1. Project Goals/Objectives:

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 others primarily for performing numerical analysis using OpenSees.

Although the focus has been on shearwalls founded on strip footings, we are attempting to produce results more generally applicable to other types of foundations and structural configurations.

2. Role of this project in supporting PEER’s mission (vision):

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.

3. Methodology Employed:

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 sub-grade 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.

4. Brief Description of past year’s accomplishments (Year 6) & more detail on expected Year 7 accomplishments:

During the Year 6 research program, we worked closely with UCD and USC researchers using a broad range of shallow foundation experimental data sets to evaluate a Winkler-based modeling approach for capturing their cyclic rocking response. Experimental datasets used included those by Rosebrook and Kutter (2001), Gajan et al. (2002), ELSA (one-g) data, and New Zealand (one-g) (Bartlett and Weissing). Parameters were evaluated in terms of their ability to capture the moment-rotation, rotation-settlement response, lateral force-sliding response and energy dissipation. We are now using the mesh generator approach used in year 6 for the design of a model frame-shearwall structure, for testing on the UCD centrifuge.

During year 7, we have focused on two things: (i) the design and analyses of the model frame-shearwall structure and (ii) expanding the shallow foundation modeling approach using the 3D brick elastic-plastic template elements in OpenSees. The model frame-shearwall system is composed of a rigid shearwall resting on a shallow strip footing and attached to two bays of flexible frames, with yielding members at their ends (with one end connected to the shearwall). The intent is to model a structure, where nonlinearity at both the foundation base, and through hinging at the beam-column joints is expected. A target prototype natural period of T~0.6 seconds (under flexible conditions) has been selected based on consultation with practicing engineers (Moore & others) and the project team (UCD and USC). The UCI team is conducting the design of the model and will assist during the testing at UCD. A diagram of the planned prototype structure is shown in Figure 1.

Figure 1. Plan, elevation, and section through prototype frame-shearwall structure being
designed for testing at UC Davis

To analyze the response of this structure, we have constructed a 2D model in OpenSees. A nonlinear Winkler mesh is generated below the strip footing and the isolated footings, to capture the nonlinear rocking, sliding, and vertical response of the foundations. The shearwall is modeled using elastic beam column elements aligned at the geometric center of the wall and connected with rigid links to receive the beam elements. Elastic beam column elements with hinges at their ends are used to model the beams, with a fiber sectional representation used to model the plastic behavior at the hinge regions. For the purposes of testing, forced disposable fuses will be used, with a fixed length of 10% of the overall beam length. In this fashion, the model frame-shearwall can be reused after testing.

5. Other Similar Work Being Conducted Within and Outside PEER and How This Project Differs:

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. In addition, UCD is developing a complementary macro-element model. Work conducted at USC involves the oversight and integration of work performed at UCD and UCI. Work performed at USC also includes interfacing with practicing engineers in the US and Europe involved in implementation of nonlinear SSI into seismic design guidelines or codes. There also useful related work on this topic being conducted in France, Italy, and England.

Our numerical studies on this topic will be unique in that most studies either include nonlinearity of soil elements, or nonlinearity of structural components of the system. Both the testing and numerical simulations incorporate these two contributions and study system response.

6. Plans for Year 8 if project is expected to be continued:

7. Describe any actual instances where you are aware your results have been used in industry:

Although we have consulted frequently with our project partner, Mark Moore, we are unaware of instances in practice were results are directly applied.

8. Expected Milestones & Deliverables:

We anticipate finalizing the design and analysis of the model frame-shearwall structure in April 2004, so we can be constructing this model in spring. This will allow us to work with these test results over summer. We can then produce comparative experimental-numerical simulation results, considering the designed model with coupled nonlinear structure and nonlinear soil behavior. Other tests will be conducted in the spring centrifuge series, and we will also prepare a ‘blind prediction’ of one of the model footings in this series, using the Winkler-approach.

In parallel with the 2D modeling, we will be exploring the use of 3D models of shallow foundations using the solid E-P template elements by Jeremic et al. Elastic models, using the 8-noded brick elements available in OpenSees have already been constructed and evaluated against well known point and strip solutions; we now need to extend these using the plastic material models and considering loading configurations from previous centrifuge tests.

Regarding reporting of project results, so far we have completed: one synopsis paper for PEER, one status report, one MS thesis (Harden 2003), and a joint paper with UCD/USC colleagues (SDEE 2004). In the spring, we plan to convert the thesis by Harden to a PEER report for broader dissemination. In the summer, we look forward to working with UCD, USC and UCLA organizing a joint workshop to present research results to academics and practicing engineers.