Strain Softening Soil Model

UCSDSoftening material is a 3D incremental plasticity constitutive model for simulating the strain softening behavior of soil materials (Qiu and Elgamal 2020)*. The constitutive model extends the UCSDCLAY formulation with a new strain softening logic as shown below. Incorporation of strain softening is an important consideration for a wide range of scenarios involving sensitive clays, cemented, over-consolidated, very dense, or frozen soils among others.
Strain Softening Model

*Qiu, Z. and Elgamal, A. (2020). "Three-Dimensional Modeling of Strain-Softening Soil Response for Seismic-Loading Applications." Journal of Geotechnical and Geoenvironmental Engineering, 146(7), p.04020053.

Download & Install OpenSees

Please download below executable OpenSees.exe and ActiveTcl if you want to test the following examples or run your own numerical models with the UCSDSoftening material

Download OpenSees.exe (16 MB, updated 5/30/2020)
Download ActiveTcl-8.5.exe (28 MB, updated 5/30/2020)

Example: 1D Site Response Analysis of Inclined Sloping Ground

A mildly inclined infinite slope with the calibrated quick Tiller clay model is employed to illustrate the salient soil strain-softening response characteristics. Representative shear behavior of the employed UCSDSoftening is shown below, along with that of the corresponding UCSDCLAY model for reference. As such, a 1D free-field ground response model is represented by ten brick elements at a 4 degrees inclination, in order to provide a static driving shear stress due to gravity. The displacement degrees of freedom at any given depth are tied together both horizontally and vertically (to reproduce the desired 1D site response representation). A base motion with a relatively high peak acceleration was employed, so as to trigger strain softening and induce significant accumulation of lateral ground deformation. For that purpose, this motion was simply taken as that of the 1994 Northridge earthquake Rinaldi Receiving Station record (Component S48W), scaled down to a peak amplitude of 0.4 g.

Strain Softening Model


Below figure shows the computed shear stress-strain at the depths of 5 and 10 m, respectively. Due to the large fling-motion pulse in the base input acceleration and the static driving shear stress (4 degrees inclination), a significant level of accumulated permanent shear strain was incurred. In this figure, the UCSDSoftening response clearly shows the strain softening effect, with shear stress reaching its residual value. As expected, the UCSDCLAY response is noticeably different, with overall lower levels of permanent shear strain.
Strain Softening Model

Please click here to download this 1D site response analysis exmaple

Potential application of the UCSDSoftening material

In addition to post-peak stress softening, cyclic degradation (Qiu and Elgamal 2020) exhibited by soils due to mechanisms such as pore pressure generation for instance can be incorporated into the developed strain softening plasticity constitutive model. As such, degradation can be defined based on mechanisms such as accumulated energy or accumulated plastic shear strain. In this model, degradation of shear stiffness and strength is defined based on the accumulated shear strain for simplicity. Other degradation logics (e.g., Elgamal 1991) may be implemented depending on the nature of the data at hand, and the intended scope of application (e.g., earthquake response versus low-strain repetitive cyclic loading).

Strain Softening Model

Please click here to download the cyclic degradation example

Elgamal, A.W. (1991). "Shear hysteretic elasto-plastic earthquake response of soil systems." Earthquake Engineering & Structural Dynamics, 20(4), 371-387.