Seismic risk assessment of adobe dwellings in Cusco, Peru, based on mechanical procedures

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1 Seismic risk assessment of adobe dwellings in Csco, Per, based on mechanical procedres N. Tarqe Istitto Universitario di Stdi Speriori - ROSE School, Pavia, Italy Civil Engineering Department, Catholic University of Per, Per H. Crowley Eropean Centre for Training and Research in Earthqake Engineering, Italy R. Pinho Strctral Mechanics Department, University of Pavia, Italy H. Varm Civil Engineering Department, University of Aveiro, Portgal ABSTRACT A procedre to evalate the seismic vlnerability of one-storey adobe dwellings located in Csco (Per) is presented here. The seismic capacity of these dwellings is based on a mechanical-based approach, where the inplane and ot-of-plane failre mechanisms are taken into accont. From a database with the principal geometrical properties of dwellings from Csco, random poplations of bildings were generated throgh Monte Carlo simlation. The capacity of each random dwelling is expressed as a fnction of its displacement capacity and period of vibration, and this is evalated for different damage limit states. The seismic demand has been represented by the displacement spectral shapes compted for different levels of intensity, considering the Pervian Seismic Code and the Erocode 8. Finally, from the comparison between capacity and demand, probability of failre have been obtained for different retrn periods. Keywords: seismic risk; adobe dwellings; displacement-based procedres; fragility crves. INTRODUCTION In this work the fragility crves for adobe dwellings placed in Csco, Per, have been derived following the Displacement-Based Earthqake Loss Assessment method (DBELA, Crowley et al. 6), where the displacement capacity and period of vibration of each random generated bilding is compted sing simple mechanics-based and empirical eqations, and compared with the seismic demand to obtain the probability of exceedance. The procedre shown here can be applied to another type of adobe bildings placed in other zones, bt taking into accont the typical geometrical properties and the seismic hazard of the zone.. CAPACITY OF ADOBE DWELLINGS.. In-plane capacity From a previos work, the seismic capacity of adobe walls in terms of displacement capacity and period of vibration has been defined (Tarqe 8). The in-plane limit states (LS) and period of vibration (T y ) were obtained based on a cyclic test carried ot at the Catholic University of Per (Blondet et al. 5) and they were related to the wall height (Table ). The damping vales (ζ) for the limit states were compted based on the hysteretic crves obtained from the test. The period of vibration for the limit states are compted with Eqations. and.. 3/4 T C H (.) y T LSi T y LSi (.)

2 where C is the period coefficient (close to.9, Tarqe 8), H is the wall height, T y is the elastic period of vibration and T LSi is the period of vibration for LS, LS3 and LS4. Table. In-plane limit states for adobe bildings Limit state Description Drift, Damping, ζ (%) Dctility, LS LSi LS Operational.5% LS Fnctional.% LS3 Life-safety.6% 5 LS4 Near or collapsed.5% 6.. Ot-of-plane capacity The ot-of-plane capacity has been defined following the work developed by Doherty et al. () and Griffith et al. (5), where the ltimate displacement ( ), measred at the top of a cantilever wall, is related to a percentage of the wall thickness (t) according to the wall spports and wall axial load, here.8t. The ltimate displacement limit state is affected by a redction factor (from.8 to ) to take into accont degradation of existing masonry walls (Restrepo-Velez 4, see Table ). Besides, two intermediate limit states (LS and LS) were considered according to the athor s experience and related to the grade of damage de to vertical cracks at wall corners (Tarqe 8). To compte the displacement capacity for LS, a 3mm width horizontal crack at the base of one cantilever adobe wall was taken. Assming that the wall will rotate as a rigid body at the base, a maximm displacement at the top of the wall of abot 7mm was compted sing.45m and.44m as the mean vales of the wall height and wall thickness from typical hoses in Csco, respectively. The displacement capacity for LS was compted directly from the displacement ratio ρ (Table, 3) times the mean vale of, reslting in 45mm approximately. The damping vale was taken as 5% de to the rocking behavior. Table. Ot-of-plane limit states for adobe bildings Limit state Displacement capacity for parapets or simply spported walls ζ (%) LS 7mm 5 LS 5 LS3 5 The period of vibration for the limit states are compted with Eq..3 and.4. LS T LSi (.3) g LS TLS (.4) g where T LSi and T LS are the period of vibration for the intermediate and ltimate limit state ( LS ), respectively; ρ and ρ are the displacement ratios for the tri-linear model of walls de to ot-of-plane forces (Table 3); is the redction factor explained before; λ is the collapse mltiplier (which depends on the failre mechanism of the wall), and g is the gravity acceleration. Table 3. Displacement ratios for the tri-linear model (Griffith et al. 3) State of degradation at cracked joint / (%) / (%) New 6 8 Moderate 3 4 Severe 5

3 The eqations for evalating the collapse mltipliers can be fond in Restrepo-Velez (4). For example, for overtrning of walls (Figre ) the Eq..5 is sed to compte the collapse mltiplier. t L hs r K r Lt pef s s b 3 (.5) tl hs K r L where t and L are the thickness and length of the front walls, β is the nmber of edge and internal perpendiclar walls, Ω pef is a partial efficiency factor to accont for the limited effect of the friction, h s is the height of the failing portion of the wall, μ s is the friction coefficient, s is the staggering length (normally it is the brick half length), b is the thickness of the brick nits, r is the nmber of corses within the failing portion (assming corses in the rocking portion); K r is the overbrden load, in which Q r is the load per nit length on the top of the front wall, and γ m is the volmetric weight of masonry. Figre. Failre mechanism for ot-of-plane (Restrepo-Velez 4). 3. GEOMETRICAL DATABASE In 4, Blondet et al. (4) carried ot a bilding-to-bilding srvey in Csco, a city located at the Pervian highland. According to the last censs (INEI 7), Csco has arond 76% of hoses bilt in adobe (Figre ) or tapial (rammed earth) and at least 54% of them are of -storey. The data which was collected inclded the dimensions of walls and bricks, the height of gable, nmber of rooms, nmber of openings, etc. With that data it was possible to define the mean vales and standard deviations of these geometrical properties. For example, it was fond that the mean wall thickness of adobe bildings in Csco is.44m, and the mean wall height is.45m for -storey bildings. The thickness of the wall is fairly niform amongst the bildings analysed, confirmed by the low standard deviation. Figre. Adobe bildings in Csco, Blondet et al. (4).

4 The variability of each of the parameters in this stdy (i.e. wall lengths, wall heights, adobe brick dimensions, etc.) were represented by histogram plots which were then fit to a probability density fnction (PDF). Figre 3 shows the histograms and the best-fit PDF for some of the geometrical parameters. 5 4 # of bildings # adobe bricks Storey height (m) Width of bricks (m) a) Height of -storey bildings b) Brick width.5 Figre 3. Histograms and PDFs for the mean geometrical properties. 3.. Generation of random data With Monte Carlo simlation it was possible to generate an artificial stock of bildings (Crowley et al. 6). The inpt data (based on the statistics of the 3 adobe dwellings; Blondet et al. 4) was represented by the mean and standard deviation vales of the principal geometrical properties (Table 4) and by the best fit for the probability density fnctions (e.g. lognormal, normal, niform and discrete distribtions). Some vales as the overbrden load for typical adobe dwellings were taken from Tejada (). The standard deviation vales for the limit states have been established p to % of the mean vale to take into accont the variability of parameters. Some parameters can be given jst as integer (Table 5). Then, the displacement capacity and the respective period of vibration for different limit states for each of the randomly generated bildings was generated (Figre 4). Table 4. Random variables sed in DBELA for the definition of strctral capacity of adobe dwellings Description Variable Mean (μ) Standard deviation (σ) Distribtion In-plane failre mechanism Inter-storey height (m) h p.45. Lognormal Pier height (m) h sp.45. Lognormal Period coefficient C.88.4 Normal Drift limit state LS.5. Lognormal Drift limit state LS.. Lognormal Drift limit state 3 LS3.6.5 Lognormal Drift limit state 4 LS4.5. Lognormal Ot-of-plane failre mechanism Wall width (m) t.44.4 Lognormal Wall length (m) L Lognormal Staggering length (m) s.3.8 Lognormal Thickness of brick nits (m) b.44.4 Lognormal Height of brick nits (m) h.5. Lognormal Overbrden load (kn/m) Q r Specific weight (kn/m 3 ) γ m Redction factor for.85.5 Normal Friction coefficient μ s Δ /Δ ρ.. Normal Δ /Δ ρ Limit state (m) LS.7. Normal # of edge and internal orthogonal walls See Table 5a Discrete # of corses within the storey height r See Table 5b Discrete

5 Table 5. (a) # of edge and internal orthogonal walls; (b) # of corses within the storey height a) Nmber Total Cmlative b) Nmber Total Cmlative Displacement capacity (mm) 5 5 LS LS LS3 LS4 Displacement capacity (mm) 3 LS LS LS a) In-plane capacity b) Ot-of-plane capacity Figre 4. Seismic capacity of adobe walls for different limit states. 4. SEISMIC DEMAND The seismic demand has been represented by many Displacement Response Spectra (DRS) compted from two code spectrm: the Pervian Seismic Code and the Erocode 8. A soil type with 8 < V s3 < 36m/s was sed for Csco. 4.. Pervian Seismic Code The Eqations 4. and 4. are sed to evalate the acceleration response spectrm (ARS) with the Pervian seismic code (VIVIENDA/SENCICO 3): Z U SC Sa g R (4.) TP C.5.5 T (4.) where S a are the vales of the spectral ordinates; Z is the expected PGA; U is a factor that depends on the importance of the bilding; S is the soil factor; C is the seismic amplification factor and shold be less than.5; R is a redction factor; and T P is the period corresponding to the end of the platea zone. For hoses, U is eqal to and the soil type in Csco has been classified as intermediate soil regarding the Pervian Seismic Code, which is close to the soil type C given by EC8, and ths the soil factor is eqal to. and T P is.6s for intermediate soils. The acceleration spectral ordinate for T = s does not give the PGA vale (as is the case in the EC8 spectrm, CEN 5). For this reason the Acceleration Response Spectra (ARS) shape starts directly from a platea zone p to T P. Since the Pervian code does not specify the corner period for displacement response spectra, from where the displacement is constant, the acceleration spectra have been directly transformed to displacement spectra even after to s. Since adobe walls have damping vales different than 5%, the acceleration response spectra are affected by the damping correction factor η (Eqation 4.3, Priestley

6 et al. 7). 7 (4.3) where the eqivalent viscos damping is given in %. 4.. Erocode 8 The acceleration spectral shape specified by EC8 (CEN 5) has been anchored to increasing levels of PGA to generate a set of acceleration response spectra which have then been mltiplied by (T/) to obtain the displacement response spectra. Following the recommendations of EC8, the displacement spectra have been taken as constant after s. The following eqations allow to compte the ARS. T T TB : Se( T) ag S.5 TB (4.4) TB T T C Se ( T ) ag S.5 : (4.5) TC T T D TC : Se( T) ag S.5 T (4.6) T D T 4s TC TD : Se( T) ag S.5 T (4.7) where S e are the vales of the spectral ordinates; a g is the PGA vale; S is the soil factor; T B, T C and T D are the characteristic periods of the spectral shape and depends on the grond type and is the damping correction factor (Eq. 4.3) that shold be for the elastic response spectra. The parameters given by Erocode 8 were taken assming that earthqakes in Csco have magnitdes higher than M w 5.5 (Ericksen et al. 954). The soil type selected was C (8 < V s3 < 36m/s ), which means soil factor S =.5. The reslting vales for T B, T C, T D were.,.6 and s, respectively. Figre 5 shows two acceleration and related displacement spectral shapes compted from the two seismic design codes considering a g.s=.7g. It seems that the spectral shapes from both codes are similar, so the compted fragility crves will give similar reslts from both seismic codes. However, it shold be important to analyze other spectral shapes from Grond Motion Prediction Eqations (GMPE) in order to see the inflence of different spectral shapes on the fragility crves..5. Acceleration (g) Pervian code EC8 Displacement (m).5..5 Pervian code EC a) Acceleration Response Spectra b) Displacement Response Spectra 3 Figre 5. Seismic demand.

7 5. FRAGILITY CURVES FOR ADOBE DWELLINGS IN CUSCO The constrction of the fragility crves starts with the comptation of the probability of exceedance, which is obtained for the first limit state by calclating the ratio between the nmber of dwellings with a displacement capacity lower than the displacement demand and the total nmber of dwellings (Figre 6). The probability of exceeding for sbseqent limit states is obtained from the ratio between the nmber of dwellings that exceeded the previos limit state and that still have a displacement capacity lower than the displacement demand at this next limit state, and the total nmber of dwellings. This evalation can be repeated for a nmber of displacement response spectra with increasing levels of peak grond acceleration (PGA) and plotted to prodce fragility crves P failre : N f /N Displacement (m) Displacement (m). Demand for a given Tr N: total nmber of N f : # of bilding having bildings capacity less than the demand a) Example of capacity vs demand b) Zoom of Figre 6a Figre 6. Evalation of the probability of exceedance for fragility crves (Tarqe 8). The elastic DRS shold be mltiplied by the modification factor η in order to take into accont the higher levels of damping for the in-plane analysis. For the ot-of-plane, the elastic DRS shold be scaled by.5 for comparison with the displacement capacity (Griffith et al. 5). The adobe bildings generated herein have in-plane limit state periods of vibration between. and.7s and ot-of-plane limit state periods of vibration between.75 and.5s. Fragility crves for adobe dwellings in Csco are showed in Figre 7. Probability of exceedance Probability of exceedance % 9% 8% 7% 6% 5% 4% 3% % % % % 9% 8% 7% 6% 5% 4% 3% % % % LS: Pervian code LS: Pervian code LS3: Pervian code LS4: Pervian code.5..5 PGA (g) Probability of exceedance % 9% 8% 7% 6% 5% 4% 3% % % % a) In-plane fragility crves LS: Pervian code LS: Pervian code LS3: Pervian code PGA (g) Probability of exceedance % 9% 8% 7% 6% 5% 4% 3% % % % b) Ot-of-plane fragility crves LS: EC8 LS: EC8 LS3: EC8 LS4: EC PGA (g) LS: EC8 LS: EC8 LS3: EC PGA (g) Figre 7. Fragility crves considering the Pervian code and the Erocode 8.

8 6. CONCLUSIONS Fragility crves for typical adobe dwellings in Csco have been derived here following the DBELA procedre. Data from 3 srveyed dwellings were sed to compte the mean, standard deviation and probability density fnctions of relevant geometrical properties. Using Monte Carlo simlation it was possible to generate bildings stock and to evalate the seismic capacity, in-plane and ot-ofplane, of the adobe dwellings. The seismic hazard was represented by a nmber of displacement response spectra. The probability of exceedance, considering each limit state, was compted by comparing the capacity with the demand. The spectral shapes from both seismic codes adopted give close spectral ordinates ntil the corner period specified by the EC8. The Pervian seismic code does not specify any corner period; therefore, the ordinates from the DRS increases in vale either after the corner period. This aspect inflences the fragility crves for LS3 of the ot-of-plane behavior de to the high period vales for LS3. For the in-plane, both seismic codes give close fragility crves. The compted fragility crves show the high seismic vlnerability of adobe dwellings. It seems that for events with PGA higher than.g, some in-plane cracking is expected to see with vertical damage at corners of walls. For events with PGA higher than.5g, a complete overtrning of walls de to ot-of-plane failre may occr, and the small blocks formed by diagonal cracking cold even overtrn. The shape of the DRS inflences on the fragility crves, so other spectral shapes shold be taken into accont in the analysis. REFERENCES Blondet, M., Tarqe, N., Acero, J. (4). Stdy of the seismic vlnerability of non-engineering bildings located at the Pervian Highlands, in Spanish, Joint Project SENCICO-PUCP, Catholic University of Per, Lima, Per. Blondet, M., Madeño, I., Torrealva, D., Villa-García, G., Ginocchio, F. (5). Using indstrial materials for the constrction of safe adobe hoses in seismic areas. Earth Bild 5Conference, Sydney, Astralia. CEN, (5). Design of Strctres for Earthqake Resistance, Part : General rles, seismic action and rles for bildings, Erocode 8. ENV-998--, Comité Eropéen de Normalisation, Brssels, Belgim. Crowley, H., Pinho, R., Bommer, J.J., and Bird, J. (6). Development of a Displacement Based Method for Earthqake Loss Assessment. Eropean School for Advanced Stdies in Redction of Seismic Risk (ROSE School), IUSS Press, Pavia, Italy. Doherty, K., Griffith, M.C., Lam, N., and Wilson, J. (). Displacement-based seismic analysis for ot-ofplane bending of nreinforced masonry wall, Jornal of Earthqake Engineering and Strctral Dynamic 3, Ericksen, G., Fernandez, J., and Silgado, E. (954). The Csco, Per, Earthqake of May, 95. Blletin of the Seismological Society of America, No., vol. 44, 97-. Griffith, M.C., Magenes, G.M., Melis, G., and Picchi, L., (3). Evalation of Ot-of-Plane Stability of Unreinforced Masonry Walls Sbjected to Seismic Excitation, Jornal of Earthqake Engineering 7, special Isse No., Griffith, M.C., Lam, M., and Wilson, J. (5). Displacement-based assessment of the seismic capacity of Unreinforced Masonry walls in bending, Astralian Jornal of Earthqake Engineering, Vol. 6, No.. INEI. Censs 7, (7). National Institte of Statistic and Informatics, Lima, Per. Available at October 9 from Priestley, M.J.N., Calvi, G.M., and Kowalsky, M.J. (7). Displacement-Based Seismic Design of Strctres, IUSS Press. Pavia, Italy. Restrepo-Velez, L. (4). Seismic Risk of Unreinforced Masonry Bildings, Doctoral Thesis, Eropean School for Advanced Stdies in Redction of Seismic Risk (ROSE School). University of Pavia, Pavia, Italy. Tarqe, N. (8). Seismic Risk Assessment of Adobe Dwellings. Eropean School for Advanced Stdies in Redction of Seismic Risk (ROSE School), University of Pavia, Pavia, Italy. Available at October 9 from: Tejada, U. (). Bena Tierra, apntes para el diseño y constrcción con adobe (in Spanish), CIDAP: Centre of Researching, Docmentation and Consltant Assistance, Lima, Per. VIVIENDA/SENCICO, NTE E.3 Technical Code for Bildings, (3). Earthqake Resistant Design (in Spanish), Ministry of Hosing, Constrction and Sanitation, SENCICO. Per.