*(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 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.

**Publications from this Research Project:**

**Yniesta, S.**, Brandenberg, S.J., and Shafiee A. “One-dimensional Non-linear Model for Ground Response Analysis” *Soil Dynamics and Earthquake Engineering* (under review)

**Yniesta, S.**, and Brandenberg, S.J. “Unloading Reloading Rule for a One-dimensional Non-linear Model for Site Response Analysis“ *Proceedings*, 6th International Conference on Earthquake Geotechnical Engineering (6ICEGE), Christchurch, New Zealand, November 1-4, 2015

**References:**

Hashash Y. M. A., Phillips C., and Groholski D. R. (2010) “Recent advances in non-linear site response analysis.” *Fifth International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego 2010*.

**Sponsors:**

Funding was provided by the George E. Brown Network for Earthquake Engineering Simulation through contract numbers 1208170. This award is part of the National Earthquake Hazards Reduction Program (NEHRP).

**Principal Investigator:**

Scott Brandenberg, UCLA, Ph.D., P.E.