Lateral Earth pressures .
The pressures exerted by an earth backfill against a retaining wall can bf commuted with reasonable accuracy on the basis of theory only for conditions rarely encountered in practice . in the first place , the designer must know what material are to be used for the backfill and in what state they will be place .
Lateral earth pressure represents pressures that are “to the side” (horizontal) rather than vertical. The objective of this course is to familiarize primarily the non-geotechnical engineer such as civil engineers, structural engineers, architects and landscape architects
with simple background theory and considerations.
Calculating lateral earth pressure is necessary in order to design structures such as:
• Retaining Walls
• Bridge Abutments
• Temporary Earth Support Systems
• Basement Walls
At the end of this course you will have learned:
• Basic method of calculating lateral earth pressure
• Other considerations when developing the total lateral force against a structure
Categories of Lateral Earth Pressure
There are three categories of lateral earth pressure and each depends upon the movement
experienced by the vertical wall on which the pressure is acting. In this course, we will
use the word wall to mean the vertical plane on which the earth pressure is acting. The
wall could be a basement wall, retaining wall, earth support system such as sheet piling
or soldier pile and lagging etc.
The three categories are:
• At rest earth pressure(Ko)
• Active earth pressure(Ka)
• Passive earth pressure(Kp)
The at rest pressure develops when the wall experiences no lateral movement. This
typically occurs when the wall is restrained from movement such as a basement wall that
is supported at the bottom by a slab and at the top by a floor framing system prior to
placing soil backfill against the wall.
The active pressure develops when the wall is free to move outward such as a typical
retaining wall and the soil mass stretches sufficiently to mobilize its shear strength. On
the other hand, if the wall moves into the soil, then the soil mass is compressed
sufficiently to mobilize its shear strength and the passive pressure develops. This
situation might occur along the section of wall that is below grade and on the oppositeside of the wall from the higher section. Some engineers use the passive pressure that develops along this buried face as additional restraint to lateral movement.
At Rest Coefficient
Ko = 1 – sin(φ) (1.0)
Where: Ko is the “at rest” earth pressure coefficient and φ is the soil friction value.
Active and Passive Earth Pressure Coefficients
When discussing active and passive lateral earth pressure, there are two relatively simple
classical theories (among others) that are widely used:
• Rankine Earth Pressure
• Coulomb Earth Pressure
The Rankine Theory assumes:
• There is no adhesion or friction between the wall and soil
• Lateral pressure is limited to vertical walls
• Failure (in the backfill) occurs as a sliding wedge along an assumed failure plane
defined by φ.
• Lateral pressure varies linearly with depth and the resultant pressure is located
one-third of the height (H) above the base of the wall.
• The resultant force is parallel to the backfill surface.
The Coulomb Theory is similar to Rankine except that:
• There is friction between the wall and soil and takes this into account by using a
soil-wall friction angle of δ. Note that δ ranges from φ/2 to 2φ/3 and δ = 2φ/3 is
• Lateral pressure is not limited to vertical walls
• The resultant force is not necessarily parallel to the backfill surface because of the
soil-wall friction value δ.
The general cases for calculating the earth pressure coefficients can also be found in
published expressions, tables and charts for the various conditions such as wall friction
and sloping backfill. The reader should obtain these coefficients for conditions other
than those discussed herein.
The Rankine active and passive earth pressure coefficient for the condition of a
horizontal backfill surface is calculated as follows:
• (Active) Ka = (1 – sin(φ)) / (1 + sin(φ)) (2.0)
• (Passive) Kp = (1 + sin(φ)) / (1 - sin(φ))
Some points to consider are:
• For the Coulomb case shown above with no soil-wall friction (i.e. δ = 0) and a
horizontal backfill surface, both the Coulomb and Rankine methods yield equal
• As the soil becomes stronger the friction value (φ) increases. The active pressure
coefficient decreases, resulting in a decrease in the active force and the passive
pressure coefficient increases, resulting in an increase in the passive force.
• As the soil increases in strength (i.e. friction value increases) there is less
horizontal pressure on the wall in the active case.