The prediction of equivalent granular steady state line of loose sand with fines

Void ratio has been used as a state variable for predicting the liquefaction behaviour of soils under the critical state, sometimes also referred to as the steady state, framework. Recent publications show that void ratio may not be a good parameter for characterising sand with fines because the steady state line (or curve) in the e-log(p) space moves downward with increase in fines content until it reaches a threshold value referred to as the threshold fines content (TFC). Recently, an alternative state variable, referred to as the equivalent granular void ratio, has been proposed to resolve this problem. To calculate this alternative state variable, an additional parameter 'b' is needed. This parameter 'b' represents the fraction of fines that actively participate in the force structure of the solid skeleton. However, predicting the 'b' value is problematic. This paper examines the factors affecting the 'b' value based on published work on binary packing. This leads to a simple semi-empirical equation for predicting the 'b' value based on fines size and fines content. The proposed equations were evaluated with published data sets. Then, the concept of an equivalent granular steady state line is proposed. This concept was used to predict the location of SSLs for sand with different fines content from either the SSL of clean sand or the SSL of sand with a given fines content. The predictions agree well with experimental results.