Analysis of Retaining Walls

Introduction

A retaining wall is any constructed wall that holds back soil a liquid or other materials where there is an abrupt change in elevation. Retaining walls have been used for thousands of years; whether in the construction of terraced fields on a steep slope, or a railway through a hillside, a retaining wall is used in some form or another.

Retaining walls can be grouped into three categories: gravity, embedded and hybrid. They all perform the function of supporting a material, which is typically soil, at an angle that exceeds the angle of repose. Each type has unique properties making them ideally suited to specific situations.

Types of Retaining Walls

There are several types of retaining walls but the most common types are the cantilever retaining walls. Cantilevered retaining walls are classified as “yielding” because they are free to rotate without any lateral restraints. Cantilevered retaining walls are generally of masonry, concrete or both but can also take different forms as will be described.

Types of retaining walls include

Masonry or Concrete Walls: Masonry walls are usually either 8″ or 12″ concrete block masonry units, partially or solid grouted and reinforced. Higher walls require 12″ blocks and are often stepped back to 8″ as the retaining height reduces.

The stems of concrete walls must be formed, can be tapered for economy, usually with a taper in the inner face (earth side) to present a vertical exposed face.

Counter-fort Walls: Counterfort cantilever retaining walls incorporates wing walls projecting from the heel into the stems. The stems between counterforts is thinner and spans horizontally between the counterforts (wingwalls). The counterforts act as cantilevered element and are structurally efficient because the counterforts are tapered down to a wider deeper base where moments are higher. Counterfort retaining walls are usually required when the retaining height is so much that a simple cantilever walls becomes uneconomical.

Counter-Fort or Buttress Retaining Wall

Buttress Walls: Similar to the counterfort retaining wall with the only difference been that the wing walls are located in the outside face of the wall, such walls are used in cases where the property line limitations on the interior face provides limited face for the heel of a traditional retaining wall.

Other types of retaining walls include, Gravity retaining walls, Bridge abutments, Restrained non-yielding walls etc.

Cantileverd Retaining Wall Terminology

Cantilever Retaining Wall Terminology

Backfill: The soil placed behind the wall.

Backfill Slope: Often the backfill slopes upward from the back face of the wall. The slope is usually expressed as a ratio of horizontal to vertical.

Dowels: Reinforcing steel placed in the footing and bent into the footing a distance at least equal to the required development length.

Toe: That portion of footing which extends in front of the front face of the stem (away from the retained earth)

Heel: That portion of the footing extending beyond the wall (under the soil).

Footing Key: A deepened section of the footing for greater sliding resistance

Stem: The vertical wall cantilevering above the foundation.

Surcharge: Any load placed in or on top of the retained soil, either in front or behind the wall.

Weep holes: Holes provided at the base of the stem for drainage

Design Overview

The four primary concern relating to the analysis and design of any retaining walls are:

1. That it has acceptable resistance with respect to overturning

2. That it has acceptable resistance against sliding.

3. That the allowable bearing resistance is not exceeded

4. That the stresses within the components are within code allowable limits.

Principles

A cantilever retaining wall must for stability resist both overturning and sliding and material stresses including allowable bearing resistance must be within acceptable limits. To resist forces tending to overturn the wall (Primarily the lateral earth pressure against the back of the wall). The wall must have sufficient weight including the soil above the footing such that the resisting moments are greater than the overturning moments.

To resist forces tending to slide the wall, the weight of the wall and the weight of the soil above the footing plus any vertical loads on the wall and permanent surcharges multiplied by the coefficient of friction of the soil must be sufficient to resist the lateral forces pushing the wall

The stem must be designed to resist both the bending caused by earth pressures including the effect of surcharges placed behind the wall, seismic if applicable, wind if applicable and any axial actions if applicable.

Derivation of Load on Retaining Walls

Pressure from retained materials can be broken down into three types: active pressure, passive pressure and surcharge. Active pressure is a force that has an adverse effect on the structure it is being supported by. Passive pressure is a force that counters the negative effects generated by the active pressure, and the surcharge is an applied load over and above the material that is exerting a lateral pressure to the retaining structure.

This note only considers relatively simple retaining structures for purposes of illustrating how loads originating from retained materials are derived. For more complex retaining structures your’re hereby directed to additional texts, which are listed under the Further Reading section.

Types of pressure that can be applied to retaining structures
Active Earth Pressure (Ka)

In order to determine the lateral force a material will exert onto a retaining structure, an appreciation of the friction between the particles the material is made up of is needed. In terms of soils, this is defined by the soil’s cohesion (c), internal angle of friction (φ) and the interface between the retaining structure and the soil.

To determine the Active Pressure, the coefficient Ka is applied to the base density of the soil.

Where γ = Soil density ; h = depth of soil ; Ka= Coefficient of active pressure; Pa = Force due to active soil pressure

This is defined thus: This only applies when the retained material is drained. Otherwise, the value of Ka is 1;

Passive Earth Pressure (Kp)

Passive Pressure acts counter to the Active Pressure and is therefore considered to be beneficial. It normally comes about due to the retaining structure being partially buried and thus creates a barrier that prevents the structure from sliding and/or overturning.

To determine the Passive Pressure, the coefficient Kp is applied to the base density of the soil. This is defined thus:

Where γ = Soil density; h = depth of soil (passive side); Kp= Coefficient of passive pressure; Pp= Force due to passive soil pressure

This only applies when the retained material is drained. Otherwise the value of Kp is 1

Surcharge (q)

Surcharge is an imposed load that is placed on top of the retained material. It is expressed as an area load, typically kN/m² or kPa and is transferred directly onto the retained structure. The active pressure coefficient Ka is applied to all surcharge forces that a retaining structure is subjected to.

Where ; Ka= Coefficient of active pressure ; q= Surcharge load ; qa = horizontal load due to surcharge; Ps = Surcharge load

Pore Water Pressure (u)

Pore Water Pressure u is based on the base density of water, which is 10 kN/m3. It is of significant importance for soil retaining walls if the water table is within the depth of the retained soil.

Where; Ka= Coefficient of active pressure; u = horizontal Pore pressure; Pw = horizontal load due to pore water pressure

Stability Against Overturning

Overturning Moments: Overturning moments are horizontally applied multiplied by the lever arm from the footing to their point of application. The primary force causing overturning is the lateral earth pressure against the wall and because it is a triangular load it moment arm will be one-third of the retained height above the bottom of the footing. If the backfill is sloped the height used to compute overturning is at a plane of the back of the footing (i.e. where the plane intersect the ground surface) Lateral pressure due to surcharge is uniformly applied to the back of the wall, therefore it point of application is 1/2 the height and the moment arm half the retained height to the bottom of the footing.

Resisting Moments: By convention resisting loads are the sum of the vertical loads about the front edge (Toe) of the footing. These forces include stem weight, footing weight, the weight of soil behind the wall and over footing, a surcharge if applicable and any axial loads on top of the wall. The total resisting moment is the product of the sum of all these loads and their moment arms taking about the front edge of the footing,

The Factor of Safety (F.O.S) is simply the ratio of the resisting moment and the overturning moment and in any case must be greater than unity

Stability Against Sliding

Sliding Force: The sliding forces are horizontally applied and consist of the lateral earth pressure, pore water pressure, and the horizontal component of any surcharge or axial load if present.

Resisting Force: The vertical loads consisting of the weight of the stem and base, weight of earth on the backfill and the resistance by the passive pressure.

The Factory of Safety is the ratio of the resisting force to the sliding force and in any case must be greater than unity

Soil Bearing Pressure

Since a retaining wall is usually subjected to lateral forces, its foundation would be eccentrically loaded. To determine this eccentricity we must first find the out of balance moment which is obtained by taken moments about the centreline of the base.

The eccentricity is then given as:

The eccentricity must be less than one-sixth of the footing width (i.e. within the middle third) for the footing to be in theoretical contact with the soil, if this is the case. The soil pressure can be computed from

If the resultant is outside the middle third the soil pressure is given as

Where: e = eccentricity; w = width of footing; W = vertical loads; M = out of balance moment; P = Bearing Pressure

Further Reading

CIRIA (2000) Publication C516: Modular gravity retaining walls: design guidance London: CIRIA
CIRIA (2003) Publication C580: Embedded Retaining Walls London: CIRIA Hugh Brooks (2010): Basics of Retaining wall design (8ed)- HBA Publications The Institution of Structural Engineers (2012): Derivation of loads to retaining structures- Technical guidance note (level2
).

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Omotoriogun Victor
About Omotoriogun Victor 66 Articles
A dedicated, passion-driven and highly skilled engineer with extensive knowledge in research, construction and structural design of civil engineering structures to several codes of practices

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