# Dynamic Properties of Calcareous Sands from Urban Areas of Abu Dhabi
## 4 Results and Discussion  
Figure 5a presents the variation of Vs with confinements for the tested samples. Vs values were normalized to the Vs value at the smallest confinement (30 kPa) for a better comparison in its trend with the confinements. Typically, a power model (Vs = a\({}^{\text{gb}}\)) is fitted to the variation of Vs with confinement (e.g., [PERSON] et al. [3]); therefore, Figure 5 also presents the exponents of the power models along with the data points to which the models are fitted. The coefficient of determination (r\({}^{2}\)) of the power models was consistently larger than 0.9, except for sample SB (r\({}^{2}\) = 0.77). The general range of exponents (b), which defines the rate of increase in Vs with confinement, for silica sands ranged from 0.25 to 0.35, which were slightly larger than the results of most calcareous sands from this study. Lower values of exponents for calcareous sands are expected due to smaller stiffness at the inter-particle contacts due to the weaker calcite minerals compared to the silica minerals. Moreover, the  
Figure 4: Illustration of hyperbolic models (Equation (1)) fitted to normalized shear modulus (N.G.) and damping ratio (sample SB, Confinement (\(\sigma\)) = 40 kPa). presence of gypsum in the sand deposits of ABD contribute to a weaker sand matrix when confinement increases (Table 1), especially in samples SA and SB. Figure 5a also shows that factors such as cementation at inter-particle contacts and inclusions such as seashells and a higher percentage of gypsum have a larger effect on the variation in Vs than the void ratio. Although smaller void ratio specimens (e.g., SC and SD) have a larger rate of increase in Vs, the trend is not clear when the results are compared with previous studies, as shown in Figure 5b. Figure 5b presents the comparison of power models with selected data for calcareous sands and for silica sands (circular markers) from the literature. [PERSON] et al. [12] presented data for natural sand deposits of ABD; however, the samples were reconstituted. Although the void ratio of the sample SC was close to the sample of [PERSON] et al. [12], the main focus of this study was not to evaluate the effect of the void ratio. The agreement between the sample SC and [PERSON] et al. [12] is good at low confinements; however, the proposed models overestimate the data. The results from other studies at different void ratios are with in the upper and lower bound for calcareous sands; however, a direct comparison based on void ratio is not appropriate due to reconstituted samples and different geographic regions. As noted earlier, the Vs of silica sand (circular markers) increases at a larger rate compared to most calcareous sands, of the present as well as of past studies. Figure 6 presents the degradation of the shear modulus for the four samples at three confinement levels of 40, 100 and 140 kPa. Corresponding hyperbolic models of damping ratios are plotted on the secondary axes. The rate of degradation in all samples increases with a decrease in confinement. Samples SB and SC not only have slightly larger damping ratios but slightly larger increases in the damping ratio with shear strain. The trend can be attributed to the presence of seashells and traces of gypsum. Samples SB and SC were collected from shallow depths, and the degree of cementation at the inter-particle contacts is expected to be less than the samples from greater depths. Figure 5: (**a**) Variation of normalized power models of shear wave velocity (Vs) with confinement (\(\sigma\)) for samples SA, SB, SC, and SD (data also shown). (**b**) Comparison of models with selected past studies on calcareous and silica sand (circular markers). The degradation behavior of the normalized shear modulus (N.G.) in Figure 6 appears to be independent of the type of sample and is almost identical at similar confinements.