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Retaining Wall/earth Pressure Theories

 

CONTRASTING POINTS OF ACTIVE AND PASSIVE PRESSURES 

 ACTIVE PASSIVE
1.Very little movement is
required to mobilise the
active pressure.(about
0.5% horizontal strain)
1.Much higher movement
is required to mobilise
the pressure (about 2%
of horizontal strain)
2.Failure plane is inclined
at 45º + Φ/2
2.Failure plane is inclined
at 45º – Φ/2
3.Width of sliding wedge
at the top of wall is H.
Cot (45 + Φ/2)
3.Width of sliding wedge
at the top of wall is H.
Cot (45 - Φ/2)

EARTH PRESSURE AT REST:
Earth pressure at rest rest is the horizontal pressure acting on the rigid structure.
Earth pressure is given by
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
For cohesive soils the Terzaghi formula for computing Kr is implemented in the program:
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
where,
ν=poisson's ratio
For cohesionless soils the Jáky expression is used:
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
where, Φ=Angle of internal friction of soil

For overconsolidated soils the expression proposed by Schmertmann to compute the coefficient of earth pressure at rest Kr is used:
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, OCR = Over Consolidation Ratio.
Typical values of Ko:
Type of soil - K o
Dense sand - 0.4 to 0.45
Loose sand - 0.45 to 0.5
Mechanically compacted sand - 0.8 to 1.5
Normally consolidated clay - 0.5 to 0.6
Over consolidated clay - 1.0 to 4.0

 ACTIVE EARTH PRESSURE:

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) 

ΔH = 0.2% to 0.5% of H  
-length of failure block = H.cot(450+Φ/2)
-ΔH= 0.2%of H for dense sand.
- ΔH= 0.5%of H for loss sand.  
-ΔH= 0.4% of H clay
Ka=(1-sinΦ)/(1+sinΦ)=tan2(450-Φ/2)
PASSIVE EARTH PRESSURE

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Langth of failure block =H.cot(450-Φ/2)
- ΔH= 2% of H For dense sand
-ΔH=15% of H For losse sand    
-ka . kp =1

where

kp = Coefficient of passive earth pressure.    
Kp=(1+sinΦ)/(1-sinΦ)=tan2(450+Φ/2)
-Pa < Po < Pp

 where, Pa = Active earth pressure.
Po = Earth pressure at rest.
Pp = Passive earth pressure.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

ACTIVE EARTH PRESSURE BY RANKINE THEORY:

 (i) Cohesionless soil on vertical smooth wall:
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

acts at (H/3) from base.
where,Pa = Active earth pressure force on unit length of wall.

 (ii) Submerged Cohesionless soil on vertical smooth wall

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
acts at (H/3) from base.
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, g ' = Submerged unit weight of soil.

  Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at a  H2+H1/3 from base =Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Pa2 =Kaγ1H22acts at H2/2 from base = Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)from base = Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) from base = Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Total Earth Pressure (Pa)

  Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) from base
where,
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Pa1 = kaq.H acts at
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)  from base
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

acts at Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)  from base

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
acts at
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
from base.

(v)

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at (H2 +H1) from base.
  • Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) acts at Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) from base.
  •  Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)acts at H2 from base.

(vi)

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

 

acts at H/3 from base but line of ation is parallel is parallel to backfill.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

acts at H/3 from base but line of action is parallel to backfill.
(vii)

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, W= Weight of soil over inclined back of wall of unit length.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Pav = Active earth pressure on imaginary wall of vertical back.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

pa = Resultant active earth pressure on the wall
a = Angle of inclination of resultant Pwith the horizontal.

 (viii)

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, Pav = Active earth pressure on Imaginary vertical back of wall. Acts parallel to back fill i.e., of b angle with hori zontal
W = Weigth of soil block of unit length.

ACTIVE EARTH PRESSURE FOR COHESIVE SOIL

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

whereNf = Influence Factor.

  •   Active Earth Pressure of Any Depth z

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Active Earth Pressure of Surface. i.e., at z = 0

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • At Z = Zc ® Pa = O

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, ZC = depth of tension crack.

  •  Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, Hc = Cirtical depth = 27º = max. Possible unsupported depth.

PASSIVE EARTH PRESSURE FOR COHESIVE SOIL

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Passive Earth Pressure at any depth ‘Z’,

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Total Pp on Unit Length

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • Coulombs Wedge Theory

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

where, a = Angle of back of wall with the hori zontal
b = Angle of sloping ground.
f = Angle of roughness between soil and wall
= 0º for smooth walls

  • When Tension Cracks are not Developed

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

acts at centroid of trapezoidal.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • When Tension Cracks are Developed

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Acts at centroid of trapezoidal

  • When tension Cracks are Developed

Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)or
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
acts at
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) 

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Remember:- Cohesion decreases the active earth pressure while increases the passive earth pressure.
Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

acts at  (H/3) from base of an angledwith the normal of wall.

 Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

The document Retaining Wall & Earth Pressure Theories | Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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FAQs on Retaining Wall & Earth Pressure Theories - Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

1. What is a retaining wall?
A retaining wall is a structure that is built to hold back or retain soil or other materials. It is commonly used to create level areas on sloping terrain, prevent erosion, or provide support to structures built on elevated ground.
2. What are the different types of retaining walls?
There are several types of retaining walls, including gravity walls, cantilever walls, sheet pile walls, anchored walls, and gabion walls. Each type has its own advantages and is suitable for different soil conditions and project requirements.
3. What is earth pressure theory?
Earth pressure theory is a set of principles that helps engineers analyze and design retaining walls. It takes into account the various forces exerted by the soil against the wall, such as lateral earth pressure, surcharge loads, and water pressure. Understanding earth pressure is crucial for ensuring the stability and safety of retaining walls.
4. How is lateral earth pressure calculated?
Lateral earth pressure can be calculated using different methods, such as Rankine's theory, Coulomb's theory, or the Mononobe-Okabe method. These methods consider factors such as the angle of internal friction, cohesion, wall friction, and wall movement to determine the lateral forces exerted by the soil against the retaining wall.
5. What are the factors that affect earth pressure on a retaining wall?
Several factors influence the earth pressure on a retaining wall, including the type of soil, its properties (such as cohesion and angle of internal friction), groundwater conditions, surcharge loads, backfill properties, and the height and geometry of the wall. Understanding these factors is essential for accurate design and construction of retaining walls.
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