The 2:1 method gives you the "stress" increase at any level below the foundation. Not really true since at any level the highest stress will be at the centre of the footing and lower stresses away from the centre - but overall average is about as per 2:1. Knowing the stress increase at the various levels, you can, for finite thicknesses determine the settlement caused by the stress. The simplest way is to use the elastic formula for strain = stress / E - or settlement = stress x thickness / E. Use average value of E over the range of stress from existing to increased stress, use correction for 3-D as (1 - mu) approximately. That is one way you can do it. There are several caveats in this method.
Another method is the Schmertmann method. You don't need to compute the "stress" increase in this method. You can also use other elastic formulas where you have correction factors for rigidity of footing, corner and centre of footing, etc. These are given in Bowles. Other methods are also available.
The above deals with "elastic sands" where the applied loading is nearly linear - not towards the failure load. It also will be good for immediate clay settlements. For clays you will need, though, your consolidation computations (with the stresses determined by your 2:1) method for determining the consolidation settlements. See any good soils text on these issues. and then, there is creep settlement, etc. Many pages of books and numerous papers dealing with this subject.
