Retaining Wall Design

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Lateral Earth Pressure

The magnitude of the lateral pressure, per geotechnical engineering theory, is

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Where  is the vertical stress of the soil and  is the coefficient of lateral earth pressure. This coefficient depends on the state of the soil. If the wall does not deflect it is at rest, if the wall deflects away from the soil causing the pressure it is considered active, and if the wall deflects towards the soil causing the pressure it is considered passive. Note: Different specifications require different deflects to be considered active/passive.

At Rest Earth Pressure

When the soil is considered at rest, the coefficient of lateral earth pressure, k, can be found to be

where,

The angle the pressure acts on, measured from the horizontal is

where, theta is the slope of the surface we are finding the lateral pressure on, taken from the y-axis with positive being clockwise and beta is the slope of the backfill

Rankine’s Active Earth Pressure

Rankine earth pressure theory was developed under the assumption that no friction exists between the wall and the soil. Using this theory we can find  to be

where,

Coulomb’s Active Earth Pressure

Coulomb’s active earth pressure theory accounts for wall friction and can be used on retaining walls with granular backfill. Using Coulomb’s active earth pressure the lateral earth pressure coefficient can be found as

Rankine’s Passive Earth Pressure

Rankine earth pressure theory was developed under the assumption that no friction exists between the wall and the soil and that the interface is vertical. Using this theory we can find  to be

Surcharge Loading

All surcharges are assumed to be uniform infinite loads applied to the surface of the backfill. For uniform loads the magnitude, , assumes the not attenuate through the soil and thus all points under the soil the vertical stress is increased by . This also translates to an increase in lateral pressure by using the selected lateral earth pressure theory.

Bearing Pressure

The bearing pressure is added as a force to the system acting on the bottom of the foundation. The bearing pressure however is unique depending on the loads being applied, thus each load combination has a unique bearing pressure. The location of this bearing pressure depends on the eccentricity, e, of the reaction which comes from the overturning analysis. The pressure distributions follow LRFD in that they are rectangular when on soil and trapezoidal when on rock.

Sliding Stress

The sliding stress is added as an axial force acting upon the bottom of the slab. It’s magnitude is the . This will result in a compressive force in the toe and a tensile force in the heel.