Question

Problem 4 Draw the active lateral pressure diagram for the wall shown (assume infinitely long wall) and determine the resultant lateral force and its location Determine the factor of safety against over-turning Given: Soil angle of internal friction 340 Dry unit weight of soil 118 PCF, Unit Weight of Concrete 150 PCF 5 ft 1.3

Answer 1

Step 1:

Calculate Ka

Ka=1-sin $\phi$ /(1+sin $\phi$ )

Ka=1-sin34/(1+sin34)

Ka=0.282

Step 2:

Pa=0.5Ka $\gamma$ H²

P_a=0.5x0.282x118x(15)²

P_a=3743.55 lbs

The lateral force acts at a distance of 1/3rd from the base that is 1/3rd of 15ft=5ft

Step 3:

Calculate the Self weight of the wall

W=5x15x150=11250 lbs

Total weight=11250 lbs

Total horizontal force=3473.55 lbs

Step 4:

Moment in vertical direction=11250x7.5=84375 lb-ft=84.375 kip-ft

Moment in horizontal direction=3473.55x(1/3x15)=5816.25 lb-ft=17.36 kip-ft

F.O.S=84.375/17.36=4.86>2.5

This wall satisfies the criteria for over turning