Sorry, I am not sure you have phrased the question correctly. The initial consumption of lime is a measure as to how much lime will be required to raise the pH value of the soil to in excess of 12. At this point it is judged that any further addition of lime will not be used to raise the pH, but instead will begin to break down the clay particles and start the stabilisation process by forming calcium silica and calcium alumina hydrates [cement]. In addition to this, once sufficient lime has been added to the soil, the structure of the clay palettes is affected by a cation exchange, which in turn changes the structure of the soil and in turn increases the plastic limit [increase OMC, therefore soil 'needs' more water to be compacted].
Therefore the recommendations from BS 1924 suggest that mix design trials should be started at the Initial Consumption of Lime PLUS 0.5%, i.e. 0.5% lime is used to stabilise the soil AFTER the pH has been raised to >12. This is just the start of the process, if the resultant 7 day strength fails to meet the specification requirement [end-performance] then further lime is used and the resultant strength determined. If the soil is unable to achieve the required strength, consideration is then given to the use of other binders including cement [OPC]. BS 1924 suggests that where the ICL is > 5%, it may be uneconomical to use stabilisation, however this document is now some years old and the economics have changed.
I would suggest that you also refer to the following document HA 74/07 which can be downloaded for free from
This document is produced by the Highways Agency in the UK and discusses the testing and specification of Capping replacement materials for road pavement design and is very useful in organising mix design trials.
Finally, please note that there are two processes which can be accomplished by using lime, the first is modification which is a short term improvement in the material and does not need the pH to be in excess of 12, the second is 'true' stabilisation which is a long-term process and requires the formation of cementitiuos products.
I hope this helps, basically the lower bound value will be the ICL plus 0.5%, the upper value will be cost driven.