Ground motion duration

Robust and efficient nonlinear structural analysis

Response history analysis validation

Amplitude, frequency content, and duration are widely recognized as the key characteristics of earthquake ground motion that influence structural response. Yet, in current structural design and assessment practice, ground motions are often explicitly characterized by just their response spectra—which quantify their amplitude and frequency content—while duration is relegated to implicit, qualitative consideration. This study evaluates the need to explicitly consider duration in structural design and assessment, in addition to response spectra.

A procedure based on the generalized conditional intensity measure (GCIM) framework is developed to characterize the seismic hazard at a site in terms of the durations of the anticipated ground motions.
The influence of duration on structural collapse risk is quantified by numerically simulating the dynamic response of structures under short and long duration ground motions, while controlling for the effect of response spectral shape.
Long duration ground motions recorded from recent large magnitude earthquakes, like 2010 Maule (Chile, M_{W} 8.8) and 2011 Tohoku (Japan, M_{W} 9.0), are used in the analyses.
Realistic, deteriorating nonlinear structural models are employed to adequately capture the effect of duration.
Strategies are then proposed to incorporate the observed effect of duration in the (i) multiple stripe analysis (FEMA P-58); (ii) incremental dynamic analysis (FEMA P-58, FEMA P695); (iii) equivalent lateral force (ASCE 7-16); and (iv) nonlinear response history analysis (ASCE 7-16) procedures.

Chandramohan R, Baker JW, and Deierlein GG (2017). “Physical mechanisms underlying the influence of ground motion duration on structural collapse capacity”. *16th World Conference on Earthquake Engineering*, Santiago, Chile.

Chandramohan R, Baker JW, and Deierlein GG (2016). “Impact of hazard-consistent ground motion duration in structural collapse risk assessment”. *Earthquake Engineering & Structural Dynamics* **45**(8), pp. 1357–1379. doi: 10.1002/eqe.2711.

Chandramohan R, Baker JW, and Deierlein GG (2016). “Quantifying the influence of ground motion duration on structural collapse capacity using spectrally equivalent records”. *Earthquake Spectra* **32**(2), pp. 927-950. doi: 10.1193/122813EQS298MR2.

Chandramohan R (2016). “Duration of earthquake ground motion: Influence on structural collapse risk and integration in design and assessment practice_Duration_thesis.pdf)”. PhD Thesis. Stanford University, Stanford, CA, USA.

The explicit central difference numerical time integration scheme is demonstrated to be a robust and efficient alternative to commonly used implicit schemes like the Newmark average acceleration scheme for nonlinear structural response simulation. Numerical non-convergence issues, which are frequently encountered using the average acceleration scheme, introduce conservative biases in the estimated structural capacity and hamper the efficiency of analysis. They are shown to be responsible for the underestimation of the median collapse capacity of a nine-story steel moment frame building by 10%. The central difference scheme, on the other hand, is non-iterative nature, and thereby immune to numerical non-convergence. Despite requiring shorter analysis time steps, the time taken to conduct an incremental dynamic analysis using the central difference scheme is 73% lower than using the average acceleration scheme. The efficiency of the central difference scheme can be further improved by using a constant damping matrix, which permits the dynamic tangent matrix to be factorized only once over the entire analysis.

Efficient parallel algorithms are developed to conduct multiple stripe analysis (MSA) and incremental dynamic analysis (IDA) on multi-core computers and distributed parallel clusters, to facilitate the adoption of these computationally intensive analysis procedures in traditional design and assessment practice. The algorithms employ dynamic load balancing schemes using a master-slave approach, which is demonstrated to significantly outperform their corresponding naïve parallel analogues that do not employ any load balancing, when using more than around 5 processors. OpenSees scripts implementing these parallel algorithms are available at the following git repository: bitbucket.org/reaganc/msa_ida_parallel.

Chandramohan R, Baker JW, and Deierlein GG (2017). “Robust and efficient nonlinear structural analysis using the central difference time integration scheme”. *1st European Conference on OpenSees*, Porto, Portugal.

Chandramohan R (2016). “Duration of earthquake ground motion: Influence on structural collapse risk and integration in design and assessment practice”. PhD Thesis. Stanford University, Stanford, CA, USA.

Response history analysis of structural and geotechnical systems has become increasingly prevalent in earthquake engineering research and practice. Proportionately little attention has, however, been paid to the verification and validation of commonly employed modelling techniques and numerical solution procedures. Hence, we are presently unable to provide quantitative estimates of the accuracy and precision of our simulation results. Improving confidence in the predictive capabilities of response history analysis procedures through a systematic validation exercise requires concerted efforts in the following four key thrust areas:

- recording seismic response data in the laboratory and the field;
- collecting and curating observational datasets;
- developing an analysis validation methodology; and
- performing validation for different problem types.

Chandramohan R, Ma Q, Wotherspoon LM, Bradley BA, Nayyerloo M, Uma SR, and Stephens MT (2017). “Response of instrumented buildings under the 2016 Kaikoura earthquake”. *Bulletin of the New Zealand Society for Earthquake Engineering* **50**(2), pp. 237–252.