Numerical study of in-plane behavior of masonry walls strengthened by vertical CFRP strips

Transcription

1 Fourth International Conference on FRP Composites in Civil Engineering (CICE2008) 22-24July 2008, Zurich, Switzerland Numerical study of in-plane behavior of masonry walls strengthened by vertical CFRP strips D. Mahjoob Farshchi & M.S. Marefat School of Civil Engineering, University of Tehran,Tehran, Iran M. Motavalli School of Civil Engineering, University of Tehran,Tehran, Iran Swiss Federal Laboratories for Materials Testing and Research (Empa), Dübendorf, Switzerland A. Schumacher Swiss Federal Laboratories for Materials Testing and Research (Empa), Dübendorf, Switzerland ABSTRACT: This paper reports on a non-linear finite element (FE) model that simulates lateral in-plane behavior of masonry walls strengthened by vertical CFRP strips. The model, which is verified by experiments found in the literature, uses the commercial finite element code ANSYS and considers orthotropic behavior and non-linear characteristics of all masonry constituents. The study shows that retrofit by CFRP strips enhances lateral strength significantly, but the wall experiences more extensive damage compared to unreinforced case. Under lateral load, the wall experiences flexural and shear cracks in the mortar joints, and sustains crushing of the brick units at the middle CFRP strips. As lateral load increases, crushing proceeds upwards and downwards and extends to other bricks located at other strips. Furthermore, the study evaluates the effect of the number of strips and different aspect ratios on the behavior of masonry walls. Simulations show that all walls exhibit a bilinear base shear versus lateral deformation behavior with a knee point. With increasing the number of vertical CFRP strips, the knee point occurs at a higher load, especially for walls with low aspect ratios. 1 INTRODUCTION There are many masonry structures throughout the world that have been built in the past decades and lack sufficient strength and enough ductility to resist strong ground motions and heavy live loads. Application of fiber reinforcement polymer (FRP) to retrofit masonry structures has increasingly been used worldwide since 1990s (Mukherjee & Jushi 2002; Karbhari & Seible 2000). Different types and shapes of FRP are used to improve seismic behavior of masonry walls (Sayed Ahmad et al. 1999; Foraboshi 2004; ElGawady 2004; Stierwalt & Hamilton 2005; Tumialan et al. 2005). To assess vulnerability of masonry structures, and to examine the efficiency of different retrofitting methods, a versatile numerical tool is needed that can take into account non-linear behavior and orthotropic characteristics of masonry. In this study, the micro nonlinear model previously developed by the authors (Mahjoob et al. 2007) for unreinforced masonry walls, is applied to masonry walls strengthened by vertical FRP strips. The commercial multi-purpose finite element code of ANSYS (1996) has been used and in-plane failure mechanisms of masonry and its non-linear phenomena such as cracking, sliding and crushing have been taken into account. It will be shown that the model is successful in predicting both local and global behavior of the strengthened wall. Furthermore, effects of the number of FRP strips and various aspect ratios on lateral behavior are investigated

2 2 EXPERMENTAL STUDIES Two independent tests series used by the authors to validate the numerical model for unreinforced masonry wall (Mahjoob et al. 2007), are briefly summarized here. ElGawady (2004) investigated the seismic, in-plane behaviour of unreinforced masonry walls and the same walls upgraded with fibre reinforced polymer (FRP) composites. The wall specimens were subjected to different axial loading and dynamic excitations (i.e. shaking table tests). Boundary conditions of the test specimens were similar to a cantilever wall. He showed that related to configuration of FRP composites, the lateral resistance would increase by a factor of 1.3 to 2.9. Laursen and Ingham (2004) tested two series of tests on two-thirds scale unbonded, posttensioned concrete masonry walls subjected to reversed, in-plane quasi-static cyclic loading. Laursen s tests showed that post-tensioned walls strengthened in the flexural compression zones with confining plates could withstand severe cyclic loading. Only localized damage occurred in the compressive zones in the lowest parts of the walls. Results of ElGawady s four unreinforced masonry specimens (two specimens with the aspect ratio of 1.0 (L1 and L2) and two specimens with the aspect ratio of 0.4 (S1 and S2)), and results of the Laursen s one unreinforced specimen (L3W15P2C), have been used to validate the results from the numerical model (see Mahjoob et al. 2007). 3 A NUMERICAL MODEL FOR IN-PLANE BEHAVIOR OF UNREINFORCED MASONRY WALL To simulate both global and local behavior of masonry walls, a numerical micro model has been used that considers all brick and joint units. Using element Solid 65, the ANSYS Concrete Brittle Model (ACBM) is used to define the vertical mortar joints (head joints) as smeared cracks. The bed joints have been modelled as discrete cracks by a contact element, Contact 52. This element supports tangential sliding based on Mohr-Coulomb theory of friction, where sliding is eliminated when the element surface is under tensile axial force. Since nonlinear behaviour of masonry walls is mainly governed by interaction at the brick/mortar interface, and in order to reduce computation time, the brick units are represented by an elastic solid element, Solid 45, and the failure of the bricks is examined manually based on ACBM (ANSYS 1996). As an example, the model specifications of Specimen L1 are presented in Table 1 (Specifications of other specimens are given in Mahjoob et al. 2007). The specimen has a fixed support at the bottom with dimensions of (m), the brick units of (mm), (length height thickness), and 10 mm for thickness of the mortar joints. The model parameters, which consist of compressive and tensile strengths, elastic module of masonry constituents, and coefficient of friction at the bed joints, have been determined either directly or indirectly by tests (Mahjoob et al. 2007). A uniform mesh in the direction of thickness and height, with finer meshing in the direction of length at locations aligned with the head joints, is used for the bricks. Distance between contact elements in the bed joints is therefore reduced. For head joints, a uniform element size with a thickness equal to that of the joints is applied throughout the model. In the model, lateral loading in the form of deformation is applied incrementally and monotonically to the upper edge of the wall. It is assumed that monotonic load conforms to the envelope of Laursen's tests with quasi-static cyclic loading and Elgawady tests with dynamic excitations produced by a shaking table. A comparison between test and numerical results shows that the model has been successful in predicting global behaviour (see Figure 1a for Specimen L1). Figure 1b illustrates crack pattern of Specimen L1. The study shows that flexural cracks initially appear at the most bottom bed joint, and, as lateral load increases, horizontal cracks propagate upwards. The damage is accompanied by sliding deformation over a large length of the bed joints, when lateral deformation reaches the stage of yielding shear force, y

3 Table 1. Model specifications of Specimen L1 Specimen f cb Bricks Head joints Bed joints Axial force [KN] ftb Eb [N/mm 2 ] fcm ftm Em [N/mm 2 ] KN [N/m] KS [N/M] µ P1 P2 L Type of lateral loading 56E6 18E Monotonic E, f c, f t =Elastic modulus; and the compressive and tensile strength (indices b and m represent brick and mortar); KN, KS= Normal and sliding stiffness used for the contact elements at the bed joints; µ=coefficient of friction at the bed joints; P1, P2= Axial loading at the first and last load step, respectively; Also observed are shear cracks with step pattern that form at the bottom corner of the wall at a lateral deformation of approximately 5 mm. These cracks, then, proceed upwards as lateral load increases. Failure of the bricks is examined manually based on ACBM. The study shows that the brick units remain undamaged throughout the loading similar to the test. Although the predicted local behaviour is not in complete agreement with the test results, it is consistent with the nature and the in-plane failure mechanisms of the masonry walls. Numerical results of other specimens are available in Mahjoob et al. (2007). Base shear force (kn) Test (L1) FE Model (L1) Lateral deformation (mm) a) Numerical results b) Local behavior predicted by the FE model Figure 1. Local and global behavior of Specimen L1 4 EXTENSION OF THE NUMERICAL MODEL TO MASONRY WALLS STRENGTHENED BY VERTICAL FRP STRIPS The FE model introduced in the previous section has been extended to masonry walls strengthened by vertical CFRP strips. The model is used to predict the behavior of Specimen L1-LAMI- C-I of ELGawady's (2004) research. Specimen L1-LAMI-C-I is completely similar to Specimen L1, but has been strengthened by two vertical plates of carbon fiber adhered to one face of the wall, each strip is 50 mm wide and 1.2 mm thick. The specimen has been tested under dynamic excitations using shaking table to a predefined degree of damage, 5.31 mm of lateral deformation. The test has been interrupted at this deformation to preserve the specimen for subsequent tests in order to evaluate the lateral resistance after changing in the configuration of FRP composites. The model specifications are given in Table 2. Specifications of CFRP strips have been determined based on information given in ElGawady (2004). Due to lack of any rupture and delaminating of CFRP strips during the tests (ElGawady 2004), they have been modeled by an elastic shell element (Shell 63, ANSYS, 1996) with a perfect contact at their interface with the - 3 -

4 wall face. A uniform mesh in the interface of strips and bricks with finer meshing in their interface with the mortar joints have been used for the CFRP strips. Other model specifications consisting of masonry constituents details and loading method are completely similar to Specimen L1 given in Table 1. The global behavior obtained by the model, is presented in Figure 2. The figure shows that the model is relatively successful in predicting the global behavior compared to the test results. Table 2. Model specifications of specimen L1-LAMI-C-I Specimen Axial load (KN) P1 P2 E (MPa) Tensile strength (MPa) CFRP Fibre orientation (degree) Thickness (mm) Type of lateral loading L1-LAMI-C-I Time history Figure 3a presents the local behavior of L1-LAMI-C-I predicted by the model at a deformation of 5.31mm. It should be noticed that the numerical model applies an incremental monotonic loading while the tests apply a cyclic dynamic incremental excitation. The flexural and shear cracks of the model seem in fairly good agreement with the test results (Fig. 3b) if only one direction of excitation is considered. It should be explained that compared to L1, there are some additional cracks in the head joints located near to interface of the wall and Strip 1. That is, due to high stiffness and strength of CFRP strips, the wall experiences higher stresses and therefore more cracks in these regions. These cracks proceed upwards through the head joints as lateral load increases. 30 Base shear force (kn) Test FE model Lateral deformation (mm) Figure 2. Global behavior of Specimen L1-LAMI-C-I It seems that stress concentration caused by CFRP strips, produces more extensive damage in L1-LAMI-C-I relative to the unreinforced masonry wall (e.g. L1) at the same deformation. a) Local behavior predicted by the FE model b) Test results Figure 3. Local behavior of Specimen L1-LAMI-C-I - 4 -

5 5 THE EFFECT OF NUMBER OF VERTICAL CFRP STRIPS AND ASPECT RATIO ON IN-PLANE BEHAVIOR In this section, the effects of the number of vertical FRP strips on in-plane behavior of walls with different aspect ratios are investigated in a framework of parametric study using the numerical model. In total, nine cases are considered: three specimens with aspect ratios of 0.44, 1.0 and 1.5, each strengthened by 2, 6, and 10 strips (see Table 3). The last step of loading is chosen to be the onset of crushing at the toes of the walls predicted by the model. The global behavior of different specimens is presented in Figure 4. As is seen, lateral strength increases significantly for all specimens with increasing in the number of strips. However, with increasing the number of strips, ductility decreases. 240 L1-AS L1-AS L1-AS L1-AS1.5-2 L1-AS1.5-6 L1-AS L1-LAMI-C-I L1-LAMI-C-I-6 L1-LAMI-C-I-10 Base shear force (kn) Drift (%) Figure 4. The response of masonry walls with different aspect ratios and various number of CFRP strips predicted by the model. This is due to fact that crushing happens at the bricks at the toes at a smaller deformation when the number of strips increases (see Table 3). As it is seen in Table 3, reduction in ductility is noticeable for specimens with aspect ratio of 0.44 due to their higher stiffness compared to other specimens. Therefore the toes of the wall should be strengthened separately e.g. with FRP sheets, if ductility should be preserved. Table 3 Damage in the bricks predicted by the FE model Specimen Number Drift (%) Aspect of Onset of the crushing at the bricks Onset of the crushing at the bricks ratio strips located at the middle strips located at the middle strips L1-LAMI-C-I Null Null L1-LAMI-C-I L1-LAMI-C-I L1-AS0.44-C L1-AS0.44-C L1-AS0.44-C L1-AS1.5-C Null Null L1-AS1.5-C L1-AS1.5-C

6 In addition, the figure shows increasing the number of strips does not have any remarkable influence on the initial stiffness of the wall with a particular aspect ratio. Simulations show that all walls exhibit a bilinear base shear versus lateral deformation behavior with a knee point. With increasing the number of vertical CFRP strips, the knee point occurs at a higher load, especially for walls with low aspect ratios. Analysis of all specimens shows that flexural and shear cracks occur in the mortar joints located between every two adjacent strips. This pattern can be described by the fact that the tensile strength and stiffness are much larger for CFRP material relative to masonry materials. As Table 3 shows, the first damage in the bricks starts at the brick units located at the middle strips. Afterwards crushing proceeds upwards and downwards and also extends to bricks at other strips. This kind of damage has also been observed in the ElGawady s (2004) tests. 6 CONCLUSION In this study, a general analysis tool which previously developed for in-plane behavior of unreiforced masonry walls by the authors, has been applied to masonry walls strengthened by vertical CFRP strips. The tool uses the general-purpose finite element code of ANSYS and has been calibrated by experimental results. The model incorporates the effects of bed joints, head joints, brick units, CFRP strips and takes into account nonlinear characteristics of masonry consisting of cracking, crushing, and sliding. The study shows that, in spite of significant improve of lateral strength, application of vertical CFRP strips causes more extensive damage in the wall and may undermine its ductility relative to unstrengthened walls. It has been observed that walls with relatively small aspect ratios are more vulnerable to reduction in ductility relative to more slender walls if vertical CFRP strips are applied. Simulations show that all walls exhibit a bilinear base shear versus lateral deformation behavior with a knee point. With increasing the number of vertical CFRP strips, the knee point occurs at a higher load, especially for walls with low aspect ratios. 7 REFERENCES ANSYS Release 5.4, ANSYS Manual Set. USA: ANSYS Inc. ElGawady, M Seismic in-plane behaviour of URM walls upgraded with composites. A Thesis for the degree of PHD, EPFL, Lausanne, Switzerland. Foraboshi, P. May-June Strengthening of masonry arches with fiber-reinforced polymer strips. Journal of Composites for Structures, ASCE; Karbhari, M.V., and Seible, F Fiber reinforced composites-advanced materials for the renewal of civil infrastructures. Applied Composite Materials;7: Laursen, P.T., and Ingham, J.M. Oct Structural testing of large-scale post-tensioned concrete masonry walls. Journal of Structural Engineering, ASCE: Mahjoob, D., Motavalli, M., Marefat, M.S. and Schumacher, A Nonlinear FE modeling of in-plane behavior of plain masonry walls and investigating effects of post-tensioning as a parametric study. 5 th Intl Conference on Seismology and Earthquake Engineering, Paper No:MA101. Mukherjee, A., and Jushi, M. February Recent advances in repair and rehabilitation of RCC structures with non-metallic fibers. Workshop on Seismic Assessment and Retrofitting Buildings, Institute of Engineers, India. Sayed Ahmad, E., Lissel, S.L., Gamiltadros, N., and Shrive, G Carbon fibre reinforced polymer (CFRP) post-tensioned masonry diaphragm walls: pre-stressing, behaviour and design recommendations. Canadian Journal of Civil Engineering;26: Stierwalt, D.D., and Hamilton, H.R Creep of concrete masonry walls strengthened with FRP composites. ELSEVEIR, Construction and Building Materials;19: Tumialan, J.G., Galati, N., and Nanni, A Strengthening with FRP bars of URM walls subject to out-of-plane loads. ELSEVEIR, Construction and Building Materials;20: