A few months ago, I was involved in a very interesting and challenging project in Bay Area, California. A portion of this project was to evaluate seismic performance of an existing wharf structure located at the project site. The subsurface soil consisted of loose silty sand fill underlain by up to 25ft deep soft young bay mud (very soft clay), and the young bay mud was underlain by loose sand with high potential for liquefaction. Due to the existing free-face at the water side and the underlying liquefiable soils, there was a significant lateral spreading.

We used PLAXIS 2D finite element program in order to evaluate the performance of the wharf  subjected to lateral spreading forces. We used the built-in constitutive models; UBCSand and HSSmall for the simulation of liquefiable soil and young bay mud, respectively. In this post, I want to share with you some details of the simulation as well as challenges and limitations of modeling:

Soil failure at model lateral boundaries: I used free-field boundary condition as available in PLAXIS 2D. Checking the outputs of the analyses, I realized that in all analyses the soil at the boundaries failed and showed up to 24 inches of lateral deformation. This happened because of the concentration of large stresses developed by the free-field boundary elements, and since the soil elements (soft clay and liquefied sand) did not have sufficient strength, they considerably deformed under these stresses. In order to minimize the effects of boundaries, I did two things:

– I made the model as large as possible in the horizontal direction to make the boundaries sufficiently far from the region of interest, i.e., location of wharf.

– I used 10 feet wide linear elastic material at the boundaries on either sides. The stiffness of the each elastic layer was the same as the corresponding layer at the region of interest. I also assigned large Rayleigh damping (about 10% damping ratio) to help out in absorbing earthquake motions.

I still had signs of soil failure at the boundaries but the level of deformations was considerably less than before.

Unexpected lateral deformations in the free-field (level ground): During analyzing the outputs, I noticed that soil lateral deformations do not decrease with increasing distance from the free face. To better investigate this issue, I performed a separate site response analysis on a column of soil with the same layers and soil properties. Interestingly, I got significant lateral deformation implying that a level ground without presence of any free-face would deform laterally. It was noticed that soil underwent up to 14% shear strains when first major motion pulse hit the layer. After reaching the 14% shear strain level, the strains remain in the same range and do not return to the original state since soil has reached its plastic state. This made sense considering the fundamentals of plasticity and the fact that the material was highly plastic. However, to date lateral movement in infinitely level grounds has not been reported in the past post-earthquake field investigations. The computed deformations initially seemed to be unrealistic. However, this discrepancy in the results of PLAXIS model was due to the fact that in the model the soft clay (YBM) was assumed to be laterally continuous with a constant thickness. In reality this layer could be discontinuous with varying thickness across the site. This has been referred to as “spatial variability” in the literature. Prof. Ross Boulnager has recently done valuable studies on effects of spatial variability on lateral spread analysis. Below you can watch one of his presentations on this topic:

Based on the above, we eventually decided to first make sure that all available site investigations showed the presence of soft clay and secondly verified that the thickness and strength of the soft clay was roughly constant throughout the site. This way we gained sufficient level of confidence in validity of the computed free field lateral deformations and reported them in our design package.

Direction of input ground motion: Direction of input motion (+X or -X) appeared to have a considerable effect on the magnitude of slope deformations. The deformations were larger when high amplitude pulses were in the same direction of slope. Therefore, if you selected a suite of five ground motions for analyses, you must run a total of ten dynamic analyses (five in dir. +X and five in dir. -X).