Furthermore, the shear modulus decreases as the shear strain amplitude increases, and the soil’s behavior becomes nonlinear. Vucetic and Dobry and Ishihara defined a volumetric cyclic threshold shearing strain γ tv, which when exceeded permanent microstructural change of soil occurs and soil stiffness changes permanently. The most used equations are presented by Hardin and Richart, Hardin and Black, and most recently by Wichtmann, Navarrete Hernández, and Triantafyllidis.

Other equations can be used as well based on extensive laboratory testing programs to calculate the initial dynamic shear modulus G max, where it is correlated to the confining stress, void ratio, and uniformity coefficient C U.

It can be determined by using seismic methods in the field to obtain in situ shear wave velocity, where the strain level is very low and the soil still behaves elastically. The shear stiffness of the soil is usually represented by the shear modulus G, which is the slope of the shear stress-shear strain curve. In this study, the Ramberg-Osgood and the Hardin-Drnevich models were used to predict and simulate the soil behavior in the TOrsional Simple Shear (TOSS) test, and the results were compared with test data for irregular loading patterns. However, the progressive development in computer technology accompanied with the increasing speed of processing complex calculations allowed the use of numerical modeling for easier and faster calibration of models for further use in real and much more complicated geotechnical problems (e.g. This has been a challenge when it comes to irregular loading patterns due to the complex nature of soils’ behavior and its dependence on many factors like the confining stress, void ratio, density and number of cycles, etc. Thus, to be able to study the soil-structure interaction numerically with adequate accuracy, it is important to have a material model that is well representative of the soil in the field conditions. It is agreed that the most important parameters to define this behavior are the dynamic shear modulus and the damping ratio, which contribute to variation in the stiffness and energy dissipation during cyclic loading. Therefore, many researchers in the past few decades focused on studying the behavior of soils subjected to dynamic loads. The response of structures to dynamic loading is directly dependent on the response of soil beneath or around it.

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