earth Pressure (Rankine's Theory)

[ P_p = \frac{1}{2} \gamma H^2 K_p ] Where:

• (\gamma) = unit weight of soil (kN/m³)
• (H) = height of the retaining structure (m)
• (K_p) = coefficient of passive earth pressure

Coefficient of Passive Earth Pressure, (K_p)

For cohesionless soil (from Rankine’s theory): [ K_p = \tan^2 \left(45^\circ + \frac{\phi}{2}\right) = \frac{1 + \sin \phi}{1 - \sin \phi} ] Where (\phi) = angle of internal friction of soil.

Summary Table for (K_p) (Typical Values)

Notes:

• IS 2809 refers to Earth Pressure generally; for detailed design, refer also to IS 456 and IS 2911.
• Passive pressure is used for design of retaining walls, pile foundations, and sheet piles resisting soil movement.

graph LR
A[Soil Mass] --> B[Retaining Wall]
B -->|Wall moves into soil| C[Passive Earth Pressure]
C --> D[Shear resistance fully mobilized]

In brief: Use (P_p = \frac{1}{2} \gamma H^2 K_p) with (K_p = \tan^2(45^\circ + \phi/2)) for passive earth pressure

IS 2809: Failure by Rupture (Shear Failure) Overview

• Definition: Failure by rupture refers to soil failure caused by shear stresses exceeding soil strength, leading to structural endangerment (Clauses 2.128, 2.282).

• Rupture Envelope: The shear strength limit is represented by the Mohr-Coulomb failure envelope (Clause 2.270), defined as:

  [ \tau = c + \sigma \tan \phi ]

  where:

  • (\tau) = shear strength
  • (c) = cohesion
  • (\sigma) = normal effective stress
  • (\phi) = angle of internal friction

• General Shear Failure: Characterized by a distinct rupture surface and sudden loss of shear strength (Clause 2.150).

Key Formulas for Shear Failure (Rupture)

Typical Rupture Modes in Soil

graph LR
A[Applied Load] --> B[Shear Stress in Soil]
B --> C[Shear Failure (Rupture)]
C --> D[General Shear Failure]
C --> E[Local Shear Failure]
C --> F[Punching Shear Failure]

Summary: Failure by rupture in IS 2809 is synonymous with shear failure, governed by the Mohr-Coulomb envelope. Design should ensure shear stresses remain below soil shear strength to prevent rupture.

IS 2809 - Flow Net Key Points

• Flow Net (Clause 2.140): Graphical tool showing flow lines (paths of seepage) and equipotential lines (lines of equal head) to analyze seepage through soils.

• Flow Channel (Clause 2.135): Area between two adjacent flow lines representing a unit flow path.

• Transformed Flow Net (Clause 2.333): Used for anisotropic soils by transforming boundaries so flow net squares become curvilinear squares, accounting for different permeability in directions.

• Flow Value, N₀ (Clause 2.142):
  [ N_0 = \tan^2 \left(45^\circ + \frac{\phi}{2}\right) ] where (\phi) = angle of internal friction of soil.

Flow Net Analysis Formula

The seepage discharge (Q) through soil can be estimated as:

[ Q = k \cdot H \cdot \frac{N_f}{N_d} ]

• (k) = coefficient of permeability (m/s)
• (H) = total head loss (m)
• (N_f) = number of flow channels
• (N_d) = number of equipotential drops

Flow Net Construction Steps

flowchart TD
    A[Define boundaries] --> B[Draw flow lines]
    B --> C[Draw equipotential lines]
    C --> D[Count flow channels (Nf)]
    D --> E[Count equipotential drops (Nd)]
    E --> F[Calculate Q = k * H * (Nf/Nd)]

Note: For anisotropic soils, transform the flow net using permeability ratio (k_x/k_y) before analysis.