# Study of Static and Dynamic Properties of Sand under Low Stress Compression
## 1 Introduction
The advantage of the AE method is its ability to characterize the destruction of different materials at all spatial scales and during the failure process itself [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Moreover, the AE method, as well as any geophysical method being an indirect tool for failure characterization, has its own restrictions. The way to overcome such limitations is to combine the AE results with the results of another method based on a different physical phenomenon for a comprehensive study. Ultrasound (US) is the standard method for assessing dynamic properties in various materials [24]. For example, [PERSON] [25] studied the dynamic Young and shear moduli of soil using the US method. [PERSON] et al. [26] measured the P and shear (S) wave speeds in the samples of dry and water-saturated natural sand samples. The exponent relationships between the P wave speed and the applied external load were found. [PERSON] et al. [27] studied the elastic wave velocity of an unsaturated silty sand. The difference in the AE and US behavior in four types of sand was studied in [28]. It was shown that when the stress level gradually increased, the US wave speed gradually increased as well, while the AE activity was sharply excited. On the other hand, during stress relaxation, the US wave speed abruptly decreased while the AE activity was minor. Such a dissimilarity in the behavior of US and AE phenomena renders them obvious candidates for the comprehensive study of sand under compression. The state-of-the-art analysis portrays that most studies of granular material loading have been carried out (1) with only one loading tool (e.g., oedometer) [18; 21; 29] or different types of compression machines or shear machines [20; 29; 30; 31; 32; 33], (2) typically under high compression stress (i.e., in the elastic and stiffness regain regimes) (e.g., [29; 32]) or during individual grains fracturing [19; 23; 34] and (3) for a very thin range of grain sizes (e.g., [22] and references therein). In addition, there are no widely agreed valuable parameters of AE to characterize sand stress-strain behavior under low stress. The studies of granular materials under low stress are significantly rare (e.g., [28; 30], as well as the combined study of US and AE measurements [28; 33]). All the above reflect the knowledge gap in the field. The goal of this paper is to fill the existing knowledge gap. This paper presents the novel results of the following:  
1. The comparison of sand loading using an oedometer and an uniaxial compression machine in the pre-yield regime (under low stress), in terms of combined AE and US measurements;
2. The analysis of sensitivity of different time domain AE parameters to the stress-strain changes;
3. The loading of the wide range of sand grain sizes of 0.075-4.75 mm (natural poorly graded dune sand) as well as its three extracted fractions as follows: 2.36-0.6 mm, 0.6-0.3 mm and 0.3-0.075 mm. Emphasis is put on the differences in stress-strain behavior of the four types of sand under loading, using these two types of loading tools with a special focus on the US and AE characteristics. The outcome of this study can be utilized in geomechanics to understand the stability of shallow infrastructure systems such as pipelines, foundations and retaining structures. For example, [PERSON] et al. (2016) in their Figure 1 presented a \"typical failure pattern and the relevant load-displacement curves for shallow foundations resting on soil\", while the most sensitive parameters observed in this paper may be used for the short-term assessment of load degree in the future. In addition, the results of this paper can be the basis for a future study of different aspects of the liquefaction process, soil sliding (e.g., (30; 31) and references therein) and sinkhole creation. For example, sinkholes in the region of the Dead Sea present a permanent hazard for the industrial and touristic facilities.