# Dynamic Characteristics of Clay-Rubber Mixtures: Perspective on Small-Strain Dynamic Shear Modulus and Damping Ratio

## TL;DR

This study examines how clay-rubber mixtures behave under small-strain vibrations, focusing on how rubber content and size affect stiffness and energy dissipation.

## Contribution

A new empirical equation for the maximum dynamic shear modulus of clay-rubber mixtures is proposed, considering confining pressure, rubber content, and particle size.

## Key findings

- Dynamic shear modulus increases with confining pressure but decreases with higher rubber content.
- Damping ratio increases with both rubber content and particle size.
- An equation for maximum dynamic shear modulus incorporating σ3, Crubber, and Drubber was successfully proposed.

## Abstract

Waste tire rubber–soil mixtures feature low density, high energy dissipation, and low shear modulus, which are widely used in geotechnical engineering for vibration attenuation. In this study, the evolution of the small-strain stiffness characteristics of clay-rubber mixture (CRM) is investigated; a resonance column test was carried out to determine the small-strain stiffness characteristics of CRM samples with different confining pressures (σ3), rubber particle contents (Crubber), and rubber particle sizes (Drubber). The test results indicate that σ3 can promote the dynamic shear modulus (G) of CRM and restrain the damping ratio (D). The rubber particles have a great influence on both G and D. Under the same conditions, G decreases significantly with the increase in Crubber and increases slightly with the increase in Drubber, which indicates that rubber particles inhibit the development of G. D increases with the increase in Crubber and Drubber. The results show that the contact area between clay particles and rubber particles increases with the increase in Crubber, resulting in the decreases in G and D. The G–γ curves are analyzed by using the Hardin–Drnevich equation. Based on the fitting results, the maximum dynamic shear modulus (Gmax) is obtained. Therefore, the evolution of Gmax with σ3, Crubber, and Drubber are analyzed, and an equation for the Gmax of CRM considering the effects of σ3, Crubber, and Drubber is proposed. In addition, the D–γ curves can be well described by an empirical equation.