Earth pressure definition, Lateral earth pressure , type of earth pressure. Rankine's theory of lateral earth pressure

Definition of  Earth pressure : —



The pressure that exists between earth's elements (such as soil or frogs) and structure (such as a wall).


1. Horizontal focus controlled by retained  soil.

2. The pressure that comes from a building, such as a wall, is the ground we retained. 



 Lateral earth pressure   —


Lateral earth pressure is the force exerted by a soil mass on its side retained by a structure, in this case a retaining wall. The magnitude of the lateral earth pressure is known to vary considerably with the displacement of retaining wall. The magnitude of the lateral earth pressure is known to vary considerably with the displacement of retaining wall and nature of soil. Depending upon the magnitude and nature of displacement, lateral pressure may be grouped into three categories. The soil retained is also known as backfill.


(1) At rest pressure 

(2) Active pressure 

(3) Passive pressure


1) At rest pressure: 

The lateral earth pressure is called at rest pressure when the soil mass is not subjected to any lateral movement. This happens where retaining wall is firmly fixed at its top and is not allowed to move or rotate. At rest condition is also

Earth pressure rest 

known as elastic equilibrium as no part of the soil mass failed and attained the plastic equilibrium. For example the bridge abutment wall which is restrained at its top by the bridge slab. 


2) Active earth pressure: 

It occurs when the soil mass yields in such a way that it tends to stretch horizontally. It is a state of plastic equilibrium as the whole soil mass is on the verge of failure. A retaining wall when moves away from the backfill, there is a stretching of soil mass and active state of earth pressure exist. 



3) Passive pressure: 

It occurs when the movement of wall is such that the soil tends to compress horizontally. It is another extreme of limiting equilibrium  condition. 



The maximum value of lateral earth pressure exerted by soil on a structure, occurring when the soil is compressed laterally, causing its internal shearing resistance along a potential failure surface to be completely mobilized; the maximum resistance of a vertical earth face to deformation by a horizontal force.






Equivalent point load method  —


This method consist of dividing the loaded area into smaller area units from point loads by assuming that an equivalent point load act at the centre of each of these units. The total vertical stress  Ïƒ z , is then the sum of all vertical stresses calculated for different area units. Since there is an approximation involved in assuming an equivalent point load in place of an area load. The dimension of small area units be kept less than one third of the depth at which the vertical stress is required.


σz= 1/2 [Q1Kb1+Q2Kb2+....QnKbn

If Q1=Q2=Q3=.......Qn
= Q, ' Ïƒz =θ/ZΣKb


ΣKb= Sum of individual influence factors of all small area units.


 Overburden pressure   —


It is also called lithostatic pressure, confining pressure or vertical stress, is the a pressure or stress imposed on a layer of soil or rock by the weight of overlying material. The over Z


burden pressure at any depth Z 



 Isobar and pressure bulb


An isobar is a stress contour - it is a line joining all points of equal vertical stress below the ground surface .



For a particular load system, many isobars can be drawn for different chosen value of stresses. The smaller the magnitude of selected stress, the greater the depth up to which an isobar extends. Since the vertical stress on a given horizontal plane is the same in all directions at points located at equal radial distances from the axis of loading, an isobar is really a spatial, curved surface of the shape of an onion bulb. Hence an isobar is often termed as pressure bulb. Within a pressure bulb, a soil mass will be stressed to stresses higher than the designated stress of the pressure bulb, while the soil beyond the pressure bulb will be stressed to lower stresses. The concept of the pressure bulb is very useful one for foundation engineers.




Rankine's theory of lateral earth pressure  —

The assumptions made by this theory are  — : —

1) The retained soil is infinite, homogenous, isotropic and cohesion less.

 2) The retaining wall is smooth vertical surface implying that there is no adhesion or friction between the wall and the soil

3) Lateral pressure is limited to vertical walls 

4) The wall yields at the base to initiate failure. This is essentially a shear failure of the backfill.

5) Lateral pressure varies linearly with depth. The resultant pressure is located at one third of the height above the base of the wall.

 6) The resultant force is parallel to backfill surface.


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