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Seismic vulnerability assessment of low-rise unreinforced masonry buildings in Northeast India considering variability of material properties

Abstract

Unreinforced masonry (URM) buildings are the most common building typology in the rural and urban areas of Northeast India. These URM buildings suffered substantial damage during earthquakes. In this context, the paper makes an effort to assess the vulnerability of URM buildings of this region through fragility analysis. Four representative URM buildings, consisting of single- and double-storey, have been selected from a group of buildings in the Northeastern part of India based on a suitable statistical parameter to reflect the commonly constructed building typology. Following the equivalent frame modelling approach, each building has been modelled with varying material properties, and thus, a total of 60 building models have been developed. Non-linear static analysis is performed for all the buildings to obtain the probability distribution function (pdf) of the damage states based on the capacity curve parameters. Inelastic displacement demands have been calculated for all the buildings based on the expressions given in FEMA 440 along with the response spectrum of Indian seismic code, IS 1893 Part I. Fragility curves are then derived from the complementary cumulative distribution function (cdf) of displacement demand and pdf of damage states. It is seen that there is a very high probability of suffering major to complete damage for URM buildings subjected to a peak ground acceleration of 0.18 g. Furthermore, derived fragility curves give reasonable predictions of observed post-earthquake building damage and can be used for the earthquake risk assessment of the same building typology of this Northeastern region of India.

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LH: conceptualization, methodology, formal analysis, and writing–original draft. SCD: supervision, writing-review, editing, and final correction, resources. PD: helping in preparation of the draft. RPS: overall supervision and correction of the draft.

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Correspondence to Sekhar Chandra Dutta.

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Appendix 1

Appendix 1

Explanation of symbols/abbreviations used

Symbols
\({\varvec{a}}\) Type of local soil class
\({\varvec{b}}\langle {\varvec{\uplambda}}\rangle\) Shear stress distribution coefficient at the centre of the pier, with respect to \(\uplambda\)
\({{\varvec{C}}}_{0}\) Factor to correlate spectral displacement of an equivalent single-degree-of-freedom
\({{\varvec{C}}}_{1}\) Modification parameter which relates the expected maximum displacement of an inelastic ESDOF system with elastic–plastic hysteresis properties to the displacement calculated from the elastic spectral response
\({{\varvec{C}}}_{2}\) Modification parameter accounts for the effects of pinched hysteresis shape, stiffness degradation, and strength deterioration on the maximum displacement response
\({{\varvec{C}}}_{\mathbf{m}}\) Effective mass factor
D Pier width
\({{\varvec{E}}}_{\mathbf{m}}\) Modulus of elasticity of masonry prism
\({{\varvec{F}}}_{\mathbf{D}|\mathbf{P}\mathbf{G}\mathbf{A}}\) Cumulative density function (cdf)
\({{\varvec{f}}}_{\mathbf{b}}\) Compressive strength of brick
fc Peak compressive strength of masonry
\({{\varvec{f}}}_{\mathbf{c}}\langle \boldsymbol{\alpha }\rangle\) Probability density function (pdf)
\({{\varvec{f}}}_{\mathbf{m}}\) Compressive strength of masonry prism
\({{\varvec{f}}}_{\mathbf{m}\mathbf{o}}\) Compressive strength of mortar
\({{\varvec{f}}}_{\mathbf{t}}\) Tensile strength of masonry
H Height of the pier
\({{\varvec{H}}}_{\mathbf{e}\mathbf{f}\mathbf{f}}\) Effective height of pier
\({{\varvec{H}}}_{0}\) Zero moment height
\({{\varvec{h}}}^{{{\prime}}}\) Calculated height of the pier as per Dolce to calculate effective height to calculate effective height
\({{\varvec{h}}}_{0}\) Height of the pier at the point of contra-flexure
\({{\varvec{h}}}_{\mathbf{p}}\) Height of the pier
\({{\varvec{h}}}_{\mathbf{s}\mathbf{p}}\) Height of the spandrel
\({{\varvec{h}}}_{\mathbf{s}\mathbf{t}}\) Storey height
\({\varvec{K}}\) Stiffness of the building
\({\varvec{k}}\) Peak compressive strength reduction factor
\(M_{w}\) Moment magnitude
N Vertical force
\({{\varvec{P}}}_{\mathbf{f}}\) Probability of failure
R Strength ratio of the system
\({{\varvec{S}}}_{\mathbf{a}}\left({{\varvec{T}}}_{\mathbf{y}}\right)\) Spectral acceleration at the fundamental period of the system
\({{\varvec{T}}}_{\mathbf{e}}\) Effective lateral period
\({{\varvec{T}}}_{\mathbf{y}}\) Fundamental period of the system
t Thickness of the wall
\({{\varvec{t}}}_{\mathbf{s}\mathbf{p}}\) Thickness of the spandrel
\({{\varvec{V}}}_{\mathbf{D}}\left({\varvec{N}},{\varvec{\uplambda}}\right)\) In-plane failure mode for diagonal cracking
\({{\varvec{V}}}_{\mathbf{R}}\left({\varvec{N}},{\varvec{\uplambda}}\right)\) In-plane failure mode for rocking
\({{\varvec{V}}}_{\mathbf{S}}({\varvec{N}},{\varvec{\uplambda}})\) In-plane failure mode for shear sliding
\({{\varvec{V}}}_{\mathbf{u},\mathbf{s}\mathbf{p}}\) Ultimate shear stress in the spandrel
\({{\varvec{V}}}_{\mathbf{y}}\) Yield strength capacity of the system
\({\boldsymbol{\alpha }}_{0}\) Zero moment coefficient
αv Shear ratio
\({\varvec{\sigma}}\langle {\varvec{N}}\rangle\) Mean compressive stress in the pier due to the axial force
λ Pier slenderness ratio
\({\varvec{\mu}}\) Masonry friction coefficient
\({{\varvec{\tau}}}_{0}\) Shear strength of masonry at zero compressive stress
Abbreviations
3D Three dimensional
ATC Applied Technology Council
cdf Cumulative density function
DSB Double storey building
DS Damage state
EFM Equivalent frame model
ESDOF Equivalent single-degree-of-freedom
FEMA Federal Emergency Management Agency
IS Indian Standard
MDOF Multi-degree-of-freedom
pdf Probability density function
PGA Peak ground acceleration
RC Reinforced concrete
SSB Single storey building
URM Unreinforced masonry

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Halder, L., Dutta, S.C., Debnath, P. et al. Seismic vulnerability assessment of low-rise unreinforced masonry buildings in Northeast India considering variability of material properties. Asian J Civ Eng 22, 843–863 (2021). https://doi.org/10.1007/s42107-021-00350-7

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Keywords

  • URM building
  • Capacity curve
  • Seismic demand
  • Damage states
  • Fragility curves
  • Vulnerability assessment