The best way to estimate the settlement of soil is by conducting consolidation test matter and/or plate load. Since you are talking about peat thus organic soil and clayey materials are present i believe that plate load can do the job
The best reference on peat is by N B Hobbs which gives full details of their origin and engineering proporties. The compression Index Cc of peat can be estimated from the natural moisture content mc or from the Liquid Limit. This correlation varies depnding on type of peat is could be taken as about Cc = 0.008 mc in the absence of more data.
You can estimate secondary compression in peat using the relationship given in NavFacs 7.1 Fig 16 (Calpha = 0.01 mc)