A central aspect of performance-based earthquake engineering (PBEE) involves simulating the performance of facilities (broadly defined to include the foundations, soil, and nonstructural components) during and after an earthquake to assess impacts in terms of direct loss, functional loss, and casualty loss. The current software for simulating the nonlinear behavior of soils and structures is inadequate, with incomplete or outdated models, problematic solution methods, and an inflexible software architecture that inhibits innovative use of modern information technology and high-performance computing. To address this shortcoming, PEER has embarked on a multiyear effort to develop the Open System for Earthquake Engineering Simulation, or OpenSees.

OpenSees is an advanced performance simulation software framework for structural and geotechnical facilities. The software is designed to integrate the implementations of models for structural behavior, soil and foundation behavior, and damage measures. Unlike traditional “codes,” OpenSees is designed to be implemented in a modular, object-oriented manner with a clearly defined application program interface (API). The modules for modeling, solution, equation solving, databases, and visualization are independent, which allows great flexibility in combining modules to solve classes of simulation problems.

One of the best features of OpenSees is its suitability to support a multidisciplinary approach to PBEE simulation problems. The modular design allows researchers from different disciplines to combine their software implementations. As one example, OpenSees is linking new models in structural and soil behavior for effecting a complete soil-foundation-structure interaction analysis. As another, parallel and distributed equation solvers developed by computer scientists and mathematicians are integrated into the framework for the simulation of very large models. The framework has been combined with advanced ground motion simulation software to investigate the earthquake behavior of structures distributed through an urban region. Researchers are developing reliability modules using the framework. In another example, other researchers are using OpenSees to develop computational reliability modules for performance-based earthquake engineering.

Fig. 1. Calculated results compared with experimental results for a reinforced concrete column

The OpenSees framework will allow combining computational simulation with physical testing. A component being tested on a shaking table or reaction wall facility is essentially a physical element in a simulation model subjected to simulated boundary conditions. Because these types of interfaces are supported by OpenSees, the framework can serve as a basis for hybrid control of physical experiments. This is an area of particular interest for PEER as it envisions its role in the NSF NEES program (http://www.nsf.eng.gov/nees/).

In addition to its furtherance of PBEE, OpenSees is an important educational tool. Students are excited about working with modern software. When learning OpenSees, its combination of sophistication and accessibility motivates students to learn more about computer science and advanced applications. The software is “open source,” meaning that all parts of the code are available for users to see, check, track changes, and make contributions to. The website at http://opensees.berkeley.edu not only provides a download center, but also supports a revision control system, a method for submitting contributions, and a bulletin board for communication. This is the first instance of an open-source, community code in earthquake engineering.

Structural Modeling

The OpenSees framework is a valuable complement to the significant progress made in developing a family of models for beam-column elements for reinforced concrete members, including a library of constitutive models for concrete and steel. A recent extension is the inclusion of large-displacement geometry, based on the co-rotational formulation, for the accurate representation of P-D effects (Filip Filippou, UC Berkeley). Another approach based on generalized plastic hinge models is nearing completion and shows promising results (Gregory Deierlein, Stanford University). The models have been verified by experimental data and other solutions, when available. Figure 1 shows computed results by Filippou using a fiber model, compared with experimental data from Laura Lowes (University of Washington) and Jack Moehle (UC Berkeley).

Structural models have been developed with a general representation of shear behavior in reinforced concrete. An accurate assessment of reinforced concrete building damage must include shear and shear-flexure modes of behavior in order to capture nonductile failure modes that can occur and to track the degradation of shear strength and stiffness during an earthquake. Shear-flexure interaction is represented in the models, and calibration of the models is under way in a joint effort by Filippou and Gregory Fenves (UC Berkeley) on the modeling side and by Moehle on the experimental and behavior side. A new model of beam-column joints (Lowes) represents the effects of joint shear, bond slip, and yield penetration.

For computation, OpenSees incorporates variable time-stepping pushover analysis procedures that increase the robustness of the solutions. Armen Der Kiureghian (UC Berkeley) and Joel Conte (UCLA) have introduced reliability-based methods, using first-order and second-order reliability analyses on structures. An initial implementation of parameterizations for models and sensitivity calculations gives not only the response for a ground motion but also the first-order sensitivity to design parameters.

For performance evaluation, OpenSees can be used with a new database for response results to evaluate damage parameters and visualization (Kincho Law, Stanford University). Additionally, a higher-level scripting language and graphical-user interface have been completed for users to create building models quickly (George Turkiyyah, University of Washington).

Geotechnical Modeling

A current emphasis in PEER is the addition of geotechnical capabilities to OpenSees. Ahmed Elgamal (UC San Diego) has implemented two-dimensional soil plasticity models that have been calibrated with experimental data developed by Juan Pestana, Raymond Seed, and Ann Marie Kammerer at UC Berkeley. Boris Jeremic (UC Davis) has implemented a three-dimensional solid element into OpenSees that enables fully three-dimensional modeling of soil-structure systems. Pestana has contributed to the modeling of deep foundations through refinement of material models and development of simplified one-dimensional elements describing the complex soil-pile response interface. The various models have been implemented in a project by Frieder Seible and Elgamal (UC San Diego) and Joel Conte (UCLA) that models an existing bridge site. Figure 2 shows the computed permanent soil deformations (amplified) for the bridge under uniform base excitation. Further modeling by Jeremic includes a three-dimensional model of the soil-foundation system.

Fig. 2. Computed permanent soil deformations under existing bridge

Many dynamic response problems involve waves propagating in semi-infinite domains, which is especially complicated if semi-discretization techniques are used to analyze the soil domain. Pedro Arduino (University of Washington) has implemented a generalized viscous boundary condition and specification of input motion.

PEER/CMU/MSU Collaboration

The most ambitious use of the OpenSees framework is perhaps PEER’s joint work with Carnegie Mellon University and the Engineering Research Center at Mississippi State. The goal of this NSF-sponsored project is to advance the science of simulating the seismic performance of entire urban regions. Jacobo Bielak at CMU is developing the ground motion simulation, including fault modeling and sedimentary basins; PEER is developing structural and soil-structure-foundation interaction (SSFI) models and simulation methods, and MSU-ERC is developing the middleware and visualization tools to link the models and computations in a web-based environment that can be used by stakeholders and decisionmakers. In the pilot project, OpenSees has been integrated with MSU-ERC’s visualization tools to show the spatial variation of damage in a region due to a point seismic source and a moving source. Figure 3 shows one set of results, specifically the spatial distribution of ductility demand for buildings in a 20 km x 20 km region subjected to a point-source. In this simple example buildings are modeled as an elasto-plastic single-degree-of-freedom system with elastic vibration period of 1 second and the strength is based on the mean spectrum for the region reduced by a factor of R=4. The results show the large spatial variation of the ductility demand for buildings in the region because of the variability of the ground motion. Results such as these are being used to provide detailed information on the spatial variability of building performance using different zonation and design procedures. The long-range goal is to provide realistic simulations of performance of the built infrastructure in urban regions with realistic models for the fault mechanisms, regional geological structures, site effects, and building and lifeline inventories.

Fig. 3. Distributions of maximum ductilities and orientations, Period =1 sec, R=4

Future Plans

With the models for soils, concrete structural components, and their interactions well under way, the next phase of OpenSees development will shift in two directions. The first is application of the models to several test bed structures; these are real facilities that will be modeled and studied in a collaboration between PEER researchers and its Business and Industry Partners. The testbed studies will examine the effectiveness of the new models and solution strategies, and will provide information on the impact of earthquakes on constructed facilities. The second new direction is to link computed performance parameters with losses. A primary objective of performance-based earthquake engineering is to provide a probabilistic statement of the likely performance of a facility in terms of losses, functionality, and casualties. The modular structure of OpenSees will facilitate the development of this new capability in the next development phase.