Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 1536 379 9

Seismic risk of monumental structures of Kathmandu Valley

PN. Maskey lnstitute oJ Engineering, Tribhuvan University, Kathmandu, Nepal

T.K. Datta /ndian lnstitute oJTechnology Delhi, New Delhi, In dia

ABSTRACT: The seismic risk ofthe peculiar monumental temples ofKathmandu Valley is evaluated using a simplified PRA procedure, considering the seismicity and the local soil conditions. After determination of the risk consistent seismic input for the temple locations, the probabilities of failure of the temples are obtained for different levels of PGA. The free field ground motion and input response spectra for the structures are obtained after one dimensional wave propagation analysis, considering both linear and nonlinear behavior of soil overlying the bedrock. The main core masonry structure ofthe temples is modeled by finite solid elements. The reliability analysis ofthe temples is carried out using first order second moment method considering various uncertainty factors for the response and the capacity ofthe structures. Major finding ofthe study shows that the fragility curves denoting the seismic risk of the monumental structures are significantly influenced by the soil characteristics.

INTRODUCTION

Many structures of the Kathmandu Valley created in the medieval period (13th to 18th century) possess heritage value. These monumental structures symbol­ize the high status of art, architecture and culture of Nepal. Of these historically important structures, the peculiar multi-tiered 'pagoda' type of temples repre­sents the best ofthe original Nepali style monumental structure. A 'pagoda ' type temple is usually a struc­ture with diminishing dimensions having a series of pyramidal roofs. These temples are made primarily of unreinforced brick masonry as the main structural sys­tem, with timber members as other elements of the structures.

The Kathmandu Valley, because of its proximity to many active faults and the peculiar neo-tectonic and geo-technical features of the Valley, has a high seis­mic risk. The unconsolidated sediments, dominating the subsurface soil condition ofthe Valley, causing the site amplification are one ofthe major factors influenc­ing the leveI of ground motion within the Kathmandu Valley. The Kathmandu Valley has been subjected to frequent earthquakes of moderate intensities, and about once in a century to disastrous earthquakes of higher magnitude. The damage records of previous earthquakes in the Kathmandu Valley indicate severe damages of many heritage structures including the temples.

The Kathmandu Valley is a region which has a long history of earthquakes but does not have enough earthquake data, absence of which indicates high uncertainty of ground motion denoting the need for assessing probable seismic input for the analysis of structures in the region. It has long been recognized that the precious monumental structures of the Kath­mandu Valley are required to be conserved against the future possible earthquakes. A systematic risk analysis for these monumental structures has yet to be carried out with the probable seismic input.

However, there have been several studies in relation to the seismic risk and probabilistic risk analysis of different kinds of structures. Hwang et a!. (1984) pro­posed a reliability analysis method to estimate the limit state probability in the life time of structures and gener­ate fragility curves. Sabol (1986) proposed a method­ology that permits the assessment of the seismic risk associated with a group of buildings, and incorpo­rates relevant aspects of seismie hazard assessment. Ravindra (1989) provided an overview of the seis­mie PRA methodology, described some of the reeent PRA applieations in the nuclear power plant. Takeda et a!. (1989) proposed a practical seismic fragility evaluation method for structures and equipment sys­tems. Mashalay & Datta (1990) developed a procedure for the seismic risk analysis of buried pipelines that provides an estimation of the annual probability of occurrence of different damage states, called damage

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indices, in a component segment of the general net­work system of buried pipelines. Other literatures on probabilistic risk analysis of structures include those by Shinozuka et aI. (1989), Stewart (1991), Gusella (1991), Matsubara et aI. (1993), Budnitz et aI. (1995) and Lee et aI. (1998).

Since the monumental structures are old and are constructed of traditional materiais like brick masonry in mud mortar and timber, a suitable method of analy­sis is required to assess their reliability. The available sophisticated methods of analysis may be difficult to employ in the reliability analysis of the monumental structures ofthe region. With an objective to assess the seismic risk of the monumental structures and use it for determining vulnerability ofthe monumental struc­tures of the Kathmandu Valley a simplified approach is presented. The proposed approach consists of proba­bilistic method to determine the risk consistent seismic input for locations with scanty records of earthquake, and the evaluation of the seismic reliability of the structures. The risk consistent seismic input is deter­mined for Bhaktapur city, best representing the typical region of the Kathmandu Valley with a large number of monumental structures. The ground motion at the bedrock is obtained considering the seismic sources in the vicinity ofthe region and modeling the occurrence of the earthquakes as Poisson processo Considering the large deposit of clay type soils in the region, the ground motion at the bedrock is modified to obtain the free-field values for the analysis. Both linear and non-linear soil conditions are taken into account in the site response analysis to obtain the free-field ground motion.

In the simplified probabilistic risk analysis, the uncertainty ofthe response is obtained by multiplying the mean response by 4 uncertainty factors, which are uncertainties in ground motion input, material prop­erty, structural modeling and analysis procedure. The uncertainty of the capacity of the structure is simi­larly obtained by a multiplying factor related with the uncertainty in material strength. The mean response is obtained by analysing the temples under vertical load and equivalent lateral load due to earthquake using eight-noded solid finite elements. A modified seismic coefficient method with the utilization of risk con­sistent response spectra is applied to determine the equivalent load due to earthquake. The probabilities of failure of the temples are determined for differ­ent leveis of PGA by the first order second moment (FOSM) method of reliability. The fragility curves denoting the risk of the temple structures are thus obtained.

The proposed method is illustrated by presenting the probabilistic risk analysis ofthe Nyatapola Temple, the tallest temple located in the protected monument zone enlisted by UNESCO after determining the risk consistent seismic input for the site.

2 MONUMENTAL STRUCTURES OF KATHMANDU VALLEY

All the traditional buildings and the monumental struc­tures including the temples of the Kathmandu Valley constitute the major parts of cultural heritage ofNepal. These historical structures, all with suitable forms of architecture, and full of arts exhibiting their crafts­manship and architecture in the best manner, represent today the civilization ofthe country. It is evident from the study of these structures that the basic concept of seismic resistant design was well understood, and the best avai lable materiais and technology were utilized in the construction of the temples and other struc­tures ofpublic importance including dwelling houses. These structures are constructed with basic materiais like brick, rich mud mortar, timber and stone.

The multi-tiered 'pagoda' style oftemples is indige­nous in form, and has been developed out of the country's long tradition. Although the oldest known reference to these temples in Nepal is at about the middle of the seventh century A.D., most developed forms of this type of temples and many in numbers were built in the Valley in the 18th century. This type oftemple, in general, is characterized by a square plan or occasionally by a rectangular plan on which the temples are laid. These temples rise in severa I stories resting on single or multi-Ieveled plinth bases. Each storey of the temple is indicated by a sloping roof of tiles or metal, supported at the eaves by a range of artistic carved struts. The roof with such detai l is repeated in each storey, but with a gradual reduction in proportion giving it grace, elegance and impression of upward ascent. Nya-ta-pola (five-tiered temple in Newari dialect) ofBhaktapur represents the best exam­pie of this type of temples. There are altogether 58 temples of'pagoda' style in Bhaktapur city only which represents the typical city ofKathmandu Valley. These temples differ from each other in terms of age, form, style, dimensions, and deities, and are distributed all over the historic city area ofBhaktapur. In view ofthe heritage value of these monumental zones, and need to conserve them UNESCO has enlisted Bhaktapur, particularly the Durbar Square, as one of the seven protected monument zones of the Kathmandu Valley under World Heritage.

Most of the existing historical monumental struc­tures are based on the structural system made ofbrick masonry in mud mortar. In the construction of the temples the masonry walls are discontinuous in verti­cal direction at different fioor leveis. The peculiarities of connecting beams and struts including the struc­tural elements at each fioor levei make a 2-dimensional modeling appear inappropriate.

In order to obtain the results nearest possible to the reality, and considering the various modes offail­ure, a solid finite element is chosen as the type of

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3-dimensional element. The three-dimensional eight noded isoparametric element has eight nodes located at the corners and has three-dimensional degrees of freedom at each node.

3 SIMPLIFIED PROBABILISTIC RISK ANALYSIS PROCEDURE

The Probabilistic RiskAnalysis (PRA) procedure con­sists basically of two main components: (I) determi­nation ofrisk consistent seismic input, and (2) seismic reliability analysis of the structures.

3.1 Determination ofrisk consistent seismic input

In order to determine the risk consistent seismic input for analysis of structures in the Monument Zone, a risk consistent response spectrum at the bedrock is first obtained. For the purpose, the risk consistent spectral shape is obtained by an empirical relationship sug­gested by Takemura et a!. (1989). The empirical rela­tionship relates the normalized ordinates of response spectrum in terms ofthe magnitude of earthquake and the source-to-site distance. The prescribed time his­tory of input ground acceleration at the bedrock is directly simulated from the normali zed risk consistent spectrum using the method proposed by Khan (1987).

A modification ofthe free field ground motion due to the local soi! effect is carried out by a one dimen­sionaI wave propagation analysis. The time history of the free field absolute ground acceleration is obtained by integrating the equation ofmotion for the soillayers subjected to the base acceleration for both linear and nonlinear condition. The obtained PGA amplification due to the overlying soil is used to modify the seis­mic hazard curve drawn for the bedrock into the same for the free field. The response spectrum of absolute acceleration at the free field is obtained from the free field time history ofthe absolute acceleration .

3.2 Seismic re/iabiliiy ana/ysis oftemp/e structures

To determine the seismic risk of the monumental structures situated in the Monumental Zone, response analysis of the structures is first carried out by the seismic coefficient method. For a chosen value of PGA, the risk consistent input spectral shape is multi­plied by the PGA to obtain the spectral ordinates. The equivalent lateralload is found by a modified seismic coefficient method. The risk consistent response spec­trum ordinate is used in this method for determining the lateral load. The fundamental time period required for finding the lateral load is obtained from the free vibration analysis ofthe monumental structures. In the modified seismic coefficient method, the base shear is

obtained by multiplying the response spectrum ordi­nate corresponding to the fundamental time period of the structure with the total mass.

The proposed probabilistic risk analysis method for the monumental structures attempts to draw a fragility curve showing the probability of failure against the seismic intensity parameter (PGA) values. The prob­ability of failure is determined considering various uncertainty factors in the reliability analysis part.

Under the seismic and vertical load condition, the expected value ofthe response is given by

(I)

where r is the response quantity of interest at a crit­icaI section for which the failure is assumed to take place, and Fi (i = 1, 2, 3, 4) are the independent ran­dom variables representing deviation of the actual response from r. The random variables F;'s take care of uncertainties arising due to ground motion input variability (FI) , material property variability (F2), uncertainty in structural modeling (F) ), and uncertainty in the method of analysis (F4 ). These factors are assumed to be log-normally distributed with median values as unity. Hence the expected response R also is a log-normally-distributed random quantity. lts mean value is In R and the logarith­mic standard deviation of the expected response R is given by

(2)

in which f3R is the logarithmic standard deviation of R, and f3i (i = 1, 2,3,4) are the coefficients ofvariation of Fi (i = 1, 2, 3, 4) respectively. Evidently, f3i, the coef­ficient of variation of Fi, is equal to the logarithmic standard deviation a'I/Fi for f3i :::: 0.25.

The median value of FI , the factor representing the variability of response caused by input motion's vari­ability, is unit and the logarithmic standard deviation f31 is evaluated as:

/31 = In (':84 J ' 50

(3)

where r 84 is the response value corresponding to input motion of 84% non-exceedence spectra, and r 50 is the value corresponding to input motion of the median spectra.

The facto r F2 represents the variability resulting from the system parameter variation. Its logarithmic standard deviation f32 is evaluated, in the same manner as the FI case, as the logarithm of the ratio between the 84th percentile non-exceedence and the median responses. The factor F) accounts for the uncertainty involved in the modeling of the system and in the analytical methods for the evaluation of response r.

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It represents the difference between the actual response and the calculated one. In general, the median value of F3 is taken as unity and coefficient of variation fh ranges from 0.15 to 0.2 (Takeda et a\. 1989). F4

is the factor accounting for the uncertainty resulting from the simplification that a Monte Carlo simula­tion is not directly performed in the evaluation of the expected response, and is assumed to have a median value of unity with a coefficient of variation of 0.15 (Takeda et a\. 1989).

The probability of failure for an assumed value of PGA, say 'a' , is given by

PAa) =P{R(a) > C}

P{R(a) - C}>O

(4)

(5)

in which, R (a) represents the expected response for an assumed value 'a ' of PGA, and C represents the capacity.

It is assumed that R (a) and C are uncorrelated, that is, they are independent variables having log normal distributions. In that event, the probability of failure, PI (a) is obtained from the value of </J, calculated as

~ = InR - ln C

J f3R 2 + f3c 2 (6)

in which, R and C are the median values of R and C; f3e is the coefficient ofvariation ofthe capacity and f3R is given by Equation 2. The fragi lity curve is obtained by plotting PI (a) against different values ofPGA. Note that PI (a) is determined from </J using standard tables (Ranganathan, 1990).

4 NUMERICAL STUDY

As an illustrative example, the proposed probabilis­tic risk analysis procedure is applied in determination of seismic risk of five-tiered 'pagoda-style' Nyatap­ola temple located at Taumadhi Square induded in the Preserved Monument Zone of Bhaktapur City in Kathmandu Valley. Bhaktapur City, in general, has a soil strata basically composed of day materiaIs hav­ing a shear wave velocity varying from 143 m/se c to 370 m/sec approximately at different layers.

The seismic hazard potential and the risk consistent response spectra at the bedrock leveI of Bhakta­pur City are determined considering the earthquake sources in the vicinity, assuming the earthquake occur­rence as Poisson's process, and considering empirical attenuation relationships. One dimensional wave prop­agation analysis is carried out, as described earlier, to obtain the free field ground motion and risk consis­tent response spectra for the acceleration at the surface of the site. The site response analysis is carried out

" 1.00 "-~------;:=====:;-l ] u x ~ -;; " " " <

0.80

0.60

'õ 0.40 Q ;.:: :E '"

0.20

~ 0.0 0.1

---- Linear _ Non-linear

0.2 0.3 OA 0.5 0.6 PGA(g)

Figure I. Free-field seismic hazard curve for Taumadhi Square, Bhaktapur City.

" 4.0 -,--------------------, o .~ 3.5 Linear Site Response

"8 3.0 u < 2.5 g g 2.0 '" {/') 1.5 ] ~ 1.0 § 0.5

Z 0.0 +-_.--_.---=:;:::::::::::;::::==::===1 0.00 0.50 1.00 1.50 2.00 2.50 3.00

Time Period (sec)

Figure 2. Normalized risk consistent response spectrum for free-field absolute acceleration (linear site response).

1.20 :§

1.00 " Non-linear Site Response

o .~ 0.80 <3 u 0.60 u < " OAO '5 Õ 15 0.20 <t:

0.00 0.00 0.50 1.00 1.50 2.00 2.50 3.00

Time Period (sec)

Figure 3. Risk consistent response spectrum for free-fie ld absolute acceleration for PGA at bedrock = 0.23 g (non-linear site response).

considering the linearity as well as the non-Iinearity ofthe soil strata ofthe location. The free-field seismic hazard curves indicating the seismic potential at the temples si te are shown in Figure 1.

The free-field response spectrum at the same site considering the linear soil condition is presented in Figure 2. Figure 3 presents the free-field response

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ELEVATION

22800

PLAN

Figure 4. Plan, elevation and section of Nyatapola temple.

0.40 .---------------------,

0.35 e ~ OJO ~ 0.25

~ 0.20

:E 0.15

" .g 0.10

~ 0.05

0.00 +--""T--,-----.-----,,---...,---i

0.00 0.05 0.10 0.15 0.20 0.25 0.30

POA (g) aI Bedrock

Figure 5. Comparison between fragil ity curves for lin­ear and non-linear soil conditions for Nyatapola temple (reference PGA at bedrock).

spectrum for the site considering non-linear site response for PGA = 0.23 g.

The plan, elevation and section of Nyatapola tem­pIe, chosen for the analysis, is presented in Figure 4. The five storied temple is located at Taumadhi Square, has an 8.80 m x 8.80 m size in plan, and a height of

SECTION

21 .984 m. rts fundamental time period is found to be 0.247 sec from free vibration analysis, and 0.667 sec calculated as per rs: 1893- 1984 (1986).

The mean values of the properties of the mate­riaIs used in the analysis are: compressive strength in axial compression (prism test result) of brick­work 3.22 MPa; permissible shear stress ofbrickwork 0.20 MPa; and the compressive strength (cube test result) of mud mortar 1.62 MPa.

The fragility curves as a result of the probabilistic risk analysis of the temple for different soil condi­tions and risk consistent seismic input are presented in Figure S.

Figures 6- 7 present the fragility curves for the same temple for different soil conditions and white noise as the seismic input.

4.1 Resulls of lhe numerical study

The seismic hazard potential, input response spec­tra and the fragility curves obtained as the result of the numerical study using the proposed simplified procedure are discussed in the following paragraphs .

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0.40

~ 0.35

::J 0.30 ~ u.. 0.25 4-o .q 0.20

:E 0. 15 '" .D 0.10 J: 0.05

0.00 0.00

- Response Spectru m

---..- White Noise

0.10 0.20 0.30 0.40 0.50 0.60 0.70 PGA(g)

Figure 6. Fragility curves for Nyatapola temple fordiffe rent types of ground motion inputs (li near soi l condition).

0.20..,-r======,---------, _Response

Spectrum ~ -= 0.15 .<õ u.. 4-

---..- White Noise

~ 0.10

~ .D 0.05 B c..

0.00 +----.. ~_r_.-.-r==*=::;=::!~,___-----j 0.00 0.05 0.10 0.15 0.20 0.25 0.30

PGA(g)

Figure 7. Fragili ty curves fo r Nyatapola temple for di fferen t types of ground motion inputs (non-linear so il condition).

4.1. 1 Seisrnic hazard potential and input response spectra for the temple location site

The seismic hazard curve obtained for the bedrock leveI is modified into free-field hazard curves con­sidering the local site amplification of the soi!. The free-field seismic hazard curves presented in Figure I shows that when soil non-linearity is considered, the probability of exceedence of PGA leveI is reduced. The reduction is more for higher leveIs of PGA.

Comparing the free-field risk consistent response spectra presented in Figures 2 and 3 for linear and non-linear soi l conditions respectively, it is seen that spectral ordinates are drastically reduced near the peaks when non-linear soil behavior is taken into con­sideration. Tt is evident that structures having natural periods within the range oftime periods corresponding to the peak of the spectra will attract lower values of earthquake forces ifnon-linear behavior of soil is duly considered in the seismic analysis of the structures.

4.1.2 Fragility curves for the temple The fragility curves for linear and non- linear soil con­ditions for the temple is compared in Figure 5.1n order

to compare, the fragility curves are shown for the prob­ability of failure versus PGA input at the bedrock. The figure highlights that the probability of fa ilure for non-linear soil condition is higher than that fo r lin­ear soil condition up to the PGA input value at the bedrock of 0.1 2 g, beyond which the probability of failure is higher for the case of linear soil condi tion. After that the difference between the probabilities of failure for linear and non-l inear conditions increases with the increase in PGA input value at bedrock.

The effect of input response spectrum at the bedrock leveI on fragility curves is clearly observed from Figures 6- 7. lt is seen from the figures that the prob­ability of fa ilure is significantly changed when the input ground motion at the bedrock is changed to white noise. The white noise input ground motion provides lower values of the probability of fai lure. This is due to the fact that the local soi l amplification is less fo r white noise input. However, the di fference between the two cases of input is significantly reduced for the non-linear soil condition. Thus, it appears that non­linear effect of soil tends to even out the differences in the probabilities offailure caused due to difference in seismic input.

5 CONCLUSTON

A simplified procedure is presented for determin­ing the seismic risk of the monumental structures of the Kathmandu Valley, the region which do not have enough recorded data. Firstly the seismic haz­ard potential and the seismic input for analysis ofthe monumental structures are established by obtaining the free field seismic hazard curves and the ri sk con­sistent response spectra for the site of monumental structures. The hazard curves and the response spectra fo r the free fie ld are obtained after duly considering the effect of overlying soillayer. Both linear and non­linear soil behaviors are considered. The monumental structures analyzed for seismic reliability using the determined seismic input. The probabilities of fail­ure of the monumental structures are obtained by considering uncertainties of ground motion, mate­rial properties, modeling and analysis procedure. The methodology is illustrated by analyzing the Nyatapola temple, best representing the original Nepali monu­mental structure. The results of the study lead to the following major conclusions.

When the soil non-linearity is considered, the prob­ability of exceedence of a PGA leveI denoted by the hazard curve is reduced; the reduction is more for higher leveIs of PGA.

The free vibration analysis of the temples show that the fundamental time periods of the temples are much below 0.4 sec., and the values are considerably different from those calculated by the co de formula.

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The natural frequencies of the temples are reason­ably wide spaced, and the first fundamental mode contributes maximum to the lateral load. The natural periods ofthe temples are such that they attract signifi­cant lateralload for the case when linear soil condition is assumed.

The probability of failure of the taller temple exhibits higher value of failure.

When non-linear behavior of the soil is taken into consideration, the seismic risk denoted by the proba­bility offailure is considerably reduced especially for highervalues ofPGA at the bedrock. The difference in the probabilities of failure due to change in soil con­dition is not only influenced by the soil behavior but also by the structures period.

When the risk consistent acceleration input spec­trum is changed to the response spectrum correspond­ing to white noise at the bedrock levei, the probabilities offailure ofthe temples are altered; the latter provides lower estimate of the probability of failure.

REFERENCES

Budnitz, R. 1. , Apostolakis , G. , Boore, D. M., Cluff, L. S. , Coppersmith, K. 1. , Comell , C. A. & Morris, P. A. 1998. Use of Teehnieal Expert Panels: Applieations to Prob­abilistie Seismie Hazard Analysis. Risk Ana!ysis 18(4): 463-469.

Gusella , V 1991. Struetural Failure and Stoehastie Diserete Proeess of Random Events. An Applieation lo Seismie Vulnerability Analysis of an Historie Building. Slruclura! Safety and Reliability 11(1): 13- 28.

Hwang, H. , Reich, M. & Shinozuka, M. 1984. Structural Reli­ability Analysis and Seismic Risk Assessment. American Society of Mechanical Ellgineers. Pressllre Vessels and Piping Division (Publica/ion) PVP, 79: 39-44. NewYork, ASME.

IS: 1983- 1984. 1986. lndian S/andard Crileriafor Ear/h­quake Resistant Design of S/ruc/ures (Fourlh Revision). New Delhi: Indian Standards Institution, India .

Khan, M. R. 1987. Improved Method of Generation of Artificial Time-Histories, Rich in Ali Frequeneies from

Floor Speetra. Ear/hquake Engineering and S/ructura! Dynamics : 15: 985- 992.

Lee, M. K. , Lum, K. Y. & Hartford, D. N. D. 1998. Calcula­tion of the Seismie Risk of an Earth Dam Suseeplible to Liquefaetion. Geo/echnica! Specia! Publicalion ASCE: 2: 1451- 1460.

Mashalay, E. A. & Datta, T. K. 1990. "Seismie Risk Analysis of Buried Pipelines, Journa! ofTransportalion Ellgineer­ing: I 15(3): 232-252.

Matsubara, M. , Takeda, M. & Kai , Y. 1993. Estimation of the Failure Probability of Building Based on Observed Earthquake Records. Proceedings oflhe IFIP WG7.5 5/h Worlâng Conference on Reliability and Oplimizalion of Structura/ Syslems: 157- 164.

Ranganathan, R. 1990. Reliability Ana!ysis and Design of Structures. New Delhi: Tata McGraw-Hill Publishing Company Limited.

Ravindra, M. K. 1989. Recent Seismie Risk Studies of Nuclear Power Plants. An Overview. Proc. ICOSSAR 89. 51h Internaliona! Conference on Slruclura! Safety and Reliabi!ity: 2211 - 2218. New York: ASCE.

Sabol , T. A. & Hart, G. C. 1986. Seismie Risk Analysis of a Multi-Site Portfolio of Buildings: 1839- 1850. EI Cerrito : Earthquake Engineering Researeh lnstitute.

Stewart, M. G. 1991 .Probabilistie Risk Assessment ofQual­ity Control and Quality Assuranee Measures in Struc­tural Des ign. IEEE Transaclions on Syslems. Man and Cybernetics: 21(5): 1000- 1007.

Shinozuka, Masanobu, Mizutani , Mamoru, Takeda, Masatoshi , Kai , & Yoshiro, 1989. A Seismic PRA Procedure in Japan and ltsApplication to a Building Performance Safety Esti­mation. Part 3 Estimation of Building and Equipment Performance Safety. Proceedings of 5th Inlernaliona! Conference on Struclura! Safely and Reliabi!ity.

Takeda, Masatoshi , Kai , Yoshiro, Mizutani , & Mamoru, 1989. A Seismic PRA Procedure in Japan and ItsApplication to a Building Performance Safety Estimation Part 2. Fragility Analysis. Proceedings of51h Inlernaliona! Conference on Slruclura! Safety and Reliabilily .

Takemura, Masayuki, Ishida, Hiroshi, Amano, Akihiko, & Mizutani , Mamoro, 1989. A Seismic PRA Procedure in Japan and Its Application to a Building Performance Safety Estimation Part I. Seismie Hazard Analysis. Pro­ceedings of 51h Internaliona! Conference on Slruclura! Safety and Reliability.

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