## 2 Materials and Methods
### Dynamic Simple Shear Apparatus and Testing Plan  
A two-dimensional simple shear test scheme was employed to assess the dynamic properties of the test sand under cyclic loading conditions. The test involved applying forces in two directions: a vertical force along the sample's axis and a shear force parallel to its horizontal surface. The cyclic shear stress was applied to the samples sinusoidally using the dynamic simple shear apparatus, and the frequency of the device was 0.5 Hz. The samples, measuring 70 mm in diameter and 20 mm in height, were prepared using dry sand following the wet damping method with a moisture content of 7%, as per [PERSON] [48]. Figure 2 provides a schematic illustration of the described dynamic simple shear test. This testing scheme is useful in determining the shear strength, deformation characteristics, and stress-strain response of sand samples [49]. The data obtained from such testing regimes are crucial in understanding the response of sandy materials to cyclic loading, which is relevant to various geoengineering applications, including the design of foundations, retaining walls and embankments. Before investigating the dynamic properties of the test sand through cyclic testing, a series of monotonic tests were also performed, which indicated a _dilative_ behavior for the investigated sand, as also noted by [PERSON] et al. [27]. The cyclic tests were carried out on samples prepared with a relative density of approximately 45%; vertical stresses of 50, 150 and 250 kPa were applied, with each test conducted using different cyclic stress ratios of 0.2, 0.3, 0.4 and 0.5. The cyclic loading involved applying a vertical load at a rate of 5 N/s, followed by sinusoidal shear loading. Constant-stress and stress-control modes were employed during cyclic testing, with the same sample being utilized for five repetitions under identical conditions. CSR loading is commonly used to evaluate the resistance of soils to cyclic loading and their ability to withstand repeated cycles of stress and strain. This method directly applies cyclic stress to the test soil, and its response is measured in terms of strain. CSR loading is particularly useful in simulating the loading conditions experienced by soils during an earthquake, particularly for soils with low plasticity index values. To quantify the shape characteristics of the sand grains, the empirical chart proposed by [PERSON] and [PERSON] [50] was employed. This chart uses an optical microscope to express grain shape in various ways; roundness \(R\), sphericity \(S\) and regularity \(\rho\) were the three shape descriptors quantified in this study using Equations (1)-(3), respectively. Note that  
Figure 2: Illustration of the employed dynamic simple shear test scheme. This study conducted a comprehensive investigation into the effects of particle shape changes on the damping ratio. To this end, 25 sand particles were randomly selected at three stages, namely, before testing, prior to the second test, and before the fifth test. The three shape descriptors (Equations (1)-(3)) were quantified for each selected particle, and their averages for the 25 particles were considered the \(R\), \(S\) and \(\rho\) parameters for each stage. This approach was employed to isolate the effects of particle shape changes on the damping ratio as other physical variables remained nearly constant. It should be mentioned that a test group was first conducted to determine the optimum number of grains. Initially, ten particles were selected; however, after conducting the investigation, it was found that the standard deviation of the three shape parameters \(R\), \(S\) and \(\rho\) was insufficient (for ten particles), with values of 0.014, 0.010 and 0.013, respectively. To address this, the study proceeded to the second step and analyzed twenty particles. The results showed that the standard deviations for the three parameters \(R\), \(S\) and \(\rho\) were acceptable at 0.0033, 0.0024 and 0.0028, respectively.