3.4.2. Parameters for Analysis

• I is the macro seismic intensity (considered equivalent to the MSK Intensity scale adopted by IS:1893) • V refers to the vulnerability index estimated in Eq (iii) • Q is the ductility factor • ���� is the mean damage calculated. The classes (A, B, C, D) of the 11 parameters are defined by qualitative as well as quantitative methods. For example, the position of the building and foundation is a qualitative aspect for the specifications for individual classes that are studied from the Eurocode – guidelines of soil type concerning earthquake phenomenon. While the parameter of conventional resistance is calculated by formulating shear strength and specific weight of the masonry. The 11 parameters are explained in the next section.

3.4.2 Parameters for analysis

As mentioned in GNDT method for calculating the vulnerability index 11 parameters are used. These 11 parameters are broadly grouped in 4 parameter groups, each parameter is defined from the existing literature, expert opinions, and parametric analysis. The classes A, B, C, and D, are formulated from the qualitative observations as well as modeling (Shakya, 2014) (modeling is not in the scope of this research). These four groups are as follows: • Structural system • Irregularities and interaction • Horizontal structure and roofing • Conservation status and other elements

Parameter 1 - Type and organization of resisting system –Parameter 1 focuses on the quality of distribution of structure, the efficiency of connections, connections between the horizontal diaphragm, and orthogonal walls. This parameter does not consider the constituents of masonry. For this parameter, the corner connections are given importance. The significant element is the presence and

effectiveness of the connections between the orthogonal22 walls, such as to ensure the efficiency of the box like behavior23 of the structure. Table 2 explains the criteria for the classification of the classes –

Table 2 Definition of the vulnerability classes for parameter P1, Source - (le, 2005 )

Class Description

A Structures built according to earthquake-resistant construction codes. Strengthening or consolidation of the building masonry complying to rules earthquake resistance codes, thus ensuring the connection requirements and efficient connection between orthogonal walls.

B The structure has good links and bonding between orthogonal walls. Existence of ring beams and/or steel ties well distributed in sufficient number with good anchorage, thus ensuring the conditions for binding and effective connection between the vertical elements.

C The structure does not have the effective connections defined in class B, however it presents good connection quality between orthogonal walls, guaranteed by the appropriate bonding or interlocking units in all the walls.

D The structure does not present effective connection of loadbearing walls. Total absence of steel tie rods and/or ring beams.

Parameter 2 - Quality of the resisting system –

Assessment of quality of masonry work is based on three dimensions, (a) homogeneity of the material, shape, size, and nature of the units, (b) unit laying configuration and arrangement of units, (c) type of cross-linking elements. Table 3 explains the criteria for the classification of the classes –

Table 3 Definition of the vulnerability classes for parameter P2, Source - (le, 2005 )

Class Description

A Brick masonry of good quality. Well-cut stone masonry units (squared) with homogeneous and uniform in size throughout the length of the walls. Irregular stone masonry well mortared and locked/arranged, existence of cross–connection between the two sides of the wall.

B Brick masonry of average quality and carved stone masonry units with homogeneity over the whole extension of the walls. Stone masonry with irregular crosslink elements between the two sides of the wall.

C Brick masonry of low quality with irregularities in laying and bonding. Masonry stone units, not squared and heterogeneous dimensions. Irregular stone masonry without cross linking elements, and average mortar quality.

D Brick masonry of poor quality with inlay of stone fragments. Stone masonry with very irregular units, nesting irregularly and without locking care (creating gaps). Irregular stone masonry without cross–connection and poor mortar quality.

22 Orthogonal – walls which are perpendicular to each other. 23 Box like behavior – when the building acts as a jointly assemblage of walls and roofs, with mainly in-plane response of the walls.

Parameter 3 - Conventional resistance –

Conventional resistance is the quantitative estimate of the shear strength available for a masonry structure, involving the quality of material, geometry of the structure and gravity loads borne by the masonry in the building. For determining the conventional resistance of the masonry building (how much resistance does this building has?) the hypothesis of a box like behavior is made for the structure.

The value of conventional resistance is calculated by the following steps and values: N – Number of floors present in the structure At – Average total area covered (m2) Ax – Area of walls excluding the openings in x direction (m2) Ay – Area of walls excluding the openings in y direction (m2) �� - Shear resistance of the masonry (kN/m2) H – Average inter-story height (m) Pm – Average specific weight of the masonry (kN/m3) Ps - Average weight per unit area for each floor (kN/m3) A – Minimum value between Ax and Ay B – Maximum value between Ax and Ay a0 - A/At (minimum structural plan density) �� – B/A (measure of the uniformity of the structural walls) The value of resistance �� is determined by the following equations –

��0���� ���� √1+

���� 1.5��0����(1+��)

α = C/0.4

Table 4 Definition of the vulnerability classes for parameter P3, Source - (Shakya, 2014)

Class A Buildings with �� ≤1 Class B Buildings with 0.6≤�� <1 Class C Buildings with 0.4≤�� <0.6 Class D Buildings with �� <0.4

Figure 21 Determining Ax and Ay where Ax = (1+2+3+4+5) c/c x tx , Ay = (a+b+c+d+e) c/c x ty

Figure 20 Determining the average height H=(a+b+c)/3

Parameter 4 - Position of the building and foundations –

This parameter assesses the importance of factors such as the topography, type, and consistency of the ground foundation and evaluates the risk of landslide or slipping of foundation soils when subjected to seismic action. The following factors are assessed here which are based on the Eurocode24 8 –• % Slope of the land • Presence of rock foundation • Presence of loose soil – thrusting or non-thrusting • Foundation height difference

24 Eurocode 8 – Eurocode 8: Design of structures for earthquake resistance (abbreviated EN 1998 or, informally, EC 8) describes how to design structures in seismic zone, using the limit state design philosophy, which is approved by the European Committee for Standardization.

Table 5 Definition of the vulnerability classes for parameter P4, Source - (Shakya, 2014)

Foundation soil

Soil type A with or without the foundation or soil type B and C with the foundation

Soil type B and C without the foundation

Soil type D and E with the foundation

Soil type D and E without the foundation

Foundation land slope

‘��’(%)

Class

��≤10 A 10<��≤30 B 30<��≤50 C ��>50 D ��≤10 A 10<��≤20 B 20<��≤50 C ��>50 D ��≤50 C

��>50 ��≤30 ��>30 D C D

Parameter 5 - Floors –

The quality and type of structural system of the floors have a major influence on the overall structural behaviour. It is proposed in this parameter the definition of the classes according to the connection of floors to the main walls. The floors must be well connected to the walls, so that, they transmit vertical and horizontal loads. The aspects of staggered floors, rigid floors, and deformable floors are used to determine the class for parameter 5. The manual of GNDT also considers the status of conservation for the floors and mentions to downgrade the class by one if the state is not good.

Table 6 Definition of the vulnerability classes for parameter P5, Source - (Shakya, 2014)

Class Structural type and connection condition of flooring

A Rigid or semi–rigid and well connected

B Deformable and well connected

C Rigid or semi–rigid and improperly connected

D Deformable and poorly connected

Parameter 6 – Configuration in plan –

The seismic behaviour of a building also depends, on the plan form of the building. In the case of rectangular buildings, the ratio of a/l is taken which is between the size of the smaller side (a) and the larger side (l). In the

Figure 22 Defining the length a and b in the building plan

case of plans that deviate from the rectangular shape, in addition to the elongated shape of the main body (b) the extent of this variance is considered.

��1=

��2=

The classes are determined as follows -

Table 7 Definition of the vulnerability classes for parameter P6, Source - (le, 2005 )

Class Ratio between the dimensions

Class A β1 ≥ 80, β2 ≤ 10 Class B 60 ≤ β1 < 80 ,10 < β2 ≤ 20 Class C 40 ≤ β1 < 60, 20 < β2 ≤ 30 Class D β1 < 40, β2 > 30

Parameter 7 – Configuration in elevation –

This parameter evaluates the elevational aspect in terms of presence of towers or porticos, and % increase and decrease of mass. The ratio between the projecting part (T) and building height (H) is used to determine the class. The classes are determined as follows

Table 8 Definition of the vulnerability classes for parameter P7, retrieved from the manual. Original text Source - (le, 2005 )

Class Configuration ratio in elevation

Class A Buildings with uniform mass and elements/ decreasing continuously and uniformly. ��/�� <10 Class B Buildings with small portico or staggered elevation. 10≤��/�� <20 Class C Buildings with towers and elevations that affect the floor area. ��/�� ≤20 Class D Buildings with major/drastic change in elevation. 20≤��/�� <40

Parameter 8 – Walls maximum inter axis –

This parameter accesses the slenderness ratio of the wall by taking the ratio of the maximum spacing between two parallel walls with the thickness of the main wall on which the parallel walls meet. It evaluates the presence of long wall which is unsupported by cross walls. If the cross-wall support is not present the long wall is susceptible to out of plane failure.

Table 9 Definition of the vulnerability classes for parameter P8, Source - (le, 2005)

Class Inter axis/thickness ratio

Class A Buildings with an inter axis/thickness ratio of not more than 15 Class B Buildings with an inter axis/thickness ratio greater than 15 and not greater than 18 Class C Buildings with an inter axis/thickness ratio greater than 18 and not greater than 25 Class D Buildings with an inters axis/thickness ratio greater than 25.

Parameter 9 – Roof –

The roofs are classified primarily as thrusting, slightly thrusting and non-thrusting roofs based on presence of tie members in the structural system. The joinery details connecting the walls with the roof are analysed for determining the class. The support length of the roof is determined by calculating the total perimeter minus the length of the openings.

Figure 23 to determine the supported roof length, l= a+b+a1+a3+b1+b3

Table 10 Definition of the vulnerability classes for parameter P9, Source - (Shakya, 2014)

Class Structural type and connection condition of roofing

A Rigid or semi–rigid and well connected

B Deformable and well connected

C Rigid or semi–rigid and improperly connected

D Deformable and poorly connected

Parameter 10 – Nonstructural elements –

Non-structural elements include the presence of balconies or chimneys. Table 11 describes the classes –

Table 11Definition of the vulnerability classes for parameter P10, retrieved from the manual. Original text Source - (le, 2005)

Class Description

A No presence of non-structural elements

B Presence of non-structural elements/projections but they are well connected to the walls

C There are projections and non-structural elements but not well connected

D Badly connected non-structural elements

Parameter 11 – Current Conditions –

This parameter considers the conservation status of the building. Table 12 describes the classes for current conditions –

Table 12 Definition of the vulnerability classes for parameter P11, Source - (Shakya, 2014)

Class Description

A Masonry walls in good condition with no visible damage.

B Walls with small cracks (less than 0.5mm), was not widespread. Signs of moisture problems which deteriorates the characteristics of the masonry and lead to degradation or decay of wood.

C Walls crack opening of about 2 to 3mm. Structures with a state of poor conservation of masonry walls. Serious problems of deformability in the structural members

D Walls with deterioration and even if not widespread severe cracking. Walls with physical features and materials that show extremely poor or severe decrease of resistance. Cracking in locations, such, as near the corners (signs of disconnection between orthogonal walls). Damage introduced by thrusts transmitted by the roof, bulging of load–bearing walls, cracking due to settlement of foundations. Slip wooden framework with respect to the walls of the framework. Decomposition and degradation of wood along the walls. Signs of rotation and walls out of plumb

These 11 parameters determine the seismic vulnerability for the building based on the structural configuration and dimensions. Parameters 1 to 10 take into account the quality of construction and structural aspects, importantly parameter 11 describes about the damages and conservation status, there by implying that to what extent the conservation status makes the building vulnerable in case of a seismic event.