On equivalent granular void ratio and steady state behaviour of loose sand with fines

Abstract

Abstract:Void ratio has traditionally, been used as a state variable for predicting the liquefaction behaviour of soils under the Critical State Soil Mechanics framework. Recent publications show that void ratio may not be a good parameter for characterizing sand with fines. An alternative state variable referred to as equivalent granular void ratio has been proposed to resolve this problem. To calculate this alternative state variable, a bparameter is needed. This b-parameter represents the fraction of fines that actively participate in the force structure of the solid skeleton. However, predicting the "b" value is problematic. Most, if not all, of the b-values reported were determined by casespecific back-analysis, that is, the b-value was selected so that a single correlation between equivalent granular void ratio and the measured steady state strength (or cyclic resistance) could be achieved. 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 value of "b" based on fines size and fines content. Published data appears to be in support of the proposed equation. A series of experiments were conducted on a specially designed sand-fines type in order to provide additional validation of the proposed equation and to reinforce the use of equivalent granular void ratio in a more generalized context. KEY WORDS:Void ratio, state variable, Steady State, Critical State, liquefaction One of the possible reasons that lead to the lack of a single Steady State Line may be due to the use of void ratio as a state variable. This is because of the non-active participation of fines in the force structure of a sand-fines mixture. To resolve this problem, a new state variable referred to as intergranular void ratio was proposed by considering the non-active fines as voids. It has been suggested that the intergranular void ratio should be used instead of void ratio for low fines content (Georgiannou et al. 1990;Georgiannou et al. 1991; Hight and Georgiannou 1995; Kuerbis et al. 1988;Ovando-Shelley and Pérez 1997, Thevanayagam 1998). However, intergranular void ratio is not applicable at higher fines content (Ni et al. 2006;Ni et al. 2004; Thevanayagam 2000;Yang et al. 2006a;2006b). Thevanayagam (2000) introduced the concept of equivalent granular void ratio for higher fines content and this approach requires an additional parameter "b" that presents the fraction of fines participating in the force structure of the solid skeleton. However, the prediction of b-value is a problematic and controversial issue (Ni et al. 2004; Thevanayagam 2001 Literature Review Intergranular void ratioMitchell (1976) pointed out the non-active role of fines in a granular phase structure and used such concept to determine the amount of non-active clay content. Kenney (1977) found that a clayey sand with a combined fines and water content of less than 40% to 50% by volume had a residual strength close to that of the host sand with a void sp...

Correlating Cyclic Strength with Fines Contents Through State Parameters

“…According to the grain size distribution of MLS and an assumed fthre of 30z, b＝0.164 and 0.577 for fc＝15 and 30z, respectively, following the method by Rahman et al (2008). However, a b value of 0.65 was required for the case of fc＝15z to establish a more consistent e * -CRR correlation, for the combined data of fc＝0, 15 and 30z.…”

“…For these reasons, natural or artiˆcially mixed M/S soils may not meet the description of binary packing in a strict sense and the thresholdˆnes content may therefore not be 30z. Some of the studies on artiˆcial silty sand specimens, mostly silica in nature, have demonstrated that the thresholdˆnes content generally ranged from 25 to 45z (Koester, 1994;Polito, 1999;Xenaki and Athanasopoulos, 2003;Papadopoulou and Tika, 2008;Rahman et al, 2008).…”

“…A higher b corresponds to an increase in the contribution ofˆnes in the force structure of the soil skeleton. Predicting the b value was considered to be problematic and controversial by Rahman et al (2008). Earlier methods generally involved the selection of a case-speciˆc,ˆnes content independent b value by a back-analysis so that the steady state or cyclic strength for a given sand-ˆnes type can be correlated with an equivalent granular void ratio irrespective of thê nes content (Ni et al, 2004).…”

“…These reports showed promising results in the use of an equivalent granular void ratio as an index to re‰ect the density state of an M/S soil. Rahman et al (2008) reported that for certain M/S soils, a series of void ratio (e) based critical state lines that correspond to various nes contents can be collapsed into one by replacing e with e * . This uniˆed e * based critical state line should be close to or the same as that of zeroˆnes content where e* ＝e.…”

On the physical meaning of equivalent skeleton void ratio for granular soil with fines

“…While the concept appears to be attractive, the physical meaning of index b in the equivalent skeleton void ratio is not yet well understood. In the literature the parameter b is commonly assumed to be a constant that can be back analyzed from test data or predicted by some empirical expression [4][5][6]. In the writers' view, the parameter b should vary during the shearing process; in other words it is a state dependent variable.…”