Identification of the critical state line of sands using coupled shear-volumetric strain paths

Abstract The identification of the critical state line projection in void ratio–mean effective stress ( $$e-p'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> ) space is an essential step in the characterization of a sand, needed both for estimations of shear strength and as input for advanced constitutive models. However, the determination of the critical state line is often an arduous process. In triaxial testing, it can be challenging to impose the large strains ( $$&gt;20\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mn>20</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> ) required to attain the critical state without excessively distorting the sample. Moreover, the axial load required to reach the critical state under high initial confining stress can be beyond the capacity of typical soil testing equipment or instrumentation. Further, the pore pressure of dilative specimens subjected to undrained compression can drop enough to reach cavitation. This paper demonstrates how in such cases, the critical state line in $$e-p'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> space can be indirectly derived through triaxial compression tests with coupled shear-volumetric strain paths that do not require axial strain beyond $$15 \%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>15</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . Congleton sand is used as an example. The process proposed is based on the observation that the locus of post-phase transformation and post-peak stress ratio instability points obtained from triaxial compression tests under the same strain coupling ratio represents a single curve in $$e-p'$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>-</mml:mo> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:math> space. The distance of this curve from the critical state is dependent on the strain coupling ratio and can be quantified within the context of double surface plasticity constitutive models through a modified state parameter function. Going further, this paper shows how the coupled strain experiments used to derive the critical state line can also serve for the calibration of additional double surface plasticity model parameters, with the final calibration shown to adequately capture triaxial compression tests under both undrained and coupled strain conditions.