Shear modulus and damping ratio of saturated coral sand under generalised cyclic loadings

The influence of complex cyclic loadings associated with earthquakes on the shear modulus and damping properties of saturated coral sands has yet to be established. This paper presents comprehensive data sets from multi-staged strain-controlled (denoted Mγ), constant-amplitude strain-controlled (Cγ) and variable-amplitude strain-controlled (Vγ) undrained cyclic triaxial (UCTX) tests on a coral sand. The strain-dependent shear modulus and damping ratio from the Mγ UCTX tests and the cyclic stiffness degradation behaviour in the Cγ and Vγ UCTX tests are investigated. A correlation-function-based method is proposed to calculate the secant shear modulus and damping ratio at different strain levels, which shows higher precision at both small and large strain levels compared with the conventional methods. An important finding of the study is that the shear modulus reduction rate of the coral sand is significantly lower than that of siliceous sands, while the damping ratio for shear strain amplitude between 0·01% and 0·1% is well below that of siliceous sands. Two quantities: one is referred to as the strain ratio (Γ_N) and used for characterising the normalised cycle-dependent strain amplitude, and the other referred to as the damage energy measure (δ_N) and used for characterising the cumulative normalised elastic strain energy absorption, are proposed such that a unique formula can be established for predicting the cyclic stiffness degradation in the UCTX tests with different loading patterns. This energy-strain-dependent formula is further validated using independent data from stress- and strain-controlled UCTX tests involving four patterns of cyclic loadings, and a satisfactory performance is demonstrated.