Mononobe Okabe Theory

Static active pressure

Dynamic active pressure

PA = E

PA =

1

2 γ.H .ka

1 2

0.6H

2

H 3

H = Height of the Retaining Wall, m

=

γ = Soil Density, kN/m3

=

18 kN/m3

φ = Angle of Friction of Soil

=

33 °

δ = Angle of Friction Between Soil and Abutment

=

16.5 °

i = Backfil Slope Angle = 0 (Level Backfill)

=

0°

β = Slope of Soil Face = 0 (Vertical Rear Face of Stem)

=

0°

θ = Seismic Angle of Friction of Soil

=

21.83 °

A = Acceleration Coefficient

=

0.27

 k   θ = arctan  h  1 − k v 

=

21.83 °

Horizontal Acceleration Coefficient k h = Horizontal

k h = 1.5A

=

0.4

k  = Vertical Acceleration Coefficient v

0.3k  h < k v < 0.5k  h

0.3k h <

0

< 0.5k h

Check horizontal acceleration coefficient (AASHTO C6.3.2 I-A):

k h ≤ (1 − k v ) ⋅ tan(φ − 1) 0.401

<

¿

0.625

Ok

4.63 m

2 γ.H . 1 - k v .kae

(

)

COULOMB EARTH PRESSURE THEORY I. Static Active Earth Pressure

PA =

1 2

⋅ γ ⋅ H 2 ⋅ K A

=

51.53 kN/m

Static Active Pressure Coefficient

K A =

cos 2 (φ − β) Ψ ⋅ cos 2β ⋅ cos(δ + β)

=

 sin( φ + δ) ⋅ sin( φ − i)  Ψ = 1 +  cos(δ + β) ⋅ cos(i − β)  

0.27

2

=

2.75

MONONOBE-OKABE THEORY II. Dynamic Active Earth Pressure (Mononobe - Okabe Theory)

PA E =

1 2

γ ⋅ H 2 ⋅ (1 - k v ) ⋅ kae

=

### kN/m

AASHTO C6.3.3 I-A

Dynamic Active Pressure Coefficient

K AE

=

cos(φ − θ − β) Ψ ⋅ cosθ ⋅ cos 2β ⋅ cos(δ + β + θ)

 sin( φ + δ) ⋅ sin( φ − θ − i)  Ψ = 1 +  cos(δ + β + θ) ⋅ cos(i − β)  

=

0.61

=

2.05

=

3.3

2

III. Equivalent Pressure

F'T =

PA ⋅

H 3

+ [ ( PAE − PA ) ⋅ 0.60H ] PA ⋅

H 3

Equivalent Pressure

PA E = F'T ⋅PA

=

### kN/m