Geotechnical and Foundation
Engineering
Chapter 1: Lateral earth pressure
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Lateral earth pressure
• Retaining structures (e.g. retaining walls, basement
walls) are commonly encountered in foundation
engineering as they support the slopes of earth
masses.
• Proper design and construction of these structures
require knowledge of the lateral forces that act
between the retaining structure and the soil mass
being retained.
• These lateral forces are caused by lateral earth
pressure.
• This chapter is devoted to study the various earth
pressure theories.
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Lateral earth pressure
• While designing retaining structures, engineer needs
to ensure only that total collapse or failure does not
occur.
• Movements of several centimeters and even meters
are often of no concern as long as there is assurance
that even larger motions will not suddenly occur.
• The approach is to analyze the conditions that would
exist at a collapse condition, and to apply suitable
safety factors to prevent collapse.
• This approach is known as limit design and requires
limiting equilibrium mechanics.
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At rest, active and passive pressures
Consider a soil mass. The mass is
bounded by a frictionless wall.
The soil element located at a depth
z is subjected to a vertical effective
pressure s’o and horizontal
effective pressure s’h.
The ratio of s’h to s’o is a
nondimensional quantity K, or
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Case 1: At-rest pressure
If the wall AB is static, i.e., if it does
not move either to right or to left of
its initial position – the soil mass
will be in a state of static
equilibrium.
In such a case, s’h is referred to as
the at-rest earth pressure, or
where Ko = at-rest earth pressure
coefficient.
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Case 2: Active pressure
If frictionless wall rotates
sufficiently about its bottom t a
position of A’B, then triangular
mass ABC’ adjacent to the wall
will reach a state of plastic
equilibrium and will fail sliding
down the plane BC’.
At this time, s’h is referred to as
active pressure, or
where Ka = active earth pressure
coefficient
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Case 3: Passive pressure
If the wall rotates sufficiently
about its bottom to a position
A”B, then a triangular mass
ABC” will reach a state of
plastic equilibrium and will
fail sliding upward along the
plane BC”.
At this time, s’h is referred to
as passive pressure, or
where Kp = passive earth
pressure coefficient
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Variation of lateral pressure with wall tilt
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Variation of lateral pressure with wall tilt
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Earth pressure coeff. at rest
Vertical effective stress = s’o = gz
Horizontal effective stress = s’h = Kogz
For coarse-grained soils, the coeff. of
earth pressure at rest is estimated by
using empirical relationship (Jaky 1944)
where f’ = drained friction angle
Jaky’s Eq. is good for loose sand
backfill. For dense sand backfill, this Eq.
may underestimate the lateral earth
pressure at rest.
This underestimation is due to the
process of compaction of backfill.
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Earth pressure coeff. at rest
For this reason, the following
relationship is used for dense sand
backfill.
where gd = actual compacted unit wt.
of the sand behind the wall
gd(min) = dry unit wt. of sand in the
loosest state.
For fine-grained, normally consolidated
soils, following relation is used for Ko
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Earth pressure at rest
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Earth pressure at rest
Partially submerged soil
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Earth pressure at rest
Partially submerged soil
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Earth pressure at rest
Partially submerged soil
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z ≥ H1
For z ≥ H1
From
hydrostatic
pressure
diagram
Earth pressure at rest - example
Example 1: Following figure shows a 15-ft retaining wall. The
wall is restrained from yielding. Calculate the lateral force Po
per unit length of the wall. Also, determine the location of the
resultant force.
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