Seismic Vulnerability Assessment of Historic Structures (A Review of Existing Methodology)

Three historic structures Shiva Parvati Temple, Jagannath temple and Indrapur temple were analyzed after an earthquake with 0.177g lateral peak ground acceleration on 25th April 2015 hit Nepal. This research makes comparison of actually observed damage state in the earthquake vs expected damage obtained by fragility curves so that the reliability of the methodology used to analyze number of other historic structures could be tested.

1. Bivek Sigdel 070/MSS/104 Seismic Vulnerability Assessment of Historic Structures (A Review of Existing Methodology) Supervisor Prof. Dr. Gokarna Bahadur Motra Dr. Huma Kant Mishra

2. Brief Introduction This research is an attempt to revise a methodology that we’ve been following before the recent 25 th April, 2015 earthquake. The methodology that is revised, is about developing fragility curves that are used to predict the vulnerability of structures. Three timber-masonry historic structures were studied i.e Shiva- Parvati temple, Jagannath temple and Indrapur temple of Kathmandu Durbar Square. Finite Element Modelling of selected structures has been carried out using SAP2000 V15. Linear Static (seismic Coefficient Method) and Direct Integration linear Time History Analysis Method has been carried out for the analysis.

3. Introduction Earthquakes are no more a matter of surprise for mountainous country Nepal with several number of active faults ( T.Nataka , 1989). The damages to the historic structures equally have histories associated with it. Nepal has always lost its precious heritages after every strong ground motion. The main events of major earthquakes recorded date back from 1255 AD, re-appearing at 1260AD,1408AD, 1681AD, 1767AD, 1810AD, 1883AD, 1934AD to 2015 AD indicating a return period of about 80 years. Several heritages, including Dharahara were lost due to the earthquakes, while leaving many other monuments to collapse completely as well as damage partially.

4. Vulnerability Assesment Safety of Historic structures against earthquake is a huge mater of concern as they represent a county’s history and ethnical values. Vulnerability assessment of those structures against seismic forces is a key way to keep them safer against any earthquake.

5. Vulnerability Assessment M ethods Many researchers around the world have proposed various methods of vulnerability assessment. Federal Emergency Management Agency (FEMA 154, 2002) prepared a hand book to conduct Rapid Visual Screening of Buildings in 1988 to evaluate the buildings in California. Revisions have been made in this handbook after obtaining new data on the performance of the buildings in earthquakes. Likewise, Lagomarsino and Giovinazzi 2006, introduced two methods of vulnerability assessment. 1 . Macro Seismic method An Observed Damage-based vulnerability method Large no. of data required: qualitative method 2 . Mechanical method Limited no. of data used: rigorous structural analysis Quantitative Method

6. Vulnerability Assessment Methods One of the Recent trend of Research found in Nepal: Mechanical method i.e Development of Fragility Curves Prem Nath Maskey , 2012 conducted Rapid Visual Screening for vulnerability assessment of 147 unreinforced brick masonry buildings at Byasi of Bhaktapur and developed fragility curves for 5 of them as a rigorous structural analysis to assess their vulnerability. Similiarly , Shrestha, Srijana Gurung, 2013 also conducted RVS method and developed fragility curves to assess the vulnerability for five typical building models located at jhatapol , Patan . She found that the results of fragility analysis are different from that of RVS methodology of assessing vulnerability . Likewise, Shrestha Saroo , 2014 developed fragility curves of Saat Talle Durbar of Nuwakot to find that the building is vulnerable to exensive damage state at considered earthquake scenarios

7. But still there is a question.., i.e to what degree can we rely upon fragility curves to point out the vulnerability of the timber-masonry structures in Nepal ? Thus, this research is an attempt to revise this methodology we’ve been following in order to predict the vulnerability of historic structures by comparing the expected damage states obtained analytically using fragility curves with the real damages observed after Gorkha Earthquake on 25 th April, 2015 with PGA 0.177g (N-S) and 0.127g (E-W) as recorded by Nepal Seismological centre . Vulnerability Assessment Methods

8. Fragility curves (Definition) Fragility functions for any structure provides the probability of exceeding a prescribed level of damage for a wide range of ground motion intensity. The curves are a cumulative log-normal distribution of probabilities of exceeding a given damage state.  

9. Fragility Curves For a structural damage, given the spectral displacement demand, S d , the probability of being in or exceeding a damage state ds, is modelled as:   Where, ds stands for the prescribed level of damage state that are namely; slight, moderate, extensive and complete is the spectral displacement demand of the structure obtained as a maximum displacement response of top level of structural support (masonry wall) obtained from linear time history analysis is the median value of spectral displacement at which the building reaches the threshold of the damage, ds : In other words it characterizes the capacity of the structure and is obtained by following the guidelines presented by Lagomarsino and Giovainnzzi , 2006 and HAZUS-MH-MR3 manual. is the standard deviation of the natural logarithm of spectral displacement of damage state, ds, and  is the standard normal cumulative distribution function.  

10. Fragility curves (defining damage states, ds) Theoritically , the description of the damage states according to HAZUS-MH-MR3 for unreinforced Masonry Bearing walls (URM) are Slight Structural Damage: Diagonal, stair-step hairline cracks on masonry wall surfaces; larger cracks around door and window openings in walls with large proportion of openings; movements of lintels; cracks at the base of parapets. Moderate Structural Damage: Most wall surfaces exhibit diagonal cracks; some of the walls exhibit larger diagonal cracks; masonry walls may have visible separation from diaphragms; significant cracking of parapets; some masonry may fall from walls or parapets. Extensive Structural Damage: In buildings with relatively large area of wall openings most walls have suffered extensive cracking. Some parapets and gable end walls have fallen. Beams or trusses may have moved relative to their supports. Complete Structural Damage: Structure has collapsed or is in imminent danger of collapse due to in-plane or out-of-plane failure of the walls. Approximately 15% of the total area of URM buildings with complete damage is expected to be collapsed.

11. Numerically , the damage states are interpreted by Lagomarsino and Giovinazzi , 2006. According to them, “ In order to identify the damage suffered by the buildings, damage limit states , are directly identified on the capacity curve as a function of the yielding d y and of the ultimate d u displacements as. Slight damage capacity = 0.7d y Moderate damage capacity = 1.5d y Extensive damage capacity = 0.5 ( d y +d u ) Complete damage capacity = d u These assumed damage states, have been defined considering how the idealized elasto-perfectely plastic capacity curves are related to the force-displacement curves obtained by implementing “pushover analysis”.   Fragility curves (defining damage states, ds)

12. Fragility curves (defining damage states, ds) Fig: Idealized elasto -perfectly plastic capacity curve related to a force-displacement curve from a pushover analysis in a masonry building. It is worth noticing that in this way, differently from the idealised system, a non-linear behaviour is observed before the yield strength is reached for the pushover curve. For this reason, the first damage state S d,1 has been identified as S d,1 = 0.7 d y , while the second one S d,2 = 1.5 d y is assumed to correspond to the maximum strength.

13. The values of yield displacement d y , and ultimate displacement d u , are suggested by “HAZUS-MH-MR3 technical manual on Multi-hazard Loss Estimation Methodology”, for unreinforced masonry structure of typical height 10.6m and pre-code design are: dy =0.27 inches du=1.81 inches Fragility curves (defining damage states, ds)

14. The displacement demand of the structures are taken as the maximum displacement response at the top level of masonry wall subjected to the time-history load of ground motions. Fragility curves (defining spectral displacement demand, S d )

15. Observation Nodes for maximum displacement response Shiva- Parvati temple Jagannath temple Indrapur temple

16. Fragility curves (Damage state variability  sd ) According to 5.4.4 section of HAZUS-MH-MR3, the total variability of each equivalent PGA structural damage state, 𝛽(𝑆𝑃𝐺𝐴) is modelled by the combination of following two contributors to damage variability: uncertainty in the damage-state threshold of the structural system (𝛽𝑀(𝑆𝑃𝐺𝐴)=0.4 for all building types and damage states), variability in response due to the spatial variability of ground motion demand (𝛽𝐷(𝑉)= 0.5. The two contributors to damage state variability are assumed to be log-normally distributed, independent random variables and the total variability is simply the square-root-sum-of-the-squares combination of individual terms i.e 𝛽(𝑆𝑃𝐺𝐴) = 0.64. = ) = 0.64  

17. Finally Fragility functions for any structure provides the probability of exceeding a prescribed level of damage for a wide range of ground motion intensity. The curves are a cumulative log-normal distribution of probabilities of exceeding a given damage state. Fragility Curves  

18. Literature review Prem Nath Maskey 2012, carried out seismic vulnerability assessment for a typical settlement area of Byasi tole of Bhaktapur city, with consideration of the traditional masonry buildings. The research used both qualitative as well as quantitative approaches of seismic vulnerability assessment in the 5 types of building representing 147 numbers of buildings in the study area. The qualitative method of EMS-98, FEMA 154 method was used to determine the vulnerability of the buildings. The buildings also were analyzed using FEM technique in SAP2000 to obtain fragility curves for different damage states.. The fragility curves were developed using Lalitpura Earthquake time history.

19. Literature review Likewise, Srijana Shrestha Gurung, 2013 also conducted Rapid Visual Screening ( RVS ) and additionally developed fragility curves to assess the vulnerability for five typical building models located at Jhatapol , Patan . She found that the results of fragility analysis were different from that of RVS methodology of assessing vulnerability. Similarly, Sharoo Shrestha, 2014 also conducted the seismic vulnerability of a historic timber masonry monumental building in Nepal. She studied the seismic vulnerability assessment of Saat Talle Durbar (Seven-storey Palace) of Nuwakot following the guidelines of HAZUS-MH-MR3 technical manual for the estimation of displacement capacity during different damage states. The seismic demand, on the other hand ,has been determined from linear Time History analysis. Finally, structural vulnerability of the building were expressed using fragility curves.

20. Literature review Giovinazzi and lagomarsino 2004, presented macroseismic method for the vulnerability assessment of built-up area. They derived the method in a conceptually rigorous way, by the use of Probability and of Fuzzy Set Theory, considering Macroseismic Scale Definitions. Later on 2006, they adopted a classification for the proposal of vulnerability methods within Risk-UE project on 2006 A.D, for European towns and regions where two approaches were proposed: (1) an observed damage-based vulnerability method referred to as “ macroseismic method”; (2) a mechanical-based method reffered to as “mechanical method”. As both the methods intend to assess the vulnerability of the same structures a cross validation was also performed.

21. Literature review Development of fragility curves require the modelling of the structure to closely represent the structure. Unreinforced Timber-Masonry Buildings in the study are made up of timber and brick in mud mortar. Floorings are timber joists with wooden boards over them. These floorings represent flexible diaphragm. According to Brignola et. al. 2008, Extensive damage observed during past earthquakes on URM buildings of different type have highlighted serious shortcomings of typical retrofit interventions adopted in the past with the intention to stiffen the diaphragm. They further state that recent numerical investigations have also confirmed that stiffening the diaphragm is not necessarily going to lead to an improved response, sometimes actually having detrimental effects on the response . Thus the flooring in this model has also been considered a flexible timber joists connection.

22. Need and objectives Fragility curves predict the probability of occurrence of a certain level of damage state of an structure subjected to a loading analytically. A real time history ground motion as load in this case. However, the reliability of the fragility curves to predict a damage state has not been tested for structures in Nepal, since, before 25 th April, 2015 no strong ground motion was felt for decades during the study period. This time on 25 th April, 2015 a strong ground motion with 7.8 magnitude on richter scale was recorded and real damage on the structures were observed. Thus, this became a good opportunity to make a comparative test between the damage states predicted by fragility curves and actually observed damages due to the real earthquake. Hence this study mainly focuses on the comparison between expected damage using fragility curves vs actual damages observed in the field and thus suggest to whether a revision is necessary or not.

23. Additional objectives Perform seismic coefficient method of analysis using the methodologies of Nepal National Building Code (NNBC:105) and IS Code (IS 1893:2002) to find the respective design base shears and make a comparative analysis with the base shear observed due to the Gorkha earthquake and other considered accelerograms . To determine the dynamic properties of the structures like natural modes of vibration, frequency, time period by conducting a modal analysis to estimate its seismic behavior .

24. Scope and Limitations The research studies only about timber-masonry structures. Non-linearity of the materials/geometry has not been considered. Only Lateral Components of Earthquakes are considered. Soil-structure interaction has not been considered. The material properties has been referenced from secondary source. Due to insufficient non-linear data and difficulty in conducting a pushover analysis of the timber-masonry structure using available software, the capacity of the structures have been assumed following the guidelines of HAZUS-MH-MR3. It is assumed that the lateral component of Gorkha Earthquake is responsible for the major damages observed in the structures and in this regard the vertical component of the earthquake is not taken into consideration.

25. The results are also based on the accuracy of the analytical modelling done in SAP2000V15. According to Dogangun and Sezen 2012, i t is difficult to model the structure that best represents the actual material properties and boundary conditions in a historical masonry structure. The idealizations in partial fixity of the connections create variations in the time period of the structures. Hence the results obtained are also based on the modelling techniques used in this research . The actual damage state observed in the structures due to the Gorkha Earthquake on April 25th, 2015 has been classified according the guidelines provided by HAZUS-MH-MR3 and based on visually observed wall cracks, diaphragm separation etc.. The damage states are classified into 4 groups namely slight, moderate, extreme, and complete. Scope and Limitations

26. Methodology

27. Field visit and selection of structures After the occurrence of Gorkha earthquake on April 25 th , 2015, at least 30 historic timber-masonry structures were observed in Patan Durbar Square, Kathmandu Durbar Square and Bhaktapur Durbar Square for rapid damage assessment. Out of them, three partially damaged structures of Kathmandu Durbar Square were selected that include Shiva Parvati Temple, Jagannath Temple and Indrapur temple for the study . The dimensioning of one of the structures i.e Shiva- Parvati temple was measured visiting the site and the dimensioning of the interior parts of remaining two structures i.e Jagannath and Indrapur were provided by Kathmandu Valley Preservation Trust (KVPT).

28. Historic Structures under Study 1. Shiva- Parvati Temple Built in 18 th century by Bahadur Shah. Materials of construction: Timber and Brick Masonry in Mud Mortar Dimensions: ( LxBxH )=10.91m x 5.21m x 7.83m

29. Plans and Elevations (Shiva- Parvati Temple)

30. 2. J agannath Temple Built in 16 th century Materials of construction: Timber and Brick Masonry in Mud Mortar Dimensions: ( LxBxH )= 8.44m x 8.44m x 11.16m Historic Structures under Study

31. Front Elevation View Sectional View Plan View Plans and Elevations ( Jagannath Temple) 11.16 m

32. 3 . Indrapur Temple Built in 16 th century Materials of construction: Timber and Brick Masonry in Mud Mortar Dimensions: ( LxBxH )= 3.49m x 3.49m x 10m Historic Structures under Study

33. Indrapur Temple Section View Plan View Front Elevation View

34. Location of the selected structures A B C A B C N Kathmandu Durbar Square: With A rial and Schematic map Shiva Parvati Temple Jagannath Temple Indrapur Temple

35. Observed Damage State (Shiva Parvati Temple) 10 cm East face West face Out of Plane tilting of wall at 1 st floor by 10 cm 1 st floor short side walls

36. 1 st floor east face wall internal All these damages presented here indicate moderate damage state . Observed Damage State (Shiva Parvati Temple)

37. Observed Damage State ( Jagannath Temple )

38. Observed Damage State ( Jagannath Temple ) The presence of only diagonal cracks in the walls indicates slight structural damage.

39. Observed Damage State ( Indrapur Temple ) Again, the presence of only minor diagonal cracks in the walls indicates slight structural damage.

40. Observed Damage States (Summary) Structure Observed Damage State Shiva Parvati Temple Moderate Jagannath Temple Slight Indrapur Temple Slight The observed damage states have been categorized into four damage states following the guidelines and definitions of the four damage states by HAZUS-MH-MR3 as shown earlier.

41. Expected Damage State Fragility Curves were developed to find out the expected damage state A finite element model was prepared in SAP2000 V15 Linear Time History Analysis was carried out using the time history data of 25 th A pril, 2015 G orkha earthquake and additionally by Elcentro and Chamauli earthquake to find the displacement demands ( S d ). Maximum displacement demand of the structure at top level of masonry was noted ( S d ). Capacity of the structure was found using the guidelines of HAZUS-MH-MR3 Development of Fragility Curves Expected damage state Expected and Observed Damage State were compared

42. Finite Element Model (Shiva- Parvati Temple)

43. Finite Element Model ( Jagannath Temple)

44. Finite Element Model ( Indrapur Temple)

45. Material Properties Brick Masonry Density (Kg/m3) 1768 Compressive Strength (N/mm2) 1.82 Shear Strength (N/mm2) 0.15 Mod. Of Elasticity, E (N/mm2) 509 Poisson's ratio (ν) 0.25 Shear Modulus (N/mm2) 204 Wood (IS 875 : 200 Density (Kg/m3) 800 Mod. Of Elasticity, E (N/mm2) 12.6e3 The material properties for the research has been cited from the work of parajuli , 2012.

46. Modelling Features The walls of the structure is modelled as thick shell element and timber as two nodded beam element. The beam bands of timber are connected to the walls using link elements to maintain the mass distribution. The floor beams are hinge connected to the walls. The timber posts to ground and timber to timber connections are hinged while the masonry to ground has been fixed. The truss rafters were hinged to the top of the walls The roof load has been manually calculated assigned as line loads to the rafters. Ritz vector algorithm were used to find the modes of vibration in specific directions. Time history analysis was carried out and the results obtained are interpreted in terms of maximum base shear and top displacement of masonry walls. Direct Integration time history data was used for the analysis.

47. Modal Analysis The time periods and modal mass participation factors were obtained using Ritz algorithm. Shiva- Parvati temple: Time period of first mode of vibration is 0.25 seconds with a mass participation of 75% towards the shorter direction of structure while second mode shows the time perioid of 0.21 second along longer direction with modal mass participation of 54%. More than 90% of the mass has participated within first 12 modes. Jagannath temple: The first translation mode of vibration is obtained on second mode with time period of 0.26 sec with mass participation 63% along North direction and symmetric. 20 modes are required for more than 90% mass participation. Indrapur temple: The time period at the mode of maximum mass participation (41%) is 0.17 sec. The structure is also symmetric and 90% mass participation has been obtained within first 24 modes.

48. Time-History Parameters ( Accelerograms ) The thesis is targeted to obtain an expected damage state due to the Gorkha earthquake 2015 using fragility curves analytically and make a comparative study with the actually observed damages. In this regard, the actual ground motion data of April 25th, 2015 was obtained from Nepal Seismological Centre, Lainchaur . Additionally, Elcentro , 1940 and Chamauli with their PGA scaled to 0.177 PGA are also used to develop fragility curves in order to maintain the spectrum compatibility of records as specified in Eurocode-8, 2004. The graphical representation of the accelerograms are shown in next slides:

49. Time-History Parameters ( Accelerograms and fourier amplitude spectrums)

50. Time-History Parameters ( Accelerograms and fourier amplitude spectrum)

51. Time-History Parameters ( Accelerograms and fourier amplitude spectrum)

52. Time-History Parameters ( Accelerograms and fourier amplitude spectrum)

53. Time-History Parameters (Comparison of maximum fourier amplitudes amongst the accelerograms )

54. Time history Parameters ( Damping) The damping associated with the analysis were used as mass and stiffness proportional damping whose values as suggested by Rayleigh, were calculated using the following Raleigh’s formula (clough and penzien ), where , = 0.05 = Fundamental frequency of MDOF system = Set among the higher frequencies of the modes that contribute significantly to the dynamic response = mass proportional coefficient = stiffness proportional coefficient Hilber -Hughes-Taylor method was used for the time integration solution.  

55. Time history Analysis (Loading directions) N Gorkha Earthquake, (0.177g) Elcentro Earthquake, (Linearly scaled to 0.177g) Chamauli Earthquake, (Linearly scaled to 0.177g) Gorkha Earthquake, (0.127g) Elcentro Earthquake, (Linearly scaled to 0.127g) Chamauli Earthquake, (Linearly scaled to 0.127g) Shiva- Parvati Temple Jagannath Temple Indrapur Temple

56. Results of Time-History Analysis (Shiva- Parvati Temple, tabular form) Ht. of Observation: 6.17m Earthquake P.G.A(g) Base shear (KN) Max. Displacement of node,mm Along East Along North Along East, node 103 Along north, node 6360 Gorkha (N-S) 0.177 - 435.4 - 6.587 Gorkha (E-W) 0.127 280.4 - 2.563 - Elcentro 0.177 - 659.5 - 13.12 Elcentro 0.127 336.3 - 3.072 - Chamauli 0.177 - 498.3 - 7.536 Chamauli 0.127 337.2 - 3.769 -

57. Maximum displacements Results of Time-History Analysis (Shiva- Parvati Temple, graphical form)

58. Earthquake P.G.A(g) Base shear (KN) Max. Displacement of node 193 Along East Along North Along East Along North Gorkha (N-S) 0.177 - 1029.3 - 7.388 Gorkha (E-W) 0.127 961.5 - 6.714 - Elcentro 0.177 - 1410 - 15.1 Elcentro 0.127 1029 - 10.56 - Chamauli 0.177 - 1293 - 10.96 Chamauli 0.127 951.2 - 7.307 - Results of Time-History Analysis ( Jagannath Temple, tabular form) Ht. of Observation: 10.23m

59. Results of Time-History Analysis ( Jagannath Temple, graphical form) Maximum displacements

60. Earthquake P.G.A(g) Base shear (KN) Max. Displacement of node 111 Along East Along North Along East Along North Gorkha (N-S) 0.177 - 134.6 - 5.483 Gorkha (E-W) 0.127 125.9 - 6.098 - Elcentro 0.177 - 230.8 - 8.113 Elcentro 0.127 159.9 - 7.311 - Chamauli 0.177 - 182.5 - 6.456 Chamauli 0.127 144.7 - 6.784 - Results of Time-History Analysis ( Indrapur Temple, tabular form) Ht. of Observation: 7.53m

61. Results of Time-History Analysis ( Indrapur Temple, graphical form) Maximum displacements

62. Fragility curves Once the maximum displacement demands at the top of masonry wall ( S d ) are obtained, the fragility curves for the structures can be plotted using the cumulative log normal function: Where, Slight damage capacity = 0.7d y = 4.801mm Moderate damage capacity = 1.5d y = 10.287mm Extensive damage capacity = 0.5 ( d y +d u ) = 26.416mm Complete damage capacity = d u = 45.974mm = 0.64    

63. Fragility curves Calculation of probabilities of failure due to N-S component of Gorkha Earthquake in Shiva- Parvati Temple (Tabular form) PGA (g) Top Displacement (mm) Probability of Failure at damage State ( ) Demand ( S d ) Capacity Displacement (mm ) ( ) Slight Moderate Extensive Complete Slight Moderate Extensive Complete 0.000 0.000 4.801 10.287 26.416 45.974 0.000 0.000 0.000 0.000 0.050 1.861 4.801 10.287 26.416 45.974 0.069 0.004 0.000 0.000 0.100 3.721 4.801 10.287 26.416 45.974 0.345 0.056 0.001 0.000 0.150 5.582 4.801 10.287 26.416 45.974 0.593 0.170 0.008 0.000 0.177 6.587 4.801 10.287 26.416 45.974 0.689 0.243 0.015 0.001 0.200 7.443 4.801 10.287 26.416 45.974 0.753 0.307 0.024 0.002 0.250 9.304 4.801 10.287 26.416 45.974 0.849 0.438 0.051 0.006 0.300 11.164 4.801 10.287 26.416 45.974 0.906 0.551 0.089 0.014 0.350 13.025 4.801 10.287 26.416 45.974 0.941 0.644 0.135 0.024 0.400 14.886 4.801 10.287 26.416 45.974 0.961 0.718 0.185 0.039 0.450 16.747 4.801 10.287 26.416 45.974 0.975 0.777 0.238 0.057 0.500 18.607 4.801 10.287 26.416 45.974 0.983 0.823 0.292 0.079 0.550 20.468 4.801 10.287 26.416 45.974 0.988 0.859 0.345 0.103 0.600 22.329 4.801 10.287 26.416 45.974 0.992 0.887 0.396 0.130 0.650 24.190 4.801 10.287 26.416 45.974 0.994 0.909 0.445 0.158 0.700 26.050 4.801 10.287 26.416 45.974 0.996 0.927 0.491 0.187 0.750 27.911 4.801 10.287 26.416 45.974 0.997 0.941 0.534 0.218 0.800 29.772 4.801 10.287 26.416 45.974 0.998 0.952 0.574 0.249 0.850 31.632 4.801 10.287 26.416 45.974 0.998 0.960 0.611 0.280 0.900 33.493 4.801 10.287 26.416 45.974 0.999 0.967 0.645 0.310 0.950 35.354 4.801 10.287 26.416 45.974 0.999 0.973 0.676 0.341 1.000 37.215 4.801 10.287 26.416 45.974 0.999 0.978 0.704 0.371 PGA (g) Top Displacement (mm) Demand ( S d ) Slight Moderate Extensive Complete Slight Moderate Extensive Complete 0.000 0.000 4.801 10.287 26.416 45.974 0.000 0.000 0.000 0.000 0.050 1.861 4.801 10.287 26.416 45.974 0.069 0.004 0.000 0.000 0.100 3.721 4.801 10.287 26.416 45.974 0.345 0.056 0.001 0.000 0.150 5.582 4.801 10.287 26.416 45.974 0.593 0.170 0.008 0.000 0.177 6.587 4.801 10.287 26.416 45.974 0.689 0.243 0.015 0.001 0.200 7.443 4.801 10.287 26.416 45.974 0.753 0.307 0.024 0.002 0.250 9.304 4.801 10.287 26.416 45.974 0.849 0.438 0.051 0.006 0.300 11.164 4.801 10.287 26.416 45.974 0.906 0.551 0.089 0.014 0.350 13.025 4.801 10.287 26.416 45.974 0.941 0.644 0.135 0.024 0.400 14.886 4.801 10.287 26.416 45.974 0.961 0.718 0.185 0.039 0.450 16.747 4.801 10.287 26.416 45.974 0.975 0.777 0.238 0.057 0.500 18.607 4.801 10.287 26.416 45.974 0.983 0.823 0.292 0.079 0.550 20.468 4.801 10.287 26.416 45.974 0.988 0.859 0.345 0.103 0.600 22.329 4.801 10.287 26.416 45.974 0.992 0.887 0.396 0.130 0.650 24.190 4.801 10.287 26.416 45.974 0.994 0.909 0.445 0.158 0.700 26.050 4.801 10.287 26.416 45.974 0.996 0.927 0.491 0.187 0.750 27.911 4.801 10.287 26.416 45.974 0.997 0.941 0.534 0.218 0.800 29.772 4.801 10.287 26.416 45.974 0.998 0.952 0.574 0.249 0.850 31.632 4.801 10.287 26.416 45.974 0.998 0.960 0.611 0.280 0.900 33.493 4.801 10.287 26.416 45.974 0.999 0.967 0.645 0.310 0.950 35.354 4.801 10.287 26.416 45.974 0.999 0.973 0.676 0.341 1.000 37.215 4.801 10.287 26.416 45.974 0.999 0.978 0.704 0.371

64. Fragility curves Calculation of probabilities of failure due to N-S component of Gorkha Earthquake in Shiva- Parvati Temple (Graphical form)

65. Fragility curves In this way, fragility curves were developed for Shiva- Parvati , Jagannath and Indrapur temples subjected to both N-S and E-W component loadings of Gorkha , Elcentro and Chamauli earthquakes.

66. Expected Damage States The expected damage state, the structure is likely to suffer can be determined from the tabular or graphical representation. The probability of failure at different damage states due to Gorkha , Elcentro and Chamauli earthquakes at 0.177g North and 0.127g East PGA can now be determined from table of graph and summarized.

67. Summary of fragility analysis (Expected Damage States) 1. Shiva parvati Temple Earthquake Base Shear (KN) Probability of failure (%) Expected Damage State Slight Moderate Extensive Complete Gorkha (N-S) (0.177g) 435.4 68.9 24.3 1.5 0.1 Slight Gorkha (E-W) (0.127g) 280.4 16.3 1.5 Slight Elcentro (Linearly scaled to 0.177g)(N-S) 659.5 94.2 64.8 13.7 2.5 Slight-Moderate Elcentro (Linearly scaled to 0.127g)(E-W) 336.3 24.3 2.9 Slight Chamauli (Linearly scaled to 0.177g)(N-S) 498.3 75.9 31.3 2.5 0.2 Slight Chamauli (Linearly scaled to 0.127g)(E-W) 337.2 35.3 5.8 0.1 Slight

68. Summary of fragility analysis (Expected Damage States) 2 . Jagannath Temple Earthquake (0.177 PGA) Base Shear (KN) Probability of failure (%) Expected Damage State Slight Moderate Extensive Complete Gorkha (N-S) (0.177g) 1029.3 75 30.2 2.3 0.2  Slight Gorkha (E-W) (0.177g) 961.5 70 25.2 1.6 0.1  Slight Elcentro (Linearly scaled to 0.177g)(N-S) 1410 96.3 72.6 19.1 4.1  Slight-Moderate Elcentro (Linearly scaled to 0.127g)(E-W) 1029 89.1 51.6 7.6 1.1 Slight-Moderate Chamauli (Linearly scaled to 0.177g)(N-S) 1329 90.1 53.9 8.5 1.3  Slight-Moderate Chamauli (Linearly scaled to 0.127g)(E-W) 951.2 74.4 29.7 2.2 0.2 Slight

69. Summary of fragility analysis (Expected Damage States) 3.Indrapur Temple Earthquake Base Shear (KN) Probability of failure (%) Expected Damage State Slight Moderate Extensive Complete Gorkha (N-S) (0.177g) 134.6 58.2 16.3 0.7  Slight Gorkha (E-W) (0.177g) 125.9 64.6 20.7 1.1 0.1  Slight Elcentro (Linearly scaled to 0.177g) (N-S) 230.8 88.1 50 6.9 0.9  Slight-Moderate Elcentro (Linearly scaled to 0.127g) (E-W) 159.9 74.4 29.7 2.2 0.2 Slight Chamauli (Linearly scaled to 0.177g) (N-S) 182.5 85.6 44.9 5.5 0.7  Slight Chamauli (Linearly scaled to 0.127g) (E-W) 144.7 70.5 25.8 1.7 0.1 Slight

70. Comparison between Expected and Observed Damage States The main focus of study being the expected damage vs observed damage due to the Gorkha earthquake of April 25 th 2015, the results are interpreted at the beginning. Structure Earthquake   Damage States Expected Observed Shiva Parvati Temple Gorkha (N-S), 0.177g  Slight Moderate   Gorkha (E-W), 0.127g  Slight Moderate Jagannath Temple Gorkha (N-S), 0.177g  Slight Slight   Gorkha (E-W), 0.127g  Slight Slight Indrapur Temple Gorkha (N-S), 0.177g  Slight Slight   Gorkha (E-W), 0.127g  Slight Slight

71. The accelerograms Elcentro and Chamauli show the following comparative results: Comparison between Expected and Observed Damage States Structure  Accelerogram Damage States Expected Observed due to Gorkha Earthquke Shiva Parvati Temple Elcentro, scaled to 0.177g (N-S) Slight-Moderate Moderate   Elcentro scaled to 0.127g (E-W) Slight Moderate   Chamauli, scaled to 0.177g (N-S)  Slight Moderate   Chamauli scaled to 0.127g (E-W) Slight Moderate

72. The accelerograms Elcentro and Chamauli show the following comparative results : Comparison between Expected and Observed Damage States Structure  Accelerogram Damage States Expected Observed due to Gorkha Earthquke Jagannath Temple Elcentro, scaled to 0.177g (N-S)  Slight-Moderate Slight   Elcentro scaled to 0.127g (E-W) Slight-Moderate Slight   Chamauli, scaled to 0.177g (N-S)  Slight-Moderate Slight   Chamauli scaled to 0.127g (E-W) Slight Slight

73. The accelerograms Elcentro and Chamauli show the following comparative results: Comparison between Expected and Observed Damage States Structure  Accelerogram Damage States Expected Observed due to Gorkha Earthquke Indrapur Temple Elcentro, scaled to 0.177g (N-S)  Slight-Moderate Slight   Elcentro scaled to 0.127g (E-W) Slight Slight   Chamauli, scaled to 0.177g (N-S)  Slight Slight   Chamauli scaled to 0.127g (E-W) Slight Slight

74. Computation of Base Shear using IS1893:2002 and NNBC:105 codal provisions 1. Shiva- Parvati Temple 2. Jagannath Temple 3. Indrapur Temple Codal Provision of: Seismic Weight (KN) Base Shear (KN) IS 1893:2002 1909.57 515.58 NNBC:105 1909.57 916.59 Codal Provision of: Seismic Weight (KN) Base Shear (KN) IS 1893:2002 4773.905 2148.26 NNBC:105 4773.905 2291.47 Codal Provision of: Seismic Weight (KN) Base Shear (KN) IS 1893:2002 760.868 342.39 NNBC:105 760.868 305.86

75. Conclusions Fragility curves have represented closely the observed damage states [refer. Sec. 4.1] in case of Jagannath and Indrapur temple and small deviations were observed in case of Shiva Parvati temple. However, it can be concluded that in the case of the structures the results of fragility curves are applicable to assess their vulnerability.

76. Conclusions The maximum base shear in the structures are induced along North-South directions. Base shear induced in the structures due to the Gorkha earthquake of April 25 th , 2015, are well within the design base shear suggested by both the codes. However, the base shear due to Elcentro , scaled to the PGA of Gorkha earthquake (0.177g), along North-South direction in Shiva Parvati temple, exceeds the base shear calculated from IS 1893:2002 code by 28% while is still lower than the base shear calculated from NNBC:105 by 28%.

77. Conclusions (Analysis of Base Shears)

78. Conclusions (Analysis of Base Shears)

79. Conclusions Though being at the same PGA level, the responses of different earthquake ground motion showed different responses in terms of displacement and base shear. This is because of their different frequency contents, which further shows that analysis of structure with only one accelerogram might become insufficient to represent the exact vulnerability.

80. Thank-you