The goals of PEER researchers (at UCD, USC, and UCI) studying the nonlinear behavior of shallow building foundations are to develop and test procedures to account for this nonlinearity in performance-based design. So far, it is established that soil yielding beneath foundations can be a very effective energy dissipation mechanism. However, foundation yielding may lead to excessive permanent deformations. The primary goal of the research at UCD (Kutter) is to produce archived test data at prototype stress levels. Collaborating researchers at UCI (Hutchinson) and USC (Martin) are using the experimental data provided by UCD and by other sources primarily for performing numerical analysis using OpenSees.

This project supports the PEER strategic plan by providing performance data, validation tests, and nonlinear models to advance the simulation capabilities of OpenSees. In addition, understanding the behavior of shallow foundations is critical to development of performance based design procedures for buildings.

Our approach has been to use a Beam-on-Nonlinear-Winkler (BNWF) framework (e.g. using spring, dashpot, gap elements) for modeling the nonlinear soil response. This allows us to capture the salient features of the rocking foundation, including distributed soil nonlinearity and uplifting of the foundation.

While generally, one may anticipate that a more rigorous model representing a physical system would lead to better results of the systems response, the uncertainty in determining the input parameters of the more rigorous model may be quite complex, leading to greater uncertainty in model response. Therefore, the intent of subgrade type modeling has always been to strike a balance between theoretically more rigorous solutions and practicality and ease of use in routine geotechnical engineering practice. Therefore, the approach of using the BNWF model is directly applicable to many practical applications. Complementary numerical modeling is being conducted at UC Davis using a plasticity based ‘macro-element’ representation.

We previously completed the development and implementation of the Template Elastic Plastic Framework. This framework is now being used in assessing the performance of deep foundations. In particular a study is underway into the performance of single piles in layered soils and the interaction effects for pile groups. Initial part of the study is conducted for static pushover loads while we are currently building and analyzing models that will be dynamically loaded. One of the important findings of the single pile study (see Figure 1) is that the effects of soft layers on stiff layers are felt further away from the interface than previously thought. In addition to that an initial study of interaction effects for piles in a pile group was conducted. The different load factors taken by the piles in a pile group are presented in Figure 2. One of important findings is that in addition to the in-plane bending, piles will undergo significant out-of loading plane bending, depending on the type of soil around them. In addition to that, the unequal distribution of loads is far more significant than previously thought and that also is a function of the type of soil surrounding the pile group. A number of additional studies is under way.

Within PEER, this work is closely coordinated with USC (Martin) and UCD (Kutter). Work conducted at UCD includes providing experimental data and guidance for use of the data in analytical modeling. While work conducted at USC entails the oversight and integration of work performed at UCD and UCI. This includes sequencing and prioritizing model tests and analysis directions and implementing analysis and experimental data into the framework of a performance based engineering design approach. Work performed by USC also includes interfacing with practicing engineers in the US and Europe involved in implementation of nonlinear SSI into seismic design guidelines or codes. In addition, input and expertise on foundation design issues will be provided for the Van Nuys building test bed including potential retrofit solutions using shear walls and shallow foundations.

There is now useful related work being conducted in France, Italy, and England. We have developed contacts with these researchers and as well are using experimental results from some of these studies in our numerical modeling. Our numerical studies will be unique in that most studies either include nonlinearity of soil elements, or nonlinearity of structural components of the system. We have begun to expand our study to combine these two contributions and studying response. Results of these numerical studies also provide extensive evaluation of modeling approaches against the available set of experimental data provided by both centrifuge (>20g) and other (~1g) tests on shallow foundations.

So far, we find that reasonable comparison between the nonlinear Winkler-based approach and the experimental data selected can be obtained, provided proper selection of properties (stiffness, strength, etc.) is considered. From our recent workshop, our primary recommendation was to work towards providing general guidance for parameter selection for the BNWF approach for modeling shallow foundations. We are now reviewing the selection of parameters for these analyses results and studying the sensitivity of response in terms of M-q and q-s results and comparing with theoretical solutions for stiffness and strength selection. Providing general recommendations for parameter selection will also require us to isolate mechanisms that contribute to response. Recent centrifuge data can help us with this. For example, data by Gajan and Kutter (SGG02) will help us isolate the sliding response of the shallow foundation, which we find can have an important influence on the overall behavior.

We also recommend that the analysis and physical modeling be extended to combine nonlinear soil and nonlinear structure behavior simultaneously. We presented preliminary results of this idea using a single and two-story reinforced concrete moment frame supported on a Winkler-foundation and received positive feedback from practicing engineers. This has not been done before and it could have significant implications on PBEE. We plan to work with engineers Mark Moore and Craig Comartin on a parameter study for this modeling.

We are currently focused on comparing our selection of BNWF parameters for the various analyses results with theoretical parameter determination. We hope to provide guidance in the selection of these parameters by Summer 2003. This will allow us to prepare a ‘blind prediction’ of the upcoming centrifuge experiments planned by UC Davis (by September 2003).

By the end of year 6 we will work with USC and UCD researchers in converting our workshop status report to a final report that covers work completed during year 5 and 6.

So far we have completed: one synopsis paper for PEER, one workshop and one status report. One MS thesis will be complete Summer 2003 and a final report at the end of year 6. Our work is using the 20-g centrifuge experimental data of UCD and contributing to the development of OpenSees.