# Dynamic Properties of Calcareous Sands from Urban Areas of Abu Dhabi
## 3 Experimental Program and Methodology
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sample Name** & **Void Ratio** & \(\mathbf{C_{C}}\) & \(\mathbf{C_{U}}\) & **Material Description** & **Depth (m)** & **SPT-N Value** \\ \hline SA & 0.81 & 0.82 & 2.45 & \begin{tabular}{c} Very dense, poorly graded sand \\ with inclusions of \\ crystalline gypsum \\ \end{tabular} & 11–12 & 50 \\ SB & 0.72 & 1 & 2.00 & \begin{tabular}{c} Medium dense to very dense, \\ poorly graded sand with silt and \\ trace crystalline gypsum \\ \end{tabular} & 1.5–2 & 21 \\ SC & 0.65 & 0.70 & 2.75 & \
\begin{tabular}{c} Medium dense, light grey to grey \\ wet, non-plastic, silty sand, trace \\ fine gravel, and shell fragments \\ \end{tabular} & 4–5 & 17 \\ SD & 0.51 & 0.72 & 2.8 &
\begin{tabular}{c} Medium dense to very dense, \\ light brown to light grey wet, \\ non-plastic, silty sand, trace fine \\ gravel, and shell fragments \\ \end{tabular} & 5–6 & 14 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of samples. Figure 1: (**a**) Typical time history recorded at the Bender Element (BE) receiver (Rx) and (**b**) Fourier spectra of receiver signals. Figure 3: Typical measured and fitted functions for (**a**) displacement amplitude, (**b**) load amplitude, and (**c**) hysteresis loops (100 kPa). Figure 2: Typical receiver signals (staked) from the Bender Element testing at different confinements for sample SB. Figure 4 illustrates the fitting of typical data from BE and CT tests with hyperbolic models. The data points at the lowest strain correspond to the results from the BE tests. The BE element data were assigned a shear strain value of \(10^{-6}\) because it is difficult to calculate the strain level from the movement of the bender elements. The variation in lowest value of assigned shear strain was assumed to have a negligible effect on dynamic properties. The difference in frequency content between BE and CT tests is large; however, no study has suggested a model to correct for the frequency. A low-strain Poisson's ratio of uncemented to lightly cemented sands can range from 0.15 to 0.25, depending upon the saturation and cementation level ([PERSON] et al. [24]). Fully saturated soil has a Poisson's ratio close to 0.5. CT typically evaluates the dynamic properties for medium to large strains; therefore, a value of 0.25 for the Poisson's ratio was selected for all conversions of elastic moduli (secant moduli) to shear moduli in this study. The sensitivity analysis showed that G will change by 8% only if the Poisson's ratio varies from 0.15 to 0.25. The damping ratios were calculated from standard procedures of analyzing hysteretic loops for energy stored and lost during one cycle (Equation (4)). \[D=\frac{1}{4\pi}\frac{A_{L}}{A_{T}} \tag{4}\]  
where \(A_{L}\) is the area of the loop, and \(A_{T}\) is the area under the line of secant modulus. The minimum damping ratios (\(D_{min}\)) corresponding to lowest shear strain levels were not measured (Figure 4). Evaluation of the low-strain damping ratio from BE and CT testing is difficult; therefore, a value of \(D_{min}\) was adopted, and a minimum shear strain level was assigned to it. Damping ratios decrease as the shear strain decreases, and then remains at a constant minimum value. The lowest damping in a best fit hyperbolic model represents \(D_{min}\).