Research On The Constitutive Model Of Saturated Sand Besed On Complex Undrained Cyclic Tests

The stress-strain characteristics of sand under the condition of principal stress axes rotation are the contemporarily hot and difficult research subject of geotechnical engineering, which is of relatively high theoretical and engineering values. Although research on the constitutive models considering complex stress conditions has attracted much attention, it is acknowledged that the problem has not been well solved. In this paper, based on an in-depth study of experimental result analysis, assumptions and computations of a constitutive model, etc., some achievements are obtained as follows:(1) Based on the tests carried out by Wang (2012) on the dynamic behaviors of saturated sand under a series of complex stress paths, the deformation of Fujian Standard Medium sand under four.different stress paths (dynamic triaxial, dynamic torsional shear, circular and ellipse paths) were selected to be analyzed. The main rule is that the cumulative compressive deformation of the sample under dynamic triaxial loading tended to be uniformly distributed in both the radial and tangential directions, while the tensile deformation increased continuously in the axial direction. Under dynamic torsional shear loading, the sample was stretched uniformly in the plane of the torsional shear stress and compressed continuously in the radial direction perpendicular to the plane. The shapes of the deviatoric stress versus deviatoric strain curves were relatively consistent and showed insignificant strain hysteresis (the stress and strain reached the peak almost simultaneously); the curves of torsional shear stress versus torsional shear strain had the same regulations. When the effective spherical stress was less than a particular value, the residual pore pressure in the sample accumulated more rapidly, and the deviatoric strain developed obviously faster. This critical value of effective spherical stress was approximated as20kPa.(2) The regulation of principal strain increment direction in the principal stress rotation plane was analyzed thoroughly, which could be concluded that if the non-coaxial angle was denoted as the angle between the principal strain increment direction and the principal stress direction, the non-coaxial angle kept decreasing with the cycles. At the peak of each stress components (i.e, the peak point of the stress path), the stain increment direction was essentially tangent to the stress path, i.e-, the strain increment direction was identical with the stress increment direction. Before liquefaction, the stain increment direction and the stress increment direction were in the same quadrant for most of the cycles, and the non-coaxial angle was able to reduce to zero only for a very small range. Based on the changing law of the non-coaxial angle, the notion of strain increment activity range was proposed in this paper, and on this basis a simplified calculation model of non-coaxial angle was established.(3) A brief introduction was given to the critical state two-surface plasticity model, and this model was optimized. The applicability of the modified model to the sand under undrained cyclic loading was analyzed, and a deformation compatibility iterative computation method was proposed to apply the modified model to undrained loading conditions. The primary parameters of the modified model was determined from the static loading tests by Li (2014). The modified model was used to predict the deformation of sand under static drained triaxial compression tests, cyclic undrained triaxial tests, respectively, which showed the applicability and reliability of the model.(4) Based on the optimized critical state two-surface plasticity model, a new module that took account of the principal stress rotation was added. The optimized model was applied to calculate the plastic deformation caused by the cyclic normal stress, and then the additional deformation induced by the cyclic torsional shear stress was incorporated. The additional deformation induced by the cyclic torsional shear stress was calculated in the light of generalized plasticity theory, and the strength, flow direction and plastic modulus were obtained directly from the experiment results. The additional deformation is divided into the deviatoric and the volumetric strains. The proportional relation between the two used the formula proposed by Yang for reference, while the additional deviatoric strain was obtained by best fitting the hollow cylinder test results. The optimized model was used to predict the deformation trends of sand under different stress paths, and agreed well with the experimental results.