Analysis of the susceptibility of infilling masonry walls to crack due to vertical deformation of concrete structures

Recent Advances in Mechanics and Materials in Design M2D’2015 1 PAPER REF: 5617 Please leave these first three lines blank for the Editors Please leave these first three lines blank for the Editors ANALYSIS OF THE SUSCEPTIBILITY OF INFILLING MASONRY WALLS TO CRACK DUE TO VERTICAL DEFORMATION OF CONCRETE STRUCTURES Rui Sousa 1(*) , Hipólito Sousa 1 , 1 Gequaltec, Department of Civil Engineering (DEC), University of Porto, Portugal (*) Email: [email protected] Please leave these two lines blank Please leave these two lines blank ABSTRACT In this paper a numerical study is presented to evaluate the masonry partitions walls susceptibility to crack due to vertical deformation of concrete structures. Common solutions used in Portuguese buildings for structural systems and non-structural partition walls were analysed in this study. The numerical study was based on a 3D FEM macro models. Two types of simulations were performed. The first type was a simulation of a masonry deep beam subjected to vertical displacements, where experimental results obtained from tests were used to calibrate a nonlinear constitutive model. The second type was the simulation of a representative part of a building concrete structure, partially filled with masonry partition walls, subjected to design loadings and creep effects. The objective of these simulations was to evaluate the partition walls susceptibility to crack by modifying some properties of these walls, and also to evaluate, as close as possible, the mechanical behaviour of partition walls affected by the deformation of concrete structures with creep effects. Keywords: Partition walls, non-structural masonry, cracking, serviceability INTRODUCTION Vertical movements/deformations of building structures in serviceability conditions can cause cracking in infilling masonry walls. This type of defect can impair the functionality of these walls, such as aesthetics, watertightness or acoustics and thermal behavior, and repairing is difficult and expensive to perform. This type of structural deformations are mainly caused by vertical loading and in the case of reinforced concrete structures these deformations are considerably aggravated by the long term/creep effects. If these structural deformations are not controlled, important loading/deformations can be imposed on more sensitive adjacent parts, such as non-structural masonry partitions and enclosure walls, and damage can occur in these elements. Masonry itself has a lower ductile capability and a lower tensile strength when compared with other building materials, therefore, masonry walls are not able to sustain significant deformations/loading without any visible damage, especially in the case of non-structural walls since these can be made with lower resistance materials. Moreover, since these sort of walls do not have any intended structural function in the building, their mechanical behavior and detailing are aspects often neglected in the design process. Taken into account that nonstructural masonry is still a solution frequently used for internal or external infilling walls, it 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 2 can be first concluded that this solution is highly susceptible to damage/cracking due to the movements of their support structure. In order to reduce the damage in non-structural elements in serviceability conditions, some concrete design codes establish limits for the vertical displacement of structural elements. Despite of this fact, cracking on masonry infilling walls have been reported with some frequency in recent years, and in some cases this seem to be related with the vertical deformation of reinforced concrete beams and slabs. In this paper a numerical study is presented to evaluate the masonry partitions walls susceptibility to crack in serviceability conditions, in particular due to vertical deformation of concrete structures. Common solutions used in Portuguese buildings for structural systems and partition walls were considered: concrete framed structure made with beams and piles and concrete slabs (beam-and-block floor system), and partition masonry walls made with horizontally perforated clay units laid with general purpose mortar. CONSTRUCTIVE SOLUTIONS FOR PORTUGUESE BUILDINGS Cracking in masonry walls is a pathology frequently associated to the constructive solutions used in buildings, in particular the solutions used in masonry walls and their support structures, and therefore a characterization of those constructive solutions is important. Since the seventy’s that Portuguese buildings are made with reinforced concrete structures filled with non-structural masonry walls. In the last decade about 67% of the buildings were constructed with this constructive technology, Fig.1 (INE, 2011). Fig.1 Example of a building being constructed with reinforced concrete structure filled with masonry walls These reinforced concrete structures are framed made with piles and beams, and at the floor level concrete slabs made with beam-and-block floor systems are frequently used (Fig.2). The spans of slabs and beams vary between 5 to 7m, and in some case may reach higher dimensions. Recent Advances in Mechanics and Materials in Design M2D’2015 3 Fig.2 Example of a beam-and-block floor system The external walls, or enclosure walls, are made with masonry cavity walls with a thickness of 30 to 35cm (without considering renderings/coatings applied on the wall), although in the last years the use of single leaf masonry walls have been growing. In general these walls include thermal insulation layers applied on the cavity of the wall or on the external face of the wall. The internal walls, or partitions walls, are made with single leaf masonry walls with a thickness of 7cm, 11cm or 15cm (without considering renderings/coatings applied on the wall), although 11cm is the most common thickness used for this type of partitions, Fig.3. Fig.3 Example of a masonry partition wall made with horizontal perforated clay units with 11cm of thickness Also higher thickness may be used in particular cases, such as single leaf or cavity walls between dwellings to improve certain functionality aspects (thermal/acoustic comfort, fire resistance, amongst others). The materials most commonly used to build masonry walls in Portugal are horizontal perforated clay units laid on general purpose mortars (factory made mortars). Other type of masonry materials may also be used, although less frequently, such as lightweight or normal concrete units and lightweight mortars or special mortars for thin joints. Partition or enclosure walls rarely include any ancillary components, such as joint reinforcement, lintels or ties. The dimensions of the walls usually vary between 3 to 6 m in length by 2,5 to 3 meters in height and for the most cases include openings for doors and windows systems. The walls are built with the units laid on vertical and horizontal mortar joints with 1 to 1,5cm of thickness. The walls are usually bonded to the surrounding structure with Cast “in situ” concrete layer Steel mesh reinforcement Precast and prestressed concrete beams Cast “in situ” reinforced concrete beams Clay or concrete block Thin rendering layer Clay units Mortar bed joints 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 4 mortars joints executed during the erection of the walls. The connection between walls is frequently made with mortar bonding, and in some few cases with the interlocking of units. Concerning the renderings/coatings, these are frequently made with traditional factory made mortars (sand and cement or sand, cement and lime, and plaster mortars). This rendering system was applied on 88% of Portuguese buildings (INE, 2011), although in the last years other techniques have been used, in particular on the external face of the walls, such as stone cladding and external thermal insulation composite systems (ETICS). The internal renderings/coatings are also made with traditional mortars, and in partitions walls the rendering layers are usually thinner than external renderings (1 to 1,5 cm for cement based mortars and 0,5 to 1cm for plaster mortars). CHARACTERIZATION OF CRACKING IN PARTITION WALLS Cracking is the main pathology on partition masonry walls and applied renderings/coatings, and it has been occurring frequently in the last few years in Portugal. The main cause seems to be associated to movements/deformations of the surrounding/supporting structure of the walls, in particular concrete slabs and beams, Fig.4. Fig.4 Examples of cracking in partitions walls due to movements of surrounding/supporting concrete structures These structural movements/deformations can affect the partitions walls, especially if these walls are connected to the structure, and are usually caused by permanent/ live loadings, foundation settlements and thermal gradients that can occur during the life time of the building, Fig.5. a) b) c) Fig.5 Causes leading to cracking on partition walls: a) vertical deflections, b) foundation settlements and c) thermal movements of surrounding/support concrete structures (Sousa et al, 2015) Recent Advances in Mechanics and Materials in Design M2D’2015 5 In the particular case of vertical deflection of beams or slabs affecting masonry partitions walls, these deformations can induce loading if the top of these walls are connected in the structure. Depending of the relative rigidity of the structure, the partition walls can act as compression members when supported on rigid elements, or act as flexural beams or deep beams, depending on the height to length ratio of the walls, if the supports are more flexible. Given the fragile nature of partition walls (lower strength and ductility when compared with its support structure), the risk for these walls to crack in serviceability conditions is high, and it is aggravated by existence of openings. Other aspects seem can also aggravate the occurrence of cracking on masonry partition walls. During the last years the evolution of concrete technology and the use of buildings with more large and open spaces, has allowed the use of more deformable and lighter structural elements (higher spans and slenderness, flat slabs). On the other hand, the fragile mechanical behavior of partitions walls and its interaction with the surrounding structure are aspects often neglected in design. Moreover, the quality of execution of these walls it is not always the best. LITERATURE REVIEW There are some scientific studies and normative/technical documents with some provisions regarding the control of the vertical deflection of structural elements and detailing aspects for the execution of partitions walls in the order to avoid the damage on these walls. Some scientific studies based on experimental tests suggests some design limits (Meyerhof, 1953; Beranek, 1987; Dias, 1994; Page,2001; Holanda et al, 2007), however it is difficult to establish from these studies a general reference since the variability of results is high. For example, limits for relative displacements of L/700 to L/3000 (being L the span of the support structure) and limits for the tensile stress in the walls of 0,1 to 0,3 N/mm 2 are found in these studies. The Belgian National Research Institute (CSTC), based on experimental tests performed on masonry walls made with clay and concrete units, recommends that the deflection of structural elements should be lower than L/500 or L/1000, depending on the existence or not of openings (Pfeffermann, 1981). More recently, the W023 commission for wall structures of the International Council for Research and Innovation in Building and Construction (CIB), has published a guidance manual with recommendations regarding the identification, prevention and repair of cracking on masonry walls (Sousa et al, 2015). For partition walls, CIB-W023 commission recommends deflection limits of L/500 to L/1000, depending on the existence or not of openings. However, it recognizes that these limits, or other more demanding, may not be affordable, therefore recommending complementary constructive measures to avoid cracking on partitions. Examples of such measures are the use reinforcement embedded in mortar joints or in mortar renderings/coatings, execution of provision joints on the walls, recommendations regarding the erection of the walls, amongst others aspects. Calculation codes for reinforced concrete and masonry structures define some deflection limits in order to limit the damage in non-structural masonry partitions walls. For example, Eurocode 2 (CEN, 2004) defines a maximum deflection of L/500 for structures submitted to a quasipermanent combination of loadings, whilst the French code (AFNOR, 2009) defines a more demanding deflection limit for structures with spans higher than 5m (L/1000 +5mm). 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 6 Calculation codes for masonry structures, such as the American code (MSJC, 2013) and the former English Code (BSI, 1995), also defines maximum deflection limits for structural masonry walls (L/600 and L/500 or 20mm) that should be verified assuming the elastic behaviour in the calculations (uncracked sections). However, in these codes it is not mentioned any admissible values for tension or compression. Nevertheless, the American code (MSJC, 2013) has section concerning specific provisions for masonry partitions, such as the establishment of minimum and maximum thickness of the wall (102 to 305mm), limiting the loading capability of the wall (e.g.vertical compression loading of 2,9kN/m and 0,2 to 0,5kN/m 2 for lateral loading), limits for the dimensions of panels and openings and support conditions of partition walls that are laterally loaded (assuming serviceability loadings and allowable stress design), definition of some constructive measures to connect/anchor partition walls to the structure and to other walls, amongst other aspects. It is also worth mentioning that European code for masonry structures, Eurocode 6 (CEN, 2005), only provides general recommendations for structural walls and does not provide any specific limits for deflection control or constructive recommendations for structural or nonstructural walls. Finally, a French normative document (AFNOR, 2008) regarding the execution and design of non-structural masonry partition walls with thickness lower than 150mm, defines deflection limits for the support structures of these walls (the same limits mentioned by the French code for concrete structures (AFNOR, 2009)) and several constructive measures, such as maximum dimensions according to the thickness of the wall, detailing provisions for the execution of joints that disconnect the walls from the surrounding structure, connections between walls, permitted type of renderings/coatings established according to the thickness of the wall, amongst other aspects. For example, for perforated clay masonry with a gross thickness of 80 to 110mm, the maximum permitted height and length are 4m and 8m, respectively. Other dimensions may be use, however the panel should not have a surface higher than 25m 2 . Moreover, the use of mortar renderings/coatings made only with cement binders is not allowed for wall thicknesses lower than 110 mm. NUMERICAL MODEL The numerical used in this study is based on a 3D FEM macro models, and was performed on Abaqus commercial software. Two types of simulations were made in this study: • simulation of a masonry panel (deep beam) in order to evaluate the susceptibility to crack by modifying some properties, such as the length to height ratio, the presence of openings, and the mechanical resistance of the masonry panel; • simulation of representative part of a building structure partially filled with masonry partition walls in order to evaluate, as close as possible, the mechanical behaviour of these walls when affected by the vertical deformations of concrete structures caused by design serviceably loading and aggravated by long term/creep effects. a) Simulation of a masonry panel (deep beam) This simulation consisted on a masonry panel subjected to vertical displacements applied on the top of the wall that simulates the flexural displacements of structural elements subjected to uniformly distributed loadings. Experimental data obtained from tests performed on a masonry Recent Advances in Mechanics and Materials in Design M2D’2015 7 deep beam were used to calibrate the constitutive model chosen for masonry, and afterwards this calibrated model was used to simulate a larger wall with some different properties. The chosen constitutive model for masonry uses the concepts of damage mechanics and classical plastic theory, in particular the strain decomposition, elasticity, and the plastic flow. This model was developed by Lubliner et al (1989) for concrete, and can be applied for other brittle or quasi-brittle materials whose fracture mechanism are mainly governed by compressive crushing and tensile cracking (unreinforced or reinforced concrete, mortars, rocks). These mechanisms are implemented in the model through uniaxial constitutive laws, usually represented by tensile and compressive stress-strain relations (σt - εt and σc - εc) that can be determined experimentally from laboratory tests or from available test data. Moreover, the tensile behaviour can be also implemented through the fracture energy concept developed by Hilleborg et al (1976), by inserting in the model the values of fracture energy, G F , and tensile strength, σ t0 , fig.6 Fig.6 Generic representation of typical uniaxial stress-strain diagrams defined in the model: (a) tensile and (b) compressive behavior The plastic strains are calculated in terms of equivalent plastic strains, which are considered in the model as tension and compression hardening variables. These variables simulate the failure mechanisms (tensile cracking and compressive crushing) and control the evolution of the failure surface. More specific details of this model and its application to masonry can be found in given literature (Lubliner et al, 1989; Sousa et al, 2013; Sousa et al, 2015). The experimental data used for calibration of the constitutive model was obtained from a flexural test performed on a double supported masonry panel, made with horizontal perforated clay units laid on general purpose mortar joints (Pereira, 2005). The panel had the dimensions of 2m x 4m x 0,11m (height x length x thickness) and no renderings/coatings were applied. A vertical load was uniformly distributed along the top of the panel trough a reaction beam. The loads and vertical displacements at middle span were measured until the maximum/breaking load, with a loading cell and displacement transducers. The values reported in this experiment for maximum/peak load and middle span deflection were 55,2kN and 1,87mm. The fracture mechanisms reported were a vertical crack near the middle span of the wall, followed by a local crushing near the corner supports of the wall, fig.6. This test was simulated by computer in order to calibrate the constitutive model of masonry. The mechanical properties and constitutive laws of masonry needed for the constitutive model (a) (b) 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 8 were estimated from experimental data available in literature (Mojsilovic 2011; Pereira 2010; Pereira, 2005; Pluijm 1997; Lourenço, 1996; Carvalho,1990), table 1. Table 1 Mechanical properties used for the constitutive model of masonry E 0 Elasticity modulus (N/mm 2 ) ν Poisson Coef. (-) σ cu Compressive strength (N/mm 2 ) σ to Tensile strength (N/mm 2 ) G F Fracture energy (Nm/mm 2 ) ψ Dilatation angle (º) 2000 0.1 1.3 0.4 0.015 11 The complete mechanical response of the masonry panel, i.e. force-displacement curve Fδ measured at middle span until maximum load, was used in order adjust the numerical results to the experimental data. By changing some specific parameters on the constitutive model, the best adjustment obtained between numerical and experimental results gave a difference of 1% for maximum/peak load and 15% for ¼ of the peak load. Also the potential fracture pattern obtained from the simulations (given by the minimum principal plastic strains just after the peak load) is similar to the fracture pattern observed in the experimental test, fig6-c. These results were considered accurate enough, considering the variability of results usually accepted for masonry tests performed in laboratory conditions (variation coefficient between 10 to 20% for the strength properties (CEN, 1998; CEN 1999)). (a) (b) (c) Fig.6 Calibration of the masonry wall constitutive model: (a) flexural test performed and fracture pattern; (b) best adjustment obtained for the mechanical response of the wall; (c) principal stresses distribution (in kPa) at peak load and minimum plastic strain vectors just after the peak load; 4m 2m δ0.5L F Corner crushing Vertical crack f (kN/m) 0,2m 0,2m Recent Advances in Mechanics and Materials in Design M2D’2015 9 After calibrating the numerical model, a reference masonry panel, made with same materials as the test sample referred before, was chosen with higher dimensions in order to represent the dimensions more commonly used for this type of masonry partition wall. The chosen dimensions were 2,75x 5,5x 0,11m (height x length x thickness). Moreover, the mechanical contribution of renderings/coatings was not considered in this reference situation, since it was assumed the existence of a thin layer of plaster mortar on both sides of the wall (most common situation for partition walls). The structural model used for this reference situation was similar to the test wall sample, fig.7. The loading was simulated by imposing a generic displacement law function on the top of the wall, δ(x): δ (x) = 16 (5kL 3 ) -1 (x 3 -2Lx 2 +L 3 ) x (1) L= span of the wall assumed equal to the span of the structure k= constant regarding the relative deflection of the structure (e.g. 500 to 1000) x= considered position on the top of the wall (between 0 an L) Fig.7 Structural model used for the simulation of the reference masonry partition wall Equation (1) was deduced from flexural elements subjected to evenly distributed loads in elastic regime and simply support conditions. This law simulates the deflection of structural beams or slabs affecting the partitions, assuming a full contact and perfect bonding conditions between the top of the wall and the structure. To evaluate the susceptibility of this particular case of masonry partition wall to crack, some changes in the geometry and in the mechanical characteristics were made in the reference masonry panel. Each one of these changes were simulated separately, therefore keeping the other characteristics equal to those of the reference situation. The variations introduced in the reference panel were: • panels with ddifferent length to height ratios by shortening of the length (L/H =0.5, L/H =0.75, L/H=1) • panel with a central or lateral door opening (1,9 x0.9m 2 ) f (kN/m) δ 0.5L H= 2.75m 0,05 L 0,05 L L= 5.5m δ (x) 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 16 Fig.12 Example of the principal stresses (in kPa) and deflections for an office building • the partition panel with top/bottom mortar joints and lateral clearance joints is affected by a top defection near L/1700 and to a maximum tensile stress close or equal to the tensile strength of masonry, especially for the case of office building, where cracks in the middle span of the wall will arise, fig.13; Fig.13 Detail view of the principal stresses (in kPa) and plastic strains indicating cracks in the middle span of the partition panel built in an office building • the partition panel with bottom/lateral mortar joints and top clearance a joint is affected by a bottom deflection near L/2200 and to a maximum tensile stress of about 2/3 of tensile strength of masonry, either for residential or office use, without any cracks on the wall, fig.14. Recent Advances in Mechanics and Materials in Design M2D’2015 17 Fig.14 Detail view of the principal stresses (in kPa) in the partition panel built in an office building CONCLUSION This study shows that masonry partitions walls, built with 11 cm horizontal perforated clay units, are susceptible to crack when affected by the structural deformations aggravated by creep effects in serviceability conditions, especially if the panels are bonded to the concrete structure by top and bottom mortar joints, since the panels are more susceptible to the structural deformations. Moreover, given the fragile nature of these type of masonry partitions, it seems very difficult to accomplish the structural deformation limits established in the design codes to avoid damage in partition walls (L/500 to L/1000). Therefore, the use of reinforcement techniques, provision joints or lower deformation limits is recommended for this type of masonry. Regarding the use of reinforcements, steel reinforcement in the mortar joints and reinforced mortar coatings are the most common techniques. Lower deformation limits for the structure can be used if affordable, and it should be evaluated case by case. From this case study, it can be concluded that displacements on the top of the wall affected by creep effects should be lower than L/1700, highlighting the fact that other parts of the structure without the influence of the partitions have higher displacements, although lower than the limits established in the design codes. Alternatively, the use of top joints made on the top of the wall, with enough clearance to avoid contact caused by structural deformations, can reduce the susceptibility for cracking to occur in the partitions. Therefore it is recommended the use of these joints filled with a material with a very low structural resistance. In any case, it should be considered that the presence of openings on the partition walls will significantly increase the susceptibility to crack, while the use of stronger rendering systems or corner reinforcement can decrease it. REFERENCES AFNOR. Règles techniques de conception et de calcul des ouvrages et constructions en béton armé suivant la méthode des états limites (DTU P 18-702). CSTB, Paris, 2009. AFNOR. Travaux de bâtiments - Cloisons en maçonnerie de petits élémentsPartie 1-1: Cahier des clauses techniques types (NF DTU 20.13 P1-1). CSTB, Paris, 2008. Beranek, W. The prediction of damage to masonry buildings caused by subsoil settlements. Heron Journal, 32(4), 1987,p.-. 6 th International Conference on Mechanics and Materials in Design Ponta Delgada/Azores, 26-30 July 2015 18 BSI. Code of Practice for the use of masonry (BS 5628Part1, 2 and 3). BSI, London, 2005. Carvalho F. Comportamento mecânico de alvenarias - Influência de alguns parâmetros nas suas resistências à compressão e ao corte (in portuguese). PhD Thesis, LNEC, Lisboa, 1990. CEB-FIP. Model Code 1990 - Design Code, Thomas Telford, Lausanne, 1990. CEB-FIP. Model Code 2010 (Final draft). International Federation for Structural Concrete, Lausanne, 2010. CEN. Eurocode 2 - Design of concrete structures - Part 1-1: General rules and rules for buildings (EN 1992-1-1). CEN, Brussels, 2004. CEN. Eurocode 6 - Design of masonry structures - Part 1-1: General rules for reinforced and unreinforced masonry structures (EN 1996-1-1). CEN, Brussels, 2005. CEN. Methods of test for masonry - Part 1: Determination of compressive strength (EN 10521). European Committee for Standardization, Brussels, 1998. CEN. Methods of test for masonry - Part 2: Determination of flexural strength (EN 1052-2). European Committee for Standardization, Brussels, 1999. Dias J. Fissuração de paredes de alvenaria devido ao movimento dos elementos de suporte (in portuguese). 2.º Encontro sobre conservação e reabilitação de edifícios, Lisboa, 1994. Hilleborg A, Modéer M, Petersson P. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6), p.773-781. Holanda G, Ramalho M, Corrêa M. Experimental and numerical analysis of masonry walls with openings subjected to differential foundation settlements. Proceedings of the 10th North American Masonry Conference, St.Louis - Missouri, 2007. INE. Censos 2011 Resultados Definitivos – Portugal. Instituto Nacional de Estatística IP, Lisboa, 2011. LNEC. Pavimentos aligeirados de vigotas prefabricadas de betão pré-esforçado. Documento de aplicação, DA 34, Lisboa, 2012. LNEC. Pavimentos aligeirados de vigotas prefabricadas de betão pré-esforçado. Documento de aplicação, DA 44, Lisboa, 2014. LNEC. Pavimentos aligeirados de vigotas prefabricadas de betão pré-esforçado. Documento de aplicação, DA 45, Lisboa, 2014. Lourenço P. Computational strategies for masonry structures. PhD Thesis, Delft University Press, Netherlands, 1996. Lubliner J, Oliver J, et al. A plastic damage model for concrete. International Journal of Solids and Structures, 1989, 25(3), p.299-326. Meyerhof G. Some recent foundation research and its application to design. The Structural Engineer, 31, 1953, p.-. Mojsilovic N. Tensile strength of clay blocks: An experimental study. Construction and Building Materials, 2011, 25, p.4156-4164. MSJC. Building Code Requirements and Specification for Masonry Structures (ASCE/SEI 513, 6-13). MSJC, USA, 2013, pp.388. Recent Advances in Mechanics and Materials in Design M2D’2015 19 Page A. The serviceability design of low-rise masonry structures. Prog. Struct. Eng. Mater, 2001, 3, p.-. Pereira M. Anomalias em paredes de alvenaria sem função estrutural (in portuguese). Msc Thesis, Minho University, Portugal, 2005. Pereira M. Avaliação do desempenho das envolventes dos edifícios face à acão dos sismos (in portuguese). PhD Thesis, Minho University, Portugal, 2013. Pfeffermann O. Deformations admissibles dans le batiment. Nit 131, CSTC Revue, Bruxelles, 1981, pp.29. Pluijm R. Non-linear behavoir of masonry under tension. Heron J, 1997, 42(1), p.25-54. Sousa H., et al. Defects in Masonry Walls - Guidance on Cracking: Identification, Prevention and Repair. CIB-International Council for Research and Innovation in Building and Construction, Rotterdam, 2015, pp.78. Sousa R, Guedes J, Sousa H. Characterization of the uniaxial compression behaviour of unreinforced masonry: sensitivity analysis based on a numerical and experimental approach Archives of Civil and Mechanical Engineering, 2015, 15, p.532-547. Sousa R, Sousa H, Guedes J. Diagonal compressive strength of masonry samples-experimental and numerical approach. Materials and Structures, 46(5), 2013, p.765-786. Veiga M. Comportamento de argamassas de revestimento de paredes - Contribuição para o estudo da sua resistência à fendilhação (in portuguese), PhD Thesis, University of Porto, Portugal, 1997.