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Design Requirement for Gravity walls - Notes - Civil Engineering (CE)

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Design Requirement for Gravity walls
Gravity Retaining walls are designed to resist earth pressure by their weight. They are constructed of the mass, concrete, brick or stone masonry. Since these materials can not resist appreciable tension, the design aims at preventing tension in the wall. The wall must be safe against sliding and overturning. Also the maximum pressure exerted on the foundation soil should exceed the safe bearing capacity of the soil.

So before the actual design, the soil parameters that influence the earth pressure and the bearing capacity of the soil must be evaluated. These include the unit weight of the soil, the angle of the shearing resistance, the cohesion intercept and the angle of wall friction. Knowing these parameters, the lateral earth pressure and bearing capacity of the soil determined.
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
                         Fig-6.12a
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
                       Fig-6.12b

Fig. 6.12a shows a typical trapezoidal section of a gravity retaining wall.
The forces acting on the wall per unit length are:
• Active Earth pressure Pa.
• The weight of the wall (Wc)
• The Resultant soil reaction R on the base. (or Resultant of weight P& Wc ).Strike the base at point D. There is equal and opposite reaction R' at the base between the wall and the foundation.
• Passive earth pressure Pacting on the lower portion of the face of the wall, which usually small and usually neglected for design purposes.
The full mobilization of passive earth pressure not occurs at the time of failure so we not consider it. If we consider it then it shows resistance against instability. So if we ignore it then we will be in safer side.

First decide which theory we want to apply for calculating the active earth pressure. Normally we calculate earth pressure using Rankine's theory or Coulomb's Earth pressure theory.
For using Rankine's theory, a vertical line AB is drawn through the heel point ( Fig 6.12-b ). It is assumed that the Rankine active condition exist along the vertical line AB. While checking the stability, the weight of the soil (Ws) above the heel in the zone ABC should also be taken in to consideration, in addition to the Earth pressure (Pa) and weight of the wall (Wc ).
But Coulomb's theory gives directly the lateral pressure (Pa) on the back face of the wall, the forces to be considered only P(Coulomb) and the Weight of the wall (Wc). In this case, the weight of soil (Ws) is need not be considered.
Once the forces acting on the wall have been determined, the Stability is checked using the procedure discussed in the proceeding section. For convenience, the section of the retaining wall is divided in to rectangles & triangles for the computation of the Weight and the determination of the line of action of the Weight.
For a safe design, the following requirement must be satisfied.

No Sliding
Horizontal forces tend to slide the wall away from the fill. This tendency is resisted by friction at the base.
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
μ = Coefficient of friction between the base of the wall and soil (= tan δ ).
∑W = Sum of the all vertical forces i.e. vertical component of inclined active force.

A minimum factor of safety of 1.5 against sliding is recommended.

No Overturning 
The wall must be safe against overturning about toe.
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)

• No Bearing Capacity Failure and No Tension
First calculate the line of action of the Resultant force ( e ) from centre of the base. (No Tension will develop at the heel)
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
The pressure at the toe of the wall must not exceed the allowable bearing capacity of the soil. The pressure at the base is assumed to be linear. The max. Pressure at the Toe & min at the Heel is given by:
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
P(max) should be less than the Safe bearing capacity(qallow ) of the soil &
P(max) should not be Tensile in any case. Tension is not desirable. The tensile strength of the soil is very small and tensile crack would develop. The effective base area is reduced.
Design Requirement for Gravity walls - Notes - Civil Engineering (CE)
 

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