Impact of Nonplastic Fines Content on the Small-Strain Shear Modulus and Water Retention Behavior of Unsaturated Sand–Silt Mixtures

Abstract This study examines the small-strain shear modulus ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> ) and water retention behavior of unsaturated sand–silt mixtures with a focus on the effects of fines content (FC), mean net stress ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Subscript n" display="inline" overflow="scroll"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> ), and hydraulic hysteresis. A comprehensive experimental program was conducted, incorporating saturated and unsaturated bender element tests, soil water retention curve measurements, and scanning electron microscope imaging. The tests were performed on compacted specimens of Firuzkooh No. 161 silica sand mixed with varying silt contents (0-100%) as fines under <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="p Subscript n" display="inline" overflow="scroll"> <mml:msub> <mml:mi>p</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:math> of 50, 100, and 200 kPa along both drying and wetting paths. Two unsaturated triaxial systems equipped with bender elements and a hanging water column controlled matric suction ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi" display="inline" overflow="scroll"> <mml:mi>ψ</mml:mi> </mml:math> ) via axis translation and water head control techniques. The results revealed significant changes in soil structure and hydromechanical behavior with increasing FC. In contrast to other soil mixtures, clean sand exhibited distinct hydraulic and mechanical behaviors, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> demonstrating a nonmonotonic variation with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi" display="inline" overflow="scroll"> <mml:mi>ψ</mml:mi> </mml:math> . As FC increased, a pronounced reduction in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> emerged at FC of 20%, at which point the soil structure began to transform from a fines-in-sand to a sand-in-fines structure. Notably, the impact of hydraulic hysteresis became increasingly prominent with FC: for mixtures with 10%–100% FC, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> during wetting was higher than during drying at the same <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi" display="inline" overflow="scroll"> <mml:mi>ψ</mml:mi> </mml:math> levels, whereas an opposite trend was observed for clean sand. Additionally, for sand specimens, the suction stress concept effectively described the variation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="psi" display="inline" overflow="scroll"> <mml:mi>ψ</mml:mi> </mml:math> , while for sand–silt mixtures (10%–100% FC), an extended framework incorporating the equivalent void ratio into a double hardening mechanism concept was adopted. The consistency between experimental observations and theoretical interpretations suggested that these concepts could provide a robust basis for predicting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript max" display="inline" overflow="scroll"> <mml:msub> <mml:mi>G</mml:mi> <mml:mi>max</mml:mi> </mml:msub> </mml:math> behavior in unsaturated sand–silt mixtures.