A Double Hyperbolic Model

Abstract eng:
A new stress-strain model, named "double hyperbolic model (DHP model)" is proposed. This model is composed of two hyperbolic models. The first hyperbolic model is used at strains less than the reference strain or strains at stiffness degradation ratio is 0.5 in which the reference strain is used as a model parameter. The second hyperbolic model is used at strains larger than the reference strain, in which shear strength is used as a model parameter. Two hyperbolic models are connected at the reference strain so that the slope is continuous. It uses only two parameters and can simulate behavior in wide range of strains from very small to large strains. Accuracy and applicability of the model is examined by using about 500 cyclic shear deformation characteristics test results. Conventional models, the hyperbolic model and the Ramberg-Osgood model, are also examined by the same method. It is shown that both the hyperbolic and the Ramberg-Osgood models can simulate stress-strain behavior well up to reference strain or strain less than 0.1 %. However, the hyperbolic model underestimate shear stress at large strains and the Ramberg-Osgood model overestimates shear stress at large strains. Therefore, these conventional models may be good in the past situations where input earthquake motion is not very large, but they are not applicable at large strains that are required in the recent Japanese design specifications. On the other hand, the error by the DHP model is much smaller than two conventional models at large strains. Among three parameters, the reference strain, the maximum damping ratio, and the shear strength, empirical equations are already shown by the authors for the first two parameters. Then statistical approach is made to get an empirical equations for the last parameter, shear strength of the model, is examined. At first it is shown that there is no good correration between reference strain and shear strength as a function with respect to corrected SPT N-value, plasticity index, fines content and average grain size, which indicates that small strain behavior and large strain behavior is independent. Then dependency of shear strength ratio (the ration of shear strength to the initial shear modulus) on these parameters are examined. It is found that shear strength ratio increases as the fines contents or the plasticity index increases of average diameter decreases. This indicates that clayey soil shows larger shear stress at large strains compared with the stress at small strains. Finally, a discussion is made on the shear strength to be used for seismic response analysis of ground and it is encouraged tor future research on this topic.

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