Source-linked AI summary
Seismic reliability assessment of classical columns subjected to near-fault ground motions
Ioannis Psycharis, Michalis Fragiadakis, Ioannis Stefanou
TL;DR
Quantifying the seismic reliability of multidrum classical columns is difficult because their three-dimensional dynamics are strongly nonlinear and highly sensitive to modelling and ground-motion characteristics. The paper combines performance-based assessment, synthetic near-fault motions, and discrete-element modelling, finding that moderate earthquakes have only a 10% probability of considerable rocking and significant residual drum dislocations.
Problem
Quantitative seismic reliability assessment of multidrum classical columns remains difficult because their three-dimensional dynamic response is strongly nonlinear and complex.
Method
The study combines performance-based earthquake engineering, Monte Carlo simulation, synthetic near-fault ground motions, and three-dimensional discrete-element modelling to generate fragility curves.
Results
Moderate earthquakes with PGA ~ 0.3 g and PGV ~ 40-50 cm/sec have only 10% probability of considerable rocking and residual drum dislocations exceeding 1% of diameter.
Takeaways & Limitations
The fragility analysis provides seismic reliability information to support restoration decisions for classical monuments.
Takeaways & Limitations
The reported results cannot be applied quantitatively to all columns because vulnerability analysis must be performed case by case.
Abstract
from arXiv · showhide
A methodology for the performance-based seismic risk assessment of classical columns is presented. Despite their apparent instability, classical columns are, in general, earthquake resistant, as proven from the fact that many classical monuments have survived many strong earthquakes over the centuries. Nevertheless, the quantitative assessment of their reliability and the understanding of their dynamic behavior are not easy, because of the fundamental nonlinear character and the sensitivity of their response. In this paper, a seismic risk assessment is performed for a multidrum column using Monte Carlo simulation with synthetic ground motions. The ground motions adopted contain a high- and low-frequency component, combining the stochastic method, and a simple analytical pulse model to simulate the directivity pulse contained in near source ground motions. The deterministic model for the numerical analysis of the system is three-dimensional and is based on the Discrete Element Method. Fragility curves are produced conditional on magnitude and distance from the fault and also on scalar intensity measures for two engineering demand parameters, one concerning the intensity of the response during the ground shaking and the other the residual deformation of the column. Three performance levels are assigned to each engineering demand parameter. Fragility analysis demonstrated some of the salient features of these spinal systems under near-fault seismic excitations, as for example, their decreased vulnerability for very strong earthquakes of magnitude 7 or larger. The analysis provides useful results regarding the seismic reliability of classical monuments and decision making during restoration process.
INTRODUCTION
Seismic reliability assessment is needed to support restoration decisions because classical columns exhibit nonlinear, parameter-sensitive responses and vulnerability involves both collapse and drum displacements. The paper proposes a record-to-record variability-aware methodology, illustrated using a typical Parthenon column rather than evaluating the Parthenon’s vulnerability.
- Background: Classical columns are generally earthquake resistant despite apparent instability, but many monuments have collapsed and their nonlinear response is highly sensitive to small parameter changes.Response and collapse depend strongly on structure size and excitation period; larger columns are more stable, while low-frequency earthquakes are more dangerous.
- Motivation: Seismic reliability assessment informs restoration by quantifying collapse risk and the expected maximum and residual drum displacements.These quantities help authorities determine necessary interventions and prioritize future work.
- Contribution: The paper presents a vulnerability assessment approach for a Parthenon Pronaos column that accounts for record-to-record variability using advanced modeling, numerical analysis, and performance-based earthquake engineering.Record-to-record variability, also termed aleatory uncertainty or randomness, can cause significant variability in seismic response.
- Scope and limitations: The Parthenon column serves only as a typical medium-size, commonly slender example, so the analysis does not evaluate Parthenon vulnerability or include damage.Case-specific assessment must consider the column’s geometry, existing damage, and seismotectonic environment.
NUMERICAL MODELLING OF MULTIDRUM COLUMNS
The model represents multidrum columns as strongly nonlinear three-dimensional systems of rigid drums undergoing sliding, rocking, and wobbling. A discrete-element formulation concentrates deformation at frictional, separable joints while using calibrated constitutive and damping assumptions.
- Dynamic behavior: Multidrum-column response is governed by independently or collectively translating and rotating drums, with continuously changing vibration modes caused by joint opening.The system’s spinal construction produces complex sliding, rocking, and wobbling behavior during seismic excitation.
- Numerical method: The study uses three-dimensional Discrete Element Method simulations with the Molecular Dynamics approach and 3DEC to model the nonlinear seismic response.DEM is presented as an efficient and validated method for dynamic analysis of masonry columns in classical monuments.
- Block and joint representation: Only rigid blocks are modeled, concentrating deformation at soft contacts where frictional sliding and complete separation can occur between drums.This approximation substantially reduces computing time while retaining the principal joint deformation mechanisms.
- Joint constitutive laws: Joint behavior follows a Coulomb-type failure criterion, whose stiffness substantially affects results and should be calibrated for specific materials using ambient-vibration measurements.The selected parameters produced good agreement for maximum top and residual drum displacements, while other materials require different stiffness values.
- Damping and connections: The model excludes artificial damping during intense rocking, applies damping afterward to dissipate free vibrations, and omits wooden dowels because their shear resistance is marginal.The dowels served mainly to center drums during erection rather than provide shear resistance.
FRAGILITY ASSESSMENT
The fragility assessment quantifies limit-state exceedance probabilities using EDPs conditioned on magnitude and distance or a scalar intensity measure. Monte Carlo sampling and collapse-aware processing support fragility surfaces and curves from nonlinear response simulations.
- FRAGILITY ASSESSMENT: Fragility is defined as the probability that an engineering demand parameter exceeds a specified limit-state threshold.EDPs include maximum or permanent deformation and drum dislocation.
- FRAGILITY ASSESSMENT: Monte Carlo simulation with Latin Hypercube Sampling evaluates fragility across magnitude–distance scenarios using nonlinear response-history analyses.The assessment conditions fragility on Mw and R, requiring many simulations for each pair.
- FRAGILITY ASSESSMENT: Assuming lognormally distributed seismic data, fragility is calculated from the mean and dispersion of the logarithms of non-collapsed EDPs.The formulation uses μ_lnEDP and β_lnEDP with the standard normal distribution and an EDP threshold.
- FRAGILITY ASSESSMENT: When simulations collapse, collapsed and non-collapsed data are separated and the conditional collapse probability is incorporated into the fragility calculation.This avoids using infinite or very large collapse EDPs to estimate μ_lnEDP and β_lnEDP.
- FRAGILITY ASSESSMENT: Fragility curves can instead condition exceedance probabilities on scalar intensity measures such as PGA, PGV, SA, or SV.A post-processing approach estimates probabilities within IM stripes after plotting scattered EDP–IM data.
GENERATION OF SYNTHETIC, HAZARD–CONSISTENT GROUND MOTIONS
The seismic reliability assessment uses synthetic near-field ground motions because natural records are too limited for the examined magnitude–distance ranges, especially on the stiff soil or rock typical of classical monuments. These motions combine high-frequency shaking, required to initiate and accurately simulate rocking/wobbling, with near-fault directivity pulses, while soil effects are neglected.
- Synthetic ground-motion selection: Synthetic near-field records were generated because natural motions are limited for the examined Mw–R pairs, particularly for the stiff soil conditions typical of monuments.Classical monuments were generally built on cliffs and founded on stiff soil or rock, motivating the use of representative synthetic motions.
- Ground-motion components: High-frequency content is necessary because rocking/wobbling is strongly nonlinear and begins only above a minimum peak ground acceleration.Long-period directivity pulses alone may not generate sufficiently intense shaking for accurate surrogate-motion simulation.
- Site conditions: Soil effects were neglected because most classical monuments stand on stiff soil or rock, although soft soil can significantly alter ground-motion characteristics.The directivity pulse itself is noted as generally unaffected by soil conditions.
Low frequency pulse
The low-frequency component was modeled as a stochastic near-fault velocity pulse calibrated to worldwide near-field motions. Pulse parameters were assigned by magnitude–distance scenario and sampled probabilistically to generate synthetic motion sets.
- Pulse model: Low-frequency motions used the Mavroeidis–Papageorgiou pulse model, whose parameters describe amplitude, frequency, phase, oscillatory character, and time shift.The model was calibrated using actual near-field ground motions from around the world.
- Scenario-dependent parameters: For each magnitude–distance scenario, pulse velocity amplitude and frequency were computed from empirical magnitude-based expressions, with magnitude capped at Msat = 7.0.For magnitudes above 7.0, Mw was set to Msat when calculating Vp.
High frequency component – The stochastic approach
The high-frequency ground-motion component is modeled using a modifiable stochastic approach based on a radiation spectrum that incorporates source, path, site, and motion-type effects. Generation involves windowing white noise in time and scaling its frequency-domain representation by the ground-motion spectrum.
- High frequency component – The stochastic approach: The stochastic method models the high-frequency component through a radiation spectrum Y(M_w,R,f) combining source, path, site, and instrument or motion-type effects.Separating these spectral contributions allows the model to be modified for different problems.
- High frequency component – The stochastic approach: White noise is generated for a duration predicted by a ground-motion prediction equation, then windowed with w(M_w,R,t) and transformed into the frequency domain.The spectrum is normalized by the square root of the mean square amplitude spectrum and multiplied by the ground-motion spectrum Y.
Combined synthetic strong ground motions
Combined synthetic motions showed that directivity pulses strongly shaped the response spectra and column vulnerability. Larger magnitude earthquakes could produce smaller top and residual displacements at greater fault distances because pulse amplitude decreased as its period increased.
- Combined synthetic strong ground motions: Directivity-pulse effects were clearest in velocity spectra near 1/fp and in combined velocity histories, but difficult to identify in acceleration histories.The synthetic records used the pulse at maximum amplitude, typically corresponding to the fault-normal direction.
- Combined synthetic strong ground motions: Most records exceeded the limited-deformation performance level, whereas only a few exceeded the significant-deformation level.The three levels ranged from limited deformation through light deformation to significant deformation, with increasing implications for future dynamic behavior and vulnerability.
- Combined synthetic strong ground motions: Strong motions generally increased both maximum top displacement and permanent drum dislocation, but substantial scatter showed that intense rocking did not necessarily produce large residual dislocations.The two engineering demand parameters were normalized top displacement and residual relative drum dislocation.
- Combined synthetic strong ground motions: For fault distances above approximately 7.5–10 km, mean top and residual displacements peaked near Mw = 6.5 and decreased at larger magnitudes.At small distances, both responses generally increased with magnitude; the decrease at larger distances was attributed to the directivity pulse’s reduced acceleration amplitude at larger magnitudes.
- Combined synthetic strong ground motions: Top displacement initially increased with pulse period but generally decreased for Tp longer than about 3 sec, consistent with response saturation at long periods.For 0.25 Hz < fp < 0.4 Hz, the safe–unsafe threshold was practically constant; above 0.4 Hz, the required PGA and pulse acceleration increased nearly linearly with fp.
- Combined synthetic strong ground motions: Very strong motions with PGV > 150 cm/sec were required to approach collapse, whereas significant drum dislocations occurred for weaker motions with PGV > 40 cm/sec.The fragility surface for utop > 1 practically coincided with the collapse probability, while ud > 0.02 represented significant drum dislocation.
CONCLUSIONS
The study assesses near-fault seismic vulnerability of a multidrum Parthenon column through Monte Carlo simulations with synthetic pulse-containing ground motions. Fragility analysis indicates that collapse and substantial drum dislocation require very strong motions, while moderate earthquakes have low probabilities of causing severe response.
- CONCLUSIONS: The risk assessment combined Monte Carlo simulation with synthetic motions containing high- and low-frequency components and an analytical near-source directivity pulse.The response was evaluated across 35 magnitude–distance scenarios, with 100 simulations per scenario and 3500 simulations overall.
- CONCLUSIONS: The assessment used two engineering demand parameters: normalized maximum capital displacement and normalized residual dislocation between adjacent drums.Three performance levels and corresponding thresholds were assigned to each parameter.
- CONCLUSIONS: Very strong ground motions are required to bring the column close to collapse and cause significant drum dislocations.Fragility surfaces were evaluated for both engineering demand parameters and all assigned performance levels.