Consider the soil profile given below from Engineering News Record article titled: "Surcharging a Big Warehouse Floor Saves $$1$ Million" in March $3,1966$ issue. The dimensions of the new Amazon Fulfillment Center warehouse are $255$ ft by $550$ ft so for practical purposes the additional vertical stress due to the surcharge is equal to the surcharge stress at the center of the warehouse, i$.$e$.,$ areal fill. The height of the surcharge fill in the building was $12$ ft$,$ which is the maximum that could be placed in the available clearance. With a unit weight of fill of $108$ pcf$,$ the vertical stress beneath the center of the warehouse due to the surcharge is $1,296$ psf$,$ i$.$e$.,108$ pcf$*12$ ft$.$ The surcharge was removed after $14$ months and the warehouse floor was installed afterwards. The organic silt has an unconfined compressive strength of $2,500$ psf and the friction angle of the underlying sand is $33$ degrees. The surficial fill is stronger than the sand. The undrained Young's modulus of the organic silt is $80,000$ psf$.$

a$.$ Which layer is of most concern for settlement under the center of the warehouse?

b$.$ Calculate the immediate settlement due to the surcharge due to the layer of most concern.