What is the common idea in the different applications of the discrete element method to masonry?

The common idea in the different applications of the discrete element method to masonry is the idealization of the material as a discontinuum where joints are modeled as contact surfaces between different blocks.

Why is linear elastic analysis used in masonry?

It must be noted that, due to its very limited capacity in tension, masonry shows a complex non-linear response even at low or moderate stress levels.

What is the main limitation of linear elastic analysis?

simple linear elastic analysis cannot be used to simulate masonry strength responses, typically observed in arches and vaults, characterized by the development of partialized subsystems working in compression.

What is the popular method for describing masonry structures?

The finite element method offers a widespread variety of possibilities concerning the description of the masonry structures within the frame of detailed non-linear analysis.

What are the main reasons for the popularity of linear elastic analysis?

During the last years, non-linear analysis is becoming more popular thanks to larger software availability and increasing computer capacity.

What is the method for generating compression-only surfaces and spatial systems?

Block and Ochsendorf [16] have presented a Thrust-Network Analysis method for generating compression-only surfaces and spatial systems based on a duality between geometry and in-plane forces in networks.

What is the main purpose of linear elastic analysis?

linear elastic analysis has been used, with partial success, as an auxiliary tool assisting in the diagnosis of large masonry structures.

What are the main problems of the study of masonry historical structures?

In spite of the important advances experienced by structural analysis methods, the study of masonry historical structures is still a challenging activity due to the significant difficulties encountered in the description of their complex geometry,materials, morphology (member composition and connections), and present condition, including damage and alterations.

What is the common example of a simple wall subjected to seismic loads?

An example concerning a simple wall subjected to seismic loads is given in Fig. 15, where the amount of horizontal forces resisted is measured as a multiplier α over the gravity forces.

What are the limitations of linear elastic analysis?

The limitations of linear elastic analysis, on the one hand, and limit analysis, on the other hand, can be partly overcome by means of simple generalizations of matrix calculation of frame structures, extended with (1) Improved techniques for the description of complex geometries (curvedmembers with variable sections . . .) and (2) Improved description of the material (for instance, including simple constitutive equations yet affording the consideration of cracking in tension and yielding / crushing in compression, yielding in shear).

What is the significance of the crushing behavior in masonry structures?

In the case of masonry crushing, hypothesis (4) might be questionable, but crushing behavior has minor importance in the response of masonry structures except for very shallow arches, pillars, towers and massive vertical structures.

(Open Access) Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches (2010) | Pere Roca

Q: What are the future works mentioned in the paper "Structural analysis of masonry historical constructions. classical and advanced approaches" ?

A wide set of possibilities have been developed to describe masonry structures to different levels of accuracy, from rough ( but useful ) engineering approaches to very detailed modelling taking into account the distinct response of the individual components. With further developments in computer technology and numerical methods, the analysis of entire complex historical structures ( including for instance, Gothic cathedrals ) using very accurate approaches, may become possible in the near future. Further developments will make very demanding analyses, such as the nonlinear time-domain dynamic one, possible even if used in combination with complex structural and material models. Sufficient validation or calibration of numerical models, based on the comparison with empirical information, will be always necessary to grant the reliability of the numerical models and their capacity to predict on the structural response and safety.

Q: What effects may have had influence on the structural response and existing damage?

The following effects linked to history may have had influence on the structural response and existing damage: Construction process, architectural alterations, additions, destruction in occasion of conflicts (wars . . .), natural disasters (earthquake, floods, fires . . .) and long-term decay or damage phenomena.

Arch Comput Methods Eng (2010) 17: 299–325

DOI 10.1007/s11831-010-9046-1

ORIGINAL PAPER

Structural Analysis of Masonry Historical Constructions.

Classical and Advanced Approaches

Pere Roca ·Miguel Cervera ·Giuseppe Gariup ·

Luca Pela’

Received: 15 January 2010 / Accepted: 15 January 2010 / Published online: 22 July 2010

Abstract A review of methods applicable to the study of

masonry historical construction, encompassing both classi-

cal and advanced ones, is presented. Firstly, the paper of-

fers a discussion on the main challenges posed by historical

structures and the desirable conditions that approaches ori-

ented to the modeling and analysis of this type of structures

should accomplish. Secondly, the main available methods

which are actually used for study masonry historical struc-

tures are referred to and discussed.

The main available strategies, including limit analysis,

simpliﬁed methods, FEM macro- or micro-modeling and

discrete element methods (DEM) are considered with regard

to their realism, computer efﬁciency, data availability and

real applicability to large structures. A set of ﬁnal considera-

tions are offered on the real possibility of carrying out realis-

tic analysis of complex historic masonry structures. In spite

of the modern developments, the study of historical build-

ings is still facing signiﬁcant difﬁculties linked to computa-

tional effort, possibility of input data acquisition and limited

realism of methods.

P. Roc a (



) · M. Cervera ·G. Gariup

Technical University of Catalonia, Jordi Girona 1-3, 08034

Barcelona, Spain

e-mail: pere.roca.fabregat@upc.edu

M. Cervera

e-mail: miguel.cervera@upc.edu

G. Gariup

e-mail: giuseppe.gariup@upc.edu

L. Pela’

University of Bologna, Bologna, Italy

e-mail: luca.pela@unife.it

1 Introduction. Purpose and Challenges

Studies oriented to conservation and restoration of histori-

cal structures have recourse to structural analysis as a way

to better understand the genuine structural features of the

building, to characterize its present condition and actual

causes of existing damage, to determine the true structural

safety for a variety of actions (such as gravity, soil settle-

ments, wind and earthquake) and to conclude on necessary

remedial measures. In short, structural analysis contributes

to all the phases and activities (including diagnosis, reliabil-

ity assessment and design of intervention) oriented to grant

an efﬁcient and respectful conservation of monuments and

historical buildings. Accurate structural analysis is needed

to avoid erroneous or defective conclusions leading to ei-

ther over-strengthen the structure, causing unnecessary loss

in terms of original material and cultural value, or to insufﬁ-

ciently intervene on it, and hence generate inadmissible risks

on people and heritage. Unsurprisingly, ancient structures

have been studied, since long time ago, using the most ad-

vanced tools available for structural assessment.

The application of advanced computer methods to the

analysis of historical structures was pioneered by the stud-

ies of the Brunelleschi Dome by Chiarugi et al. [30], the

Pisa Tower by Macchi et al. [79],theColosseoinRomeby

Croci [34], see also Croci and Viscovik [36], Mexico Cathe-

dral by Meli and Sánchez-Ramírez [88] and San Marco’s

Basilica in Venice by Mola and Vitaliani [93], among oth-

ers (Figs. 1 and 2). By then, the development of methods

for accurate analysis of steel and concrete structures, includ-

ing non-linear applications, was already at a very advanced

stage thanks to the work of Zienkiewicz and Taylor [136],

Ngo and Scordelis [97] and many others. Notwithstanding,

analysts attempting to use computer tools for the study his-

torical structures were by then facing overwhelming chal-

lenges. Methods then available were not yet prepared to

300 P. Roca et al.

tackle the speciﬁc problems of ancient constructions con-

cerning materials, structural arrangements and real preser-

vation condition. In fact, the difﬁculties posed by histori-

cal structures are still very challenging, and still reminiscent

of those encountered by the pioneers, in spite of signiﬁcant

progress during the last decades.

Some of difﬁculties encountered are related to the de-

scription of geometry, materials and actions, all of which

acquire remarkable singularity in the case of historical con-

struction. Additional important difﬁculties are related to the

acquisition of data on material properties, internal morphol-

ogy and damage, as well as to the adequate interpretation

of structural arrangements, overall organization and histori-

cal facts. Because of all these difﬁculties, it is generally ac-

cepted (Icomos/Iscarsah Committee [60]) that the study of

a historical structure should not only base on calculations,

but should integrate as well a variety of complementary ac-

tivities involving detailed historical investigation, deep in-

spection by means of non destructive techniques (NDT)

and monitoring, among other. Structural analysis of histor-

ical structures constitutes in fact a multidisciplinary, mul-

tifaceted activity requiring a clever integration of different

approaches and sources of evidence. These difﬁculties are

discussed into more detail in the following paragraphs.

1.1 Material

Historical or traditional materials such as earth, brick or

stone masonry and wood are characterized by very com-

plex mechanical and strength phenomena still challenging

our modeling abilities. In particular, masonry is character-

ized by its composite character (it includes stone or brick

in combination with mortar or day joints), a brittle response

in tension (with almost null tensile strength), a frictional re-

sponse in shear (once the limited bond between units and

mortar is lost) and anisotropy (for the response is highly sen-

sitive to the orientation of loads). In spite of the very signif-

icant effort invested to characterize and mathematically de-

scribe masonry mechanics and strength, the accurate and ef-

ﬁcient simulation of masonry response is still a challenge in

need of further experimental and theoretical developments.

Important results by Ali and Page [1], Lourenço [70], Binda

et al. [12] and many others have yielded a very signiﬁcant

level of understanding.

Historical materials, including brick or stone masonry,

are normally very heterogeneous even in a single building

or construction member. Moreover, historical structures of-

ten show many additions and repairs done with different ma-

terials. Material characterization is constrained by due re-

spect to the monument and original material. Non- destruc-

tive, indirect, tests (NDT) and minor destructive tests (MDT)

should be preferred. If any, only a very limited number of

pits or cores allowing direct observation and laboratory test-

ing are normally acceptable. In practice, only limited and

partial information can be collected. Additional assumptions

on morphology and material properties may be needed in or-

der to elaborate a model.

1.2 Geometry

Historical structures are often characterized by a very com-

plex geometry. They often include straight or curved mem-

bers. They combine curved 1D members (arches, ﬂying

arches) with 2D members (vaults, domes) and 3D ones

(ﬁllings, pendentives ...). They combine slender members

with massive ones (massive piers, walls buttresses, foun-

dations ...). However, today numerical methods (such as

FEM) do afford a realistic and accurate description of geom-

etry. Due to it, geometry is perhaps one of the least (although

still meaningful) challenges to be faced by the analysis.

1.3 Morphology

A more signiﬁcant problem lays in the characterization and

description of the internal morphology of structural mem-

bers and their connections. Structural members are often

non-homogeneous and show complex internal structures in-

cluding several layers, ﬁlling, material, cavities, metal inser-

tions and other possible singularities. Connections are sin-

gular regions featuring speciﬁc geometric and morphologi-

cal treats. The transference of forces may activate speciﬁc

resisting phenomena (contact problems, friction, eccentric

loading). Modeling morphology and connections in detail

may be extremely demanding from a computational point of

view. Nevertheless, the main difﬁculty is found in physically

characterizing them by means of minor- or non-destructive

procedures.

1.4 Actions

Historical structures may have experienced (and keep on ex-

periencing) actions of very different nature, including the

effects of gravity forces in the long term, earthquake, envi-

ronmental effects (thermal effects, chemical or physical at-

tack), and anthropogenic actions such as architectural alter-

ations, intentional destruction, inadequate restorations ....

Many of these actions are to be characterized in historical

time. Some are cyclic and repetitive (and accumulate signiﬁ-

cant effect in the long term), some develop gradually in very

long time periods, and some are associated to long return

periods. In many cases, they may be inﬂuenced by historical

contingency and uncertain (or at least, insufﬁciently known)

historical facts.

1.5 Damage and Alterations

Existing and general alterations may affect very signiﬁcantly

the response of the structure. Damage and deformation are to

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches 301

(a)

(b)

Fig. 1 Some pioneering FEM studies on historical structures.

(a) Tower of Pisa: FEM model and substructuring of the colonnade sys-

tem (Macchi et al. [79]). (b) Mexico City Cathedral (Meli and Sánchez

Ramírez [88]). (c) The Colosseum in Rome. Tensile horizontal stresses

due to the seismic action (Croci [34])

be modeled, as present features of any existing structure, to

grant adequate realism and accuracy in the prediction of the

actual performance and capacity. Damage encompasses me-

chanical cracking, material decay (due to chemical or phys-

ical attack) or whatever phenomena inﬂuencing on the orig-

inal capacity of materials and structural members.

(c)

Fig. 1 (Continued)

1.6 History

History is an essential dimension of the building and must

be considered and integrated in the model. The following ef-

fects linked to history may have had inﬂuence on the struc-

tural response and existing damage: Construction process,

architectural alterations, additions, destruction in occasion

of conﬂicts (wars ...), natural disasters (earthquake, ﬂoods,

ﬁres ...) and long-term decay or damage phenomena. His-

tory constitutes a source for knowledge. In many occasions,

the historical performance of the building can be engineered

to obtain conclusions on the structural performance and

strength. For instance, the performance shown during past

earthquakes can be considered to improve the understanding

on the seismic capacity. The history of the building consti-

tutes a unique experiment occurred in true scale of space and

time. In a way, knowledge of historical performance makes

up for the mentioned data insufﬁciency.

2 Desirable Features of Methods Applied to Historical

Structures

Because of the aforementioned challenges, attempts to

model and simulate the response of a historical structure

should try to satisfy some basic requirements. Firstly, any

modelling technique should be able to adequately describe

the geometry and morphology of the real construction, in-

cluding the structural form, internal composition, connec-

tions and support conditions. An accurate description of the

distribution of mass and external forces is essential for both

gravity and seismic analyses.

Secondly, constitutive equations should be adopted al-

lowing an adequate description of the essential mechanical

302 P. Roca et al.

and strength features of the different materials existing in the

building. It is important to highlight that simple linear elas-

tic analysis fails to simulate essential features of non-tension

resisting materials such as stone and masonry. More sophis-

ticated, non-linear constitutive equations will normally be

Fig. 2 The ﬁnite element model of the St. Mark’s Basilica: Top: global

discretization; Bottom: soil foundation discretization including defor-

mation (Mola and Vitaliani [93])

necessary. In turn, the use of such constitutive equations

will require the availability of non-linear properties to be ob-

tained by means of different laboratory or in-situ mechanical

tests.

Actions (mechanical, physical, chemical ...)arealsoto

be modelled by means of mathematical formulations de-

scribing their mechanical effect in terms for forces on the

structure, imposed movements or deformations, or possible

variations of the material properties.

An accurate model of the structure should also afford the

description of damage and alterations existing in the struc-

ture, including cracks, disconnections, crushing, deforma-

tion and out-of-plumb, and construction defects. Some dam-

age types can be modelled indirectly as a disconnection be-

tween elements or a local reduction of material properties. In

order to characterize the actual capacity in the present con-

dition of a building, the analysis should be carried out on the

model accounting for its real damaged and deformed state.

As the analysis of historical structures will normally be

oriented to identify needs for restoration and strengthening,

analysis methods should able to incorporate and model pos-

sible stabilization, repair or strengthening measures. In some

cases, these can be taken into account in an indirect way

by adequately modifying material properties, modifying the

sectional dimensions or conﬁguration, or by adding forces

to represent their mechanical effect.

The interaction of the structure with the soil is also to be

taken into account except in cases it is judged to be irrele-

vant. Taking it into account will often require the inclusion

of a large portion of foundation soil as part of the entire FEM

model as done in the analysis of San Marcos Basilica by

Mola and Vitaliani [93] or the modal analysis of a masonry

tower by Fanelli [44] (Figs. 2 and 3).

Fig. 3 Examples of graphical rendering for a FE mathematical model of a masonry tower: discretized geometry, including the soil foundation,

and ﬁrst two vibration modal shapes (Fanelli [44])

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches 303

Fig. 4 Different stages of the

model (a)to(d) and successive

boundary conditions variation

(Casarin [21]). The surrounding

buildings are taken into account

by directly modelling their walls

or by simulating them with

translational springs

Fig. 5 Deformed meshes and

maximum displacements (in

grey scale) for seismic load

acting along the longitudinal

direction of the building.

Monastery of Jerónimos

(Lourenço and Mourão [72])

Fig. 6 Detailed modelling of Mallorca cathedral, in Spain, including the different parts of the structure which can inﬂuence on the modal analysis

(tower, façade, choir) and ﬁrst modal shapes (Roca et al. [126])

Certain types of analyses, as in particular dynamic one,

may require the inclusion of neighboring buildings into the

model with an adequate description of existing connections.

This is so because of their possible effect on the modal

shapes and overall dynamic response. Modelling accurately

the dynamic response will often require to construct a global

model incorporating all the distinct parts of a complex struc-

ture as in the analysis of Reggio Emilia Cathedral (Casarin

[21], Casarin and Modena [22]), of the Monastery of Jerón-

imos (Lourenço and Mourão [72]) or of Mallorca Cathedral

(Roca et al. [126]) (Figs. 4–6). The connection between the

different parts should be modelled accurately by taking into

account the real contact conditions, which requires a pre-

vious detailed inspection and investigation. The agreement

between numerical and experimental vibration modes and

frequencies may be considered as a way to validate the de-

scription of connection among different parts in the struc-

ture.

Studies on different historical structures (Roca [121],

Roca et al. [123]) have shown that real deformations are nor-

mally much larger (one or even two orders of magnitude)

than those predicted by conventional instantaneous calcu-

lations. This is due to the fact that these analysis neglect

history-related aspects such as (1) deformations occurred

Structural Analysis of Masonry Historical Constructions. Classical and Advanced Approaches

Figures

Citations

Modeling Strategies for the Computational Analysis of Unreinforced Masonry Structures: Review and Classification

Damage and performance evaluation of masonry churches in the 2009 L’Aquila earthquake

Simulating masonry wall behaviour using a simplified micro-model approach

An innovative numerical modeling strategy for the structural analysis of historical monumental buildings

From Laser Scanning to Finite Element Analysis of Complex Buildings by Using a Semi-Automatic Procedure.

References

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Frequently Asked Questions (15)

Q1. What are the contributions mentioned in the paper "Structural analysis of masonry historical constructions. classical and advanced approaches" ?

Q2. What are the future works mentioned in the paper "Structural analysis of masonry historical constructions. classical and advanced approaches" ?

Q3. What is the common idea in the different applications of the discrete element method to masonry?

Q4. Why is linear elastic analysis used in masonry?

Q5. What is the main limitation of linear elastic analysis?

Q6. What is the popular method for describing masonry structures?

Q7. What effects may have had influence on the structural response and existing damage?

Q8. What are the main reasons for the popularity of linear elastic analysis?

Q9. What is the method for generating compression-only surfaces and spatial systems?

Q10. What is the main purpose of linear elastic analysis?

Q11. What can be considered to improve the understanding on the seismic capacity?

Q12. What are the main problems of the study of masonry historical structures?

Q13. What is the common example of a simple wall subjected to seismic loads?

Q14. What are the limitations of linear elastic analysis?

Q15. What is the significance of the crushing behavior in masonry structures?