Executive Summary:
Spatially varying ground motion (SVGM) refers to the differences in the phase and amplitude of ground motions recorded over an extended area. Phase and amplitude variability may affect the SVGMs to various degrees depending on the separation distance. Amplitude variability is contributed from the change in magnitude (scaling) and spectral shape of auto-spectral density (ASD). The recorded ground motions represent the characteristics of seismic excitation at one single point. Past studies have demonstrated that the SVGMs could have significant effect on the structural response of certain civil engineering structures. Coherency, which is generally used as a descriptor of the spatial variability, is defined as the normalized (with ASD) cross-spectral density (CSD) and lagged coherency is given by its absolute value. Several procedures are available to simulate the spatially varying ground motion using lagged coherency conditioned to a seed ground motion. Most of the existing procedures assume the spatially uniform ASD and use either CSD or the evolutionary cross-spectral density (ECSD) to simulate the spatially varying ground motion around a chosen reference station. These CSD / ECSD based procedures account only for the phase variability and hence, lead to a good prediction at short separation distance (for example, 0~20 m). Since these procedures do not account for the amplitude variability, the resulting SVGMs do not exhibit close resemblance with the recorded data, at moderate to large separation distances.
One way of investigating the extent of spatial variability in ASD is through its parameterisation. For this purpose, a multi-modal lognormal functional form is proposed and a close resemblance with the ASD from the recorded components is observed. Possible correlation of the parameters of the proposed ASD model against site characteristics is investigated based on selected ground motions from PEER database. An attempt has been made in synthetically predicting the ASD at a given site. ASD of the recorded components at LSST and SMART1 arrays is parameterised through the lognormal form and similarity of spectral shapes of ASD is assessed through the “spectral contrast angle” based on “distance correlation”. At short separation distances (for example, LSST array), spatial variability of ASD of horizontal motions is negligible while that for the vertical motion varies considerably. All three translational components exhibit considerable variability in ASD over the footprint of a large array (for example, SMART1 array) and hence, the assumption of spatially uniform ASD in simulating SVGMs is questionable.
Conditional simulation of SVGM requires a calibrated coherency model and a seed ground motion. For this purpose, a new coherency model is proposed accounting for the phase as well as amplitude variability of ASD and assessed that along with some of the other coherency models available in the literature against the data recorded over the footprint of LSST and SMART1 arrays. However, the scope of the coherency model was first restricted to the variation of lagged coherency against frequency for a particular separation distance (and not to study its variation along the separation distance). Numerical studies on the spatial variability of ASD did not show a monotonic decay against the separation distance. Attributing this to the contribution from random component, the same coherency model is then extended so as to account for the contribution of random component to ASD.
A new framework for conditional simulation of SVGM based on ASD is proposed. This ASD based framework simulates the SVGM through the calibrated coherency model (proposed) and mapping of the ASD over the footprint of an array. The proposed ASD based framework accounts for both the phase as well as amplitude variability and hence, exhibited good resemblance with the horizontal components recorded over LSST and SMART1 arrays. Hence, for conditionally simulating SVGM, use of the proposed ASD based framework is recommended over the CSD based framework. However, investigations specific to the recorded vertical components are limited in the literature and the proposed ASD based framework is further explored using the vertical components. Once again, a close resemblance between recorded vertical components and those from the proposed ASD based framework is noted.
Description of the ground motion input cannot be completed without specifying the rotational ground motion. Rotational motion is the spatial derivative of the associated translational motion and hence, rotational coherency model does not exist precluding the study of its spatial variability. However, if the rotational component can be expressed as a time derivative of an apparent translational component (ATC) with due scaling through apparent velocity, one may prove that the lagged coherency of rotational components computed by treating it as a mere time series is identical to that of its ATC. A semi-empirical procedure has been proposed to estimate ATC without the knowledge of rotational motion a priori. Time derivative of ATC has been assessed against the rotational components extracted using the single station procedure (SSP) reported by Basu et al. (2012). Both rocking and torsional components are found to be reasonably well described by the respective ATC. A novel window-based procedure has been proposed to estimate the required apparent velocities without the knowledge of rotational motion. Next, applicability of proposed ASD based framework for simulation of spatially varying rotational ground motion (SVRGM) is explored. SVRGM is simulated using the proposed framework through two approaches. In the first approach, spatially varying translational components simulated using the proposed framework are considered and SVRGM are extracted through the SSP by Basu et al. (2012). In the latter approach, SVRGM is directly simulated using the proposed framework on extracted rotational components. SVRGM from both the cases exhibit close resemblance with the extracted rotational components irrespective of separation distance unlike the CSD based framework. Therefore, proposed ASD based framework is recommended for conditional
simulation of spatially varying rotational ground motion.
Proposed ASD based framework is next extended to account for non-stationarity (in both intensity and frequency content) effects in the SVGM through the use of Hilbert transform. Nonstationary spatially varying ground motion is simulated through the mapping of both lagged coherency and evolutionary power spectral density over the spatial footprint.
As a closure, this thesis presents a novel framework for conditional simulation of six-component spatially varying ground motion (6C-SVGM) for seismic design of structures with spatially extended sub- and / or super- structures.
Publication out of this Project:
Publications:
- Rodda, G.K. and Basu, D. (2020). “A novel framework for conditional simulation of fully nonstationary spatially varying ground motion field.” Earthquake Engineering and Structural Dynamics.
- Rodda, G.K. and Basu, D. (2020). “Spatially correlated vertical ground motion for seismic design.” Engineering Structures, Elsevier. Vol. 206.
- Rodda, G.K. and Basu, D. (2019). “Parameterisation of Auto-Spectral Density of Earthquake Induced Strong Ground Motions.” Soil Dynamics and Earthquake Engineering, Elsevier. Vol. 118: 52–64.
- Rodda, G.K. and Basu, D. (2019) “On conditional simulation of spatially varying rotational ground motion” Journal of Earthquake Engineering, Taylor and Francis.
- Rodda, G.K. and Basu, D. (2018) “Spatial Variation and Conditional Simulation of Seismic Ground Motion.” Bulletin of Earthquake Engineering. Vol. 161(10): 4399–4426.
- Rodda, G.K. and Basu, D. (2018). “Coherency model for translational and rotational ground motions.” Bulletin of Earthquake Engineering, Springer, Volume 16, Issue 7, pp 2687–2710.
- Rodda, G.K. and Basu, D. (2018). “Apparent translational component for rotational ground motions.” Bulletin of Earthquake Engineering, Vol. 16(1): 67–89.
- Rodda, G.K. and Basu, D. (2017). “On extracting rotational components of ground motion using an empirical rotational window.” International Journal of Earthquake and Impact Engineering, Vol. 1 (3): 253-288.
Invited Papers/Abstracts in Published Conference Proceedings:
- Rodda, G. R. and Basu, D. (2015). “Development of a Window Based Approach for Simplified Estimation of Rotational Ground Motion”, 5th Tongji-UBC Symposium on Earthquake Engineering, May 4-8, 2015 Tongji University Shanghai, China.
Contributed (Non-Invited) Papers/Abstracts in Published Conference Proceedings:
- Rodda, G.K. and Basu, D. (2016). “Coherency model for dense seismic array.” Structural Engineering Convention, SERC, Chennai.
Published Book Chapters
- Rodda, G.K. and Basu, D. (2019). “Coherency model for dense seismic array.” Recent Advances in Structural Engineering, Volume 1, Springer, Select Proceedings of Structural Engineering Convention (SEC)-2016
