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Acquiring reference parameters of masonry for the structural performance analysis of historical buildings

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Abstract

The structural performance of historical masonry elements can be understood provided the following factors are known: geometry; the characteristics of its masonry texture and morphology, state of damage and decay, physical, chemical and mechanical characteristics of the components (units, infill, mortar); the characteristics of built masonry as a composite material. In order to quantify the mechanical properties of the masonry both laboratory and in-situ tests are required. However, in the case of cultural heritage assets, the setting up of an effective knowledge procedure is strictly related to the minimization of invasiveness on the structure, with the aim of its conservation, rather than the cost–benefit optimization: thus it is essential to have available reference parameters to be adopted for different masonry types. Within this context, this State-of-the-Art paper on this topic is organized with integrated outcomes from the test campaigns carried out through the PERPETUATE project, that are also briefly presented. Reference parameters for effective seismic assessment are provided both for brick and stone masonry together with their upper and lower bound values for both mechanical parameters and damage limits for which proper limit states (LS) may be associated. Apart from the LS for structural elements (SE), the relevant LS’s for artistic assets attached to the SE are also presented in this paper.

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Abbreviations

A2:

Damage level corresponding to drift at which the first structural crack on the plaster occurred

A3:

Damage level corresponding to drift at which plaster was largely detached from the wall but still repairable

A4:

Damage level corresponding to drifts at which plaster collapsed

\(A_{w }\) :

Gross wall cross-section

AA:

Artistic asset

\(b \) :

Shear distribution factor

D:

Destructive test

\(D_{cr}\) :

Displacement at which first crack is attained

\(D_{cr,x}\) :

Displacement at which first flexural crack is attained

\(D_{e}\) :

Elastic displacement of an idealized bilinear curve

\({D}_{{ FC}}\) :

Drift capacity corresponding FC state

\(D_{max}\) :

Maximum attained displacement

\({D}_{{NC}}\) :

Drift capacity corresponding NC state

\({D}_{{SD}}\) :

Drift capacity corresponding SD state

\(D_{u }\) :

Ultimate displacement of an idealized bilinear curve

\(D_{Vmax}\) :

Displacement at which maximum resistance is reached

\(E_{b}\) :

Modulus of elasticity of the unit

\(E_{M}\) :

Modulus of elasticity of the masonry

\(E_{m}\) :

Modulus of elasticity of the mortar

FC:

First Cracking

\(f_{bc}\) :

Compressive strength of the unit

\(f_{bc,n}\) :

Normalised compressive strength of the unit

\(f_{bt}\) :

Tensile strength of the unit

\(f_{bta}\) :

Axial tensile strength of the unit

\(f_{bts}\) :

Splitting tensile strength of the unit

\(f_{bx}\) :

Flexural tensile strength of the unit

\(f_{jx}\) :

Bond strength of mortar–unit junction determined with Bond Wrench test

\(f_{Mc}\) :

Compressive strength of the masonry

\(f_{Mc,k}\) :

Characteristic compressive strength of the masonry

\(f_{Mt}\) :

Diagonal tensile strength of the masonry

\(f_{mc}\) :

Compressive strength of the mortar

\(f_{mx }\) :

Flexural strength of the mortar

\(f_{St}\) :

Equivalent tensile strength aimed to characterize the masonry behaviour at spandrel scale and not at material scale

\(f_{v0}\) :

Initial shear strength of the masonry

\(f_{vk0}\) :

Characteristic initial shear strength of the masonry

\(G_{M}\) :

Shear modulus of the masonry

\(H_{p}\) :

Tensile resistance of the horizontal tension element coupled to spandrel

\(h_{0}\) :

Span height of wall/pier

\(h_{j}\) :

Height of the mortar joint

\(h_{S}\) :

Spandrel length

\(h_{s}\) :

Free height between two storeys

\(h_{w}\) :

Height of wall/pier

\(K_{eff}\) :

Effective stiffness of the wall/pier

\(K_{w}\) :

Resulting effective stiffness for composite wall sections

LS:

Limit States

\(l_{0S}\) :

Span height of spandrel

\(l_{S}\) :

Spandrel height

\(l_{w}\) :

Length of wall/pier

\(l_{wc}\) :

Length of the compressed part of the wall/pier

MD:

Minor (partly) destructive tests

NC:

Near collapse

ND:

Non-destructive tests

\(P_{d}\) :

Maximum force at diagonal test

SD:

Significant damage

SE:

Structural elements

\(t^{e}\) :

Thickness of exterior leaf

\(t^{i}\) :

Thickness of the infill

\(t_{S}\) :

Spandrels thickness

\(t_{w}\) :

Thickness of the wall/pier

\(V_{cr }\) :

Shear resistance of the wall corresponding to first cracking

\(V_{max}\) :

Maximum in-plane shear resistance of the wall

\(V_{Rd}\) :

Design value of shear resistance

\(V_{Rd,r}\) :

Design value of shear resistance considering rocking

\(V_{Rd,s}\) :

Design value of shear resistance considering sliding

\(V_{Rd,t}\) :

Design value of shear resistance considering diagonal cracking

\(V_{u }\) :

Idealized shear resistance

\(\varepsilon \) :

Strain

\(\gamma _{S}\) :

Coefficient considering the actual distribution of stress at the end section of spandrel

\(\Delta _{y}\) :

Unit height

\(\mu \) :

Coefficient of friction

\(\nu _{M}\) :

Poisson’s ratio for masonry

\(\rho \) :

Density

\(\sigma \) :

Stress

\(\sigma _{0}\) :

Average compression stress due to vertical loading

\(\sigma _{d}\) :

Average vertical stress over the compressed part of the wall/pier

\(\sigma _{0S}\) :

Normal compressive stress on the spandrel

\(\tau _{{M}0}\) :

Equivalent diagonal shear strength

\(\tau _{Hmax}\) :

Average shear stress over the whole cross section of the wall at the attained maximum resistance of the wall

\(\phi \) :

Interlocking parameter considering the texture of masonry

\(\psi \) :

Corrective factor in dependence from boundary conditions

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Acknowledgments

The results were achieved through the project PERPETUATE (www.perpetuate.eu), funded by the European Commission in the 7th Framework Programme (FP7/2007-2013), under Grant Agreement No. 244229 and by the Ministry of Science and Technology of the Republic of Slovenia. We would also like to thank Prof. Adrian W. Page from the University of Newcastle, Australia and two anonymous reviewers for their valuable comments, effort and time allocated to improve the paper.

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Authors and Affiliations

  1. University of Ljubljana, Ljubljana, Slovenia

    Meta Kržan & Vlatko Bosiljkov

  2. Building and Civil Engineering Institute ZRMK, Ljubljana, Slovenia

    Samo Gostič

  3. University of Genova, Genoa, Italy

    Serena Cattari

Authors
  1. Meta Kržan
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  2. Samo Gostič
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  3. Serena Cattari
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  4. Vlatko Bosiljkov
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Correspondence to Vlatko Bosiljkov.

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Kržan, M., Gostič, S., Cattari, S. et al. Acquiring reference parameters of masonry for the structural performance analysis of historical buildings. Bull Earthquake Eng 13, 203–236 (2015). https://doi.org/10.1007/s10518-014-9686-x

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  • DOI: https://doi.org/10.1007/s10518-014-9686-x

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