Approximate limit analysis of full scale FRP-reinforced masonry buildings through a 3D homogenized FE package

A 3D homogenized FE limit analysis software for the numerical prediction of collapse loads and failure mechanisms of entire masonry buildings reinforced with FRP strips is presented. In particular, a two steps approach is adopted: in step I, masonry homogenized failure surfaces are obtained through an admissible kinematic FE approach in the representative element of volume (REV), constituted by a brick interconnected with its six neighbors with finite thickness mortar joints. 8-Noded rigid infinitely resistant parallelepiped elements interconnected with interfaces with frictional behavior and limited tensile and compressive strength are utilized to model the REV. A simple linear programming problem in few variables is obtained, suitable to recover numerically masonry failure surfaces when loaded in- and out-of-plane. In step II, homogenized failure surfaces are implemented in the novel FE kinematic limit analysis software for an inexpensive evaluation of collapse loads of entire buildings. Delamination is considered in the model imposing to FRP–masonry interfaces a limited resistance in agreement with Italian code CNR-DT-200. 6-Noded rigid infinitely resistant 3D wedge-shaped elements are used to model homogenized masonry, whereas FRP strips are modeled by means of triangular 3-noded rigid elements.     

FE homogenized limit analysis model for masonry strengthened by near surface bed joint FRP bars

A homogenized limit analysis model for the prediction of collapse loads and failure mechanisms of masonry walls reinforced with near surface bed joint GFRP bars is presented. Reinforced masonry homogenized failure surfaces are obtained by means of a compatible identification procedure, where each brick is supposed interacting with its six neighbors by means of finite thickness mortar joints, filler epoxy resin and FRP rods.In the framework of the kinematic theorem of limit analysis, a simple constrained minimization problem is obtained on the unit cell, suitable to estimate – with a very limited computational effort – reinforced masonry homogenized failure surfaces.A FE strategy is adopted to solve the homogenization problem at a cell level, modeling joints, bricks, filler and FRP rods by means of eight-noded infinitely resistant parallelepiped elements. A possible jump of velocities is assumed at the interfaces between contiguous elements, where plastic dissipation occurs. For mortar and bricks interfaces, a frictional behavior with possible limited tensile and compressive strength is assumed, whereas for epoxy resin and FRP bars some formulas available in the literature are adopted in order to take into account in an approximate but effective way, the delamination of the bar from the epoxy and the failure of the filler at the interface with the joint.In order to validate the model proposed, two meaningful examples are critically analyzed. The first relies on a reinforced masonry beam in four-point bending, whereas the second is a full scale wall constrained at three edges and loaded until failure with a distributed out-of-plane pressure. While the first example is useful to test the model at a cell level, since only horizontal ultimate bending moment is involved in the failure mechanism, the second provides a full assessment of the procedure proposed at a structural level. In both cases, very good agreement is found with literature data, meaning that the model proposed may provide useful information for all practitioners interested in the design of masonry walls reinforced with bed joint FRP bars.     

Textile reinforced mortar (TRM) versus FRP as strengthening material of URM walls: out-of-plane cyclic loading

The application of a new structural material, namely textile reinforced mortar (TRM), as a means of increasing the load carrying capacity and deformability of unreinforced masonry walls subjected to cyclic out-of-plane loading is experimentally investigated in this study. The effectiveness of TRM overlays is evaluated in comparison to the one provided by fiber reinforced polymers (FRP) in the form of overlays or near-surface mounted (NSM) reinforcement. TRM systems may be considered as alternative to FRPs, tangling with some of the drawbacks associated with the application of the latter without compromising performance. Medium-scale tests were carried out on 12 masonry walls subjected to out-of-plane bending. The parameters under investigation comprised mortar-based versus resin-based matrix materials, the number of layers, the orientation of the moment vector with respect to the bed joints and the performance of TRM or FRP jackets in comparison to NSM strips. It is concluded that TRM jacketing provides substantial increase in strength and deformability. Compared with their epoxy-resin counterparts (FRP), TRM may result in generally higher effectiveness in terms of strength and deformability. NSM strips offer lower strength but higher deformability, due to controlled debonding. From the results obtained in this study it is believed that TRMs comprise an extremely promising solution for the structural upgrading of masonry structures under out-of-plane loading.     

Out-of-plane behavior of unreinforced masonry walls strengthened with FRP strips

The out-of-plane behavior of unreinforced masonry walls strengthened with externally bonded fiber reinforced polymer (FRP) strips is analytically studied. The analytical model uses variational principles, equilibrium requirements, and compatibility conditions between the structural components (masonry units, mortar joints, FRP strips, and adhesive layers) and assumes one-way flexural action of the strengthened wall. The masonry units and the mortar joints are modeled as Timoshenko’s beams. The FRP strips are modeled using the lamination and the first-order shear deformation theories, and the adhesive layers are modeled as 2D linear elastic continua. The model accounts for cracking of the mortar joints and for the development of debonding zones near the cracked joints. Numerical and parametric studies that reveal the capabilities of the model, throw light on the interaction between the variables, and quantitatively explain some aspects of the behavior of the strengthened wall are also presented.     

Nonlinear finite element analysis of masonry wall strengthened with CFRP strips

In many experimental studies, it has been proved that unreinforced masonry (URM) brick walls have high strength against lateral forces acting in plane. However, out-of-plane strength of URM brick walls against lateral forces has found to be quite low. According to the experiences that were obtained from the major earthquakes, the low out-of-plane performance of URM brick walls resulted in excessive loss of human lives during an earthquake, hence the strengthening of URM brick walls with CFRP strips has been appeared to be a very important subject. However, very limited literature has been found. Especially, the data obtained from experimental studies must be increased for the true understanding of the behavior of strengthened brick walls under out-of-plane lateral forces. However, in most cases, this procedure required large number of expensive experiments. At this stage, numerical analysis can be an appropriate choice, thus in this paper a finite element model is presented for modeling URM brick walls that are strengthened with CFRP strips. The numerical results are compared with the experimental ones and consistent results are obtained from the finite element model. General purpose finite element analysis software ANSYS is used throughout this study. Contact elements are used along the masonry wall–CFRP strip interfaces for the investigation of the stress distribution and load – strain behavior.     

Experimental analysis of historic masonry walls reinforced by CFRP under in-plane cyclic loading

External bonding of Fiber Reinforced Polymers (FRPs) has become a popular technique for strengthening historic masonry wall buildings in seismic area. Although FRPs seem to improve response of historic masonry walls under in-plane shear loading, further investigations must specify a number of aspects for both researchers and practitioners. This paper presents an experimental analysis pertaining to the response of unreinforced and reinforced historic masonry walls built using full clay bricks in scale 1/3rd. On the basis of previous experimental research carried out by shear tests on triplets and unreinforced walls, a shear criterion for historic unreinforced masonry (HURM) has been assumed. In this experimental analysis two HURM walls, characterized by double T shape, were subjected to in-plane cyclic loading to shear cracking. The damaged walls were reinforced using horizontal–vertical and diagonal Carbon FRP strips. An anchorage system was also put into place to improve the adhesion of the strips used; the historic reinforced masonry (HRM) walls were tested by cyclic loading until failure. The experimental results are illustrated and discussed taking into account the delamination failure of the CFRP strips. Finally, the increase obtained in walls’ shear capacity is analysed considering theoretical bilinear diagrams and the coefficient of ductility.     

Experimental analysis of historic masonry walls reinforced by CFRP under in-plane cyclic loading

External bonding of Fiber Reinforced Polymers (FRPs) has become a popular technique for strengthening historic masonry wall buildings in seismic area. Although FRPs seem to improve response of historic masonry walls under in-plane shear loading, further investigations must specify a number of aspects for both researchers and practitioners. This paper presents an experimental analysis pertaining to the response of unreinforced and reinforced historic masonry walls built using full clay bricks in scale 1/3rd. On the basis of previous experimental research carried out by shear tests on triplets and unreinforced walls, a shear criterion for historic unreinforced masonry (HURM) has been assumed. In this experimental analysis two HURM walls, characterized by double T shape, were subjected to in-plane cyclic loading to shear cracking. The damaged walls were reinforced using horizontal–vertical and diagonal Carbon FRP strips. An anchorage system was also put into place to improve the adhesion of the strips used; the historic reinforced masonry (HRM) walls were tested by cyclic loading until failure. The experimental results are illustrated and discussed taking into account the delamination failure of the CFRP strips. Finally, the increase obtained in walls’ shear capacity is analysed considering theoretical bilinear diagrams and the coefficient of ductility.     

Monte Carlo homogenized limit analysis model for randomly assembled blocks in-plane loaded

A simple rigid-plastic homogenization model for the limit analysis of masonry walls in-plane loaded and constituted by the random assemblage of blocks with variable dimensions is proposed. In the model, blocks constituting a masonry wall are supposed infinitely resistant with a Gaussian distribution of height and length, whereas joints are reduced to interfaces with frictional behavior and limited tensile and compressive strength. Block by block, a representative element of volume (REV) is considered, constituted by a central block interconnected with its neighbors by means of rigid-plastic interfaces. The model is characterized by a few material parameters, is numerically inexpensive and very stable. A sub-class of elementary deformation modes is a-priori chosen in the REV, mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating the power dissipated in the heterogeneous model with the power dissipated by a fictitious homogeneous macroscopic plate. Due to the inexpensiveness of the approach proposed, Monte Carlo simulations can be repeated on the REV in order to have a stochastic estimation of in-plane masonry strength at different orientations of the bed joints with respect to external loads accounting for the geometrical statistical variability of blocks dimensions. Two cases are discussed, the former consisting on full stochastic REV assemblages (obtained considering a random variability of both blocks height an length) and the latter assuming the presence of a horizontal alignment along bed joints, i.e. allowing blocks height variability only row by row. The case of deterministic blocks height (quasi-periodic texture) can be obtained as a subclass of this latter case. Masonry homogenized failure surfaces are finally implemented in an upper bound FE limit analysis code for the analysis at collapse of entire walls in-plane loaded. Two cases of engineering practice, consisting on the prediction of the failure load of a deep beam and a shear wall arranged with random texture are critically discussed. In particular, homogenization results are compared with those provided by a heterogeneous approach. Good agreement is found both on the failure mechanism and on the distribution of the collapse load.     

Out-of-plane flexural behavior of unreinforced red brick walls strengthened with FRP composites

This paper presents the results of a study focused on evaluating the out-of-plane flexural behavior of two fiber reinforced polymer (FRP) composite systems for strengthening unreinforced red brick masonry walls. The full-scale tests followed the International Code Council Evaluation Service (ICC-ES) AC 125 procedure. In the experimental program, a total of four full-scale destructive tests were conducted on UMR red brick walls. One wall specimen was used as control (as-built) specimen without composites, and the remaining three wall specimens were strengthened with either E-glass/epoxy or carbon/epoxy composite systems with different fiber architecture. The effect of applying a cross-ply laminate on the ultimate failure mode has been investigated. Full-scale experimental results confirmed the effectiveness of the FRP composite strengthening systems in upgrading the out-of-plane flexural structural performance of URM walls. In addition, an analytical model was developed to predict the ultimate load capacity of the retrofitted walls. The analytical modeling is based on deformation compatibility and force equilibrium using simple section analysis procedure. A good agreement between the experimental and theoretical results was obtained.     

Analytical model for the in-plane shear behavior of URM walls retrofitted with FRP

This paper presents an analytical model for in-plane shear behavior of unreinforced masonry (URM) walls retrofitted using fiber reinforced polymers (URM-FRP). The proposed model idealizes masonry, epoxy, and FRP in a URM-FRP as different layers with isotropic homogenous elastic materials. Then, using principles from the theory of elasticity, the governing differential equation of the system is formulated. A double Fourier sine series is used as a solution for the differential equations. A simple computer program was developed to combine the solution of the differential equations with material nonlinearity. The material nonlinearity was represented by step-by-step layer stiffness degradation; after each step the equations are resolved linearly. The proposed basic analytical model allows the fundamental investigation of in-plane shear behavior of URM-FRP. Finally, effects of epoxy and masonry ductility as well as allowable shear stresses and FRP axial rigidity on the shear strength of URM-FRP are examined. In addition, comparisons with three existing models are carried out.     

考虑填充墙平面内外相互作用评估RC框架-填充墙结构抗整体性倒塌能力

首先简要阐述了可模拟填充墙平面内外相互作用的纤维离散化梁-柱单元模型。其次,基于OpenSees分析软件,对某倒塌试验的4层钢筋混凝土框架-填充墙结构进行了数值模拟,数值模拟结果与试验结果的对比表明考虑平面内外相互作用的纤维离散化梁-柱单元模型模拟框架-填充墙结构中的填充墙是有效的。最后,基于校准后的数值分析模型,利用OpenSees分析软件对某钢筋混凝土框架-填充墙结构教学楼,区分考虑和不考虑填充墙平面内外相互作用两种情况,分别建立三维空间模型,进行了静力推覆分析和增量动力分析,进而利用24条地震动记录输入下的增量动力分析结果,给出了具有50%倒塌概率的结构抗整体性倒塌能力。分析结果对比表明不考虑填充墙平面内外相互作用会明显低估结构的抗倒塌能力。     

Limit analysis of masonry walls using discontinuity layout optimization and homogenization

A numerical limit analysis model for masonry walls subject to in-plane loading is posed as a discontinuity layout optimization (DLO) problem, with the masonry conveniently modeled using a smeared continuum (“macromodeling”) approach and a homogenized yield surface. Unlike finite element limit analysis, DLO is formulated entirely in terms of discontinuities and can produce accurate solutions for problems involving singularities naturally, without the need for mesh refinement. In the homogenized model presented, masonry joints are reduced to interfaces, with sliding governed by an associative friction flow rule and blocks are assumed to be infinitely resistant. The model takes account of the interlock ratio of the masonry blocks, their aspect ratio and the cohesion and coefficient of friction of interfaces in both the vertical and horizontal directions. Results from the proposed model are compared with those from the literature, showing that complex failure mechanisms can be identified and that safe estimates of load carrying capacity can be obtained. Finally, to demonstrate the utility of the proposed modeling approach, it is applied to more complex problems involving interactions with other elements, such as voussoir arches and weak underlying soil layers.     

Computer-aided strengthening of masonry walls using fibre-reinforced polymer strips

Studies on the use of fibre-reinforced polymers (FRP) as strengthening materials of masonry walls have been numerous. FRP materials, particularly in the form of unidirectional strips, provide a highly effective method of structural intervention in masonry walls. However, the selection of the reinforcing pattern (positioning of the strips) and the calculation of respective cross sectional FRP areas still remains a problem, which is solved in this study through the development of a methodology that relies on strut-and-tie modelling. This methodology has been implemented in a computer programme that enables the definition of the locations where FRP strips should be placed in masonry walls subjected to in-plane loading. Moreover, the tensile forces in the ties can be used to calculate the required FRP cross section areas, hence the number of strips in each location. Hence, a valuable tool for the dimensioning of interventions in masonry walls using FRP materials in the form of strips has been developed. Applications of the tool in simple case studies (masonry walls with openings subjected to both vertical and horizontal loads) are also provided. Finally, a comparison between results predicted by this strut-and-tie model and those from an experimental study found in the literature adds some confidence to the model.     

FRP reinforcement of stone arch bridges: Unilateral contact models and limit analysis

A method for the estimation of the limit load and the failure mode of fiber-reinforced polymer (FRP) reinforced stone arch bridges is hereby presented. Unilateral contact interfaces with friction simulating potential cracks are considered in the finite element model of the bridge. FRP strips are then applied to the intrados and/or the extrados of the arch. The possible failure modes of the reinforced structure are sliding of the masonry, crushing, debonding of the reinforcement and FRP rupture. Identical failure modes arise from the computer simulation and from experiments on reinforced arches published in the literature.     

纤维布加固砖砌体墙平面内受力性能有限元模型

考虑一顺一丁的砌筑形式,针对纤维布加固前后砖砌体墙的特点,利用ABAQUS提供的零厚度粘结单元,建立纤维布加固砖砌体墙有限元分离模型,通过前期拟静力试验数据和相关规范公式计算结果,验证所建模型在单调荷载和往复荷载作用下的适用性。结果表明,有限元模型能有效模拟纤维布加固砖砌体墙的抗震性能,分析纤维布的加固效果,计算纤维布加固前后砖砌体墙在单调荷载作用下的受剪承载力。     

The performance of unreinforced masonry walls subjected to low-velocity impacts: Finite element analysis

A simplified discrete-crack finite element modelling approach has been developed to model the performance of unreinforced brickwork and blockwork masonry walls subject to out-of-plane impacts. The approach involves the use of linear elastic solid elements for masonry units in conjunction with a specially formulated contact interface model for masonry joints. Key features of the latter include: (i) a Mohr–Coulomb failure criterion; (ii) a cohesive crack model for initial fracture; (iii) inclusion of dilatancy. The contact interface model has been implemented in LS-DYNA, a three-dimensional non-linear explicit finite element program. The modelling approach was used to simulate the behaviour of a series of unreinforced walls tested previously in the laboratory. It was found that the dynamic response of full-scale masonry walls could be predicted with reasonable accuracy. However, parametric studies showed that wall response was highly dependent on small changes in loading impulse, base friction, fracture energy, joint failure stress and angle of dilatancy.     

Experimental FRP/SRP–historic masonry delamination

The preservation of the architectural heritage presents one of the important challenges in civil engineering due to the complexity of the geometry of the structures, the variability of the materials used and the loading history of the buildings. This objective increases for existing constructions in the seismic area. External bonding of fiber or, more recently, steel reinforced polymer composites has become a popular technique for strengthening historic monumental masonry buildings. The performance of the interface between composites and masonry is one of the key factors affecting the behaviour of strengthened structures: shear walls, arches and vaults. This paper aims to present the results of an experimental study to evaluate the bond between fiber reinforced polymer (FRP) – glass and carbonFRP – and steel reinforced polymer (SRP) with historic masonry: pull–push shear tests on FRP/SRP-to-historic brick bonded joints specimens were carried out. Modes of failure are discussed in detail and analytical results are compared with experimental data. Experimental strains recorded on FRP/SRP strips were processed to evaluate shear–slip laws of tested specimens; energy fracture and failure load values are compared with theoretical values by simplified models for shear stress–slip. Finally, a simple model of FRP/SRP design suitable for practical application to historic masonry is proposed.     

Shear effect on seismic behaviour of masonry walls

Firstly, a finite element numerical model for nonlinear dynamic analysis of masonry walls is briefly presented. The model can simulate the main nonlinear effects of masonry and reinforced concrete. It is simple and intended to the engineering application. A macro model of masonry is adopted for simulation its behaviour in compression and for cracks modelling in tension. Two constitutive models are implemented to describe the shear resistance of the masonry wall: One that does not take the effect of the shear failure of masonry (Model 1), and second which takes into account shear failure of masonry (Model 2). By using the numerical model, the shear effect of masonry on the behaviour of two‐storey unreinforced and confined masonry walls exposed to harmonic base acceleration was investigated. The height to length ratio of the walls and the quality of masonry are varied. Analysis results for Model 1 and Model 2 are significantly different. Model 1 gives a significantly higher load bearing capacities of masonry. It was concluded that the shear effect of masonry significantly depends on the type of the masonry walls (unreinforced, confined), the quality of the masonry and height to length ratio of masonry walls.     

高延性混凝土加固蒸压加气混凝土砌体墙抗震性能试验研究

蒸压加气混凝土(AAC)砌块砌体墙自重轻,但其抗震性能较差,为提高该类墙体的抗震性能,提出采用高延性混凝土(HDC)面层和条带对其进行加固。设计制作了4个无筋砌体墙和2个构造柱约束墙体试件,其中2个试件采用HDC面层加固,2个试件采用HDC条带加固,通过拟静力试验,研究AAC砌体墙的破坏形态、滞回性能、承载力及变形能力等性能。试验结果表明:HDC面层可改变AAC墙体的破坏模式;对于无筋砌体墙,加固后试件的承载力、变形及耗能能力均得到了不同程度的提高,墙体裂缝数量明显减少,刚度退化较为平缓;对于构造柱约束墙体,单面HDC面层使加固试件的侧向刚度、水平承载力及耗能能力均大幅提高,且加固试件具有较高的残余承载力,墙体的开裂和损伤程度较小。基于试件的破坏形态,提出加固墙体的水平承载力计算方法,其计算结果与试验结果吻合较好,可为HDC加固AAC砌块墙体的承载力计算提供参考。     

组合材料加固砖砌体的有限元模拟方法

基于ABAQUS有限元软件,提出了组合材料加固砌体数值建模方法。该方法是在未加固砌体整体式模型的基础上,结合分离式思想建立组合材料加固砌体模型。通过对8片采用粘钢-聚合物砂浆组合材料加固的砖砌体墙体（其中,4片采用粘贴正交钢片,4片采用粘贴斜撑钢片）的拟静力试验结果进行了数值模拟对比分析,结果显示:模拟所得墙体滞回、骨架及刚度退化曲线与试验曲线基本吻合;仿真破坏形态与试验现象一致;计算所得荷载、位移、延性和耗能等全部指标中有81%的误差在20%以内。