Coulomb Theory
Coulomb (1776) first studied the problem of lateral earth pressures on retaining structures. He used limit equilibrium theory, which considers the failing soil block as a free body in order to determine the limiting horizontal earth pressure. The limiting horizontal pressures at failure in extension or compression are used to determine the Ka and Kp respectively. Since the problem is indeterminate, a number of potential failure surfaces must be analysed to identify the critical failure surface (i.e. the surface that produces the maximum or minimum thrust on the wall). Mayniel (1908) later extended Coulomb's equations to account for wall friction, symbolized by δ. Müller-Breslau (1906) further generalized Mayniel's equations for a non-horizontal backfill and a non-vertical soil-wall interface (represented by angle θ from the vertical).
Instead of evaluating the above equations or using commercial software applications for this, books of tables for the most common cases can be used. Generally instead of Ka, the horizontal part Kah is tabulated. It is the same as Ka times cos(δ+θ).
The actual earth pressure force Ea is the sum of a part Eag due to the weight of the earth, a part Eap due to extra loads such as traffic, minus a part Eac due to any cohesion present.
Eag is the integral of the pressure over the height of the wall, which equates to Ka times the specific gravity of the earth, times one half the wall height squared.
In the case of a uniform pressure loading on a terrace above a retaining wall, Eap equates to this pressure times Ka times the height of the wall. This applies if the terrace is horizontal or the wall vertical. Otherwise, Eap must be multiplied by cosθ cosβ / cos(θ − β).
Eac is generally assumed to be zero unless a value of cohesion can be maintained permanently.
Eag acts on the wall's surface at one third of its height from the bottom and at an angle δ relative to a right angle at the wall. Eap acts at the same angle, but at one half the height.
Read more about this topic: Lateral Earth Pressure, Active and Passive Pressure
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