your project is very broad , i mean that slope failure happens for many reasons
I highly recommend that you read "an introduction to geotechnical engineering by Holtz et al" , also read Terzaghi's book if you can
Slope instabilities occur because of either : decrease in shear strength by environmental or human activity or increase in driving forces also by the same causes .
Granular loose materials fail under UU conditions by liquefaction , to make it simple they fail when pore water pressure is equal or greater than effective stresses . Dense granular materials however can behave quiet well , but they do fail under CD conditions or when erosion remove part of the materials .
Cohesive materials are most troublesome , since they can fail after considerable time or spontaneously w/o warning . Normally consolidated clays fail under UU condition by compression or lateral active spreading ( think erosion , chemical alteration , PWP ) . OC clays fail only under CD conditions , but they are a hard bit : intact unfissured clays can be good , highly fissured clays are not . The latter tend to suffer creep and progressive failure by reduction of shearing strength because mostly of water , the shearing strength lowers down to a residual value or fully softened one . Therefore , shales or claystone can be tricky rocks .
But bear in mind ,organic soils or fill materials are highly hazardous , in fact one slope i am working on failed catastrophically because of this reason.
If you just want to study mathematically how variation of the parameters affect slope stability well , its already done watch for the basic analytical methods such as Bishop's or Fellenius methods . If you want to try and quantify erosion and or other processes leading to failure then good luck i will see if i can help