| Summary: | The shear modulus is an essential parameter that reflects the mechanical properties of the soil. However, little is known about the shear modulus of coral sand, especially under complex consolidation conditions. In this paper, we present the results of a multi-stage strain-controlled undrained cyclic shear test on saturated coral sand. The influences of several consolidation state parameters: effective mean principal stress (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula>), consolidation ratio (<i>k</i><sub>c</sub>), consolidation direction angle (<i>α</i><sub>0</sub>), and coefficient of intermediate principal stress (<i>b</i>) on the maximum shear modulus (<i>G</i><sub>0</sub>), the reference shear strain (<i>γ</i><sub>r</sub>) and the reduction of shear modulus (<i>G</i>) have been investigated. For a specified shear strain level, <i>G</i> will increase with increasing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula> and <i>k</i><sub>c</sub>, but decrease with increasing <i>α</i><sub>0</sub> and <i>b</i>. However, the difference between <i>G</i> for various <i>α</i><sub>0</sub> and <i>b</i> can be reduced by the increase of shear strain amplitude (<i>γ</i><sub>a</sub>). <i>G</i><sub>0</sub> shows an increasing trend with the increase of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula> and <i>k</i><sub>c</sub>; on the contrary, with the increase of <i>α</i><sub>0</sub> and <i>b</i>, <i>G</i><sub>0</sub> shows a decreasing trend. To quantify the effect of consolidation state parameters on <i>G</i><sub>0</sub>, a new index (<i>μ</i><sub>G0</sub>) with four parameters (<i>λ</i><sub>1</sub>, <i>λ</i><sub>2</sub>, <i>λ</i><sub>3</sub>, <i>λ</i><sub>4</sub>) which is related to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>p</mi><mn>0</mn><mo>′</mo></msubsup></mrow></semantics></math></inline-formula>, <i>k</i><sub>c</sub>, <i>α</i><sub>0</sub>, <i>b</i> is proposed to modify the prediction model of <i>G</i><sub>0</sub> in literature. Similarly, the values of <i>γ</i><sub>r</sub> under different consolidation conditions are also evaluated comprehensively by the four parameters, and the related index (<i>μ</i><sub><i>γ</i>r</sub>) is used to predict <i>γ</i><sub>r</sub> for various consolidation state parameters. A new finding is that there is an identical relationship between normalized shear modulus <i>G</i>/<i>G</i><sub>0</sub> and normalized shear strain <i>γ</i><sub>a</sub>/<i>γ</i><sub>r</sub> for various consolidation state parameters and the Davidenkov model can describe the <i>G</i>/<i>G</i><sub>0</sub>–<i>γ</i><sub>a</sub>/<i>γ</i><sub>r</sub> curves. By using the prediction model proposed in this paper, an excellent prediction of <i>G</i> can be obtained and the deviation between measured and predicted <i>G</i> is all within ±10%.
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