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This research is based on the results of 120 determinations of the shear modulus (G) of a saturated granular medium (20-40 Ottawa sand) for different conditions of relative density (Dr), effective consolidation pressure (σ’c), and level of torsional excitation (Te) obtained through the measurement of the resonant frequency (Fr) in resonant column equipment. The tests were performed with relative density values equal to 20, 40, 60, and 80 %; effective consolidation pressures of 50, 100, 150, 200, 250, and 300 kPa; and torsional excitations of 0.025, 0.05, 0.1, 0.2, and 0.4 V. The proposed experimental program is described in detail, in addition to the systematic process of analysis to properly study and interpret the results obtained for samples subjected to cyclic loading. In general, the results indicate that it is possible to establish very simple empirical functions of the resonant frequency as a function of the angular strain and of the effective consolidation pressure. It is concluded that is statistically significant to consider the shear modulus and the resonant frequency related by a constant value M for each type of soil. In this sense, a methodology is proposed herein to be able to obtain from a very small number of tests the variation trends of the shear modulus as a function of the angular strain for different effective consolidation pressures.

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