IS 4651 Part 41989AI Search Enabled✦ AI Generated

Code of practice for planning and design of ports and harbours, Part 4: General design consideration

IS 4651 Part 4:1989 provides comprehensive guidelines for the general design considerations of ports and harbour structures, focusing on load factors, material selection, corrosion protection, and structural design methods. It applies to engineers and designers involved in planning and constructing durable marine infrastructure, ensuring safety and serviceability under various environmental and operational loads.

11Sections
68Clauses Indexed
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1989Edition
Ports and HarboursCategory
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What This Standard Covers

IS 4651 Part 4:1989 provides comprehensive guidelines for the general design considerations of ports and harbour structures, focusing on load factors, material selection, corrosion protection, and structural design methods. It applies to engineers and designers involved in planning and constructing durable marine infrastructure, ensuring safety and serviceability under various environmental and operational loads.

Who Uses This Standard

  • Marine Structural Engineers
  • Port and Harbour Designers
  • Civil Engineers specializing in Marine Construction
  • Geotechnical Engineers
  • Construction Project Managers for Ports
  • Materials Engineers focusing on Marine Environments
  • Consultants in Coastal Infrastructure

Key Topics Covered

Load types and combinations including dead, live, berthing, wind, seismic forces
Limit state and working stress design methods
Permissible stresses for concrete, steel, timber, and prestressed concrete
Material selection and durability in aggressive marine environments
Corrosion protection techniques including coatings and cathodic protection
Concrete mix design requirements for marine structures
Design and spacing of expansion joints
Fender design and energy absorption considerations
Use of precast concrete elements
Timber preservation and protection against marine borers
Safety factors and partial safety factors for loads and materials
Guidelines for allowable stresses and bearing pressures
Structural detailing to control cracking and ensure serviceability
References to related Indian Standards for materials and loads
Design considerations for secondary and erection stage stresses

Table of Contents

1Scope

IS 4651 Part 4 (1989) - Scope: Key Formulas, Tables & Specifications


1. Scope Overview

  • Applies to design and construction of port and harbour structures.
  • Covers load combinations, material specifications, and safety factors.
  • Refers to related IS codes for materials and loadings.

2. Partial Safety Factors for Loads (Table 1)

Load TypeServiceability (γ)Collapse Limit State (γ)
Dead Load (DL)1.01.5
Vertical Live Load (LL)1.01.5
Earth Pressure1.01.0
Hydrostatic/Hydrodynamic1.01.2
Berthing & Mooring Forces1.01.5
Wind Forces-1.5
Seismic Forces-1.5

Note: Some factors have alternative values (e.g., 0.9) depending on conditions.


3. Increase in Permissible Stresses & Bearing Pressure (Table 2)

Load CombinationIncrease in Permissible Stress (%)Increase in Allowable Bearing Pressure (%)
i) DL + LL + impact + vehicle forcesNilNil
ii) DL + LL + impact + earth pressure1515
iii) DL ± LL + impact + earth pressure + hydro + berthing/mooring forces25 (RC), 33⅓ (Steel/Timber)25
iv) Wind forces + (i), (ii), or (iii)Refer IS 875 (Part 3)-
v) Seismic forces + (i), (ii), or (iii)Refer IS 1893-
vi) Secondary stresses + (i)1515
vii) Erection stage stresses + DL + LL + earth + hydro + wind forces15
2Definitions

IS 4651 Part 4 - Definitions: Key Formulas, Tables & Specifications


1. Partial Safety Factors for Loads (Table 1, Clause 5.1)

Load TypeServiceability FactorCollapse Factor
Dead Load (DL)1.01.5
Vertical Live Load (LL)1.01.5
Earth Pressure1.01.0
Hydrostatic/Hydrodynamic Forces1.01.0
Berthing & Mooring Forces1.01.5
Wind Forces-1.5
Seismic Forces-1.5

Note: For serviceability limit states, factors apply to short-term effects; consider creep for long-term.


2. Increase in Permissible Stresses (Table 2, Clauses 5.1 and 7.1.2)

Load CombinationIncrease in Permissible Stress (%)
DL + LL + impact + braking/traction + centrifugal forcesNil
DL + LL + impact + braking/traction + centrifugal + earth pressure15
DL ± LL + impact + earth pressure + hydrostatic/hydrodynamic + berthing/mooring25 (RC), 33⅓ (Steel/Timber)
Wind forces + above combinationsSee IS 875 (Part 3)
Seismic forces + above combinationsSee IS 1893
Secondary stresses + DL + LL15
Erection stage stresses + DL + LL + earth pressure + hydrostatic + wind15 (RC), 33⅓ (Steel/Timber)

3. Referenced Indian Standards (Annex A)

  • IS 875 (Part 3): Wind Loads
  • IS 1893: Earthquake Resistant Design
  • IS 456: Plain & Reinforced Concrete
  • IS 800: Structural Steel Design
  • IS 2911: Pile Foundation Design
3Loads, Forces and Stresses

IS 4651 Part 4 — Loads, Forces, and Stresses Key Points

1. Loads to Consider (Clause 4.1)

  • Dead Load (DL)
  • Vertical Live Load (LL)
  • Impact/Dynamic effects of live load
  • Forces from tractive effort/breaking of vehicles, cranes, etc.
  • Centrifugal forces on curves
  • Earth pressure
  • Hydrostatic & hydrodynamic forces
  • Berthing & mooring forces
  • Wind forces
  • Secondary stresses (shrinkage, creep, temperature)
  • Erection stage stresses
  • Seismic forces

2. Partial Safety Factors (Table 1)

LoadingServiceabilityCollapse Limit State
Dead load (DL)1.01.5 (or 0.9)
Vertical live load (LL)1.01.5 (or 0.9)
Earth pressure1.01.0
Hydrostatic/hydrodynamic forces1.01.0
Berthing & mooring forces1.01.5
Secondary stresses1.0-
Wind forces-1.5
Seismic forces-1.5

Note: For serviceability limit states, consider short-term effects. For long-term creep effects, only permanent parts of DL and LL are considered.


3. Design Formula (General Load Combination)

[ \text{Design Load} = \gamma_D \times DL + \gamma_L \times LL + \gamma_E \times \text{Earth Pressure} + \ldots ]

Where:

  • (\gamma_D), (\gamma_L), (\gamma_E) = partial safety factors from Table 1.

4. Summary Diagram of Load Types

graph LR
  A[Loads & Forces] --> B[Dead Load]
  A --> C[Live Load]
  A --> D[Impact/Dynamic Effects]
  A --> E[Earth Pressure]
  A --> F[Hydrostatic Forces]
4Combination of Loads, Forces and Stresses

IS 4651 Part 4: Combination of Loads, Forces, and Stresses

1. Partial Safety Factors (Table 1)

Load TypeServiceabilityCollapse Limit State
Dead Load (DL)1.01.5 (or 0.9)
Vertical Live Load (LL)1.01.5 (or 0.9)
Earth Pressure1.01.0
Hydrostatic/Hydrodynamic Forces1.01.2 (for collapse)
Berthing & Mooring Forces1.0 (service)1.5 (service)
Wind Forces-1.5 (collapse)
Seismic Forces-1.5 (collapse)

2. Increase in Permissible Stresses (Table 2)

Load CombinationIncrease in Permissible Stress (%)Increase in Allowable Bearing Pressure (%)
i) DL + LL + impact + breaking/traction + centrifugal forcesNilNil
ii) DL + LL + impact + breaking/traction + centrifugal + earth pressure1515
iii) DL ± LL + impact + breaking/traction + centrifugal + earth + hydro + berthing2525 (RC), 33⅓ (Steel/Timber)
iv) Wind forces + (i), (ii), or (iii)Refer IS 875 (Part 3): 1987-
v) Seismic forces + (i), (ii), or (iii)Refer IS 1893: 1984-
vi) Secondary stresses + (i)1515
vii) Erection stresses + DL + LL + earth + hydro + wind1525 (RC), 33⅓ (Steel/Timber)

3. Notes

  • Loads should be computed as per **IS 4651 Part 3 (1974
5Method of Design

IS 4651 Part 4 — Method of Design: Key Points

Design Methods (Clause 6.1)

  • Working Stress Method (WSM)
  • Limit State Method (LSM)

Working Stress Method (Clause 7.1)

  • Use permissible stresses under working loads.
  • Stresses must not exceed allowable limits for materials.

Load Combinations & Partial Safety Factors (Clause 5.1, Table 1)

Load TypePartial Safety Factor (Limit State of Collapse)
Dead Load1.5
Vertical Live Load1.5
Earth Pressure1.0
Hydrostatic/Hydrodynamic1.0
Berthing and Mooring Forces1.5
Wind Forces1.5
Seismic Forces1.5

Summary:

  • WSM: Use permissible stresses directly on working loads.
  • LSM: Multiply characteristic loads by partial safety factors (γ) before design.
  • Refer to Clause 5.1 Table 1 for specific γ values per load type.
  • Combine loads as per IS 4651 guidelines for design checks.
flowchart TD
    A[Start Design] --> B{Select Method}
    B -->|Working Stress| C[Use permissible stresses]
    B -->|Limit State| D[Apply partial safety factors]
    D --> E[Calculate design loads]
    E --> F[Check stresses against design strength]
    C --> F
    F --> G[Design Structural Element]

This concise approach ensures safety and economy in structural design per IS 4651 Part 4.

6Permissible Stresses

IS 4651 Part 4: Permissible Stresses Summary

1. Basic Permissible Stresses (Clause 7.1)

  • Use Working Stress Method for design until full adoption of Limit State Method.
  • Permissible stresses are based on safe working loads, ensuring stresses do not exceed yield or 0.2% proof stress.

2. Increase in Permissible Stresses (Clause 7.1.2 & Table 2)

Load CombinationIncrease in Permissible Stress (%)Increase in Allowable Bearing Pressure (%)
i) DL + LL + impact, breaking/traction + centrifugal forcesNil (0%)Nil (0%)
ii) DL + LL + impact, breaking/traction + centrifugal + earth pressure15%15%
iii) DL ± LL + impact, breaking/traction + earth + hydro + berthing/mooring forces25% (RC) / 33⅓% (Steel/Timber)25%
iv) Wind forces + (i), (ii), or (iii)Refer IS 875 (Part 3):1987-
v) Seismic forces + (i), (ii), or (iii)Refer IS 1893:1984-
vi) Secondary stresses + (i)15%15%
vii) Erection stage stresses + DL + LL + earth + hydro + wind forces15% (RC) / 33⅓% (Steel/Timber)25%

Notes:

  • DL = Dead Load, LL = Live Load.
  • Permissible stresses must not exceed yield stress or 0.2% proof stress.
  • For wind and seismic forces, refer to IS 875 (Part 3) and IS 1893 respectively.

Visual Summary:

flowchart TD
    A[Load Combinations] --> B[Permissible Stress Increase]
    B --> C{i) DL+LL+Impact+Traction+Centrifugal}
    B --> D{ii) + Earth Pressure}
    B --> E{iii) + Hydro + Berthing/Mooring}
    B --> F{iv) +
7Choice of Construction Material

IS 4651 Part 4 — Choice of Construction Material: Key Points

1. Increase in Permissible Stresses (Clause 7.1.2, Table 2)

Load CombinationIncrease in Permissible Stress (%)Reinforced ConcreteSteel & TimberIncrease in Allowable Bearing Pressure (%)
i) DL + LL + impact + breaking/traction + centrifugal forcesNilNilNilNil
ii) DL + LL + impact + breaking/traction + centrifugal + earth pressure15151515
iii) DL ± LL + impact + breaking/traction + centrifugal + earth pressure + hydro + berthing/mooring252533⅓25
iv) Wind forces + (i), (ii), or (iii) combinationsRefer IS 875 (Part 3): 1987---
v) Seismic forces + (i), (ii), or (iii) combinationsRefer IS 1893: 1984---
vi) Secondary stresses + (i)15151515
vii) Erection stage stresses + DL + LL + earth + hydro + wind1533⅓2525

2. Permissible Stresses per Material (Clause 7.1.1)

  • Reinforced Concrete: IS 456 : 1978
  • Prestressed Concrete: IS 1343 : 1980
  • Structural Steel: IS 800 : 1984
  • Timber: IS 883 : 1970
  • Piles (Timber/Concrete): IS 2911 (Parts 1 & 2)

3. Partial Safety Factors for Loads (Table 1, Clause 5.1)

Load TypeServiceabilityCollapse State
Dead Load1.01.5
8Corrosion Protection Measures

Corrosion Protection Measures (IS 4651 Part 4)

Key Remedial Measures (Clause 8.2.3):

  • a) Protective Coatings
    • Barrier to environment; delays corrosion.
    • Important factors: coating type, application method, thickness, recoating possibility.
  • b) Cathodic Protection
    • Effective for steel submerged or buried with electrolytic corrosion risk.
    • Methods: Impressed current or sacrificial anode systems.
  • c) Increased Section / Reduced Stresses
    • Use thicker steel if coatings/cathodic protection not feasible.
    • Minimum thickness:
      • With cathodic protection: 6 mm
      • Without cathodic protection: 10 mm
    • Always use protective coatings in marine conditions.
  • d) Use of Special Steel
    • Alloy steels (e.g., with 2% copper) reduce corrosion rate.

Additional Specifications:

  • Concrete Cover (Clause 8.3.5):
    • Increase cover by 25 mm over IS 456:1978 for marine exposure (sea water, splash zone, marine atmosphere).

Summary Table: Minimum Steel Thickness in Marine Environment

ConditionMin. Steel Thickness
With Cathodic Protection6 mm
Without Cathodic Protection10 mm

Corrosion Severity Zones (Clause 8.2.2):

  • Severe corrosion in:
    • Saline water
    • Splash zone (wet/dry cycles)
    • Tidal range
    • Buried steel under certain conditions

Related Load Increase Table (Clause 5.1):

Load CombinationIncrease in Permissible Stress (Reinforced Concrete)Increase in Permissible Stress (Steel/Timber)
DL + LL + impact + centrifugal forcesNilNil
DL + LL + impact + earth pressure15%15%
DL ± LL + impact + earth + hydro + mooring forces25%33⅓%
Secondary stresses + DL15%15%

(DL = Dead Load, LL = Live Load)


9Design of Fenders

IS 4651 Part 4 – Design of Fenders: Key Points

1. Design Parameters (Clause 9.3)

  • Berth loads: As per IS 4651 Part 3 (1974).
  • Ship size & frequency: Fender capacity depends on ship size and arrival frequency.
  • Berthing velocity: Adopt values from IS 4651 Part 3 (1974).
  • Importance of structure: Consider consequences of failure.
  • Energy absorption:
    • Energy stored as strain energy.
    • Shear > tension/compression in energy absorption.
    • Torsion effective for thin-walled tubes.
    • Include flexibility of berthing structure + fender system.
  • Reaction force & deflection:
    • Consider hull and structure strength.
    • Use manufacturer data with a factor of safety = 1.4 on ultimate energy absorption.
  • Fender disposition:
    • Longitudinal spacing: 0.3 to 0.4 × length of smallest ship (L).
    • Vertical range: From cope level to low water level to protect hull and structure.

2. Types of Fenders (Clause 9.2)

  • Rubber (cylindrical, rectangular, sandwich types)
  • Steel spring, timber, brushwood, rope, concrete, floating, torsion, etc.
  • Choice based on specific berth conditions.

3. Functional Requirements (Clause 9.1)

  • Absorb berthing energy.
  • Prevent direct hull-structure contact.
  • Transmit controlled thrust to structure.

4. Partial Safety Factors for Loads (Table 1, Clause 5.1)

Load TypeServiceabilityCollapse
Dead Load1.01.5
Vertical Live Load1.01.5
Earth Pressure1.01.0
Hydrostatic/Hydrodynamic Forces1.01.0
Berthing & Mooring Forces1.01.5
Wind Forces-1.5
Seismic Forces-1.5

**Typical Energy Absorption

10Expansion Joints

Expansion Joints: Key Specifications from IS 4651 Part 4

1. Spacing of Expansion Joints (Clause 10.2):

  • Recommended spacing: 39 m for solid quay walls or walls on piles.
  • For better stiffness, spacing can be increased to 60 m.

2. Design Requirements (Clause 10.1 & 10.3):

  • Provide sufficient expansion joints to accommodate movements due to:
    • Shrinkage
    • Temperature changes
    • Foundation yieldings
  • Steel reinforcement should be designed to control shrinkage and temperature cracks.
  • Joints must be keyed to transfer shear forces and allow free length changes.
  • Key arrangement depends on soil, structure, and loading.
  • Expansion joints must be covered to prevent backfill washout.

Summary Table for Expansion Joint Spacing

Structure TypeRecommended Joint Spacing (m)Notes
Solid quay walls or pile walls39General rule
Same structures for stiffness60Provides better stiffness

Design Considerations

  • Shear transfer: Use keyed joints to transfer shear between sections.
  • Movement accommodation: Joints must not hinder thermal/shrinkage movement.
  • Protection: Cover joints to avoid backfill erosion.

flowchart LR
    A[Structure Length] -->|Divide into sections| B[Expansion Joints]
    B --> C{Spacing}
    C -->|39 m| D[Standard spacing]
    C -->|60 m| E[For better stiffness]
    B --> F[Keyed joints for shear transfer]
    B --> G[Allow free expansion/contraction]
    B --> H[Covered joints to prevent backfill washout]

For detailed design, refer to related IS codes:

  • IS 456 (Concrete design)
  • IS 800 (Steel structures)
  • IS 2911 (Pile foundations)

These ensure proper detailing of reinforcement and joint construction.

Annex AList of Referred Indian Standards

List of Referred Indian Standards in IS 4651 Part 4

IS No.Title
IS 226 : 1974Specification for structural steel (standard quality)
IS 800 : 1984Code of practice for use of structural steel in general building construction
IS 401 : 1982Code of practice for preservation of timber
IS 875 (Part 3) : 1987Code of practice for design loads - Wind loads
IS 455 : 1976Specification for portland slag cement
IS 456 : 1978Code of practice for plain and reinforced concrete
IS 883 : 1970Code of practice for design of structural timber in buildings
IS 1343 : 1980Code of practice for prestressed concrete
IS 2911 (Parts 1-3) : 1979Code of practice for design and construction of pile foundation
IS 1489 : 1976Specification for portland pozzolana cement
IS 1893 : 1984Criteria for earthquake resistant design of structures
IS 2062 : 1984Specification for weldable structural steel
IS 4651 (Part 3)Code of practice for planning and design of ports and harbours

Notes:

  • These standards cover materials (steel, cement, timber), design codes (loads, earthquake), and construction practices relevant to ports and harbours.
  • Always refer to the latest edition or amendments for compliance.
  • BIS ensures quality and conformity through inspection and certification under the BIS Act, 1986.

flowchart LR
    A[IS 4651 Part 4] --> B[Structural Steel - IS 226, IS 800, IS 2062]
    A --> C[Cement - IS 455, IS 1489]
    A --> D[Concrete - IS 456, IS 1343]
    A --> E[Timber - IS 401, IS 883, IS 2911 Part 2]
    A --> F[Loads - IS 875 Part 3, IS 1893]
    A --> G[Ports & Harbours Design

Popular Questions About IS 4651 Part 4

?What types of loads and forces must be considered in the design of port structures according to IS 4651 Part 4?

According to IS 4651 Part 4 (1989), the design of port structures must consider the following loads and forces (Clause 4.1):

  • Dead Load (DL)
  • Vertical Live Load and its impact/dynamic effects
  • Forces from tractive effort or braking of vehicles, cranes, ship loaders, etc.
  • Centrifugal forces from vehicles on curves
  • Earth pressure on structures
  • Hydrostatic and hydrodynamic forces due to water
  • Berthing forces from vessels
  • Mooring forces holding vessels in place
  • Wind forces acting on structures
  • Secondary stresses from shrinkage, creep, temperature changes
  • Erection stage stresses during construction
  • Seismic forces for earthquake resistance

Note: For serviceability limit states, short-term effects of these loads are considered, while long-term effects focus on dead load and permanent parts of live load.


Summary Table of Loads

Load TypeDescription
Dead Load (DL)Self-weight of structure
Vertical Live LoadVariable loads from traffic, equipment
Impact/Dynamic LoadSudden load effects
Tractive/Braking ForcesFrom moving machinery/vehicles
Centrifugal ForcesOn curved tracks
Earth PressureSoil lateral pressure
Hydrostatic & HydrodynamicWater pressure & wave forces
Berthing ForcesVessel impact forces
Mooring ForcesTension from mooring lines
Wind ForcesWind pressure on exposed surfaces
Secondary StressesShrinkage, creep, temperature effects
Erection StressesDuring construction
Seismic ForcesEarthquake-induced forces
Loading diagram...
?Which design methods are recommended for reinforced concrete and steel members in harbour structures?

Recommended Design Methods for Harbour Structures (IS 4651 Part 4):

  • Reinforced Concrete (RCC) and Prestressed Concrete:

    • Can be designed using Working Stress Method (WSM) or Limit State Method (LSM) (Clause 6.1.1).
    • In marine environments, stresses should be reduced to minimize cracking (Clause 8.3.4).
    • Steel stresses in WSM are limited to 165 N/mm².
    • Crack width near main reinforcement should not exceed 0.004 × cover.
  • Steel and Other Materials:

    • Design should follow Working Stress Method (Clause 6.1.1).
    • Special attention to durability due to aggressive marine environment (Clause 8.1).

Summary Table:

MaterialDesign MethodStress Limits in Marine EnvironmentCrack Control
RCC & PrestressedWSM or LSMSteel stress ≤ 165 N/mm² (WSM)Crack width ≤ 0.004 × cover
Steel & OthersWorking Stress MethodAs per WSMDurability considerations critical
Loading diagram...

Note: Always check for crack formation explicitly if higher stresses are used.

?What are the concrete grade and mix requirements for durability in marine environments?

Concrete Grade and Mix Requirements for Durability in Marine Environments (IS 4651 Part 4):

  • Concrete Grades:

    • RCC: Minimum M30
    • Prestressed Concrete: Minimum M40
    • Mass Concrete: Minimum M15
  • Cement Type:

    • Prefer Sulphate Resistant Cement or Blast Furnace Slag Cement (IS 455, IS 1489).
    • Ordinary Portland Cement can be used if a higher grade concrete than strength requirement is adopted.
  • Cement Content & Water-Cement Ratio:

Concrete TypeMinimum Cement Content (kg/m³)Maximum Water-Cement Ratio
RCC & Prestressed4000.45
Trimmed Concrete400Up to 0.50 (Engineer’s discretion)
Plain Cement Concrete3100.50
  • Durability Focus: Concrete must be dense and impermeable to prevent sea water penetration.

  • Preferred Practice: Use precast concrete elements for better quality control and durability.

Loading diagram...

Summary: Use dense concrete (M30+), sulphate resistant cement, minimum cement content 400 kg/m³, and low water-cement ratio (≤0.45) to ensure durability in marine environments.

?How does the standard recommend protecting steel against corrosion in marine conditions?

IS 4651 Part 4 recommends the following for protecting steel against corrosion in marine conditions:

1. Protective Coatings

  • Form a barrier against environmental exposure.
  • Selection & application (type, thickness, recoating) are crucial.
  • Coatings degrade over time, especially due to barnacle growth.

2. Cathodic Protection

  • Effective for steel fully immersed or buried.
  • Uses impressed current or sacrificial anodes.
  • Significantly reduces corrosion in wet/dry cycles.

3. Increased Section / Reduced Stresses

  • If coatings/cathodic protection are impractical, increase steel thickness.
  • Minimum thickness:
    • 6 mm with cathodic protection.
    • 10 mm without cathodic protection.
  • Always use protective coatings regardless.

4. Use of Special Steel

  • Alloy steels with ~2% copper content help arrest corrosion.

Additional Recommendations

  • Concrete cover: Add 25 mm more than IS 456:1978 cover for marine exposure.
  • Stress reduction: Limit steel stress to 165 N/mm² in working stress design to minimize cracking.
Loading diagram...

Summary: Use coatings + cathodic protection where possible; otherwise, increase thickness and reduce stresses. Always ensure adequate concrete cover and crack control for durability in marine conditions.

?What are the guidelines for the design and placement of expansion joints in port structures?

IS 4651 Part 4: Guidelines for Expansion Joints in Port Structures

  • Spacing:

    • Recommended length between expansion joints: 39 m for solid quay walls or pile-supported walls.
    • For better stiffness, spacing can be increased up to 60 m.
  • Design Requirements:

    • Expansion joints must be keyed to transfer shear forces between sections.
    • They should allow free length changes due to temperature, shrinkage, and foundation yielding without hindrance.
    • Keys for vertical support depend on soil conditions, structure type, and loading.
  • Protection:

    • Joints must be covered to prevent backfill washout.
  • Reinforcement:

    • Steel reinforcement should also control shrinkage and temperature cracks.
Loading diagram...

These provisions ensure structural integrity and durability of port structures under environmental and operational movements.

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