# Experimental Study on Small-Strain Shear Modulus of Unsaturated Sility-Fine Sand
## 1 Introduction  
In actual engineering, foundation soil is often unsaturated. There are significant differences in the mechanical behaviours of saturated and unsaturated soil. Saturation vibration in soils causes serious engineering problems, such as the cracking and settlement of roadbeds, dams, shallow foundations and other structures [1]. Soil strain is divided into three intervals according to size: very small strain (\(\leq\)\(10^{-6}\)), small strain (\(10^{-6}\)-\(10^{-3}\)) and large strain (\(>\)\(10^{-3}\)) [2]. Large amounts of engineering monitoring data have shown that the soil strain around the foundation of a geotechnical structure under a normal working load is generally small, mostly being concentrated in 0.01-0.1%. This is almost in the small-strain range [3]. Therefore, it is necessary to study the small-strain characteristics of unsaturated soils. In geotechnical dynamic analysis and design (e.g., the prediction of soil deformation behaviour under seismic, blasting, traffic loads and soil-structure interactions), the soil dynamic shear modulus is one of the key dynamic parameters and its value must be reasonable to accurately predict the deformation of geotechnical structures under a dynamic loading condition [4, 5]. At present, there are three main methods used to determine the small-strain dynamic characteristic parameters of soils, which are the resonant column (RC) method, the bending element (BE) method and the torsional cyclic loading method (TCL). For more than 50 years, RC devices have been successfully used in the field of soil dynamics [6, 7, 8, 9] and they are considered the most reliable method in the determination of the shear modulus and dampingcapacity in soils. In the USA, the RC technique has become the standard ASTM method [10]. However, it is worth noting that the strain range of soils in RC tests is \(10^{-5}\)\(\sim\)\(10^{-3}\). [PERSON] et al. [11] first applied the BE technique to the field of geotechnical engineering. [PERSON] et al. [12] further developed the technique and compared the BE and RC testing techniques. Since then, the BE test has been widely used as a convenient and promising method to measure the maximum shear modulus \(G_{max}\) of soils [13; 14; 15; 16]. Generally, the strain range of soils in the BE test is \(10^{-6}\). Based on RC and BE apparatus, extensive studies have been carried out to investigate the influences of saturation degree or matrix suction on the shear modulus of unsaturated soils. [PERSON] et al. [17] studied the decay of shear modulus with strain in different types of soils; the results revealed that shear modulus of different soils all decreased with an increase in strain, but the decay rates of different soils are different. [PERSON] and [PERSON] [18] indicated that the \(G_{max}\) of clay continues to increase with increasing saturation through BE testing. [PERSON] and [PERSON] [19] studied the effect of saturation on the small-strain shear modulus of clay based on BE tests and they found that the \(G_{max}\) increases with a decrease in saturation and the increasing trend is obvious when the saturation is low. [PERSON] et al. [20] studied the effect of saturation on the dynamic shear modulus of clay by RC tests and the results showed that the shear modulus increases with increasing suction in unsaturated clay. The results of these studies indicate that there is a clear trend for \(G_{max}\) versus saturation in clay. However, the evolution of the shear modulus of sand has been observed to be different from clay. [PERSON] and [PERSON] [21] studied the dynamic shear modulus of unsaturated sand based on RC tests and the results showed that the degree of saturation has a small effect on the small-strain shear modulus at a low confining pressure. [PERSON] et al. [22] studied the effect of different saturation levels on the small-strain shear modulus of five fine-grained cohesionless soils based on RC tests and it was found that the small-strain shear modulus increases and then decreases with the increase in saturation. [PERSON] et al.