Code of practice for planning and design of ports and harbours, Part 2: Earth pressure

IS 4651 Part 2: Scope - Key Formulas, Tables & Specifications

Scope (Clause 3.0 & 4.1):
Defines symbols and parameters for earth pressure and soil mechanics related to excavation and retaining walls.

Important Symbols (Clause 4.1)

Key Table: Excavation in Clay (Clause 7.7)

IS 4651 Part 2: Key Definitions & Symbols

Important Symbols (Clause 4.1)

Key Formula for Flow Value N_φ

[ N_φ = \tan^2(45^\circ + \frac{\phi}{2}) ]

Table: Values of ( K_y ) for Cohesionless Soils (Vertical Walls, Horizontal Ground)

Table: Excavation in Clay (Clause 7.7)

| Parameter | 2 < N₀ < 5 | 5 < N₀ < 10 | 10 < N₀ < 20 | 20 < N₀ | |

IS 4651 Part 2: Types of Earth Pressure

1. Earth Pressure at Rest (Po)

• Formula:

  [ P_o = K_o \cdot \gamma \cdot z ]

  Where:

  • (P_o) = Earth pressure at rest at depth (z)
  • (K_o) = Coefficient of earth pressure at rest (from Table 1)
  • (\gamma) = Unit weight of soil
  • (z) = Depth below ground surface

• Table 1: Field Values of (K_o)

2. Active Earth Pressure (PA)

• Formula:

  [ P_A = K_A \cdot \gamma \cdot z - K_{Ac} \cdot C ]

  Where:

  • (P_A) = Active earth pressure at depth (z)
  • (K_A) = Active earth pressure coefficient (from Table 3)
  • (K_{Ac}) = Adhesion factor coefficient (from Table 4)
  • (C) = Cohesion of soil

• Parameters:

  • (K_A) and (K_{Ac}) depend on soil friction angle (\phi), wall friction (\delta), and adhesion-to-cohesion ratio.

3. Effect of External Causes on Earth Pressure (Clause 7.8)

• External loads (traffic, surcharge) increase earth pressure.
• Adjusted earth pressure should consider surcharge loads and dynamic effects.

Summary Diagram

flowchart TD
    A[Soil Type & Properties] --> B[Determine \(K_o\), \(K_A\), \(K_{Ac}\)]
    B --> C{Type of Earth Pressure}
    C -->|At Rest| D[\(P_o = K_o \gamma z\)]
    C

IS 4651 Part 2: Properties of Backfill & Soil Parameters

1. Earth Pressure at Rest (Clause 6.1)

[ P_0 = K_0 \cdot \gamma \cdot z ]

• (P_0): Earth pressure at rest at depth (z)
• (K_0): Coefficient of earth pressure at rest (from Table 1)
• (\gamma): Unit weight of soil
• (z): Depth below surface

Table 1: Field Values of (K_0)

2. Active Earth Pressure Coefficients (Clause 7.8.4)

• For hydraulic fills, (K_a) ranges:
  • Clean sands: ~0.35
  • Silty fine sands: ~0.50

3. Lateral Earth Pressure Due to Surcharge (Table A-3)

4. Coefficients (K) for Cohesionless Soils (Table B-1)

Key Design Considerations for Retaining Walls (IS 4651 Part 2)

1. Earth Pressure Coefficients

• Active Earth Pressure, (K_A) depends on soil friction angle (\phi) and wall friction (\delta).
• Passive Earth Pressure, (K_P) and Earth Pressure at Rest, (K_0), also defined.

2. Earth Pressure Formulas

• Active Earth Pressure (inclined wall):

[ P_A = K_A \gamma H^2 \cos \beta ]

Where:

• (K_A) = coefficient of active earth pressure (including wall friction)

• (\gamma) = bulk unit weight of soil

• (H) = height of soil retained

• (\beta) = wall back inclination angle

• Resultant Active Force Location:

[ \text{Acts at } 0.48H \text{ to } 0.5H \text{ above base depending on soil} ]

3. Coefficients (K) for Different Soils (Partial Table)

4. Pressure Distribution for Excavations

• Dense Sand:

[ P_A = 0.64 K_A \gamma H^2 \cos \beta ]

• Loose Sand:

[ P_A = 0.72 K_A \gamma H^2 \cos \beta ]

5. Wall Friction and Inclined Back Wall

• Use Clause 7.3.2: Apply earth pressure equations at different heights and sum to get total resultant.

6. Table of (K) for Cohesionless Soils (Vertical Walls, Horizontal Ground)

| Wall Friction (\delta) | (\phi=25^\circ) | (\phi=30^\circ) | (\phi=35^\circ) | (\phi=40^\circ) | |--------------------------|-------------------|-------------------|-------------------|

IS 4651 Part 2: Active Earth Pressure Calculation

1. Active Earth Pressure Formula (Clause A-1.1 & A-2.1)

For cohesionless soils at depth Z: [ P_a = K_A \cdot \gamma \cdot Z - K_{Ac} \cdot c ]

• (P_a) = active earth pressure intensity at depth (Z)
• (K_A) = active earth pressure coefficient (depends on soil friction angle (\phi) and wall friction (\delta))
• (\gamma) = unit weight of soil
• (c) = soil cohesion
• (K_{Ac}) = adhesion coefficient ratio (depends on (\phi), (\delta), and adhesion/cohesion ratio)

2. Coefficients (K_A) and (K_{Ac}) (Table 3 & 4)

• Values depend on:
  • Soil friction angle (\phi)
  • Wall friction angle (\delta)
  • Adhesion/cohesion ratio (for cohesive soils)
• Refer to Table 3 for (K_A) and Table 4 for (K_{Ac}).

3. Earth Pressure at Rest (Clause 6.1, Table 1)

[ P_0 = K_0 \cdot \gamma \cdot Z ]

• (K_0) values for typical soils:

Summary Diagram: Active Earth Pressure Components

graph TD
    Z[Depth, Z]
    gamma[Unit Weight, γ]
    phi[Soil Friction Angle, φ]
    delta[Wall Friction Angle, δ]
    c[Cohesion, c]
    KA[Active Earth Pressure Coefficient, K_A]
    KAc[Adhesion Coefficient, K_Ac]
    Pa[Active Earth Pressure, P_a]

    Z --> Pa
    gamma

IS 4651 Part 2: Passive Earth Resistance for Vertical Walls (Horizontal Ground Surface)

1. General Approach (Clause 8.3, Annex B)

Passive earth resistance is computed per Annex B for vertical walls with horizontal ground surface.

2. For Cohesionless Soils (Clause B-1)

• Effective friction angle for passive resistance:
  [ \delta = \frac{2}{3} \phi ] where (\phi) = soil friction angle.
  (For silty sands, (\delta) ranges between (\frac{1}{3}\phi) to (\frac{2}{3}\phi))

• Passive earth pressure coefficient (K_p):
  [ K_p = \tan^2 \left( 45^\circ + \frac{\phi}{2} \right) ]

3. For Cohesive Soils (Clause B-2)

• Cohesive soils have cohesion (c) and friction angle (\phi = 0).
• Passive earth resistance includes cohesion component and friction component.
• Total passive resistance (P_p) can be approximated as:
  [ P_p = c N_c + \gamma H K_p ] where:
  • (N_c) = bearing capacity factor (usually 5.7 for deep foundations)
  • (\gamma) = unit weight of soil
  • (H) = height of wall
  • (K_p) = passive earth pressure coefficient (for (\phi=0), (K_p=1))

4. Summary Table

Effect of External Factors on Earth Pressure
(IS 4651 Part 2 - Clause 7.8 and related clauses)

Key Formulas:

• Resultant Earth Pressure:
  [ P_H = K \times W_L ]
  Where:

  • (K) = Earth pressure coefficient (active or passive)
  • (W_L) = Load intensity (line or point load)

• Horizontal Pressure due to Surcharge (Sand Excavation):
  For dense sand:
  [ P_A = 0.64 \times K_A \times \gamma \times H^2 \times \cos \theta ]
  Acting at (0.5H) above base of cut.

  For loose sand:
  [ P_A = 0.72 \times K_A \times \gamma \times H^2 \times \cos \theta ]
  Acting at (0.48H) above base of cut.

• Wall Deflection Effect (Trapezoidal Pressure Distribution):
  [ 6H = 0.8 \times K_{ATH} \times \cos 6 ]

Table: Earth Pressure Coefficient (K_A) for Cohesionless Soils (Clause A-1.1)

Earth Pressure Due to Surcharge Loads (IS 4651 Part 2)

1. Key Formulas

For a horizontal ground surface and vertical retaining wall with surcharge ( q ):

• At depth ( z ), ( 0 \leq z < D ):

[ P_A = K_y \cdot (q + \gamma z) - 2c \sqrt{K_y} ]

• At depth ( z ), ( D \leq z < h ):

[ P_A = K_y \cdot (q + \gamma D + \gamma' (z - D)) - 2c \sqrt{K_y} + \gamma_w (z - D) ]

• For ( h < z < H ):

[ P_A = K_y \cdot \left( q + \gamma D + \gamma' (h - D) + \gamma'_1 (z - h) \right) - 2c \sqrt{K_y} + \gamma_w (z - D) ]

• Note: Negative ( P_A ) (tension) should be ignored, but hydrostatic pressure due to water intrusion in cracks must be considered.

2. Lateral Earth Pressure Coefficients

• For cohesionless soils (Table A-3):

Effect of Earthquake Forces on Earth Pressure (IS 4651 Part 2 & IS 1893)

• For seismic earth pressures, refer to IS 1893 (latest revision) for detailed earthquake load criteria.
• Earthquake forces increase lateral earth pressure on retaining structures.

Key Formulas & Concepts from IS 4651 Part 2:

• Active Earth Pressure with Wall Friction (Excavation in Sand):

  [ P_A = K_A \gamma H^2 \cos \delta ]

  Where:

  • (K_A) = coefficient of active earth pressure (includes wall friction)
  • (\gamma) = unit weight of soil
  • (H) = height of excavation
  • (\delta) = wall friction angle

• Resultant Pressure Location:
  Acts at about 0.5H above base for dense sand, 0.48H for loose sand.

• Horizontal Pressure on Wall due to Surcharge:

  [ P_H = K \times W \times L ]

  Where:

  • (K) = earth pressure coefficient (see table below)
  • (W) = surcharge load per unit length
  • (L) = length of surcharge

Earth Pressure Coefficients (K) for Various Soils:

Seismic Earth Pressure (Conceptual):

• Earthquake increases lateral pressure by a factor related to seismic coefficient (k_h).
• Use pseudo-static approach:
  [ P_{seismic} = P_{static} (1 + k_h) ]

Summary Diagram (Pressure Distribution in Braced Cuts):

graph LR
A[Top of Excavation] -->|Pressure increases with depth| B(Trapezoidal Pressure Distribution)
B --> C[Resultant Force at ~0.5H]
C --> D[Wall Deflection Increases with Depth]

References:

• IS 465

IS 4651 Part 2: Pressure Distribution & Resultant Force Key Points

1. Resultant Pressure from Line Load (WL)

• Resultant PHE = 0.64 WL (m² + 1)

• Approximate resultant force for low retaining walls from line load WL:

  [ P_H = K \times W \times L ]

• Line of action: Constructed by drawing a 40° line from the center of loaded area (Clause 7.6.1).

2. Pressure Distribution in Soil (Boussinesq Modified)

• Horizontal pressure due to surcharge:

  [ 6H = 0.8 K_A T H \cos \theta ]

• Resultant active earth pressure in dense sand:

  [ P_A = 0.64 K_A \gamma H^2 \cos \theta ]

  Acting at 0.5 H above base.

• In loose sand:

  [ P_A = 0.72 K_A \gamma H^2 \cos \theta ]

  Acting at 0.48 H above base.

3. Coefficient (K) for Point Loads (Table from IS 4651)

4. Resultant Force from Point Load (W_p)

• Use Boussinesq equation modified by experiments.

• Resultant force:

  [ P_H = K \times W_p ]

Summary Diagram (Pressure Distribution on Wall)

flowchart LR
    A[Soil Surface] --> B[Pressure Distribution]
    B --> C{Shape}
    C -->|Dense Sand| D[Trapezoidal, PA=0.64 K_A γ H² cosθ]
    C -->|Loose Sand| E[Trapezoidal, PA=0.72 K_A γ H² cosθ]
    C -->|Clay| F[Depends on Stability Number]
   

IS 4651 Part 2: Special Cases - Hydraulic Fills & Layered Soils

1. Hydraulic Fills (Clause 7.8.4)

• Active Earth Pressure Coefficients (Ka) for loose hydraulic fill:
  • Clean sands: Ka ≈ 0.35
  • Silty fine sands: Ka ≈ 0.50
• Account for increased earth pressure due to loose nature of hydraulic fill.

2. Layered Soils (Clause 7.3.1)

• Method applicable for more than two layers.
• Consider surcharge and water table effects on pressure distribution.
• Use superposition of pressures for each layer.

3. Key Formulas

4. Table: (K_y) Values for Cohesionless Soils (Vertical Walls, Horizontal Ground)

Key Formulas, Tables & Specs for Braced Excavations & Wall Movement (IS 4651 Part 2)

1. Braced Excavations (Clause 7.7)

• Bracings placed progressively, restraining lateral movement at top, allowing increasing movement with depth.
• Pressure distribution is trapezoidal, not Coulomb's.
• Use Fig. 5 & Table 2 (empirical) for pressure magnitude & resultant position.

2. Earth Pressure in Excavations

• Active Earth Pressure (Sand):

  [ P_A = (0.64) K_A \gamma H^2 \cos \delta \quad \text{(Dense Sand)} ]

  [ P_A = (0.72) K_A \gamma H^2 \cos \delta \quad \text{(Loose Sand)} ]

• Resultant acts approx. at 0.5H (dense) and 0.48H (loose) above base.

• (K_A) = active earth pressure coefficient (includes wall friction).

3. Pressure in Clay Excavations

• Pressure shape & magnitude depend on stability number (function of cohesion, unit weight, and depth).

4. Wall Movement & Earth Pressure Coefficients (Clause 1.1, Table B-1)

IS 4651 Part 2 — Annex A: Active Earth Pressure for Vertical Wall with Horizontal Ground

Key Formulas

1. For Cohesionless Soils (Clause A-1.1):

[ P_a = K_A \cdot \gamma \cdot Z ]

• (P_a): Active earth pressure at depth (Z)
• (K_A): Active earth pressure coefficient (from Table 3)
• (\gamma): Unit weight of soil
• (Z): Depth below ground surface

2. For Cohesive Soils (Clause A-2.1):

[ P_a = K_A \gamma Z - K_{Ac} C ]

• (C): Cohesion of soil
• (K_{Ac}): Cohesion factor (from Table 4)

Important Tables Summary

Notes:

• (K_A) depends on soil friction angle (\phi) and wall friction (\delta).
• For cohesive soils, adhesion reduces active pressure by (K_{Ac} C).
• Depth (Z) is measured from the ground surface.

graph TD
    Soil_Properties -->|Input| Calculate_KA_and_KAc
    Calculate_KA_and_KAc -->|Use Table 3 & 4| Determine_Coefficients
    Determine_Coefficients -->|Apply Formula| Compute_Active_Pressure
    Compute_Active_Pressure -->|Output| Active_Earth_Pressure

This concise framework helps compute active earth pressures for vertical retaining walls with horizontal backfill per IS 4651 Part 2 Annex A.

IS 4651 Part 2 - Annex B: Passive Earth Resistance for Vertical Walls on Horizontal Ground

Key Points:

B-1: Cohesionless Soils

• Passive earth resistance is computed using soil friction angle (φ).
• Typical assumption:
  [ \delta = \frac{2}{3} \phi ] where δ = wall friction angle.
• For silty sands, δ ranges between (\frac{1}{3} \phi) to (\frac{2}{3} \phi).

B-2: Cohesive and Mixed Soils

• For cohesive soils ((c \neq 0)) and mixed soils, passive resistance includes cohesion effects.
• Passive pressure (P_p) can be estimated by: [ P_p = K_p \gamma H + 2c \sqrt{K_p} ] where:
  • (K_p) = passive earth pressure coefficient
  • (\gamma) = unit weight of soil
  • (H) = wall height
  • (c) = cohesion

Passive Earth Pressure Coefficient (K_p) (Rankine's Theory for cohesionless soil):

[ K_p = \tan^2 \left( 45^\circ + \frac{\phi}{2} \right) ]

Notes:

• Use IS 1893 for seismic earth pressure considerations.
• Passive resistance is critical for design against lateral loads.

Summary Table for δ (Wall Friction Angle):

flowchart TD
    A[Vertical Wall] --> B[Horizontal Ground Surface]
    B --> C{Soil Type}
    C -->|Cohesionless| D[Use φ and δ = 2/3 φ]
    C -->|Silty Sands| E[δ = 1/3 φ to 2/3 φ]
    C