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Application of Predictive Models to Assess Failure of Museum Artifacts under Seismic Loads Constantine C. Spyrakos a*, Charilaos A. Maniatakisb, Ioannis M. Taflampasc School of Civil Engineering, National Technical University of Athens, Greece
Abstract In recent years there has been a growing interest in the protection of cultural heritage structures and artifacts from seismic excitations. Nevertheless, although the vulnerability of museum exhibits under seismic excitations has been repeatedly verified, it has not been given proper attention. In this work emphasis is placed on efforts for mitigating seismic risk of museum artifacts elucidating the necessity to identify artifact failure not only based on code design spectra that mainly account for far-fault conditions but also considering near-source phenomena. A general methodology is proposed and demonstrated with representative examples. The methodology considers the detailed geometry of the artifacts, its support conditions, relative distance from the soil surface, the fundamental frequency of the housing structure as well as relevant seismological data, such as vicinity with active faults and soil type, and provides the critical distance from an active fault within which the artifact could fail. The proposed methodology can serve as an easy-to-apply analytical means to assess the seismic risk of museum exhibits for preserving cultural heritage. Keywords: museum artifacts; rigid body motion; seismic risk; failure criteria; ground motion prediction equations; near-fault region.
1.
Research aims
This work presents a simple methodology that allows assessing seismic risk for museum artifacts. According to the proposed procedure the maximum distance from an active fault is defined, within which the artifact is threatened by failure either because of rocking or overturning. The calculation of this “critical distance” is performed considering the geometry and mass of the artifact, the support conditions, the soil conditions at the site and the special characteristics of strong ground motion at small distances from active faults; namely, near-fault phenomena. The proposed procedure can be used as a means to engineer protection measures of cultural heritage assets in museums at seismic prone regions. Representative museum artifacts placed in the National Museum of Athens, Greece, are selected as case studies and the reliability of the procedure is verified based on failures observed after three significant earthquake events in Greece.
2.
Introduction
Eastern Mediterranean countries such as, Greece, Italy, Cyprus and Turkey, are well known not only for the noteworthy history of the native civilizations but also for their high seismic activity [1].
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Laboratory for Earthquake Engineering, National Technical University of Athens, 9, Heroon Polytechneiou str., Zografos 15780, Athens, Greece. * Corresponding author, Tel: 00302107721187; Fax: 00302107721182; E-mail adresses:
[email protected] (C.C. Spyrakos),
[email protected] (C.A. Maniatakis)
[email protected] (I.M. Taflampas)
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Recently there has been increased concern on a global scale for the protection of museum artifacts from seismic threats, after the failure of significant exhibits from major devastating earthquake events, such as: (i) the 17 August 1999 Izmit (Kocaeli) M W =7.5 and the 12 November 1999 Duzce M W =7.1 earthquakes in Turkey that caused extensive damage to monuments and historic structures [2]; (ii) the M W =6.3 earthquake in L’Aquila, Italy on April 6, 2009 that caused extended failure not only to numerous historic and monumental structures but also to the contents of the National Museum of Abruzzo [3] and (iii) the M S =6.0 and M S =6.1 earthquakes that occurred on January 26th and February 3rd, 2014, respectively, in Cephalonia, Greece and caused significant damage to museum artifacts in the Archaeological Museum of Argostolion. Unfortunately there is a lack of seismic regulations regarding the protection of museum artifacts even in countries with high seismic activity. Usually museum artifacts are treated as non-structural components in light of provisional requirements [4-7] since they do not constitute a bearing part of the structure. Some easy-to-apply directives are also available in the literature for the support of museum artifacts, e.g., [8, 9], while the experimental work in this area remains limited, e.g., [10]. The available directives generally include simple analytical calculations related to stability and empirical rules to form the artifact supports based on the type of the artifact and its constituent material [9]. A typical procedure to design the supports for non-structural acceleration sensitive components is the development of approximate floor acceleration spectra, e.g., [11]. Caution should be paid to the amplification of floor accelerations caused by higher mode effects that should be considered in the design [12]. The current European seismic code, Eurocode 8, EC8, [13] suggests that the design of nonstructural components should be based on the force F a that is applied at the center of gravity of the object and may be calculated by the following formula:
Fa = (S a ⋅ Wa ⋅ γ a ) / q a
(1)
where S a is the seismic coefficient, W is the weight of the component, γ a is its importance factor varying between 1.0 and 1.5, and q a is the behavior factor of the component that varies between 1.0 and 2.0. Eurocode 8 [13] accepts that a non-structural component can be designed to respond inelastically depending on its type. The behavior factor q a is a reduction factor applied to the seismic forces accounting for the nonlinear behavior of the component (artifact). The seismic coefficient S a is the design seismic acceleration of the non-structural component divided by the acceleration of gravity and can be calculated from
3 1 + z H − 0.5 ≥ a ⋅ S Sa = a ⋅ S ⋅ 2 1 + 1 − Ta Tn
(2)
where a =a g /g is the ratio of peak ground acceleration for ground type A, a g , to the acceleration of gravity g, S is the soil factor, T a is the fundamental vibration period of the component, T n is the fundamental vibration period of the structure in the considered direction, z is the height from the level of the application of base shear to the center of mass of the component and H is the total height of the structure within which the non-structural component is placed above the level of the application of base shear. Ground type A according to EC8 [13] refers to a stratigraphic profile with an average value of shear wave velocity in the upper 30 m of the profile v S,30 >800 m/s. The most widely used approaches for the protection of artifacts are: (i) fixing of the base, and (ii) base isolation. The use of isolators for museum artifacts, even though well studied [e.g., 14-
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17], is a technology that has been applied in practice only to a limited extend, e.g., [18]. Recent unpublished experimental and analytical research performed at LEE-NTUA on artifacts and showcases to be placed at the Louvre-Abu-Dhabi museum has revealed the advantages and disadvantages of both approaches [19]. In the literature the study of the seismic response of artifacts with analytical means is more extended compared to the available experimental results [20-24], while there exist only limited research that combines experimental and analytical work, e.g., [25]. The dynamic response of a museum artifact simply supported can be studied with the equations of motion describing the response of a single or multiple blocks under ground excitation. From that point of view, a large number of formulations and analytical and numerical solutions may be found in the literature for the governing nonlinear equations for rocking motion of single or multiple rigid blocks, e.g., [26-31] as well as slender structures allowed to overturn [32]. In the present investigation, previous work of the authors [20-22] is extended regarding the vulnerability of museum artifacts under seismic excitation with emphasis on near-fault seismic motions. A number of representative museum artifacts placed in the National Museum of Athens are selected and simplified criteria are used in order to define the acceleration and velocity required to cause failure. Then applying recent attenuation relationships that consider near-fault effects, the minimum distance needed to provoke failure as well as the type of failure is determined for every artifact. Finally, the results of the procedure are verified based on representative case studies of significant earthquake events.
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Seismicity in Greece with emphasis on damage of artifacts
The particular vulnerability of artwork to seismic excitations in Greece, regarding the historic years, has been recognized through paleoseismological, archaeological and historical studies, e.g., [33, 34]. During modern years, the vulnerability of museum artifacts was re-confirmed. Representative strong earthquakes during the last decade are listed in Table 1, in terms of the surface wave magnitude scale M S . Damages of both the museums and their artifacts have been observed in all cases. Referring to the M L =6.7 Alkyonides earthquake on February 24, 1981, dramatic artifact failures were recorded at the Perachora Museum, located a few kilometers from the epicenter [35], (Figure 1). These failures have been attributed to overturning and impact of artifacts, while failure of weak areas caused by excessive stresses has been also observed at the support connections of statues. Even though the epicenter of the main earthquake was located 77 km away from Athens, severe damage was inflicted to 500 buildings and minor damage was recorded also at the Parthenon [36]. The 1999 Athens earthquake, originated from a normal fault rupture located at the mountain of Parnitha with a focal depth of 9 to 14 km at a distance of 18-20 km from the historical centre of Athens, caused severe damages to numerous engineered structures. Also numerous damages were observed to artifacts and statues in museums (Figure 2a). The earthquake magnitude was defined as M S =5.9 in the surface wave magnitude scale [37, 38]. In Figure 2a the overturn of a showcase in the National Museum of Athens is depicted caused by the 1999 Athens earthquake. The small width of the support and the small distance from the other cabinets is characteristic. More recently, during the M S =6.0 and M S =6.1 earthquakes that occurred in Cephalonia on January 26th and February 3rd, 2014 the Argostolion museum at the island of Cephalonia, one the most highly active seismic regions of Greece, suffered significant damage, as shown in Figure 2b. The main reason for the vessel failure was the fact that they were unanchored, as was the case during a former earthquake with M S =5.9 on 2007. The 2014 Cephalonia earthquakes are considered to be one of the highest sequences of ground motions ever recorded in Europe because of the vicinity of the epicenters, the characteristics of the recorded strong ground motion
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and the near-source phenomena [39]. The epicenters where located at 13 km and 15 km from Argostolion for the first and the second event, respectively [39].
4.
Analysis of rigid artifacts
In the present study the representative museum artifacts, on pedestals, as shown in Fig. 3, are studied for their vulnerability under seismic excitation considering near-source phenomena. The first five artifacts are made of marble and are located at the ground floor of the National Archeological Museum of Athens, N.A.M.A., while the artifacts numbered from “6-10”, ancient Greek ceramic vessels, are located at the second floor of the museum. Every artifact is placed on a pedestal, that is the support on which the artifact is mounted. The assumption of rigid body behavior is made for all artifacts and pedestals. Two possible alternatives are considered: (I) artifact rigidly connected to the pedestal; (II) artifact placed unanchored on the pedestal that is rigidly connected to the floor. In the first case the system pedestal-artifact is vibrating as a rigid body, while in the second case only the artifact is responding as a rigid body to base excitation, as shown in Fig. 4. Assuming that the earthquake response of an artifact can be adequately described using rigid body kinematics, three failure modes are identified: rocking, sliding and overturning. The critical peak ground acceleration PGA and velocity PGV that can cause rocking and overturning, respectively, for the artifacts shown in Figure 3 are determined for the two cases described above and shown in Fig. 4(I) and 4(II). Sliding is not examined, since its proper consideration requires experimental measurement of the friction coefficient at the interface of the artifact and its supporting surface. The equation of motion of a rigid block rocking about the centers of rotation 0 and 0΄, as shown in Fig. 5a when excited by a base horizontal acceleration agh ( t ) , is given by the equations 3(a) and 3(b) for rocking about 0 and 0΄, respectively, provided that the friction coefficient is large enough to prevent sliding [27]:
θ + p 2 ⋅ ( a − θ ) = − p 2 ⋅ agh ( t ) g
(3a)
− p 2 ⋅ agh ( t ) g θ − p 2 ⋅ ( a + θ ) =
(3b)
where θ is the angle of the rigid block from the vertical, α is the angle given by the arctan(B/H), as shown in Fig. 5, and g is the acceleration of gravity. The Eqs. (3a) and (3b) are governed by the parameter p that is given by the relationship:
= p
W ⋅ R I0
(4)
where I 0 is the mass moment of inertia of the rigid block about 0 or 0΄, W is the total weight of the rigid block, R is the distance from point 0 to the center of mass,= R b 2 + h 2 and b and h are the half-width and the half-height of the rigid block, respectively, as shown in Fig. 5a. For a continuous mass distribution, the moment of inertia I 0 is given by integrating over the total mass M the contribution of each differential mass element dm according to the following relationship: I 0 = ∫ rm2 dm
(5)
M
where r m is the distance from the axis of rotation to the mass element dm [40]. For a more complex geometry, as it is usually the case for museum artifacts, an equivalent rigid block should be studied, as shown in Fig. 5b. Since Eqs. (3) are governed by the parameter p and the angle α, the equivalent block should have the same values for both parameters. In this case, the distance R denotes the distance from the center of mass, CM, to the point 0. The point CM results from the geometry of the artifact and the pedestal considering their weights, as depicted in Fig. 5b as W a and W p , respectively.
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The total weight of the “equivalent” rigid block W is taken as, W= W a + W p . An equivalent height H΄ is determined in order to obtain the same mass moment of inertia I 0 with the original geometry about the point 0. The mass moment of inertia about point 0 (see Figure 5a) for an “equivalent” rigid rectangular block with dimensions B� H� D is I = ( 4 3) ⋅ M ⋅ R 2 , where D is the depth [27]. The 0 mass moment of inertia around an axis that passes through the body center of mass, CM, denoted as I 0CM is related to the mass moment of inertia about point 0, according to the parallel axis theorem with the following equality:
( 4 3) ⋅ M ⋅ R 2 =
I 0CM + R 2 ⋅ M
(6)
The total mass of the equivalent block, retaining the dimensions of the base B and D, may be considered as a product of its volume V = B ⋅ D ⋅ H ′ with the mass density ρ. Also, the radius of gyration i can be determined by the equation i 2 = I 0CM M . Applying the necessary algebra, Eqn. (4) and (6) lead to the following expression that defines the height of the equivalent block: 2 3 V i ′ H =⋅ ⋅ + 1 4 B ⋅ D R
(7)
Determination of the exact radius of gyration, the volume and the distance R requires a thorough recording of the geometry considering any modifications in thickness and may be performed with the use of standard CAD tools. The first two failure modes that are rocking and overturning are governed by the PGA and the PGV, respectively [20-22]. The minimum horizontal acceleration that can provoke rocking motion is given by the relationship [27]:
agh g
=
B H
(8)
Ishiyama [28] proposed the following simple expressions in order to estimate the horizontal velocity vgh capable to cause overturning of a rigid body for significant values of the angle a 0.4 ⋅ vgh =
1 − cos ( a ) 2g 2 i + R2 ) ( cos 2 ( a ) R
(9)
Considering a rectangular body and for small values of a, Eq. (9) takes the form
vgh = 10
Β Η
(10)
According to the more general expression given in [32], the overturning stability of a flexible structure is determined by the following criterion: 2 m ⋅ φ I2 ⋅ α 1 m ⋅ φI 2 Svo − WRα 2 = 0 TK +Κ e * Svo − W * m ⋅H⋅ω 2 m ω
(11)
where m is the mass per unit length, 𝜔 is the fundamental natural circular frequency, S vo is the spectral velocity required to cause overturning and W is the total weight of the structure. The spectral velocity S v0 is the maximum velocity developed by a single degree-of-freedom system with period equal to the fundamental period of the structure under the same seismic excitation. The parameters m*, 𝜑𝛪 and K e are given by the expressions
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m* =
2 ∫ m ⋅ ϕ ( y ) dy ϕI = 0
1
∫ ϕ ( y ) dy K e = 0
1
1 2 EIϕ′′ ( y ) dy ∫ 20
(12)
where 𝜑(𝑦) is the normal mode shape, E is the Young’s modulus and I is the second moment of area. Equations (11) and (12) refer to the dynamic response of slender structures that can be obtained with beam type models [32]. The second moment of area, I, refers to an axis that lies in the plane of the beam section and passes through the centroid. The parameter T K is related to the incremental change of the kinetic energy during the rocking motion. For the limit case of a rigid structure, the criterion of Eqn (11) simplifies to the following: S B = vo H gR
(13)
as also proposed by Housner [26]. Equations (8), (9) and (10) are applied in order to calculate the thresholds (critical values) of the horizontal acceleration and velocity that can cause failure to the artifacts of Figure 3. Using the exact three-dimensional geometry of the exhibits and pedestals, the equivalent height H ′ is calculated for complex geometry according to Equation (7). The minimum PGA and PGV values that can cause rocking or overturning for the two conditions of inter-connection between the pedestals and the artifacts are listed in Table 2. The axis x-x refers to the longest dimension of every artifact-pedestal. As a rule, the results of Table 2 show that it is easier to provoke either rocking or overturning of the artifacts about the x-x axis. The artifacts at the second storey of the museum are symmetrical for both axes; thus, the same values of PGA and PGV result for both directions. Eurocode 8 [13] applies Eq. (2) in order to account for the modification of the spectra applied to non-structural components depending on their location along the height of the housing structure. Neglecting the artifact height, for a two-storey building with equal storey heights, z/ H may be considered as equal to approximately 0.5. Consequently, assuming rigid behavior of the artifact compared to the fundamental structural period, i.e., Ta/Tn� 0, Eq. (2) yields an amplification coefficient equal to 1.75. Thus, an artifact placed at the first floor would rock under a 1.75 lower PGA than the same artifact located at the ground floor. Similar expressions are proposed in other seismic design codes and provisions, such as the ASCE 7-10 [41]. These formulas are based on the assumption that the first mode dominates the storey acceleration, an assumption that it is not proven to be always valid, even for a structure where the first mode dominates storey displacements [12]. The proposed methodology is a simplified approach useful in engineering practice as a first level assessment of risk accounting for near-fault and far-fault phenomena. A rigorous nonlinear dynamic analysis should be applied in order to calculate the real response of a rigid block considering the vertical component, the high frequency content of strong ground motion, the significance of scale effects and the response of the structure itself properly accounting for higher mode effects [12, 42-44]. Such an analysis is beyond the scope of a first level assessment of failure for the artifacts.
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Hazard estimation
The determination of the minimum PGA and PGV that can provoke failure of the artifacts may be considered as a valuable tool in the context of a probabilistic seismic hazard analysis, PSHA. In this study, prediction models that account for near-fault effects are used in order to calculate the maximum distance at which the minimum PGA or PGV values needed to provoke failure may occur. When the median value, μ, of predictive models is used, then a 50% probability of exceeding the PGA or PGV values is considered, while when use is made of the median plus one
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standard deviation value, μ+σ, then a 16% probability of exceeding is considered for normal distribution [45]. 5.1 Characteristics of Strong Ground Motion in the Near-Fault Area The increasing availability of ground motion recordings from seismic events at a region located a few kilometers from the source, in the so-called near-fault area, has lead to the identification of specific phenomena. According to these phenomena large pulses with relatively short duration may be expected in the ground velocity time history at sites towards which the fault ruptures, a phenomenon called forward directivity, while in the opposite direction the motion is characterized by a relatively long duration and low amplitude, a phenomenon called backward directivity. At directions parallel to the fault slip, a permanent displacement may be expected, a phenomenon called fling-step [46-50]. Furthermore, the strong motion that is recorded at a specific site is affected not only by the direction of the site relative to the direction of rupture evolution but also by the position of the site compared to the fault plane. The strong motion significantly differs for sites located on the hanging wall, which is the part of the fault over the fault plane, compared to sites lying on the footwall. This differentiation is valid even for equidistant sites from the upper edge of the fault rupture [46-50]. 5.2 Predictive models considering near-fault effects In the present study the far-fault motion is estimated with the predictive model proposed by Boore and Atkinson [51] that provides PGA and PGV accounting for: (i) the magnitude and distance scaling; (ii) soil category and inelasticity effects; (iii) hanging wall and foot-wall effects by using the Joyner-Boore distance R jb , i.e., the shortest distance from the site to the horizontal projection of the fault rupture. In order to account for the increase in PGV due to forward directivity effects, the empirical relationships proposed by Bray and Rodriguez-Marek [47] are employed to calculate PGV in the near-fault region. Thus, the PGA and the PGV are plotted in Figure 6 for three different earthquake magnitudes, that is, M W =5.5, 6.5 and 7.5 based on [51]. Also, three different soil categories are considered according to EC8 [13]: (i) ground type A with shear wave velocity at the upper 30 meters, V S,30 =1130 m/s; (ii) ground type B with V S,30 =560 m/s; (iii) ground type C with V S,30 =270 m/s. Both median and median plus one standard deviation curves are plotted and denoted with continuous and dashed curves, respectively. The reference peak ground acceleration, a gR , for ground type A and for stiff soil conditions is depicted with dashed lines for the three seismic zones considered in Greece; namely, a gR =0.16 g, 0.24 g and 0.36 g for seismic Zones I, II and III, respectively [52]. With dotted lines the PGA according to the first Greek Seismic Code of 1959 (GC-59) are also depicted: namely, 0.04g, 0.06g and 0.08g for seismic Zones I, II and III, respectively, referring to stiff soil conditions [53]. The final objective is the estimation of the R jb distances that define the areas within which rocking or overturning failures are expected. The results are shown on Table 3. Two different R jb values are determined corresponding to the PGA and PGV causing rocking and overturning, respectively. The maximum R jb , denoted as R max , is depicted on Table 3 since the aim is to identify the first mode of failure, denoted with (r) for rocking and (o) for overturning. It should be noted that the critical distances are overestimated using attenuation relations based on time-history samples from far-field regions [20-22]. In Table 4 the derivation of the critical distance is repeated considering the effects of forward directivity in PGV as accounted for according to the Bray and Rodriguez-Marek relationships [47]. Two soil categories are considered: (a) rock/ shallow stiff soil (0–20m of soil or weathered rock over competent rock with no soil having shear wave velocity V S 180 m/s) that represents ground type C. For
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ground type B the parameters defined by Bray and Rodriguez-Marek [47] as appropriate for all conditions are applied. From Table 3 it can be observed that for earthquake magnitudes M W =5.5 and 6.5 the dominant mode of failure is rocking, while for M W =7.5 significant PGV values are predicted; thus, overturning may dominate for some cases. Also, for the smallest earthquake considered, that is M W =5.5 for some artifacts no failure is caused even for R jb =0 km. On the contrary, for M W =7.5 there are cases of artifacts for which failure occurs even for distances greater that R jb =100 km. The main failure mode alters when the near-fault effects on PGV are considered, as shown in Table 4. The dominant failure mode becomes overturning for all earthquake magnitudes, while only a few artifacts that are expected to fail in rocking are detected for magnitude M W =6.5 and M W =7.5 specially when median plus one standard deviation values are considered for ground type C conditions. Also the consideration of near-fault effects results in a significant increase of the critical distance. This increase suggests that the failure of artifacts is probable at even greater distances from active faults because of directivity. However, it should be noted that the Rodriguez-Marek relationships are based on a dataset of earthquake records obtained at distances smaller than 15 km [47]; thus, the application of these relationships at greater distances might result in an overestimation of PGV values attributed to the decrease of the effects of directivity with distance. It is essential to mention that extended failures such as the ones shown in Figs. 1 and 2 observed after significant earthquakes may be attributed most probably to overturning, since rocking would preserve the failure to a less extend. This observation provides an insight of the significance to consider near-fault earthquake effects for the design of the support of artifacts and museum showcases. As shown in Fig. 6 the a gR acceleration, according to current provisions for soil type A, especially for seismic zone I, is significantly smaller than the one expected on average from the applied predictive models; namely, at distances R jb
