Linking the macro-scale response of granular materials during drained cyclic loading to the evolution of micro-structure, contact network and energy components
Tara S. Sassel, Fernando Patino-Ramirez, Kevin J. Hanley, Catherine O’Sullivan
Abstract
Abstract This study has considered the behaviour of granular materials subjected to drained cyclic loading under constant mean effective stress. Using the discrete element method, cubical, isotropically compressed samples were subjected to 50 loading cycles at different values of mean stress ( $$p' =$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>p</mml:mi><mml:mo>′</mml:mo></mml:msup><mml:mo>=</mml:mo></mml:mrow></mml:math> 100, 200, 300 kPa) and different loading amplitudes ( $$\zeta =$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math> 5%, 10% and 20% of $$p'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>p</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> ). At low cycle numbers, the deformation mechanism is controlled by contractive volumetric strains, before transitioning to the ratcheting regime, characterised by the persistent accumulation of plastic strains. An energy/work analysis showed that the volumetric work per cycle decreased as hysteresis loops tighten. During ratcheting, most boundary work was dissipated by contact sliding. The mechanical response was controlled by $$\zeta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ζ</mml:mi></mml:math> , with little to no influence of $$p'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>p</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> . For $$\zeta = 5\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> , deformations were confined to the elastic range, with no increase in secant stiffness $$G_{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>sec</mml:mi></mml:mrow></mml:msub></mml:math> or shear strength after cyclic loading. For $$\zeta = 10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo><mml:mn>10</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> , $$G_{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>sec</mml:mi></mml:mrow></mml:msub></mml:math> and the shear strength increased after cyclic loading, although no significant expansion of the yield surfaces was observed. The largest loading amplitude ( $$\zeta = 20\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn><mml:mo>%</mml:mo></mml:mrow></mml:math> ) induced yielding at low cycles, leading to significant changes in the fabric, volume and yield surfaces of the samples, and a significant increase of shear strength and $$G_{sec}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>G</mml:mi><mml:mrow><mml:mi>sec</mml:mi></mml:mrow></mml:msub></mml:math> . At the micro-scale, graph theory was used to quantify the evolution of the contact network. After $$\sim 20$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>∼</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math> loading cycles, the network reached a steady-state of constant but persistent topology changes in the material, with most of the topology retained between loading cycles.