Coupled shear strain-damage state model for prediction of shear modulus of coral sand

Four series of cyclic triaxial tests with different loading forms are conducted on saturated coral sand from Nansha Islands. The relationships between shear modulus ratio G_1st/G₀ of the first loading cycle and shear strain amplitude $\gamma_{a}$ under different relative densities D_r and effective confining pressures $\sigma_{0}^{'}$ are studied. D_r shows no influence on G_1st/G₀, and G_1st/G₀ increases with the increasing $\sigma_{0}^{'}$. When γ_a is larger than 3×10^-4, the G_1st/G₀ -$\gamma_{a}$curves obtained from the strain-controlled multistage loading tests (UMγ-CTX) are higher than those obtained from strain-controlled single-stage loading tests (USγ-CTX) because of the change of the soil structure and the relative density during the reconsolidation process of UMγ-CTX. A new damage parameter P_d is proposed based on the elastic strain energy theory, and the relationships between shear modulus ratio G/G₀ and damage parameter P_d under different loading forms are studied. The (1-G/G₀) - P_d curves are almost linear in the log-log coordinate, and the slopes are dependent on the shear strain amplitude $\gamma_{a}$ and the maximum shear strain amplitude $\gamma_{a.max}$. Based on the G_1st/G₀ -$\gamma_{a}$and G/G₀ - P_d relationships, a new G/G₀ prediction model is proposed to predict the shear modulus of coral sand considering the effect of coupled shear strain amplitude and damage state.