Sorry, been on site for a couple of weeks and missed the original post, so you may have to scroll back up when you read this.
As for the chemistry element, when you add quick lime to a soil and increase the pH to over 12 [around 12.4 for quick lime in UK], any further lime you add will start to 'break' down the clay minerals [note, not clay size fraction]. This will allow the calcium [lime] to combine with the silica and/or allumina from the clay minerals, with water and form calcium allumina hydrates and silica allumina hydrates - i.e. weak cements. This accounts for the requirements for the PI as from experience, clay soils with PI in this range have sufficient allumina and silica within them that when they break down they will form the cementitious products. This also accounts for the 'Initial Consumption of Lime' [ICL] test, which is a measure of how much lime you need to add to increase the pH of the soil to over 12, after this any further lime is then free to combine with the silica and allumina.
If the soils do not contain sufficient allumina and silica, or where the lime addition is less than the ICL, then you are into 'modification' and not 'stabilization'. So if you need to assess the potential impact/imprvement of the material, you can begin by looking at the chemical composition of the silt [XRD etc..] and assess the clay mineral content.
On the plus side, when ettringite and/or thaumasite form from a detrimental sulfate reaction, they also use the silica and allumina, if they are not present in the parent soil, you may not get heave with sulfates. A bit left field but we have a site in the UK with very high sulfates but sulfate heave did not occur, no silica and no allumina to drive the reaction, unfortunately no stabilizaion either!!