DAMAGE INDICATORS FOR UNREINFORCED MASONRY BUILDING WALLS SUBJECTED TO SEISMIC ACTIONS

Seizmička aktivnost u Bosni i Hercegovini (BiH) uzrokovana je postojanjem dubokih, lateralnih i reverznih rasjeda. Tektonska aktivnost ovog područja povezana je i s činjenicom da drugi po veličini pojas (Alpski pojas) prelazi preko Bosne i Hercegovine, a proteže se od Himalaja, preko Irana Turske i Grčke [1, 2, 3, 4]. Prema evromediteranskoj seizmičkoj mapi rizika, BiH se svrstava u zemlje sa srednjim stepenom seizmičkog rizika, s vršnim ubrzanjem tla (PGA) u rasponu od 0,08 do 0,24 g, dok je jugozapadni dio zemlje okarakterisan visokim rizikom (PGA>0,24 g). Konstrukcija koja je prikazana u ovom članku (vidjeti sliku 1) karakteristična je za široko područje Zapadnog Balkana, građena pedesetih i šezdesetih godina prošlog stoleća. Više detalja o tipologiji same konstrukcije može se naći na drugim mjestima [1, 2, 3, 4]. Ova vrsta nearmirane (URM) obične zidane konstrukcije izgrađena je od industrijskih opečnih elemenata, ali bez vertikalnih sekrlaža. Osjetljivost ovih konstrukcija povezana je s njihovom velikom visinom, lokacijom nosivih zidova koji se nalaze uglavnom samo u jednom pravcu i činjenicom da nema vertikalnih armiranobetonskih (AB) serklaža. Razaranje ove vrste zgrada dobro je dokumentovano nakon zemljotresa u Skoplju 1963. godine (prikazano na slici 2).


INTRODUCTION
Seismic activity in Bosnia and Herzegovina (B&H) is connected to the existence of deep lateral and reverse faults.The fact that the second biggest belt (Alpine Belt), going from the Himalayas over Iran, Turkey and Greece, passes through B&H verifies the tectonic activity of this region [1,2,3,4].As per Euro Mediterranean Seismic Hazard Map, B&H falls in the Moderate Seismic Hazard having the peak ground acceleration (PGA) in the range of 0.08 to 0.24g, while a south-west part of the country experiences a High Hazard (PGA>0.24g).
The building presented in this paper (see Figure 1) is characteristic for the wider region of Western Balkans, built in the 1950's and 1960's.More details about the building typology can be found elsewhere [1,2,3,4].This type of unreinforced masonry (URM) buildings were constructed with industrial bricks, but without vertical confining elements.The vulnerability of these buildings lies in its high height, structural walls placed mostly in only one direction and the fact that there is no vertical reinforced concrete (RC) confining elements.The devastation of this type of buildings is well documented after the 1963 Skopje earthquake, as illustrated in Figure 2.

DYNAMIC CHARACTERISTICS
Dynamic identification methods are often used for determination of the vibration characteristics (eigenfrequencies and mode shapes) of civil engineering structures.These dynamic characteristics are important for understanding the dynamic behaviour of structures under earthquake actions.
The relevant eigen-modes and eigen-frequencies obtained by the FEM calculations [1,2] are presented in Figure (a), (b) and (c).The first mode is the prevailing mode of the response with the largest effective modal mass contribution in the x-direction (67.33%).This is a "typical" box behaviour of a masonry structure with stiff connections between the walls and the slab (diaphragm effect).
The value of the frequencies were compared with the data provided by Tomaževič [20], indicating that for higher structures, "even up to 11-storeys the values are close to 2Hz even though buildings have been built with different materials".This is very important in order to be able to "verify" the model as there are no experimental data.

DIAPHRAGM HYPOTHESIS
When subjected to earthquakes, the shear failure mode evidenced by the building typology studied highlights the critical aspect of stiffness degradation, as a damage indicator, of the masonry walls.For the masonry structures with reinforced concrete slabs the horizontal floor loads are distributed according to the stiffness of the vertical resisting elements.In the example of the existing structure [1,2] that has been investigated and modelled, it was proven that slabs made of semi-prefabricated elements "Herbst" concrete hollow elements (Figure 4) behave as a rigid floor (diaphragm).

TIME HISTORY ANALYSIS
The structure was exposed to the 1979 Petrovac short-period earthquake recorded during the earthquake in Petrovac on 15 April 1979, (Montenegro), with peak acceleration of 0.43g, in order to analyze the dynamic response of the structure.This is one of the accelerograms being frequently used for different verifications throughout former Yugoslavia [19,20].The differences in the soil conditions between Sarajevo and Petrovac in this case were not taken into account in this case.The accelelogram was scaled in order to have a maximum PGA of 0.1g corresponding to the Zone VII (MCS-Scale) for the Sarajevo region, where the building is located, and filtered using the software Seismosignal [18].The value for the damping ratio (ξ)was taken as 5%.

Damping characteristics
The classical damping hypothesis, precisely the Rayleigh damping, shown in Figure 7, has been chosen since the building has a similar structural system and structural material over its height.Rayleigh damping composes of mass-proportional and stiffness proportional damping defined by the following equation [6].
where and are the first and second Rayleigh coefficients.
Correct choice of modes i and j is essential in order to ensure reasonable values for the damping ratios in all the modes contributing to the response.Frequencies of the mode 1 and 3 were taken in the analysis, even though the cumulative effective modal mass was of 73%, as the contribution of the other modes was rather low.In this way the contribution of the undesirable higher modes is avoided.
The Newton-Raphson iteration method was used in this computation, while it was necessary to use an implicit Hilbert-Hughes-Taylor (HHT) method in DIANA 9.4 [8], for time integration.The HHT method (known as α methods) is actually a generalization of the Newmarks method.By this method it is possible to introduce numerical dissipation in higher modes without degrading the order of accuracy [8].
The reasoning behind the adoption of the HHT method lies in the fact that masonry has a very low tensile strength, so there is a rapid transition from the elastic range to the fully cracked stage with development of a large number of distributed cracks, leading to almost no stiffness.This all leads to problems of convergence and, additionally taking into account that the stiffness matrix has to be updated at each step, making the calculation time consuming.Secondly, this method has proven useful in structural dynamic simulations with many degrees of freedom.[1,2,11].
The increment value of ∆t = 0.01 sec was selected due to the values of the most important periods of the structure and the need to have an accurate time response.

Constitutive modelling laws
Physical non-linear behaviour of the masonry walls is defined through the total strain fixed crack model detailed in Diana [8].In this way the cracks are fixed in the direction of the principal strain vectors being unchanged during the loading of the structure.
For hysteretic behaviour of masonry as indicated in Figure 8 parabolic stress-strain relation for compression, based on Hill-type yield criterion, was chosen with no lateral confinement and no lateral crack reduction, with the compressive strength in the value of, and the corresponding compressive fracture energy amounting to Gc = 6,51 N/mm.
The post-cracked shear behaviour was defined by taking i nto account the retention factor of its linear behaviour, which reduces its shear capacity according to the following equation: (1) gdje je β r (retention factor) koji se kreće u granicama od 0 < βr ≤ 1, a G predstavlja modul smicanja za neispucali materijal.
Tension path, based on Rankine-type yield criterion, was described by an exponential tension softening diagram having a tensile strength of ft = 0.2 N/mm 2 , and respectively the tensile fracture energy being equal to
The shear retention factor, β r , was left at the default value of 0.01.This means that the shear strength of the material will be reduced to one percent of the original shear strength when cracks form.[1,2].Slika 8. Nelinearne karakteristike materijala [1,2,11] Figure 8. Hysteretic Behaviour of Masonry [1,2,11]

Analysis and discussion of Results
In order to view the development of the damage and stiffness degradation, as a damage indicator, in the structure it was necessary to investigate the damage pattern (principal tensile strains distribution) in different time steps.The displacement vs. time of the control node 44014 was chosen and plotted as indicated Figure 9. Several time instances during the earthquake action are presented and stiffness degradation evaluated.The time instances that have been selected are indicated in Figure 9. ment and stiffness degradation of the wall W-Y6 (see also Figure 5) will be discussed.The first peak is evident at t1 = 3.29 s and the damage pattern is shown in Figure 10.The formation of the first cracks is located at the contact between the basement, made of reinforced concrete, and ground floor, made of masonry.The same pattern is kept at the time t2 = 3.41 s just in the opposite side of the wall (Figure 10a) and b)).
The second sets of peaks are and (t3 = 7.79 s) in the two opposite direction.The crack development is shown in Figure 11(a) and (b) respectably.Finally, the damage pattern on the structure after the earthquake, meaning at the time ts = 23.87 s is shown in Figure 12.The concentration of damage is located at the openings as well as in the ground level and the first floor.The creation of the typical "X" cracks for shear behaviour is evident in Figure 12.

STIFFNESS DEGRADATION AND ENERGY DISSIPATION
Determining, or rather estimating the correct stiffness is of the utmost importance, for example for the deformation-based design of masonry structures [12,17].It is the hysteresis curve that can be used for the estimation of the deformation capacity of masonry.Usually the Young's and shear modulus is determined from the applicable codes and not through experimental tests.It is commonly the characteristic compressive strength that is determined from experiments and then used as the basis for calculation of other mechanical characteristics of masonry.This value does not represent the actual stress state in the masonry wall subjected to cyclic shear loading [12].

Stiffness degradation
The shear wall stiffness is assessed from the hysteresis curve shown in Figure 13.The aspect ratio (height over length) of the wall is 1.50.Maximal resistance is defined with values: Hmax obtained from the calculations is 474.88kN and dHmax=8.53mm.Maximal displacement at the ultimate resistance amounts to dmax = 11.38mm and the corresponding Hu amounts to 430.73kN.
Da bi se procenila degradacija zida, potrebno je izračunati sekantnu krutost (Ks,i) za svaki ciklus.Ova vrijednost izračunata je prema sledećoj formuli: As it can be seen the stiffness degradation as a damage indicator occurs at shear failure modes due to reverse cyclic loads.The horizontal loads are distributed according to the stiffness of the walls and this is seen by the transmission of the number of cracks from one wall to the other.As the cracks occur on one wall, the transfer of the load changes as different distribution is obtained in respect to the residual wall stiffness [1,20].
In order to evaluate the degradation of the wall it was necessary to calculate the secant stiffness (Ks,i) for each cycle.This value was calculated according to the formula: (2) gdje je: -sekantna krutost za i ciklus -horizontalna sila pri maksimalnom pomaku za i ciklus -maksimalni pomak za i ciklus Degradacija krutosti jasno je vidljiva na slici 14.. Kako se pomjeranje povećava, smanjuje se sekantna krutost zida, što dovodi do jasnog zaključka o oštećenju zida i njenom smanjenom kapacitetu.Rezultati [19,21] ukazuju na to da je oblik degradacije krutosti -kao funkcije bočnog pomeranja u nedimenzionalnom oblikuprilično sličnog oblika, bez obzira na tip zidova (obični, omeđeni ili armirani). where: -secant stiffness as i cycle -horizontal load at maximum displacement at i cycle -maximum displacement at i cycle Degradation of the stiffness is clearly seen in Figure 14.As the displacement increases the secant stiffness of the wall decreases leading to the clear conclusion regarding the damage of the wall and its reduced capacity.The results [19,21] indicated that the shape of the stiffness degradation a s a function of lateral displacement in the non-dimensional form is of a rather similar form regardless of the masonry type (plain, confined or reinforced masonry).

Disipacija energije
Drugi, prilično važan parametar u analizi cikličnih odgovora konstrukcija jeste koeficijent disipacije energije zidova.Ovakav kapacitet procijenjuje se putem koeficijenta ekvivalentnog viskoznog prigušenja ( ζ eq), where: -secant stiffness at elastic limit -displacement at maximum horizontal load , -stiffness degradation parameters In the absence of experimental data it was suggested to use the value of , and for the case of normal compression stresses, not exceeding 20% of masonry's compressive strength, and cyclic lateral loads [6,22].In this case the parameters , were obtained by the regression analysis of the calculated curve resulting in , and . The obtained coefficient of determination, or the coefficient of multiple determination for multiple regression is equal to R 2 =0.91 and the proposed power function follows the trend of stiffness degradation in a good manner.
Energija disipirana viskoznim prigušenjem u jednom ciklusu harmonijskih vibracija, kako je definisano u [9], data je jednačinom (4) (ζeq), which is obtained when the energy dissipated in a vibration cycle of the actual structure is set to be equal to the equivalent viscous system [6].Damage indicators that consider the energy dissipation reflected in the strength and stiffness deterioration can be used successfully to control the design parameters [16].
In order to make an approximation of the equivalent viscous damping connected to the hysteretic behaviour, the concept of dissipated (ED) and stored (ESo)energy can be utilized.The dissipated energy in the wall is given by the area ED enclosed by the hysteresis loop in one cycle loading.
Graphical representation of the respective energies is illustrated in Figure 15.
The calculated values of the strain/stored potential energy and dissipated energy, as explained above for this particular case, is presented in the Figure 16.A similar trend of the energy dissipation was obtained in [7], which is comparable as the input material characteristics of the masonry structure are quite similar [1,2,7].The ratio between dissipated and input energy was in the range from 14 to 49%. ), s obzirom na to što je početno viskozno prigušenje ( ) jednako nuli, što ukazuje na to da zavisi samo od histeričnog ponašanja, iznosi 11,48%.Kada se govori o URM, ove veličine u funkciji su oblika loma, iz eksperimentalne i analitičke studije [10].U istraživanju, Magenes i Calvi predložili su ultimni međuspratni pomak od 0,5% i 1,0%, a ekvivalentno prigušenje jednako je 10% i 15%, usljed otkazivanja na smicanje i savijanje respektivno.Priestley i ostali [15], u istraživanju koje je sprovedeno nekih deset godina nakon [10], smanjuje ove granice međuspratnog pomjeranja za 20%, tj.0,4% za smicanje i 0,8% za lom On the basis of obtained values of dissipated and stored potential energy and utilizing the equation ( 7), the average value of the coefficient of equivalent viscous damping ( ), taking into account that the initial viscous damping ( ) ,is equal to zero, indicating that it is dependent only on the hysteretic behaviour, amounts to 11.48%.Regarding URM, these quantities are indicated in function of the failure mode, from an experimental and analytical study [10].In their research, Magenes and Calvi suggested an ultimate drift of 0.5% and 1.0%, and an equivalent damping equal to 10% and 15%, for shear and flexural failure respectively.Priestley et al. [15], in a research carried out some 10 years later than [10],reduced these drift limits by 20%, i.e. 0.4% for shear and 0.8% for flexural failure.These are also the limits
imposed by Italian Technical Code.So, now the equivalent viscous damping is assumed to be 15% for shear and 10% for flexural failure behaviour.A good consistency is obtained with the values proposed in [10,15].

CONCLUSION
In the presented paper, the seismic behaviour of a masonry building typical from Western Balkans under cyclic loading is presented and exploited.Its seismic behaviour seems to be controlled by the fundamental global modes.
With the increase of displacement, the concentration of damage is located at the openings as well as in the ground level and the first floor.The walls parallel to the load direction exhibit diagonal cracking caused by horizontal forces, as well as the diagonal "X" type cracking due to cyclic loading, leading to its reduced capacity.
From the calculations, it was confirmed that also for this building the stiffness degradation shape follows a power function trend.The obtained value of the coefficient of equivalent viscous damping amounts to 11.5%, which agrees with the proposals given by from other researchers.Investigations confirm that the effects of in-plane cyclic strength and stiffness degradation are crucial in determining the possibility of lateral dynamic instability.Here damage indicators take into account energy dissipation which is reflected in the strength and stiffness deterioration giving a clear indication of the behavior URM building.