Small strain constrained modulus of dry sands: The impact of anisotropic loading

Abstract

In recent years, there has been a growing recognition of the importance of vertical ground motions in the seismic design of engineering structures. A comprehensive understanding of the small-strain constrained modulus M₀, which is a key input soil parameter, is essential for conducting a reliable analysis of vertical site response. Natural soils in engineering scenarios are often subjected to various anisotropic stress states, and the role of such loading on M₀ is a critical concern that remains incompletely understood. This paper presents a systematic experimental program aimed at addressing this issue. Using a triaxial apparatus, sand specimens initially isotropically consolidated were subjected to various anisotropic stress states, including triaxial compression and triaxial extension. The evolutions of M₀ at different stress states were captured by exciting elastic compression waves through embedded bender-extender elements. The specimens were tested under a wide range of states in terms of void ratio, axial stress, and radial stress. The study demonstrates that the impact of stress anisotropy is complex, depending on the magnitude of the stress ratio, the loading mode, and the initial state of the specimen. A practical model is suggested for the improved characterization of M₀ under the anisotropic stress states. This model considers two primary mechanisms that are associated with the effects of stress anisotropy.