Elsevier

Computers & Structures

Volume 253, September 2021, 106576
Computers & Structures

Mechanics of structure genome applied in the homogenization of masonry reinforced by FRP repointing technique

https://doi.org/10.1016/j.compstruc.2021.106576Get rights and content

Highlights

  • MSG is applied to the homogenization of masonry reinforced by FRP.

  • The results agree with numerical or theoretical methods, including a 3D FEA.

  • MSG considerably reduces the computational cost.

  • 3D properties are obtained from the solution of 2D problems.

  • Absence of necessity of applying boundary conditions.

Abstract

This paper presents the newly developed Mechanics of structure genome (MSG) technique as an alternative for homogenizing masonry without reinforcement or reinforced by the FRP repointing technique. In the numerical examples analyzed, the results obtained with MSG were compared to those presented by Barbieri and Cecchi (2007), as well as with the finite element method (FEM). For unreinforced masonry, it is observed that the results obtained with MSG are closer to those of the FEM than those presented by Barbieri and Cecchi (2007). For the reinforced masonry, three values were considered for the FRP Young’s modulus. The analyses performed show an increase in the stiffness of the reinforced masonry, but the increase in FRP Young’s modulus only showed respective growth in the stiffness of the masonry in the horizontal direction. Finally, it is added that the MSG technique has advantages over the solution of a boundary value problem by the FEM, which is the classic and referential formulation for the masonry homogenization process.

Introduction

Masonry, one of the oldest and most widely used building materials in the world, is basically formed by the manual arrangement of blocks and mortar. Although apparently a simple material, masonry is in fact a composite material very difficult to characterize. First, because the very characterization of the constituent materials is not an easy task. Blocks and mortar can be considered isotropic materials, however, due to the differences between the mechanical properties of these materials and the different possibilities of arrangements, masonry usually presents anisotropy. Masonry presents quasi-fragile behavior with low tensile strength, where fracture usually occurs in the mortar.

While masonry presents itself as a relatively simple production material and can have both partition or structural function, on the other hand, the diversity of factors involved in its construction, including the process labor, make it a material with great uncertainties in its characterization. In general, masonry has low resistance to out-of-plane loads, especially in regions subjected to seismic shocks.

Considering old or historic masonry structures, challenges are even greater. In these cases, the dimensions of the blocks (or units) and the mortar are often not so regular. Since the Young’s modulus of historic masonry mortars is usually much lower than the Young’s modulus of blocks, these structures usually present large anisotropies, Cecchi and Sab [2], [3], and Cecchi et al. [4], [5]. Historical constructions usually undergo reforms and changes in their use over the years, in addition to the very action of the environment on these structures and the effect of time on applied loads. There are several forms of intervention in masonry at risk. Years ago, the most common ones involved the use of concrete or steel bars as reinforcement. In general, the reinforcement can be classified as external, internal or near to the surface. The first type, externally bonded (EB), can be symmetric when applied to both faces of masonry, or asymmetric when applied to only one face; the latter being more indicated in case of masonry with artistic value on one side (frescoes, for example). The internal reinforcement has as advantages the aesthetic issue, since the reinforcement is not exposed; the protection of the reinforcement of external actors; and the possibility of applying prestressing, increasing the strength and ductility of the structure. The disadvantages are due to being a more invasive technique, requiring greater care in its application, and the difficulty of anchoring the reinforcement to neighboring structural elements. Near surface mounted (NSM) reinforcement basically consists of cutting at a certain depth, usually in bed joint mortar, removing material, cleaning (by water or air blasting), partial filling with a bonding material (usually an epoxy or cement based paste), applying reinforcement and covering with material, which can be the same color as the original mortar. This has been the chosen technique in many cases since it also has no aesthetic problems and is simple and quick to apply, Turco et al. [6].

More recently, new materials have been used in place of steel to reinforce these structures. These new materials include composites known as FRP (fiber reinforced polymer), which consist of fibers – commonly carbon (CFRP), glass (GFRP) or aramid (AFRP) – embedded in a polymeric matrix (epoxy resin, for example). The fibers have high tensile stiffness and the matrix serves to transmit the stresses to the fibers and protect them. FRP can be applied in the form of rods, grids or sheets. The ease of molding these parts in different ways is one of the advantages of FRP, adding to this the high stiffness/weight ratio, low corrosion and long durability. A disadvantage is the higher material cost, where GFRP may be an alternative to higher cost CFRP; however, it should be remembered that the tensile strength and Young’s modulus of the GFRP is much lower than that of the CFRP, De Lorenzis and Teng [7]. Gabor et al. [8] conducted comparative analyzes on FRP reinforced masonry with both glass and carbon fibers. A recent review of various FRP masonry reinforcement techniques can be found at Babatunde [9].

It is observed that FRP is usually considered as a linear elastic material, more resistant to tension than to compression. However, like any composite material, it presents some complexities in its characterization, presenting, for example, anisotropy. In the case of masonry, which is already a composite material, reinforced by FRP, the characterization of the material is even more complicated. Several techniques can be used in the computational modeling of masonry. Basically, they can be classified into 3 different approaches: micro-modeling, macro-modeling and homogenization, Milani et al. [10], Milani [11], and Milani and Lourenço [12]. In micro-modeling, each masonry element (blocks and mortar) is modeled individually, thus, the computational cost is very high and this approach is only possible for masonry with reduced size. In the case of macro-modeling, masonry as a whole is made up of a single equivalent material, usually orthotropic. Such approach presents a reduced computational cost, but the numerical results obtained usually differ from the real behavior of the structure. The third approach is an intermediate technique between the previous two, and consists of two steps: obtaining the physical properties of masonry (homogenization) and modeling the masonry structure as a whole considering the mortar joints as zero thickness elements or other finite value. The homogenization step, as far as the authors know, is done by solving a boundary value problem in a representative volume element (RVE) using the finite element method (FEM).

One of the earliest works involving the modeling of masonry reinforced by FRP is the article by Luciano and Sacco [13], who present a micromechanical approach to obtain the general properties of masonry and then analyze the case of a masonry wall reinforced by a sheet of FRP applied to the surface of both faces of the wall.

Later, Tinazzi et al. [14] studied masonry panels reinforced by FRP bars, where the repointing technique was used, concluding that this technique may be the ideal solution in cases where aesthetic and durability issues are relevant. The repointing technique is a classical retrofitting technique commonly used in masonry, consisting basically of a NSM reinforcement variant. Tumialan and Nanni [15] approached the application of GFRP structural repointing, where bars were inserted in the horizontal bed joints to increase the shear stiffness considering loads applied in the masonry plane. The authors compared the performance of reinforcement by GFRP bars with sheets of the same material applied to the masonry surface and observed that the gains were similar. Bajpai and Duthinh [16] also analyzed masonry reinforced by GFRP NSM bars, but with a focus on out-of-plane bending behavior, in the case of walls subject to lateral loading, caused by wind gusts, earthquakes or blasts. Still on the reinforcement of masonry structures by repointing, Valluzzi et al. [17] studied the mechanical behavior of historic masonry reinforced by steel bars applied to bed joints, emphasizing the use of relatively common tools, ease and speed of application, and aesthetic preservation. The authors conclude that the studied technique is particularly interesting for masonry with regular topology presenting a pattern of critical cracking by high compressive loads. Recently, Casacci et al. [18] presented results of diagonal compression tests on reinforced masonry, where two reinforcement techniques were compared: NSM structural repointing by inserting basalt bars into bed joints and the application of a single layer of fiber reinforced cementitious matrix (FRCM) with glass fibers.

Cecchi et al. [19] presented a comparison between different homogenization methods for CFRP reinforced masonry walls subjected to plane loading, where it was observed that homogenization of this type of structure requires greater attention than the case without reinforcement, especially for low relations between Young’s moduli of mortar and blocks, a typical case of historic masonry. Milani [11] presents a finite element homogenization limit analysis model for masonry reinforced by NSM repointing with GFRP bars. Milani and Bucchi [20] is another example of application of this formulation.

Recently, Almeida and Lourenço [21] presented in an unprecedented way the application of mechanics of structure genome (MSG) technique for the homogenization of unreinforced masonry in the elastic range. In the cases studied in the paper, the three-dimensional elastic constants of masonry, calculated from Young’s modulus and Poisson’s ratio of blocks and mortar, were calculated and compared with results from numerical and theoretical methods from different authors, showing good agreement.

Yu [22] presented to the scientific community the multiscale modeling technique for composite materials entitled MSG. This technique is implemented in a general computer code called SwiftCompTMwhich has been used in both industry and academic research. This computational code can also be used in conjunction with commercial finite element programs to treat composites in structural analysis and design. Basically, the SwiftCompTM, program considers the geometry and material properties of a structure gene (SG) (described in the next section) discretized by a finite element mesh as input and calculates the effective properties for macroscopic analysis, that would be the homogenization process. After the macroscopic analysis, SwiftCompTM, can still calculate the local fields in SG based on the global behavior of the structure, which consists of the process of dehomogenization (or localization), a step that many multiscale modeling methods do not present.

It can be said that MSG is a generalization of the technique created by Drs. Carlos Cesnik and Dewey H. Hodges and collaborators known as “variational asymptotic beam section analysis” (VABS), to treat all types of structures, including beams, plates, shells and three-dimensional (3D) structures, Yu et al. [23], [24].

Therefore, the present study aims to apply the MSG technique in the homogenization of masonry reinforced by FRP by the repointing technique, where there is the insertion of an FRP plate at half height of the horizontal mortar bed joints. The present paper then follows with a section on the MSG technique, followed by a section with the results obtained in the numerical analyses carried out in the study, ending with a section with the conclusions of the research and suggestions for its continuation.

Section snippets

Mechanics of structure genome

Mechanics of structure genome (MSG) – or mechanics of structure gene, as used in Almeida and Lourenço [21] – is a newly developed technique for multiscale and multiphysics constitutive modeling that can be applied to all types of composite structures including beams, plates and shells and three-dimensional (3D) structures. Since it is a semi-analytical technique, MSG considerably reduces the computational cost and maintains the same accuracy of 3D analysis, for example in finite elements.

Numerical results

The numerical analyses carried out in this work consider a masonry with running bond texture, one of the simplest and most used topologies, especially in historical masonry; formed by blocks of dimensions 250 × 55 × 120 mm3 (UNI 5628/65), Fig. 3a, where it is observed that the thickness of the masonry measures 120 mm. It was considered a mortar with thickness t=10 mm, Young’s modulus Em=1 GPa and Poisson’s ratio νm=0.2. For the blocks, it was considered Poisson’s ratio νb=0.2 and variable

Conclusion

This paper presents the newly developed Mechanics of structure genome (MSG) technique as an alternative for homogenization of unreinforced (URM) or reinforced (RM) masonry by the FRP repointing technique. It is observed that the repointing technique considered in this work consisted of the application of a 1.2 mm thick FRP plate along the entire length of the bed joints, t=10 mm, and width coinciding with the thickness of the masonry. In the numerical examples analyzed, the results obtained

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The first author would like to thank Dr. Wenbin Yu for being his host during his one-year sabbatical at Purdue University, School of Aeronautics and Astronautics, West Lafayette, IN, USA. Thanks also to the Federal University of Alagoas (UFAL), Maceio, AL, Brazil, for granting the respective concession.

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