Structural analysis of masonry buildings

From early fact-finding to finite element modelling

 

Prior to the structural analysis of an existing building and to design, the following actions must be put in place:
_collecting information about the building;
_numerical modelling of the structural system.

UNDERSTANDING THE BUILDING

The diagnostic and fact-finding step plays an essential role prior to modelling, analysing and engineering any works.
Therefore, the results obtained with various survey methods are of major relevance. (Figure 1).
The different testing methods help understand with sufficient accuracy the mechanical characteristics of the materials in place and offer some essential parameters to formulate a model of operation of the structure as a whole.
Studying the interventions to be implemented in an existing building is a very delicate step, owed to the special nature of the issue on its own, as well as to the uncertainties linked to the knowledge of the materials and the reliability of the results of any survey and calculation procedure.
It is therefore necessary that the results obtained from surveys are both qualitatively and quantitatively wholly representative of the characteristics of the work.

 

NUMERICAL MODELLING

Another delicate step lies in structural modelling and analysis. Based on the information obtained from surveys (geometrical characteristics, material specifications and construction details), modelling is aimed at simulating as much accurately as possible the structural behaviour of a building with regard to the vertical loads and to the horizontal actions of a seismic event.
There are several modelling procedures now available in literature. Certainly, the most widely used methods to analyse both the local and the global collapse mechanisms are based on simplified models, for instance the macro-element modelling method, which reduces the number of degrees of freedom and therefore makes both the input and output procedures easier, as well as the interpretation of results. Another modelling approach falling in this class is based on the  association of a masonry wall to an equivalent frame, whose vertical and horizontal elements are constituted by shear walls and masonry beams, respectively. They are all modelled as a beam element  provided with axial, flexural and shearing stiffness. The nodes at the intersection of shear walls and masonry beams are considered as infinitely stiff and resistant. The collapse of a masonry wall under the effect of horizontal action is generally owed to the failure of shear walls becoming increasingly vulnerable because the masonry beams have become weaker. (figure 2)

More complex finite element methods can be used, where macro-modelling and micro-modelling strategies are involved. As for macro-modelling, a masonry wall is generally rendered with (2D or 3D) finite elements capable of describing the mechanical behaviour of masonry as a homogeneous and isotropic continuous material. (figures 3a-c)

On the other hand, detail micro-modelling is based on modelling the individual components of a masonry structure. In particular, both bricks and mortar are rendered as continuous elements. The behaviour of the system as a whole is then governed by specific elements with a non-linear behaviour that describe the mechanical characteristics of the brick-mortar interface. (figures 4a-c)

 

THE CONVENT OF SPIRITO SANTO IN AVERSA (CE) – ITALY

A survey campaign and a structural behaviour analysis were performed in the framework of the functional upgrading of a former nunnery to be used as university residence.

Historical-critical analysis
The complex of Spirito Santo is located at the heart of the Norman city of Aversa in its 12th century extension, that is between the first and second ring, near the Cathedral and the bishop's residence, and was home to the Franciscan Clarist Order, who first settled in Aversa in 1562.
After the Italian Unification (1868), the convent was abolished and turned into a junior high school. After the Second World War, some areas of the school were refurbished, including roof and masonry reparations, as well as replacements of floors, doors and windows.
After the school was moved elsewhere, the convent failed to be maintained and was eventually assigned by the Municipality to ADISU, which decided to turn it into a university residence.
The convent is a listed building and bears constraints under the Cultural Heritage Regulations.

Geometrical-structural survey
A planometric and altimetric survey of the building was carried out, followed by renderings of plans, sections and construction details. (figures 5-8)

Diagnostic investigations and fact-finding step
The investigation campaign consisted in performing a number of tests aimed at understanding the type of construction method and the mechanical characteristics of the materials, as well as the construction details of masonry, vaults, foundations and floors.
All these data proved essential to set up a numerical calculus model. (figures 9-16)

On-site diagonal compression test – Testing Method
Diagonal compression tests are aimed at assessing the shear strength and stiffness of masonry walls. They are governed by the ASTM E 519- 81 standard and are generally carried out on square panels sized 120 x 120 cm. During on-site testing, panels are isolated from the neighbouring wall with four cuts made with a diamond wire or circular blade. Unlike in laboratory testing, during on-site testing the bottom portion of the panel remains toothed to the wall masonry. However, theoretical and numerical analyses have demonstrated that this has a trivial influence on results, at least during the elastic phase.
The testing equipment consists in a set of metallic elements placed at the two edges of a diagonal of the panel. One of the two edges also accommodates a hydraulic ram, which operates between two metallic elements, of which the inner one leans onto the panel edge and the outer one is connected with steel bars to the metallic element located on the opposite edge. This layout makes a closed system, where the ram induces stress along a diagonal of the panel. The panel is equipped with 4 displacement transducers positioned along two sides of the diagonals, so that strain under load can be measured.

> Identifying the mechanical characteristics of masonry

Mechanical characteristics of masonry

Parametres

Values

fm

36,3 daN/cm2

to

0,63 daN/cm2

E

10.500 daN/cm2

G

3.600 daN/cm2

W

16 KN/m3

 

> Load analysis (figure 17)

> Numerical modelling
A finite element modelling aimed at assessing the structural behaviour of the building was carried out in compliance with Directive 2011, which provides for three different levels of increasing accuracy to evaluate safety conditions.
In this case, the complexity of the structure imposed using all three levels of verification.
In particular, the following procedures were followed:

Simplified global verification – LV1; 
Local collapse mechanism verification – LV2; 
Accurate global verification – LV3.

_Level LV1
A simplified global analysis of the building in current conditions was performed with the use of a simplified method named “VM – Assessment of vulnerability of masonry buildings”. The global strength of the building was assessed on each floor as the sum of the shear strength of the individual masonry walls.

_Level LV2
Local collapse mechanisms analyses were executed under the prescriptions of point C8A.4 of NTC Information Letter. An accurate analysis of the building layout allowed identifying the macro-elements prone to instability and suggesting the corresponding local mechanisms. In particular, the following collapse mechanisms were detected and studied: simple overturning of monolithic wall; combined overturning of a diagonal wedge; break owed to vertical deflection, etc. (figures 18a,b)

_Level LV3
Global numerical analyses and corresponding verifications were carried out with an equivalent frame model by using the pushover or non linear static analysis method in compliance with the procedure prescribed by NTC 2008 standards and related Information Letter n. 617/2009. Special care was given to the fact that the building was an aggregate. Any interferences with neighbouring buildings were therefore analysed and taken in consideration. (figures 19-20)

A safety assessment was carried out in compliance with Chapter 8 of “NTC” standards, for “Ultimate Limit State”, with reference to the “Life Safety Limit State”, and for the “Operational Limit State” with reference to both the “Damage Limit State” and the “Operation Limit State”.

[by Pasquale Crisci, Gennaro Di Lauro, Gianfranco Laezza]

   

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