Structural Analysis of Historic Construction – D’Ayala & Fodde (eds)© 2008 Taylor & Francis Group, London, ISBN 978-0-415-46872-5

Experimental survey on seismic response of masonry models

A. Baratta, I. Corbi & O. CorbiDepartment of Structural Engineering, University of Naples “Federico II”, Naples, Italy

D. RinaldisENEA Casaccia Research Center, Italy

ABSTRACT: This paper is focused on the elaboration of the results recorded during some dynamic experi-mental tests executed on a masonry arch placed on a shaking table facility at Laboratory of the ENEA CasacciaResearch Center. The experimental results are correlated to the theoretical results obtained by means of somecalculus codes, which have been elaborated for applications on masonry structures by the researchers of theDepartment of Structural Engineering of the University of Naples “Federico II” and suitably modified for thestudy model. The results have shown that the curves solved by the static calculus may be given an exponentialform as the dynamic curves by the tests; moreover, it is evident that the static degradation is much faster than inthe seismic response, probably thanks to kinetic energy absorption that helps the structure to resist inertia forces.

1 INTRODUCTION

Some interesting experimental tests have been devel-oped at Laboratory of the ENEA Casaccia ResearchCenter (New Technology Department, Rome, Italy)on some masonry arches within a national conven-tion with the Authority of the Monumental HeritageSupervision in Benevento and Caserta Provinces as apreliminary step finalized to the strengthening for seis-mic risk of the San Rocco’s church in Benevento and ofthe S. Francesco’s bell tower in Montesarchio (Campa-nia, Italy). More in general, the study spaces from thedynamic characterization of the considered structures,realized by means of the monitoring of environmentaland forced vibrations of the churches, to the analysisof the seismic conditions at the site where the ancientstructures are built, to the tests on shaking table ofselected structural elements (in real and reduced scale)and of some scale models of the churches.

This paper is focused on the experimental testsexecuted on some masonry prototypes placed on ashaking table at the ENEA laboratory. The experi-mental investigation consists of seismic tests actedon some masonry arches, made of tufa bricks andcement mortar; the prototype is solicited under quakesof increasing intensities up to the collapse condition.

This work starts from the collection of the existingrecorded data of the laboratory tests: a pretty consistentnumber of response diagrams in the time and fre-quency domains (time history of acceleration, powerspectrum, frequency response and coherency func-tion), produced by the sensors placed on the structure.

The scope of the present study, and, in general, ofthe experimental campaign, is to characterize the ownvibration frequency of existing structures and to elab-orate a rationale to correlate the theoretical results toin situ dynamic identification and to the laboratorytests that have been performed. The static analyseshave been carried on by calculus codes that havebeen implemented for no-tension material structuresat the Department of Structural Engineering of theUniversity of Naples “Federico II”.

2 APPLICATION OF THE NO-TENSION (NT)STRESS ANALYSIS: THE MASONRY ARCH

In structural patterns of the type of arches (or vaults),the stress field can be inferred from the internal forceson every cross section by a pattern as in Figure 1(Baratta & Corbi, 2003; 2005).

Figure 1. Stress pattern on cross sections.

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Figure 2. Superposition schemes for managing equilibriumstress fields.

The set of stress fields in equilibrium with appliedloads can be built up by a superposition scheme of thetype shown in Figure 2.

The solution of the no-tension (or NT) structuralproblem is approached by the Minimum principle ofthe Complementary Energy, and the procedure aims atidentifying the redundant reactions allowing internaland external constraint compatibility.

Let Do be the definition set of the admissible NTstress fields in equilibrium with the applied loads; thestress field σo is found as the constrained minimum ofthe Complementary Energy functional U (σ) under thecondition that the stress field is in equilibrium with theapplied loads and compressive everywhere

The admissibility of the stress field (Baratta & Corbi,2003; 2005) is guaranteed by the condition that theforce funicular line is everywhere in the interior of thearch profile (Fig. 3)

Figure 3. Admissible funicular line.

Figure 4. Specimen (in cm) of the masonry arch for thelaboratory tests.

3 DYNAMIC EXPERIMENTAL TESTS ONMASONRY ARCH BY MEANS OFSHAKING TABLE

3.1 Testing model: the masonry arch

For the tests executed on the shaking table, at Labo-ratory of the ENEA Casaccia Research Center (Newtechnology Department) two similar arches are builthaving a circular round-headed axis and the geometryshown in Figure 4. The arcade built in tufa bricks restson two piers, which continue over the imposts of thearch in order to contain the overload imposed on thetop of the portal arch with the help of a tie-rod.

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The structure is made by yellow tufa bricks tiedby a poor mortar, which is a most common masonryencountered in South Italy. The intrados profile of thearcade is semicircular with a radius of 100 cm. Thearcade is composed by two rows of bricks determininga masonry thickness of 20 cm; the two pillars whichsupport the arcade have a rectangular base 50 cm andan height 70 cm; the depth of the whole is 100 cm. Thewing walls, continuing in height the pillars, which haveto contain the overload, are characterized by thickness35 cm and an height 110 cm.

Moreover, some steel tie-beams fixed by means offlexible elastic ties are placed between the structureand the wing walls used for containing the overload,in order to guarantee the stability during the tests. Thetotal weight of the masonry structure is 5,1 tons. On thetop of the portal arch an overload of material composedby crushed tufa and lime and having a weight of 1,4 tonis applied, in order to simulate the structural contextwhere the real arcade is included. Sliding is preventedthrough steel profiles attached to the shaking table.

The total weight of the structure plus the overloadand the steel bars is 7,0 tons.

3.2 Characteristics of the shaking table andof the recording instruments

As described in the above, during the tests, the seis-mic input is transmitted to the structure by means ofa shaking table; the table has the following techni-cal characteristics: dimension of 4 × 4 m, maximumsupported weight of 10 ton, six degrees of freedom,frequency range of 0–50 Hz, maximum peak accel-eration of 3 g, maximum velocity of 5 m/sec andmaximum span of 25 cm.

In order to evaluate the time histories of the accel-eration and displacement some recording instrumentsare located at some “critical” positions on the arch,which are fundamental for the determination of thestructures’ response.

The recording instruments consist of two differenttypologies of accelerometers:

• n. 20 piezoelectric accelerometers with feed-through band of 2–15000 Hz (± 10%), and nominalsensitivity of 10 pC/g,

• n. 8 transducers of displacement (LVDT) subdi-vided in:– transducers with nominal sensitivity of 0,1Vmm-

1 (± 3%), maximum displacement of ± 2 inch,and feed-through band of 50 Hz,

– transducers with nominal sensitivity of 0,2V/mm(± 3%), maximum displacement of ± 1 inch,and feed-through band of 50 Hz.

The accelerometers are directly applied on themasonry arch, while the transducers are located in cor-respondence of the external sides of the two piers, and

Figure 5. Sensors locations on the masonry arch byBuffarini et al. (1997) modified.

are fixed to some steel trestles integral with the shak-ing table. A scheme of the arch with the locations ofthe sensors composing the monitoring equipment isshown in Figure 5 (Buffarini et al., 1997; Clementeet al., 1999).

3.3 Description of the laboratory tests

At first the tuning of the shaking table is realized inorder to check the response of the table. To this pur-pose, the table is loaded with a fictitious structuresimulating the testing structure both in its total weightand in its barycentre position, and the fictitious struc-ture is subject to the selected profile, consisting inthe selected time history of the acceleration. The finalobjective of the tuning phase is the realization of thetest profile (Buffarini et al., 1997).

3.3.1 Tests developed on the 1st portal archThe first arch is tested in two phases up to the collapse.In the first phase (Phase A) only an horizontal input isused; thereafter, in order to approach the collapse con-dition of the structure, in the second phase (Phase B),a vertical input is also added to the horizontal one. Inboth the two phases the applied excitation acts in theplane of the structure, orthogonally to its side at thebottom of the portal arch.

In the first phase (Phase A) the characterization ofthe arch having an overload on the top of the arcadefixed to 14,1 kN is developed by means of a whitenoise with amplitude of 0,1 g (as well known, thetheoretical white noise is a disturbance with infiniteenergy uniformly distributed over the whole frequencyrange. After the initial characterization of the struc-ture, an excitation corresponding to the time history

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Figure 6. Curve of the structural frequencies f vs the seismiccoefficient c during the laboratory tests on the first arch.

recorded in Sturno during the earthquake occurred inCampania-Lucania on the 23rd November 1980 withdirection W-E, and increasing amplitude from 0,3 g upto 1,5 g, is transmitted to the arch. The recorded dataare, then, filtered by means of a high-pass filter witha cut-off frequency of 2 Hz, in order to contain themaximum value of the displacement within the max-imum table stroke of 12,5 cm. Thereafter, the recordis suitably scaled in order to obtain a peak excitationof 0,1 g. After any test a white noise having a fixedamplitude of 0,05 g, and lasting 60 sec, and finalizedto the characterization of the structure, is tested onthe arch.

The first cycle of laboratory tests was stopped at thepeak acceleration 1.5 g and caused some damages onthe structure never leading to its collapse. This unex-pected result may be due to two major reasons: the firstis because for any increment of the damaging a reduc-tion of the own frequencies of the total apparent modesof the structure occurs, and the second reason is dueto a-priori filtering applied on the lower-frequenciesof the Sturno accelerogram (Fig. 6).

In the second phase (Phase B) a vertical input withamplitude of 1,5 g is added to the horizontal input,which continues to increase its amplitude from 1,5 g upto the collapse condition encountered at 1,8 g (Fig. 7).

3.3.2 Tests developed on the 2nd portal archOn the basis of the results obtained on the first arch,a sequence of seismic tests with increasing intensityis transmitted to the second arch, by assuming asbase signal the W-E component of the accelerationtime history recorded at Sturno during the earthquakeof Campania-Lucania (Italy) on the 23rd November1980; moreover, a varying overload on the top of thearcade is introduced.

A preliminary filtering at low frequencies up to2 Hz has been introduced to avoid displacements largerthan the maximum allowable for the shaking table.Then the accelerogram is scaled in order to obtain

Figure 7. Two phases of the arch collapse during thelaboratory tests (a) and (b).

a peak acceleration of 0,1 g, and its peak accelera-tion is amplified of 0,1 g at any step. The subsequenttests with increasing intensity have been staggered tosome tests for the dynamic characterization, realizedby soliciting the structure with a white noise having afixed peak of 0,1 g. Moreover a varying pink noise of8–16 Hz (a signal where the energy is transmitted in theinterior of a well defined frequency band, and can becreated by high-low or band pass filtering white noise)is introduced in the tests, probably becoming the causeof the premature and unexpected damaging of thestructure.

For all the records a sampling step equal to 0,02 secis adopted and the total time of the record amountsat 102,38 secs for the characterizations and the testswith the pink noise, and at 61,42 sec for the seismictests. The time of the effective signal is respectively of60 sec and 40 sec.

The base acceleration is always applied into the lon-gitudinal direction, determining a plane stress state,unless of spatial effects due to the presence of unavoid-able executive defects.

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Three cycles of tests with different overload andexcitation are developed in order to study the behaviorof the second arch:

Cycle 1) in the first cycle an overload of 8,5 kN isapplied on the top of the portal arch, and the seis-mic input consists of a white noise for the seismiccharacterization of the structure, a pink noise andtwo tests of 0,1 and 0,2 g.Cycle 2) In the second cycle an overload of 14,1 kN(equivalent to the one acting on the first arch) isapplied and the structure is subjected to two seismictests with peak 0,1 and 0,2 g; the cycle is then inter-rupted because of the detachment of some stonesat the intrados.Cycle 3) In the third cycle, started after the restora-tion of the broken bricks, an overload of 14,1 kN iskept, the pink noise which is probably the cause ofthe masonry slack is removed, and the seismic testsare continued up to the peak acceleration of 0,7 g.

By analyzing the results, on the basis of the testprogram shown in Table 1 (from the laboratory tests’schemes by Buffarini et al., 1997 modified) andFigure 8, some considerations can be outlined.

After the dynamic characterization (C1) developedon the undamaged structure, the first test (T1) has beendeveloped with the acceleration time history scaled toa peak of 0,1 g. At any step the peak value is increasedby 0,1 g, and so on up to a maximum peak value of0,7 g (T7R), about twice the real peak accelerationrecorded to Sturno, which is equal to 0,34 g. The testwith a peak of 0,7 g (T7) was interrupted because ofthe detachment of some stones at the intrados and thenrepeated (T7R) (Clemente et al., 1999). After any testa characterization of the structure has been developedby operating a white noise input (C1 to C9) plus a pinknoise having an increasing peak value of 0,1 g at anystep (P1 to P8).

In the first three characterizations (C1 to C3) anoverload of 8,5 kN has been imposed on the top of thearch, then the tests have been interrupted and startedagain by a peak value of 0,1 g and an overload of14,1 kN has been imposed (C1R to C9R) in order tomake tests homogeneous to the 1st arch.

3.4 Comparison between the dynamic resultsin the laboratory tests

By the comparison between the curves in Figures 6and 8, which plot the results by the dynamic tests inlaboratory on the masonry arches, some general con-siderations can be made about the behavior of the twoarches (Fig. 9).

The laboratory tests put to evidence some differ-ence between the two arches. Both the arches showa typical behavior where the trend of the recordedfrequencies decreases with respect to the seismicintensity (the coefficient “c = ap/g”) the arch has been

Table 1. Scheme of the laboratory tests executed on thesecond arch pre-consolidation.

Test Solicitation Note

Cl white noise Overload 8.5 kN. Testsstart (cycle 1)

Pl pink noise_01TI test 01

C2 white noiseP2 pink noise_02

T2 test 02C3 white noise

ClA white noise Overload 14.1 kN. Newstart of tests (cycle 2)

PIA pink noise_0lT1A test 01

C2A white noiseP2A pink noise_02

T2A test 02C3A white noise

P3A pink noise_03 Test stop for breakingoff of some stones

C1R white noise Restoration of thebroken bricks andnew start of the test(cycle 3)

T1R test 01C2R white noise

T2R test 02C3R white noise

T3R test 03C4R white noise

T4R test 04C5R white noise

T5R test 05C6R white noise

T6R test 06C7R white noise

T7R test 07 Test stop for breakingoff of some stones.

C8R white noise Characterizationfollowing to theprevious test

C8RB white noise Characterizationbefore the testingstart

C8RATT white noise Characterization witha scale spectrum 1/2

T7RB test 07 Final testC9R white noise

subjected, approximately according to an exponentialcurve. Nevertheless the dynamic curve of the first archdecreases more quickly than the curve of the secondarch. Probably this effect is due to the different pro-gram of the shaking sequences to which the archeshave been subjected during the tests: in the tests of thesecond arch an increasing pink noise has been cou-pled to the Sturno input, with the result to anticipatethe damage of the arch.

This different behavior is pointed out in Figure 9where the decay of the first own frequencies of thetwo arches is shown. The fact is however that the trendof both curves can be approximated by an exponential

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Figure 8. Dynamic curve of the structural frequencies f(Hz)vs the seismic coefficient c = ap/g during the laboratory testsfor the second arch.

Figure 9. Comparison between the dynamic curves of thestructural frequencies f vs the seismic coefficient c duringthe laboratory tests on the two arches.

curve, the curve relevant to the first arch decreasesmore quickly than the second one.

4 AN INSIGHT ON VULNERABILITYFORECASTING OF A MASONRYSTRUCTURE

4.1 Procedure for vulnerability evaluation

In order to have an estimate of the seismic vulnerabilityof a existing masonry structure under a seismic input,an attempt is made to draw conclusions on the basis ofdynamic identification coupled with static analysis, inthe light of the above experimental survey.

At first, the static analysis yielding the fundamentalelements of the examined masonry structure can besolved by considering only the geometric dimensionsand some other easily collectable data. So the trend ofsome characteristic displacement parameter uc (e.g.the maximum displacements of points of the structureumax) with respect to the seismic coefficient “c” (with

Figure 10. Trend of the seismic coefficient c vs the maxi-mum displacements umax by the static calculus.

Figure 11. Trend of the tangential stiffness K = c′(u) vs theseismic coefficient c (b) by the static calculus.

c = ap/g) can be inferred up to the collapse conditionfor c = cf (Fig. 10).

By deriving the seismic coefficient c one getsthe trend of the tangential stiffness K = K(c) = c′(u)as a function of the displacement umax and of thecoefficient c (Fig. 11).

It can be conceived that the own frequency of thestructure is a function of the type f2

o = α2Ko, where Kois the stiffness of the structure. Since the structure has aNT non-linear behavior (Fig. 10), one expects that thefrequency depends on the stress intensity, that is mea-sured by “c”. So, referring to the tangential stiffnessK(c), one grossly puts f2(c) = α2K(c).

After dynamic characterization on the structure insite (e.g. by soliciting the fabric with a white noiseor other) one identifies the own frequency fo beforeany earthquake strikes on the building. This allows toestimate the coefficient α = fo

/√Ko, after calculating

the initial stiffness Ko. It is found that, heuristically, thecurve f(c) = α

√K(c) follows a exponential proceeding

(Fig. 12). This curve is referred to in the following asthe “static damage progression”.

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Figure 12. Comparison between the trend of the frequencyf vs the seismic coefficient c by the static calculus (trian-gles) and by the seismic tests (squares), and the relevantexponential approximations, for the first masonry arch.

Figure 13. Comparison between the trend of the frequencyf vs the seismic coefficient c by the static calculus (trian-gles) and by the seismic tests (squares), and the relevantexponential approximations, for the second masonry arch.

A second sentence can be assumed, i.e. that also theprogression of damage in a sequence of earthquakeswith increasing intensity is of the exponential type,as observed in the experiments that have been sum-marized in the above. This curve is referred to in thefollowing as the “dynamic damage progression”.

So the static and the dynamic curves, f∗ (c) and f(c)respectively, can be directly compared, after havingbeen reported to the same initial frequency f(0) = f∗ (0)(Figs 12–13).

4.2 Exponential damage progression

Considering that damage and consequent proneness toseismic collapse evolves according to an exponentiallaw, e.g. having the form assumed in the following

where “c” is the intensity of the worst earthquake thestructure has suffered in the past and to which it hassurvived. At the same time the own frequency “fo”, i.e.the easiest parameter that can be evaluated by dynamicidentification, evolves with increasing the damage ofthe structure.

So, if one considers the derivative of the expressionin Eq. (4)

and the ratio

The rate of decay of the own pulsation turns out to beconstant, despite the fact that in a nonlinear structureit is to be expected that the hazard increases with theintensity of the ground shaking.

4.3 Comparison between the static and dynamicresults

Looking at the diagrams of the static analysis and oflaboratory tests, some observations can be outlined.

The first one is that the experimental seismic decayof the own frequency of the arch when increasingthe seismic intensity can be modeled by means of anexponential curve (Fig. 7).

Moreover, the static degradation of the arch,inferred by means of the static calculus on an NT arch,can be approximated by an exponential curve as well(Fig. 11). The degradation is here measured by thevariations of the tangential stiffness with respect to theincreasing of the seismic component of the overload.

By the comparison of the exponential approxi-mations of the static and dynamic curves, shown inFigures 12–13, it is evident that the static degradationis much faster than the dynamic one.

This effect is probably caused by the opening ofthe fractures in the arch that produces an increasingabsorption of the oscillation energy as kinetic energyat the limit for the mechanism activation, rather thanas elastic energy.

It is possible to emphasize some tentative forecastthat is possible to draw on the basis of the experimentalresults.

By the observation of the diagrams, it can be con-sidered that the two exponential curves (“static” and“dynamic” curves) can assume a very similar form bychanging the scale of the abscissas “c”.

So, considering that the static curve obeys theequation

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Figure 14. The experimental evidence shows that dynamicinteraction with inertial forces strongly improves the seismicperformance of the structure.

while the dynamic curve obeys Eq. (4), it is clearthat if the “static” c is multiplied times q∗/q, the twocurves become very similar. If the same transforma-tion is applied to the ordinates in the static calculusline (Fig. 10), one obtains a very significant increasein the seismic capacity of the structure, approximatelya seismic peak acceleration that is 5 times larger thanthe limit static force.

This result would agree with test, so that it has beennecessary to rise the peak ground acceleration up to1.8 g to bring the arch to collapse.

It is necessary to remark that the difference betweenthe “seismic” and the “static” curve is due to iner-tial forces due to accelerations involved in the archdeformation.

Such accelerations “a” can be grossly related to themaximum displacements umax through the pulsationωo by a relation of the type

It should be expected that the difference �c betweenthe two curves in Figure 14 can be referred to someadditional displacements �umax that, according toEq. (11), is given by

where �a = g�c.This is a necessary condition for additional inertial

forces absorption. In Figure 15 the experimental valuesof �c are plotted versus umax as expressed in Eq. (9).

By adding the additional displacement to the abscis-sas in Fig. 14, one gets a possible reconstruction ofthe relationship between the peak acceleration and themaximum displacement under seismic excitation

Figure 15. Experimental absorption of inertia forces inaccordance with Eq. (12).

Figure 16. Final pseudo-force/displacement curve underseismic action.

Figure 17. Comparative seismic forecasts for both arches.

The procedure can be applied to both arches, yield-ing comparative results of the seismic forecast as inFig. 17.

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5 CONCLUSIONS

By comparing the dynamic curves of the tested arches(Fig. 9), which can be well approximated to an expo-nential form, one observes that the curve relevant tothe first arch decreases more quickly than the secondone. Moreover, by the comparison of the exponen-tial approximations of the static and dynamic curves(Fig. 12), it is evident that the static degradation ismuch faster than the dynamic one. This effect is prob-ably caused by the opening of the fractures in the archthat produces an increasing absorption of the oscil-lation energy as kinetic energy, mainly due to theprogressive activation of a collapse mechanism, ratherthan as elastic energy. The considerations illustrated inSec. 4.3 enable a transformation of the static analysisresults to produce a "seismic response expectation" asin Fig. 16. Looking at the results of the static analysiselaborated to yield seismic expectation (Fig. 17) thesecond arch has to produce larger displacements thanthe first one, to store a given amount of elastic energy.This means that a larger part of the external energydisplayed by the earthquake has to be transformed bythe second arch in kinetic energy through the activa-tion of a mechanism. The larger the amplitude of suchmechanism the faster the arch approaches collapse.

ACKNOWLEDGEMENTS

The laboratory tests were funded by the ENEACasaccia Research Center (New technology Depart-ment, Rome, Italy) and by the Authority of the Monu-mental Heritage Supervision in Benevento and CasertaProvinces. The recent advancements have been per-formed thanks to the financial support by the Depart-ment of Civil Protection of the Italian Government,through the RELUIS Pool (Convention n. 540 signed07/11/2005, Research Line no. 8).

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