# Investigation of Geotechnical Seismic Isolation Systems Based on Recycled Tire Rubber-Sand Mixtures
## 2 Materials and Methods  
In this study, the dynamic properties of granular rubber-sand mixtures were investigated through numerical analyses and laboratory experiments carried out by [12]. The laboratory component primarily relied on consolidated undrained cyclic triaxial tests to determine the shear modulus and damping ratio under various confining pressures. Specimens were prepared using well-graded sand mixed with granular rubber particles derived from recycled tires. The granular rubber content varied between 0%, 5%, and 10%, while confining pressures of 50, 100, 200, and 300 kPa were applied to assess the influence of overburden pressure on dynamic behavior [12]. A GDS Instruments cyclic triaxial testing system was employed for the experiment procedures. This system was equipped with an automated load frame capable of applying cyclic axial loads at a controlled frequency range of 0.1-10 Hz. The system recorded stress-strain responses using high-precision displacement transducers and pressure sensors, allowing for the derivation of modulus reduction and damping curves. The hysteresis loops obtained from cyclic loading were analyzed to compute the shear modulus and damping ratio, which were subsequently normalized to generate G/Gmax and damping ratio curves shown in Figure 1.  
The experimental data was subsequently used to calibrate numerical models developed in the DeepSoil software. The validation of the numerical framework was achieved through a comparative analysis of response spectra, Fourier amplitude ratios, and acceleration time histories. This integration of laboratory testing with numerical modeling enhances the reliability of the results and provides a more comprehensive understanding of the seismic isolation performance of granular rubber-sand mixtures. In the dissection of most soil dynamics problems, determining the shear modulus and damping ratio based on shear strain amplitude is a critical parameter for defining dynamic properties or estimating stiffness and energy absorption ability. Soil-structure interaction response to dynamic loads, such as earthquakes, vibrating equipment foundations, explosive forces, and the response of marine structures to ocean waves, is exceptionally convoluted. Under dynamic loading, stress-strain behavior is represented by hysteresis loops. The slope of lines connecting the peaks of these loops indicate stiffness, while the area enclosed by the loops represents material damping [12]. In Figure 1, experimental results on damping ratio and shear modulus reduction were presented. The graph demonstrates the influence of varying rubber content (0%, 8%, 10%, and 14%) and confining pressures (50, 100, 200, and 300 kPa) on dynamic soil properties, such as damping ratio and shear strain amplitude. These experimental data complement the numerical results discussed in this study and validate the trends observed under seismic loading conditions. In the research presented herein, the research conducted by [PERSON] and [PERSON] [12] on consolidated undrained cyclic triaxial testing was utilized to obtain the shear modulus and damping ratio of the isolation soil. As shown in Table 1, samples were mixed in various proportions with granular rubber of a specific particle size and specific granular soil. Models were introduced to estimate the maximum shear modulus (Gmax) and normalized shear modulus (G/Gmax) for different confining pressures (\(\sigma_{3}\)) and granular rubber percentages (R). This research inquiries into how the dynamic properties of soil vary with the supplement of granular rubber and how augmenting the rubber content influences soil stiffness and damping capacity. Shear modulus-shear strain amplitude curves for soil-granular rubber mixtures are presented in Figure 2 for 50 and 100 kPa confining pressures and granular rubber content ratios of 0.0%, 5%, and 10%. The results indicate that, under constant confining pressure, the shear modulus diminishes as the percentage of granular rubber increases.