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

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

where, g ' = Submerged unit weight of soil.

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

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

Total Earth Pressure (Pa)

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

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

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

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

(v)

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

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

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

(vi)

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

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

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

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

whereNf = Influence Factor.

  •   Active Earth Pressure of Any Depth z

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

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

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

  • At Z = Zc ® Pa = O

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

where, ZC = depth of tension crack.

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

  • Passive Earth Pressure at any depth ‘Z’,

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

  • Total Pp on Unit Length

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

  • Coulombs Wedge Theory

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

acts at centroid of trapezoidal.

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

  • When Tension Cracks are Developed

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

Acts at centroid of trapezoidal

  • When tension Cracks are Developed

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

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

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