Question

A retaining wall with sloping back, of vertical height 9m retains soil of density 1.6 Mg/m³, and angle of friction 30^o. The soil slopes upwards at 20^o to the horizontal from the back edge of the wall, the angle between the slope and the back of the wall is 100^o. Cohesion 10kN/m², angle of friction between soil and wall is 25^o but there is no cohesion between them. Find the thrust on the back wall per metre run using trial values of 25, 30, 40, and 45^o for the inclination for the plane of rupture to the vertical.

Answer 1

soil density = 1.6mg/m3 or 16kN/m3

angle of friction = = 30⁰

^{depth = z = 9m}

soil slope (upwards) == 20⁰

the angle between slope and back of wall = 100⁰

so angle of wall with horizontal =w= 100⁰-20⁰ = 80⁰

Cohesion =C = 10 kN/m2

angle of friction between wall and soil ==25⁰

Possible values to run trail are = 25, 30, 40 and 45⁰

Thrust = K * (effective vertical stress)

Using coulomb.'s earth pressure theory,

assuming active state,

K_a = sin²( w + )/(sin²( w)sin(w - )[1+(sin(+)sin(-) / (sin(w - )sin( + w))]²)

Using Rankine theory of cohesive soil,

thrust = (effective vertical stress)* K_a - 2C(K_a)^0.5

Putting values in the standard formulaes,  K_a =0.5513

for = 25 ⁰ , thrust = 16*9*.5513 - 2*10*.5513^.5 = 64.5373 kN/m2

similarly for different values of theta, phi will change and we can solve accordingly