Sir how do we solve for cohesion for the sloping backfill, you have given the formula for Ka and Kp, but what of the Pa if there is cohesion too. And Secondly Sir do we have formula for ∆.
Did you reverse your Force sums for m and n. I do not see how you have the shear force acting in the n direction when to me it looks like it is acting on the m axis based on the coordinate system you choose.
Can you assume a flat backfill and use an equivalent surcharge for the sloped soil wedge with superposition? If so, how would you assume the width of the surcharge from the top of the wall?