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

Retaining Wall/earth Pressure Theories

CONTRASTING POINTS OF ACTIVE AND PASSIVE PRESSURES 

EARTH PRESSURE AT REST:
Earth pressure at rest rest is the horizontal pressure acting on the rigid structure.
Earth pressure is given by

For cohesive soils the Terzaghi formula for computing K_r is implemented in the program:

where,
ν=poisson's ratio
For cohesionless soils the Jáky expression is used:

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 K_r is used:

where, OCR = Over Consolidation Ratio.
Typical values of K_o:
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:

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
K_a=(1-sinΦ)/(1+sinΦ)=tan²(45⁰-Φ/2)
PASSIVE EARTH PRESSURE

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

where

k_p = Coefficient of passive earth pressure.    
K_p=(1+sinΦ)/(1-sinΦ)=tan²(45⁰+Φ/2)
-P_a < P_o < P_p

 where, P_a = Active earth pressure.
P_o = Earth pressure at rest.
P_p = Passive earth pressure.

ACTIVE EARTH PRESSURE BY RANKINE THEORY:

 (i) Cohesionless soil on vertical smooth wall:

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

 (ii) Submerged Cohesionless soil on vertical smooth wall

acts at (H/3) from base.

where, g ' = Submerged unit weight of soil.

 acts at a  H₂+H₁/3 from base =
P_a2 =K_aγ1H₂²acts at H₂/2 from base =
 acts at from base =
 acts at  from base =

Total Earth Pressure (P_a)

   acts at  from base
where,

P_a1 = k_aq.H acts at
  from base

acts at   from base

acts at

from base.

(v)

•  acts at (H₂ +H₁) from base.
•  acts at  from base.
•  acts at H₂ from base.

(vi)

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

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

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

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

p_a = Resultant active earth pressure on the wall
a = Angle of inclination of resultant P_a with the horizontal.

 (viii)

where, P_av = 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

whereN_f = Influence Factor.

•   Active Earth Pressure of Any Depth z

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

• At Z = Z_c ® P_a = O

where, Z_C = depth of tension crack.

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

PASSIVE EARTH PRESSURE FOR COHESIVE SOIL

• Passive Earth Pressure at any depth ‘Z’,

• Total P_p on Unit Length

• Coulombs Wedge Theory

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

acts at centroid of trapezoidal.

• When Tension Cracks are Developed

Acts at centroid of trapezoidal

• When tension Cracks are Developed

or

acts at
 

Remember:- Cohesion decreases the active earth pressure while increases the passive earth pressure.

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