Predicting the Maximum Shear Modulus of Sands Containing Nonplastic Fines

There are some attempts to evaluate Hardin’s equation for transition soils, i.e., sand mixed with a systematic increase of fines ($\text{particle size}\le 0.075\mathrm{mm}$) content, $f_c$. The most common finding is that maxmium shear modulus, $G_{\max }$, decreases with increasing $f_c$, and there are attempts to capture the effect of $f_c$ on $G_{\max }$ by considering $G_{\max }$ of clean sand as a reference. These are done by (1) developing empirical relations of $A$, $n$, $c$, or $d$ with $f_c$; (2) using equivalent granular void ratio, $e^{*}$, instead of void ratio, $e$ in Hardin’s equation; and (3) using a critical state (CS) approach. This paper presents 288 resonant column $G_{\max }$ data for clean Hostun sand and Hostun sand mixed with 5, 10, 20, and 30% nonplastic quartz powder. It is found that when $e$ in a pre-established Hardin equation for clean Hostun sand is replaced by $e^{*}$, Hardin’s equation can predict $G_{\max }$ for Hostun sand with $f_c$ with good accuracy. Only soil grading properties, e.g., $D_{10}$ and $d_{50}$, are required as inputs to convert $e$ to $e^{*}$. This is a significant advantage over a recently proposed CS approach which requires critical state lines (CSLs) data for each $f_c$.