Failure of masonry arches under impulse base motion

Recent seismic events have caused damage or collapse of invaluable historical buildings, further proving the vulnerability of unreinforced masonry (URM) structures to earthquakes. This study aims to understand failure of masonry arches—typical components of URM historic structures—subjected to horizontal ground acceleration impulses. An analytical model is developed to describe the dynamic behaviour of the arch and is used to predict the combinations of impulse magnitudes and durations which lead to its collapse. The model considers impact of the rigid blocks through several cycles of motion, illustrating that failure can occur at lower ground accelerations than previously believed. The resulting failure domains are of potential use for design and assessment purposes. Predictions of the analytical model are compared with results of numerical modelling by the distinct element method, and the good agreement between results validates the analytical model and at the same time confirms the potential of the distinct element framework as a method of evaluating complex URM structures under dynamic loading. Copyright © 2007 John Wiley & Sons, Ltd.     

The masonry arch as a four-link mechanism under base motion

The dynamic response of an unreinforced masonry arch is examined, modelling the rigid body motions of arch segments under the influence of gravitational and inertial forces. This extends earlier studies of single rocking blocks, stacked blocks, and portal mechanisms of blocks; the masonry arch is analysed as another kinematic form of such a system. In this first effort a part-circular planar arch ring is studied and excitation is restricted to horizontal ground acceleration of the base. The mechanism kinematics are presented and the governing equation of motion is derived in non-linear form. The instantaneous form is determined for small rotations about the initial geometry and is used to study the conditions for the onset of mechanism motion. Possible failure conditions are posed and bounding principles are stated. One possible failure condition, direct overturning as a four-link mechanism, is studied for one simplified base motion. The results show that an arch geometry establishes good resistance to earthquake excitation in that ground acceleration must exceed a rather high threshold before any mechanism motion would develop; however, once that threshold has been passed the arch has relatively modest resistance before failure. Other possible failure conditions are discussed; one emerges from pounding effects between segments at impact, and another develops from sliding of blocks over one another as the internal forces (normal and tangential to the masonry joint) vary with the inertial forces.     

Model for multiblock columns subjected to base excitation

A new model is presented for multiblock columns subjected to earthquakes, which contains an impact and an opening model. Both in the impact and in the opening model, all the possible opening configurations are investigated because it was found that in many practical cases, unexpected patterns may occur. The model is purely mechanical: assuming rigid blocks and classical (inelastic) impact. The effect of energy dissipation during impact was investigated. Using our model in accordance with the literature, it was found that monolithic blocks are more vulnerable to overturning than multiblock systems.     

Introduction to dynamics of stone arches

The dynamic analysis of stone arches, made up of rigid voussoir laid dray, can be performed in two phases. First of all the value of the horizontal acceleration necessary to turn the structure into a mechanism and the corresponding mechanism must be determined. Then the dynamic behaviour of such a mechanism under a given acceleration time history can be studied. The first step is a static matter. The second one requires the solution of the non-linear equation of motion of the one-degree-of-freedom system in which the arch is turned. In this paper an iteration procedure is proposed to find out the mechanism. Then the structural behaviour of the mechanism is analysed. Both free and forced vibrations are investigated and the study is limited to the first-half cycle of vibration. Damping is not considered and sliding between the blocks at the hinge sections is not allowed. © 1998 John Wiley & Sons, Ltd.     

Dynamic analysis of stacked rigid blocks

The dynamic behavior of a structural model of two stacked rigid blocks subjected to ground excitation is examined. Assuming no sliding, the rocking response of the system standing free on a rigid foundation is investigated. The derivation of the equations of motion accounts for the consecutive transition from one pattern of motion to another, each being governed by a set of highly nonlinear differential equations. The system behavior is described in terms of four possible patterns of response and impact between either the two blocks or the base block and the ground. The equations governing the rocking response of the system to horizontal and vertical ground accelerations are derived for each pattern, and an impact model is developed by conservation of angular momentum considerations. Numerical results are obtained by developing an ad hoc computational scheme that is capable of determining the response of the system under an arbitrary base excitation. This feature is demonstrated by using accelerograms from the Northridge, CA, 1994, earthquake. It is hoped that the two-blocks model used herein can facilitate the development of more sophisticated multi-block structural models.     

Seismic behavior of concrete filled steel tubular arch structures

Shaking table tests of a 1:10 scale arch model performed to investigate the seismic behavior and resistance ofconcrete filled steel tubular (CFT) arch structures are described in this paper. The El-Centro record and Shanghai artificial wave were adopted as the input excitation. The entire test process can be divided into three stages depending on the lateral brace configurations, i.e., fully (five) braced, two braces removed, and all braces removed. A total of 46 tests, starting from the elastic state to failure condition, have been conducted. The natural vibration frequencies, responses of acceleration, displacement and strain were measured. From the test results, it is demonstrated that the CFT arch structures are capable of resisting severe ground motions and that CFT arches offer a credible alternative to reinforced concrete arches, especially in regions of high seismic intensity.     

Response of jointed arches to earthquake excitation

An efficient method for accurately modelling the gradual opening and closing of joints in two-dimensional slabs and arches has been devised. The method is used in computing the earthquake response of an arch which is a representative horizontal cross-section of a concrete arch dam. Responses of the arch with and without joints are compared to assess the effect of joint opening. An extension to three-dimensional arch dams is proposed.     

Simulation of damage in RC frames with variable axial forces

The purpose of this paper is to describe how the methods and concepts of continuum damage and fracture mechanics can be applied to the modelling of the hysteretic behaviour of Reinforced Concrete (RC) frame members under variable axial loads. A frame member is considered as the assemblage of an elastic beam-column and two inelastic hinges, as in conventional nonlinear analysis of RC frames. As a result of the combination of damage mechanics and standard RC theory, a simplified model of damage is proposed and implemented as a finite element (FE). This new element can be used with any non-linear commercial FE program. The numerical simulation of several experiments, for which data were available in the literature, verifies the accuracy of the model. Copyright © 1999 John Wiley & Sons, Ltd.     

DETERMINATION DE L'IMPULSION SISMIQUE*

Determining the shape of a pulse generated by an explosion solely from the data provided by the recorded seismic trace is a difficult and even ambitious task. Knowledge of parameters such as length and number of “arches” of the pulse under study is, in fact, indispensable in solving this problem. These parameters cannot be found directly in the seismic trace, which nevertheless contains a great amount of information. Autocorrelation, with its mathematical and statistical properties, is an efficient way of making the best of this information. We compute all the autocorrelations of reflections having a given number of arches which fulfil certain conditions determined in advance. Then, after statistical testing of some parameters pertaining to the autocorrelations (abcissae of zeros, of extrema …), we select only those with a maximum likelihood. It is sufficient to consider only the reflections whose autocorrelations have been selected and to arrange them in groups according to their shape and arch number in order to obtain average pulses. In so doing several solutions are arrived at, but when considering a given number of traces, a single record for instance, it is possible by comparing these results with each other to considerably reduce their number. In the last part of the paper the nature of the impulse obtained with our method is examined in order to find out whether it is “minimum phase” for carrying out deconvolutions.     

Mechanisms and models of iridium anomaly shape across the Cretaceous–Paleogene boundary

The interpretation of the Cretaceous–Paleogene (K–Pg) iridium anomaly – and other impact ejecta – as the result of a single, large asteroid impact has been the subject of much debate, in part due to the distribution of impact markers beyond the narrow confines of the K–Pg boundary sedimentary layer. Here, we revisit the hypothesized processes leading to the shape of K–Pg iridium profiles including geochemical remobilization and/or diffusion, prolonged deposition, volcanism, multiple impacts, and sediment mixing. Using evidence from the literature and modeling of one North Pacific site, we find that sediment mixing of a single impact event provides the most parsimonious mechanism for iridium profile shape in open ocean oxic sediments, while the increase in background iridium bracketing the boundary likely has a volcanic origin. In some past studies, a sediment mixing mechanism for iridium profile shape was ruled out based on an overly simplified set of expectations for the effect of sediment mixing on markers of geologically instantaneous events. Thus, we introduce and use a Lagrangian sediment mixing model to illustrate the theoretical effects of mixing on records of rapid events. The sediment mixing origin for iridium anomaly shape, the correspondence in mixing extent between iridium and microfossils, and the fit of sediment mixing models to an empirical iridium profile indicate that iridium may provide a better tracer of mixing than previously proposed K–Pg mixing tracers such as Ni-spinels.     

Internal structural variations in a debris-avalanche deposit from ancestral Mount Shasta,California, USA

Various parameters of the internal structure of a debris-avalanche deposit from ancestral Mount Shasta (size and percentage of block facies in each exposure, number and width of jigsaw cracks, and number of rounded clasts in matrix facies) were measured in order to study flow and emplacement mechanisms. Three types of coherent blocks were identified: blocks of massive or brecciated lava flows or domes, blocks of layered volcaniclastic deposits, and blocks of accidental material, typically from sedimentary units underlying Shasta Valley. The mean maximum dimension of the three largest blocks of layered volcaniclastic material is 220 m, and that of the lava blocks, 110 m. This difference may reflect plastic deformation of blocks of layered volcaniclastic material; blocks of massive or brecciated volcanic rock deformated brittly and may have split into several smaller blocks. The blocks in the deposit are one order of magnitude larger, and the height of collapse 1100 m higher, than the Pungarehu debris-avalanche deposit at Mount Egmont, New Zealand, although the degree of fracturing is about the same.This suggests either that the Shasta source material was less broken, or that the intensity of any accompanying explosion was smaller at ancestral Mount Shasta. The Shasta debris-avalanche deposit covered the floor of a closed basin; the flanks of the basin may have retarded the opening of jigsaw cracks and the formation of stretched and deformed blocks such as those of the Pungarehu debris-avalanche deposit.     

Dynamic analysis of dams with nonlinear slipjoints

A nonlinear, slip-joint element for analyzing the effect of discontinuities on a concrete, arch dam's seismic response is developed. The joint element has been incorporated into a finite-element-based, solution for predicting dynamic structural response. This joint model, plus the numerical procedure incorporated into the incremental solution, models inter-element impact across a joint when adjacent, structural elements separate and later collide. Collision is incorporated into the incremental analysis by calculating the exchange of momentum and energy with the equations describing eccentric, rigid-body impact. Joint material's force-deflection relations are multi-linear with hysteresis. Coulomb friction is also modeled. The joint element and numerical procedure have been tested with two models. The first is a segmented arch of seven, straight beam elements connected to one another. The arch dam has been experimentally tested. Analytical results are compared with experimental results from the sealed model. Second is a rectangular plate model subject to lateral base accelerations. One horizontal edge is fixed and the opposite edge is free. The vertical edges may be fixed or connected to the base by joint elements.     

Nonlinear earthquake analysis of high arch dam–water–foundation rock systems

A nonlinear finite element model for earthquake response analysis of arch dam–water–foundation rock systems is proposed in this paper. The model includes dynamic dam–water and dam–foundation rock interactions, the opening of contraction joints, the radiation damping of semi‐unbounded foundation rock, the compressibility of impounded water, and the upstream energy propagating along the semi‐unbounded reservoir. Meanwhile, a new equivalent force scheme is suggested to achieve free‐field input in the model. The effects of the earthquake input mechanism, joint opening, water compressibility, and radiation damping on the earthquake response of the Ertan arch dam (240 m high) in China are investigated using the proposed model. The results show that these factors significantly affect the earthquake response of the Ertan arch dam. Such factors should therefore be considered in the earthquake response analysis and earthquake safety evaluation of high arch dams. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of seismic disaster failure mechanism and dam-break simulation of high arch dam

Based on a Chinese national high arch dam located in a meizoseismal region, a nonlinear numerical analysis model of the damage and failure process of a dam-foundation system is established by employing a 3-D deformable distinct element code(3DEC) and its re-development functions. The proposed analysis model considers the dam-foundation-reservoir coupling effect, infl uence of nonlinear contact in the opening and closing of the dam seam surface and abutment rock joints during strong earthquakes, and radiation damping of far fi eld energy dissipation according to the actual workability state of an arch dam. A safety assessment method and safety evaluation criteria is developed to better understand the arch dam system disaster process from local damage to ultimate failure. The dynamic characteristics, disaster mechanism, limit bearing capacity and the entire failure process of a high arch dam under a strong earthquake are then analyzed. Further, the seismic safety of the arch dam is evaluated according to the proposed evaluation criteria and safety assessment method. As a result, some useful conclusions are obtained for some aspects of the disaster mechanism and failure process of an arch dam. The analysis method and conclusions may be useful in engineering practice.     

钢筋混凝土分体柱的抗震机理

为揭示钢筋混凝土分体柱的抗震机理,在以前模型试验基础上,考虑隔板与单元柱之间的非线性接触及钢筋与混凝土之间的黏结滑移,数值模拟了钢筋混凝土分体柱的抗震性能。结果表明:分体柱可实现变短柱为“长”柱的设想;分体柱具有理想的变形能力和延性,延性系数达到4.0;分体柱的刚度随变形增加呈指数衰减,后期刚度退化较为缓和;分体柱具有较高的耗能能力,其耗能系数达1.44;隔板与单元柱的切向接触应力较小,可忽略隔板对单元柱的变形协调作用。进一步验证了钢筋混凝土分体柱具有理想的抗震性能,完善和发展了钢筋混凝土分体柱的设计理论和应用技术。     

Simplified multi-block constitutive model predicting earthquake-induced landslide triggering and displacement along slip surfaces of saturated sand

Slopes consisting of saturated sand have recently moved down-slope tens or hundreds of meters under the action of earthquakes. This paper presents a simplified but accurate method predicting the triggering and displacement of such landslides. For this purpose, a simplified constitutive model simulating soil response of saturated sands along slip surfaces is proposed and validated. Then, this constitutive model is coupled with the multi-block sliding system model to predict the triggering and displacement of such slides. The multi-block model considers a general mass sliding on a trajectory which consists of n linear segments. The steps needed to apply this method are described in detail. The method was applied successfully to predict the triggering, the motion and the final configuration of the well-documented (a) Higashi Takezawa, (b) Donghekou and (c) Nikawa earthquake-induced slides.     

Impulsive Dirac‐delta forces in the rocking motion

In this work the classical theory of one block rocking motion is revisited. A Dirac‐delta type interaction as impact mechanism is found to be an alternative for the traditional model. Numerical computations with this new formulation have shown that the agreement with the classical theory is excellent for the case of slender blocks and small displacements. Good agreement with experimental data has also been found for the case of arbitrary angles and slenderness. The approach presented in this paper opens new lines for further theoretical developments and computational applications. Copyright © 2004 John Wiley & Sons, Ltd.     

A comparative study of concentrated plasticity models in dynamic analysis of building structures

Concentrated plasticity (CP) models are frequently used in static and dynamic building analysis and have been implemented in available commercial software. This investigation deals with three different CP‐models, a simplified macroelement model (SEM) for a complete building story, a frame element with elasto‐plastic interaction hinges (PH), and a frame element with fiber hinges (FB). The objectives of this work are to evaluate the quality of the earthquake responses predicted by these models and to identify important aspects of their implementation and limitations for their use in dynamic analysis. The three elements are tested in a single‐story asymmetric plan building and in a three‐story steel building. Results show that base shear and global response values are usually computed with better accuracy than interstory deformations and local responses. Besides, the main limitation of elasto‐plastic CP models is to control the displacement offsets that result from perfect elasto‐plastic behavior. On the other hand, calibration of the SEM‐model shows that global responses in steel structures may be computed within 20% error in the mean at a computational cost two orders of magnitude smaller than that of the other CP elements considered. However, the three element models considered lead to increasing levels of accuracy in the dynamic response and their use depends on the refinement of the analysis performed. Copyright © 2005 John Wiley & Sons, Ltd.     

Arch responses to correlated multiple excitations

This paper analyses the in-plane stochastic responses of incompressible circular arches to spatially correlated multiple excitations. The dynamic, quasi-static and total structural displacements, moments, shear and axial forces are calculated. The results are compared with those obtained by various simplified excitations. The effects of the ground motion spatial variations on arch responses are examined. The results indicate that the responses may be underestimated or overestimated by neglecting the ground motion spatial variations, depending upon the structure and ground motion properties, the locations where the responses are evaluated, and the response quantity under consideration.