3D Constitutive Model for Site Response Analysis

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

Dynamic curves are typically not used in 2D or 3D models because their inclusion in a plasticity framework is complicated due to their dependence on confining pressure, which can change during earthquake loading (e.g. when excess pore pressure develops under undrained loading). Hence, the damping behavior is not an input of current 3D constitutive models.

In order to facilitate the inclusion of dynamic curves in constitutive models, a new concept was created that plots modulus reduction and damping curves against stress ratio instead of shear strain. This results in pressure-independent modulus reduction and damping curves for three empirical relationships commonly-used to derive modulus reduction and damping curves. This finding is useful for implementation in one-dimensional effective stress ground response analysis codes for undrained loading conditions, and in advanced plasticity models.

The unloading-reloading rules derived for the 1D case (see here) are extended and included in a 3D constitutive model that uses modulus reduction and damping curves that are plotted against stress ratio by using the aforementioned concept. The formulation of the model allows to match dynamic properties (i.e., modulus reduction and damping curves), in 1D and 2D site response. At large strains the strength is controlled by a bounding surface algorithm following the formulation from Dafalias and Manzari (2004). The volumetric response is controlled by a dilation surface that introduces plastic volumetric strains based on deviatoric plastic strains. Most of the input parameters are well-known engineering properties easily measured in laboratory tests. Default values are defined for the input parameters that are not easily measured. The model is implemented in FLAC.

Publications from this Research Project:

Yniesta, S., Brandenberg, S.J., “A 3D Constitutive Model for Dynamic Applications” International Journal of Geomechanics (In Preparation)

Yniesta, S., Brandenberg, S.J., “Stress-Ratio-Based Interpretation of Modulus Reduction and Damping CurvesJournal of Geotechnical and Geoenvironmental Engineering, 10.1061/(ASCE)GT.1943-5606.0001585 , 06016021.


Dafalias YF, Manzari MT. (2004) “Simple plasticity sand model accounting for fabric change effects.” Journal of Engineering Mechanics, 130(6), 622–634.


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.