Experimental and statistical investigation of the relationship between static and dynamic modules of soils

In contemporary geotechnical engineering, the stiffness parameters (moduli) that govern the stress–strain behavior of soils from very small to large deformation levels constitute the fundamental inputs of constitutive models used in finite element analyses and are therefore critical for accurately representing soil behavior. However, obtaining these parameters directly in the laboratory is challenging due to the experimental complexity, high cost, and the need for specialized equipment and expertise. Consequently, establishing accurate and meaningful transitions between stiffness moduli corresponding to small and large deformation ranges is essential for engineering analyses. In the existing literature, Alpan's empirical relationship is virtually the only method proposed for constructing such transitions.Within the scope of this thesis, the validity, limitations, and representational capability of this empirical relationship in engineering applications have been thoroughly evaluated. The investigations revealed several constraints of this approach. In particular, the concept of the static modulus of elasticity (Estat) used in Alpan's formulation is not explicitly defined and is open to various interpretations. In this study, the Estat concept has been discussed together with its theoretical foundation. Moreover, Alpan's proposed relationship does not account for soil index properties or stress conditions; instead, it classifies soils into only two broad categories (cohesive and cohesionless), which is insufficient for accurately estimating the moduli that govern soil behavior under static and dynamic loading conditions.The relationship between the static and dynamic moduli of sandy soils was comprehensively investigated using both experimental data and an extensive database compiled from the literature. Resonant column and triaxial compression tests were performed on five sand specimens with varying characteristics, yielding 34 new data points. These were combined with 469 data points from the literature, resulting in a large dataset of 503 measurements. Based on this dataset, new correlations were developed for sandy soils to explain the maximum shear modulus (G₀), secant Young's modulus (E₅₀), dynamic Young's modulus (Edyn), and the dynamic/static modulus ratios (G₀/E₅₀ and Edyn/E₅₀) as functions of soil index properties and stress conditions. Since sufficiently comprehensive studies including both static and dynamic moduli for clayey soils are lacking, the topic was discussed within the framework of the Alpan approach. Given the limited number of studies in the literature on dynamic/static modulus ratios and the inability of existing approaches to adequately represent soil behavior, the correlations developed in this thesis offer a novel and practically applicable approach, particularly for sandy soils. By providing new relationships that are sensitive to soil index properties and stress conditions, the study presents high-fidelity correlations that can be directly implemented in engineering practice.