ESTIMATION OF SEISMIC DEMAND IN POST-TENSIONED ROCKING WALLS
Prepared by Reza Kordani of ACH Consulting for the NZSEE Pacific Conference on Earthquake Engineering 2019 in conjunction with the Departments of Mechanical and Civil Engineering at the University of Canterbury.
Design and development of rocking structures is an advanced method to ensure the seismic resilience of structures by creating a non-linear elastic response. However, there are some issues that need to be addressed to enable designers to develop quick, robust designs of rocking structural systems that can provide hysteretic energy absorption in a repeatable manner.
Post-tensioning Tendons (PT) are often used in rocking systems to provide a conventional fixed base response under low levels of shaking, add inherent self-centring and prevent the structure from excessive drifts.
These systems dissipate earthquake response energy in a damage free manner and unlike ﬁxed-based conventional designs, can accommodate inelastic behaviour without suﬀering from excessive residual drift. However, disincentives exist for a wider use of rocking systems in industrial applications. There is a lack of practical design standards and guidelines accepted by building consent authorities. The simpliﬁed design guides must enable practicing engineers to estimate force and displacement demand in rocking systems without the need to full non-linear analysis.
A simplified Finite Element Model is developed to study the global dynamic behaviour of structural rocking walls of 4, 8, and 12 storey. The FE mesh and degrees of freedom for a 4 storey rocking wall are presented in the figure below. The rigid footing is located on top of non-linear elements that represent post-tensioning tendons and energy dissipaters.
Numerical analysis is performed to obtain the structural response of the 4, 8, and 12 storey rocking walls under the design level ground motion time histories. Where η is a ratio, indicating the amount of loss in the initial post-tensioning force.
The medium suite of earthquake records from the SAC project (Somerville, 1997) is selected to perform response simulations. The medium suite have probability of exceedance of 10% in 50 years and includes 20 ground motion records.
Two simplified methods are compared to the non-linear dynamic analysis results to estimate the displacement demand in rocking systems:
1) Direct Displacement Based Design (DDBD) procedure Priestley, Calvi, and Kowalsky (2007)
2) Steel Construction New Zealand (SCNZ) guideline Wiebe, Sidwell, and Gledhill
For the 4, 8 and 12 storey walls, the DDBD method provided a very good prediction of the median structural displacement. The SCNZ method underestimated the structural response of the 4 storey rocking wall and the method became conservative for taller walls.
Four analytical approximation methods are used to estimate the force demand of structural rocking walls 1) Steel Construction New Zealand (SCNZ) 2) Weighted Capacity Design (WCD) 3) Substitute structure (SS) 4) The Wiebe method.
It was concluded that the Wiebe and SS methods provided the best approximation compared to the median results. The robustness of these methods were independent to the structural height and strength reduction factor at the base.
The support of the University of Canterbury Quake Centre (UCQC) and ACH Consulting to the first author is gratefully acknowledged.