Example $4-$ Failure stress due to a foundation using Mohr$-$Columb Criterion

The figure below shows the soil profile at a site for a proposed building. The soil is a homogeneous, poorly graded sand. Determine the increase in vertical effective stress at which a soil element at a depth of $3m,$ under the centre of the building, will fail if the increase in lateral effective stress is $20\%$ of the increase in vertical effective stress.