(This project was done as part of my doctoral work at UCLA)

1D ground response analysis typically include modulus reduction and damping curves as input parameters (Hashash et al. 2010), which represent the desired behavior of the soil. Nonlinear one dimensional ground response models generally present a compromise between fitting the backbone curve or the hysteretic damping curve. Fitting the damping curve depends on unloading and reloading rules. Most of the models use Masing rules or extended Masing to correct the overdamping at high strains resulting from using Masing rules. Frequency dependent Rayleigh damping is used to introduce damping at low strains. Existing models typically introduce a misfit of the input curves, resulting in an undesirable mismatch of the desired behavior (Hashash et al. 2010).

To solve this problem a one dimensional nonlinear stress-strain model called ARCS, capable of reproducing any user-input modulus reduction and damping curve was created. Unlike many previous nonlinear models, the proposed model does not utilize Masing’s rules, nor does it require a specific functional form for the backbone curve such as a hyperbola. Rather, the model utilizes a coordinate transformation technique in which one axis lies along the secant shear modulus line with the other axis in the orthogonal direction for a particular unload-reload cycle. Damping is easily controlled in the transformed coordinate space. An inverse transformation returns the desired stress for any increment of strain. The returned stress value is independent of the amplitude of the strain increment. Small-strain hysteretic damping is achieved using the proposed model, avoiding the need for supplemental damping. The model is shown to match the results of laboratory cyclic simple shear tests involving deliberately irregular stain histories. The model does not explicitly account for rate effects, cyclic degradation, or pore pressure generation. However, the equations can potentially be adapted in more advanced constitutive models to capture these effects.

The model was implemented in Deepsoil 6 as a user-defined model, and is fully compatible wih Deepsoil 7:

ARCS Model dll

The input parameters are the following three vectors composed of 15 elements each:

• Shear strain levels (g1 to g15), ordered from the lowest to the highest level, in percent,
• Modulus reduction (MR1 to MR15) at said shear strain levels,
• Damping (D1 to D15) at given shear strain levels, in percent.

Notes:

• The model automatically adds a value at zero shear strain internally, for which the modulus reduction is equal to 1, and the damping is equal to D1, i.e. the damping value at the lowest strain level specified.
• Although the model is able to achieve purely hysteretic damping at low strains by defining a minimum damping of 0, it is advised to use the frequency independent damping scheme of Deepsoil for the minimum damping to avoid unwanted numerical noise. To do so, specify the minimum damping, and subtract its value from the input damping curve, so that the hysteretic damping at low strain is nil.

To report a bug or give a suggestion, please email me.