Anisotropic Consolidation Effects on the Dynamic Shear Modulus of Fujian Sand: Experimental Investigation and Predictive Modeling

The dynamic shear modulus of soil is a critical parameter for evaluating the seismic response of geotechnical structures. Although extensive research has been conducted on soil dynamics under isotropic conditions, the understanding of soil behavior under anisotropic stress states, characterized by the consolidation stress ratio ( K c ), remains inconsistent. This study investigates the effects of anisotropic consolidation on the dynamic shear modulus ( G ) of Fujian sand through a series of strain-controlled cyclic triaxial tests, covering a medium-to-high shear strain range. The influences of lateral effective confining pressure ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> m ), consolidation stress ratio ( K c ), and saturation condition (dry and saturated) on the maximum dynamic shear modulus ( G max ), dynamic shear modulus (G), and normalized dynamic shear modulus ( G/G max ) were systematically investigated under two stress paths: constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> m and constant mean effective confining pressure ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> ). The results indicate that the maximum dynamic shear modulus ( G max ), G , and dynamic shear modulus ratio ( G/G max ) all increase with the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> m . Under two different methods of applying consolidation stress ratio (keeping <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> m constant and keeping average effective confining pressure ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> ) constant), <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> has the same influence pattern on G max , G, and G/G max . When <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>σ</mml:mi> </mml:math> m or <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>σ</mml:mi> <mml:mi>m</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">′</mml:mi> </mml:mrow> </mml:msubsup> </mml:math> is kept constant, G max increases with the increase in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> </mml:mrow> </mml:msub> </mml:math> for both dry and saturated sand, with the ratio G max(aniso) / G max(iso) ranging from 1.0 to 1.8. Before <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>γ</mml:mi> </mml:math> reaches 10 -4 , the increase in G with increasing K c is significant. However, after <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>γ</mml:mi> </mml:math> exceeds 10 -4 , with the increase of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>γ</mml:mi> </mml:math> , higher K c leads to faster attenuation of G. When <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>γ</mml:mi> </mml:math> is around 10 -2 , the results of G under different K c values are essentially consistent. On the other hand, G/G max decreases gradually with the increase of K c , and the ratio of reference shear strain