Charles Augustine Coulomb (1776), a popular French scientist and military engineer, was the first to try to put the surreal and subjective ideas about lateral earth pressure on walls that existed at the time on a scientific basis.
Coulomb’s Wedge Theory considers the soil behind the wall as a whole rather than as a single part. If there isn’t a wall supporting granular soil, it can sink down to its angle of repose or internal friction. As a result, it’s fair to think that even though the wall just shifted forward slightly, a rupture plane will form between the wall and the surface of repose.
The ‘Sliding Wedge’ is the triangular mass of soil between this plane of failure and the back of the wall. The soil inside the sliding wedge would sag downward if the retaining wall was abruptly withdrawn, it is reasoned.
As a result, an examination of the forces acting on the sliding wedge at the time of emerging collapse would expose the thrust from lateral earth pressure that the wall must endure in order to keep the soil mass in place.
Coulomb’s theory is known as the “Wedge theory“, since it implies the presence of a plane rupture surface. Coulomb, on the other hand, recognised the possibility of a curved rupture surface, though he preferred a plane rupture surface for mathematical reasons.
In reality, studies have shown that assuming a plane rupture surface introduces substantial error in the calculation of passive earth resistance, with a curved rupture surface being closer to reality.
Coulomb’s theory has undergone some changes and new advances over time. The theory lends itself well to graphical representation, and the effects of wall friction and batter are taken into account automatically. Coulomb’s theory was further developed by prominent figures such as Poncelet (1840), Culmann (1866), Rebhann (1871), and Engesser (1880).
The importance of Coulomb’s work is best shown by the fact that, with a few exceptions, his theories on earth pressure still hold true in their main points and are still considered valid in the design of retaining walls today.
Assumptions of Coulomb’s Wedge Theory
Coulombs wedge theory assumes that :
- The backfill soil is a dry, homogeneous, and isotropic granular substance that is elastically underformable but breakable, with internal friction but no cohesion.
- For the sake of ease of study, the rupture surface is believed to be a plane. It goes right through the wall’s heel. Coulomb was aware that it is not a plane, but rather a curved surface.
- The earth thrust is calculated by considering the equilibrium of the sliding wedge, which functions as a rigid body.
- The earth thrust’s location and direction are believed to be understood. The thrust acts on the back of the wall at a point one-third of the wall’s height above the foundation, forming an angle with the usual to the back face of the wall. The angle of friction between the wall and the backfill soil is commonly referred to as “wall friction.”
- On the basis of a two-dimensional case of plane strain, the problem of calculating the earth thrust is solved. This means that the retaining wall is considered to be very long and that all of the wall’s and fill’s conditions remain constant along its length. As a result, a unit length of wall perpendicular to the plane of the paper is taken into account.
- The theory provides two limiting values of earth pressure, the least and the greatest (active and passive), consistent with equilibrium, when the soil wedge is on the verge of failing or slipping.
The following are some of the Coulomb’s Theory’s other underlying Assumptions:
- Without rupture or sliding, the soil creates a normal slope angle,, with the horizontal. This is known as the angle of repose, and it is nothing more than the angle of internal friction in dry cohesionless soil. Coulomb was aware of the principle of friction.
- A soil wedge is ripped away from the rest of the soil mass if the wall yields and the backfill soil ruptures. The soil wedge slides sideways and downward over the rupture surface in the active case, putting lateral pressure on the wall. The soil wedge slides sideways and upward on the rupture surface due to the wall’s force against the fill in the case of passive earth resistance. These are depicted in figure below.
- Newton’s law of friction applies to a rupture plane within the soil mass, as well as between the back of the wall and the soil. The physical properties of the materials concerned determine this angle of friction, whose tangent is the coefficient of friction.
- On the rupture surface, friction is evenly distributed.
- Back face of wall is a plane.
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Determination of Active & Passive Earth Pressure
The most dangerous of the infinitely many rupture surfaces that can be passed through the heel of the wall is the one with the maximum active earth thrust.
The most dangerous rupture surface in the case of passive earth resistance is the one with the lowest resistance. The requirement is the minimum force required to tear the soil wedge from the soil mass when the wall is pressed against the soil, since failure is inevitable at greater force. This is in contrast to the minimum and maximum values for active and passive scenarios, respectively, in terms of wall movement away from or towards the fill.
It’s also worth noting that Coulomb’s theory considers the entire soil mass in the sliding wedge. The assumptions allow the problem to be treated as statically determinate.
Coulomb’s principle may be applied to inclined wall faces, broken wall faces, sloping backfill surfaces, angled backfill surfaces, broken backfill surfaces, and concentrated or distributed surcharge loads.
Coulomb’s theory has a number of flaws, one of which is that it does not, in general, fulfill the static equilibrium condition that occurs in nature. When the sliding surface is believed to be planar, the three forces acting on the sliding wedge (weight of the sliding wedge, earth friction, and soil reaction on the rupture surface) do not meet at a common point. Even the wall friction was not considered at first and was only added later.
Despite this flaw and other assumptions, the theory produces useful results in practice. However, soil constants should be calculated as precisely as possible.