Aseismic retrofitting of unreinforced masonry walls using FRP

Transcription

1 Composites: Part B 37 (26) Aseismic retrofitting of unreinforced masonry walls using FRP Mohamed A. ElGawady*, Pierino Lestuzzi, Marc Badoux Swiss Federal Institute of Technology at Lausanne EPFL, Ecole Polytechnique Fédéral de Lausanne (EPFL-ENAC-IS-IMAC), Lausanne 115, Switzerland Received 8 September 24; accepted 2 June 25 Available online 15 September 25 Abstract Many of existing unreinforced masonry (URM) buildings are seismically vulnerable and require retrofitting. This paper investigates in-plane seismic behaviour of URM walls before and after retrofitting using fiber-reinforced polymers (FRP). Dynamic in-plane tests were carried out on five half-scale specimens with two different effective moment/shear ratios namely.7 and 1.4. The specimens were retrofitted on a single side using different types and structures of FRPs. The test specimens were subjected to a series of synthetic earthquake motions on a uni-axial earthquake simulator. The retrofitting technique improved the lateral strength and stiffness of the URM walls. Moreover, the fundamental frequency and the initial stiffness of each specimen remained approximately constant before and after retrofitting. During the test, the slender specimens failed in flexural. For specimens failed in flexural, the measured FRP axial strains showed that the strain distributions along the specimens cross-sections are approximately linear even at failure. Hence, the flexural strengths of the specimens were calculated using linear elastic approach. The measured lateral resistances of slender specimens are approximately 13% of the calculated flexural strength. This difference attributed to the difference in the nominal ultimate strains of FRPs and the real values at failure. The measured axial strains in FRPs during this test were approximately 5% of its nominal values. In addition, the shear strengths of the squat specimens were calculated using two different models. The calculated shear strengths approximately range from 99 to 177% of the measured lateral resistances. q 25 Elsevier Ltd. All rights reserved. Keywords: Seismic retrofitting 1. Introduction Existing unreinforced masonry (URM) buildings constitute a significant portion of existing buildings around the world. Recent earthquakes have repeatedly shown the vulnerability of URM buildings. Moreover, based on modern design codes most of the existing URM buildings need to be retrofitted. For example, in Switzerland, a recent research [1] carried out on a target area in Basel shows that from 45 to 8% of the existing URM buildings, based on construction details, will experience heavy damage or destruction during a moderate earthquake event. * Corresponding author. Present address: Civil and Environmental Engineering Department, The University of Auckland, Private Bag 9219, Auckland, New Zealand. Tel.: C ; fax: C address: melg3@ec.auckland.ac.nz (M.A. ElGawady) /$ - see front matter q 25 Elsevier Ltd. All rights reserved. doi:1.116/j.compositesb This brought to light the urgent need to improve and develop better methods of retrofitting for existing seismically inadequate. The main structural elements that resist earthquakes in these buildings are the old URM walls URM buildings. Several conventional techniques are available to improve seismic performance of existing URM walls. Surface treatments (ferrocement, shotcrete, etc.), grout injections, external reinforcement, and center core are examples of such conventional techniques. Several researchers (e.g. [2]) have discussed the disadvantages of these techniques: available space reduction, architecture impact, adding heavy mass, corrosion potential, etc. Modern composite materials offer promising retrofitting possibilities for masonry buildings and present several well-known advantages over existing conventional techniques. A recent literature review for using of composites for retrofitting of URM walls have been presented in [3]. This paper presents a pioneer dynamic in-plane tests carried out on half-scale single leaf unreinforced masonry walls retrofitted with composites (URM-WRC). The objective of this study was to

2 M.A. ElGawady et al. / Composites: Part B 37 (26) (a) Mass Level (4.2) a a. Head beam (R.C.).15 b. Masonry specimen c. Foundation (R.C.) d. Post-tensioning bars a.25 b c Table Top Level (1.125) b c Sec (1-1) d (b) Mass (2.66) Level a b c Table Top Level (1.125) Sec (1-1) a d b c a. Head beam (R.C.) b. Masonry specimen c. Foundation (R.C.) d. Post-tensioning bars Fig. 1. Specimens dimensions in meter, (a) slender and (b) squat. compare the seismic behavior of URM walls before and after retrofitting with composites. Another objective was to examine the ability of existing simple analytical models to predict the lateral strength of URM-WRC. 2. Experimental program 2.1. Test specimens The test specimens had two aspect ratios (Fig. 1): slender walls and squat walls; also, two mortar types were used: weak (M2.5) and strong (M9). In addition, different types of FRP (Table 1) and retrofitting configuration (Figs. 2 and 3) were used to retrofit the specimens. Anchorage failure of the FRP was prevented by clamping the FRP ends to specimen s footing and cap beam using steel plates and screw bolts (since anchorage problem is out of the scope of this research). Both the cap beam and footing pad were pre-cast reinforced concrete. The test walls were tested twice: first, the URM specimens were tested, as reference specimens, till a predefined degree of damage; secondly, these reference specimens were retrofitted using composites and retested. The focus of this paper is on the comparisons between the retrofitted and URM specimens. More details about the behavior of the URM specimens are presented in [4]. The specimens were retrofitted on a single side only. This way of retrofitting was successfully used in different research programs for retrofitting of URM walls using composite material (e.g. [5]). Each specimen is designated by a name that reflects their characteristics; Tables 2 and 3 explain the specimens names and give a complete list of the tested specimens. For instance, L1-WRAP-G-X means a slender specimen (L) which was constructed using mortar type (1) and was retrofitted with fabric (WRAP) of glass (G) fiber in a diagonal (X) configuration. Also, Figs. 2 and 3 show summary of the tests that were carried out on the specimens. It should be noted that specimen L1-LAMI-C-I where a virgin URM specimen was upgraded with two vertical plates of CFRP was designed to study the shear resistance of slender URM walls rather to investigate the effect of using vertical plates as retrofitting of existing URM walls. Since, in this specimen and in order to force a shear failure, the flexural strength of the specimen was increased with minimal increment in its shear strength. As such, this specimen herein after is considered as a reference Table 1 FRP used in the experimental program Commercial name FRP (Fiber) Warp W (g/m 2 ) Weft W (g/m 2 ) f t (MPa) E (GPa) 3 (%) SikaWrap-4A /9 Aramid SikaWrap-3G /9 Glass MeC Grid G4 Glass Sika CarboDur S512 Carbon * 165 ** 1.7 Sika CarboDur T1.214 Carbon * 135 ** 1.6 Warp w and Weft w, Weight of fiber in the warp and weft directions respectively; f t and E, Fibers nominal tensile strength and E-modulus respectively; 3, Ultimate strain; *, Composite tensile strength; **, Composite E-modulus.

3 15 M.A. ElGawady et al. / Composites: Part B 37 (26) Fig. 2. Overview of the tested slender specimens. specimen. More discussion about this specimen is published in [6]. Finally, after testing of L1-LAMI-C-I and S1-LAMI- C-X the CFRP plates were taken off using hammer and chisel. These specimens were retrofitted, one more time, using glass fiber and retested again as L1-WRAP-G-X and S1-WRAP-G-F, respectively Test set-up The walls are tested on the uni-axial earthquake simulator of the Swiss Federal Institute of Technology in Zurich (ETHZ). A test specimen is fixed on a shaking table measuring 2 m by 1 m. It has a maximum displacement

4 M.A. ElGawady et al. / Composites: Part B 37 (26) Fig. 3. Overview of the tested squat specimens. of G1 mm and is driven by a 1 kn servo-hydraulic actuator (Fig. 4). The specimen is connected at its top to a 12-ton substitute mass placed on bearing wheels with a low coefficient of friction in the order of.5%. This 12-ton mass represents approximately the mass of approximately 55 m 2 of a floor due to 2 mm thick reinforced concrete slab, flooring, and live load. At its top, the specimen is guided with a low friction set-up to ensure that out-of-plane displacements are limited. More details about the test set-up are available in [4] Loading system A test specimen was constructed on a pre-cast reinforced concrete footing. After allowing the specimen to cure (from 3 to 7 days), the pre-cast reinforced concrete cap beam was fixed to the top of the specimen using strong mortar (M2). Superimposed gravity load of approximately 3 kn was simulated using two external post-tensioning bars. This was in addition to 12 kn of self-weight from steel elements at wall top (due to the test set-up), reinforced concrete cap beam, and masonry panel weight. This normal force corresponded to a stress of.35 MPa. During testing of specimens L1-REFE, L1-WRAP-G-F and L1-WRAP-G-X and due to increase of the wall height as result of opening of Table 2 Legend for specimens names Slenderness Mortar type L Long (Slender) 1 Type 1 S Short (Squat) 2 Type 2 Retrofitting products Retrofitting materials WRAP Loose fabric A Aramid fibers GRID Rigid fabric C Carbon fibers LAMI Plates G Glass fibers REFE Reference Retrofitting configurations F One face fully covered I Vertical elements X Diagonal elements

5 152 M.A. ElGawady et al. / Composites: Part B 37 (26) Table 3 List of the tested specimens Tests carried out on slender specimens with type 1 mortar L1-REFE L1-WRAP-G-F L1-LAMI-C-I L1-WRAP-G-X Tests carried out on slender specimens with type 2 mortar L2-REFE L2-GRID-G-F Tests carried out on squat specimens with type 1 mortar S1-REFE S1-LAMI-C-X S1-WRAP-G-F Tests carried out on squat specimens with type 2 mortar S2-REFE S2-WRAP-A-F Reference specimen Specimen L1-REFE after retrofitting with fabrics of glass fibers Specimen has been retrofitted with plates of carbon fiber and is considered as a reference specimen Specimen L1-LAMI-C-I after taking off the carbon plates and re-retrofitting the specimen with fabrics of glass fiber Reference specimen Specimen L2-REFE after retrofitting with grids of glass fibers Reference specimen Specimen S1-REFE after retrofitting with plates of carbon fibers Specimen S1-LAMI-C-X after taking off the carbon plates and retrofitting it with fabrics of glass fibers Reference specimen Specimen S2-REFE after retrofitting with fabrics of aramid fibers flexural cracks the post-tensioning force increased many times; in the next specimens two railcar springs were used with the post-tensioning bars. These springs prevent to a certain extend the increment in the post-tensioning force. of the reference earthquake acceleration. For space limitations in this paper, the detailed test runs are not presented and interested reader is referred to [4] Dynamic excitations The displacement inputs were based on synthetic acceleration time-histories compatible with Eurocode 8 [7] for rock soil Type A and with a peak ground acceleration of 1.6 m/s 2 (Fig. 5). The specimens were subjected to acceleration histories of increasing intensity until failure occurred. The tests started by subjected the specimens to an earthquake with acceleration of 1% of the reference earthquake acceleration followed by an increment in the acceleration of usually 1% 3. Experimental results In this section, the experimental results of the test specimens are discussed in terms of lateral strength, drift, maximum strain in composites, and specimen asymmetry. Detailed results regarding URM specimens (i.e. specimens without composites) are available in [4]. It should be noted that effects of mortar on specimens behavior were examined during testing the reference specimens; the effects were very limited. Fig. 4. Test set-up.

6 M.A. ElGawady et al. / Composites: Part B 37 (26) Fig. 5. UG1, Eurocode 8 for rock soils type A, spectrum-compatible synthetic earthquake Lateral strength and mode of failure All the composite materials increased the lateral strength by a factor ranging from 1.3 to 2.9. Different failure modes happened during the test; Fig. 6 shows the test specimens at the test end. For slender specimens, the full-face retrofitted specimens (L1-WRAP-G-F and L2-GRID-G-F) developed a rocking mode with masonry crushing at toes and fiber rupture at heals (Fig. 7); see the video in Appendix A in the online version of this paper. For the reference specimens a rocking mode of failure was observed. However, in case of retrofitted specimens the failure happened at level corresponding to the first brick course and this was not always the case for the reference specimens [4]. For both retrofitted specimens Fig. 6. Failure modes of specimens (a) L2-GRID-G-F, (b) L1-WRAP-G-F, (c) L1-WRAP-G-X, (d) S1-WRAP-G-F, (e) S2-WRAP-A-F, and (f) S1-LAMI-C-X.

7 154 M.A. ElGawady et al. / Composites: Part B 37 (26) Fig. 7. L1-WRAP-G-F at the test end (a) fabric rupture in the bottom western north side, (b) masonry failure in the bottom eastern north side. and under a constant normal force of 57 kn, the retrofitting increased the lateral strength by a factor of 2.6 for fabric and 2.9 for grid. A superposition of the hysteresis loops of reference slender specimens (L1-REFE and L2-REFE) and the corresponding retrofitted specimens (L1-WRAP-G-F and L2-GRID-G-F) is presented in Fig. 8. For L1-WRAP-G-F and at the test end, the normal force tripled (due to increments of wall height as a result of opening of flexural cracks and due to the absence of the railcar springs); this increment in the normal force had insignificant effect on the specimen lateral strength. Nevertheless, the lateral strength of the reference specimen (L1-REFE) approximately tripled when the normal force tripled. As a consequence, the enhancement in the lateral strength in case of high normal force reduced to 1.9 times the original lateral strength. For squat specimens, the lateral strengths of the full-face strengthened specimens (S1-WRAP-G-F and S2-WRAP-G- F) were higher than the capacity of the shaking table hydraulic jack. At the tests end, there were no significant signs of failure; in addition, the retrofitting increased the lateral resistance of the specimens by a factor of 2.6. A superposition of the hysteresis loops of reference squat specimens (S1-REFE and S2-REFE) and the corresponding retrofitted specimens (S1-WRAP-G-F and S2-WRAP-A-F) is presented in Fig. 9. Specimens (L1-WRAP-G-X and S1-LAMI-C-X) that retrofitted with diagonal shape (X) were less successful. The behaviors of both specimens were affected by the previous tests, which was carried out on the specimens before retrofitting: before retrofitting, L1-WRAP-G-X was tested as L1-LAMI-C-I while S1-LAMI-C-X was tested as S1- REFE. These testes developed several cracks in both specimens. So, the retrofitting could be considered as retrofitting of URM wall that have been severely damaged during a recent real earthquake event. For L1-WRAP-G-X and at failure, the FRP failed at the specimen mid-height due to shear and flexural cracks, which had developed first through mortar joints. For S1-LAMI-C-X and during the test, one plate failed due to anchorage failure at foundation level since no steel plates (which were used in the other specimens to prevent anchorage failure) were used in this specimen. Both retrofitting configurations enhanced the lateral resistance by a factor of 1.5 for L1-WRAP-G-X and 1.3 for S1-LAMI-C-X. A superposition of the hysteresis loops of the reference specimens (L1-REFE and S1-REFE) and the corresponding retrofitted specimens (L1-WRAP-G- X and S1-LAMI-C-X) is presented in Fig. 1. It should be noted that the cracks, which were exist in the specimens before the diagonal retrofitting influenced the results. Hence, it is not recommended to use the diagonal configuration as the only retrofitting scheme in the case of real URM wall, which suffers sever damage after a real earthquake. Recently [13] a similar conclusion has been experimentally explored in static cyclic tests on URM walls retrofitted using diagonal strips of carbon fiber. Finally, as mentioned, the goal of testing specimen L1-LAMI-C-I was not to examine the effect of retrofitting; since, in such retrofitting configuration shear cracks were expected to occur. However, it was interested to compare the hysteresis of this specimen (L1-LAMI-C-I) and the corresponding reference specimen. Fig. 11 shows such comparison; as expected this retrofitting system changed the wall mode of failure (from rocking to shear) and increased the specimen lateral strength by a factor of Fig. 12 shows step-cracks passing through bed and head joints during the test Lateral drift The ultimate lateral drifts of retrofitted specimens were dependent on the aspect ratio and mostly independent of the reinforcement ratio (r). For slender specimens (L1- WRAP-G-F, L2-GRID-G-F, and L1-WRAP-G-X) the ultimate drifts were approximately 1%. As an example

8 M.A. ElGawady et al. / Composites: Part B 37 (26) (a) 8 7 L2-REFE 6 L2-GRID-G-F [mm] (a) S1-REFE S1-WRAP-G-F [mm] (b) 8 7 L1-REFE 6 L1-WRAP G F [mm] (b) 8 7 S2-REFE 6 S2-WRAP-A-F [mm] Fig. 8. Superposition of the hysteresis loops of reference and fully covered retrofitted slender specimens. Fig. 13 shows the envelopes of the hysteresis loops of all the test runs of specimen L2-GRID-G-F and the corresponding reference specimen L2-REFE; the peak lateral force values are normalized by kn, the weights sum of the 12-ton mass, the head beam, half of the masonry panel, and the other test set-up steel elements at specimen top. This normalization makes it similar to what is known by base shear coefficient in design codes. The envelope clearly shows that approximately 8% of the drift was attributed to specimen rocking. In addition, examinations of the measured displacements using the LVDTs along the specimen full-height and half-height (Fig. 14) showed that approximately all the deformations concentrated in the bottom half of the specimen. Note that in the presented figure the negative values represent an opening of the crack. Fig. 9. Superposition of the hysteresis loops of reference and fully covered retrofitted squat specimens. It is also worth to note the feature of the crack opening/ closing histories and how it had a regular pattern, which existed for the opening and closing of the horizontal cracks. This repetitive, regular opening and closing motion was indicative of a specimen rocking. For squat (short) specimens (S1-WRAP-G-F, S2-WRAP- A-F, and S1-LAMI-C-X), it is difficult to establish the relationship between reinforcement ratio and lateral drift since the specimens (S1-WRAP-G-F, S2-WRAP-A-F) did not reach its ultimate state due to the test set-up capacity. However, the measured maximums drifts for the squat retrofitted specimens were ranging from.1 to.5%. Ongoing static cyclic test is carried out by the authors to study the behavior of similar squat specimens.

9 156 M.A. ElGawady et al. / Composites: Part B 37 (26) (a) S1-REFE S1-LAMI-C-X [mm] 8 7 L1-REFE 6 L1-LAMI-C-I [mm] (b) L1-WRAP-G-X L1-REFE [mm] Fig. 1. Superposition of the hysteresis loops of reference and X (diagonal) shape retrofitted specimens Maximum strains at failure Recently, several researchers proved that, during testing reinforced concrete beams, the FRP strain at failure is many times lower than its nominal ultimate strains. This phenomenon has been reported for reinforced concrete beams that have been tested in shear [8,9] as well as in bending [1]; moreover; this phenomenon was presented [11] for URM walls that had been retrofitted using glass fiber reinforced plastic and tested for out-of-plane failure. All these researchers proposed empirical efficiency factors for FRP; these efficiency factor are inversely proportional to FRP area and Young s modulus. In order to investigate this phenomenon for the tested specimens, the maximum strains, Fig. 11. Superposition of the hysteresis loops of reference and retrofitted slender specimens. calculated based on the measured deformations using the LVDTs, at the masonry and strengthened faces of the failed test specimens were examined. The results show that just before failure, the maximum vertical strain for the GFRP fabrics was 1.2% (the nominal ultimate strain for fabric fiber is 3%), while for GFRP grids was 2.5% (the nominal ultimate strain for grid fiber is 4%). For the other retrofitting materials, no strains at failure were recorded since the FRP did not fail in tension (either debonding and anchorage or no failure at all). It should be noted that these values are measured along approximately 156 mm long distance; so, it corresponds to the average strain along that distance. It is expected that the ultimate strain at the ruptured section will be higher than these measured values Plane section Vertical deformations, at the first brick course, along a specimen cross-section were measured using four LVDs. The measured displacement were divided by the original measuring length (156 mm) and this gave the strain timehistory along the specimen cross-section. These measurements were used to verify the main assumption of Bernoulli Navier hypothesis (plane section remains plane before and after deformations) for slender URM-WRC. As an example of these strain distributions, measured strains during the several test runs of specimen L2-GRID-G-F, are plotted in Fig. 15. Note that, the points and the lines in the figure represent the experimental measurements and the best-fit of these measurements, respectively. A salient feature of this figure is that the vertical strain distribution along the specimen cross-section is approximately linear even at failure. The verification of this assumption of plane

10 M.A. ElGawady et al. / Composites: Part B 37 (26) Fig. 12. Step cracks in specimen L1-LAMI-C-I during the test: (a) cracks propagation, and (b) close up view of a 2 mm crack opening. section is very important to use the usual linear elastic approach to calculate the lateral strength of URM-WRC Specimens asymmetry As mentioned earlier all the test specimens were retrofitted on a single-side only. As shown by other researchers [5,12] this system did not result in any asymmetry in deformations, which may result in more complicated failure mechanism. In order to evaluate this issue for the tested specimens, a comparison between the vertical strains, calculated based on measured displacements using LVDTs, on the masonry face bare face and the retrofitted side was carried out. The comparison showed the following points: For slender specimens, the retrofitting system succeeded in producing complete symmetric response in case of tension while there was asymmetry in the case of compression. The strains indicated that the asymmetry increased by increasing the earthquake intensity, the rate of increase in the asymmetry during compression was many times larger than tension. The maximum asymmetry in tension was recorded during testing L2-GRID- G-F; the average vertical strain along the masonry face was approximately 118% of the average vertical strain along the FRP face. In compression, the maximum asymmetry was recorded during testing L1-WRAP-G-F; the average vertical strain along the masonry face was approximately 5% of the average strain along the FRP face. For squat specimens, the retrofitting system did not succeed in producing symmetric response. The maximum asymmetry in tension was recorded during testing S1-WRAP-G-F; the average vertical strain along the masonry face was approximately 29% of the average vertical strain along the FRP face. In compression, the maximum asymmetry was recorded during testing S2- WRAP-A-F; the average vertical strain along the masonry face was approximately 56% of the average strain along the FRP face Anchorage and delamination As mentioned earlier, the study of the anchorage system was out of the scope of this research; hence, the anchorage failure was prevented by using steel plates at the FRP ends; the steel plates were used in all specimens except in the beginning of testing specimen S1-LAMI-C-X. In all specimens, except S1-LAMI-C-X, this technique prevented the anchorage failure. Delamination is an important event, since it could be either a reason for stiffness degradation or early sign of failure. The stiffness degradation due to delamination was reported by others (e.g. [11]) for out-of-plane failure of URM-WRC. In order to examine the effect of the strengthening material characteristics on delamination and hence on a specimen behavior, the lateral resistances from each test run were plotted versus earthquake intensity. As an example, Fig. 16 compares the behavior of specimens L1- WRAP-G-F and L2-GRID-G-F both of them retrofitted using a single-side full-face glass fiber but with different characteristics. The figure shows that, the behavior of both specimens can be described through two phases: before and after delamination. The first phase (before delamination), by increasing the earthquake real intensity (acceleration) F/W L2-REFE L2-GRID-G-F Rocking Rocking Lateral Drift [%] Fig. 13. Normalized lateral force versus wall drift for slender specimens (L2-REFE and L2-GRID-G-F).

11 158 M.A. ElGawady et al. / Composites: Part B 37 (26) Vertical Displacement [mm] Wall Full Height Wall Half Height Time [S] Fig. 14. The vertical displacement time-histories measured along the specimen full and mid-height. the lateral resistance of both specimens increased linearly, approximately, in an identical way. In this phase no large variations in the post-tensioning forces, in both specimens, were recorded. The second phase started with delamination; after delamination both specimens behaved in a nonlinear way; there was nonlinear increase in the lateral resistance with increasing earthquake real intensity. This nonlinear behavior was combined with high increase in the posttensioning force in case of L1-WRAP-G-F (note that no railcar springs were used). In the case of L2-GRID-G-F, 1.5 Strain [%] UG1R 2% UG1R 15% UG1R 21% UG1 4% UG1R 2% UG1R 15% UG1R 21% UG1 4% L [m] Fig. 15. Vertical strain distribution along specimen L2-GRID-G-F cross-section L1-WRAP-G-F (F) L2-GRID-G-F (F) L1-WRAP-G-F (P) L2-GRID-G-F (P) No Difference P Approx. Constant F Approx. Coincident Fabric Delamination Grid Delaminatio P [kn] Real Earthquake Intensity [%] Fig. 16. Measured lateral resistances (F) and post-tensioning forces (P) vs. real earthquake intensity (acceleration) for slender retrofitted specimens L1-WRAP- G-F and L2-GRID-G-F.

12 M.A. ElGawady et al. / Composites: Part B 37 (26) (a) 4 Fourier Amplitude [m/s 2 /Hz] f=3.37 Hz Frequency [Hz] (b) 2 18 f=2. Hz Frequency [Hz] Fourier Amplitude [m/s 2 /Hz] Fig. 17. Fourier amplitude spectra for relative mass accelerations of specimen L2-GRID-G-F, (a) before cracking, and (b) at the test end. the post-tensioning force remained approximately constant till 232% of real earthquake intensity; after rupture of the grids, the real earthquake intensity decreased while the corresponding post-tensioning force increased many times. Moreover, examination of FRP strains at first delamination for all the tested specimens shows the following comments: The lateral resistance at the first delamination (F d )is proportional to the fiber ultimate strength and inversely proportional to the reinforcement ratio. Qualitatively F d is influenced by three factors: the aspect ratio, the FRP product and material type, and the retrofitting configuration. The glass fiber fabrics delaminated at average tensile strains approximately ranging from.6 to.32%, depending on the reinforcement ratio. The glass fiber grids delaminated at an average vertical tensile strain of approximately.9%. The thermoplastic plates of CFRP Sika CarboDur T exhibited anchorage failure at average tensile strains of.4%; after reparation using fast epoxy, it delaminated at average tensile strain of.5%. For all specimens, that had delaminated, the average vertical compression strains along the masonry panel, at delamination, was approximately.4% independent of the reinforcement ratio or FRP type Natural frequencies Fast Fourier transforms (FFTs) were computed from the relative horizontal acceleration response time-histories of the mass collected during the dynamic test runs. The relative horizontal acceleration of the mass is the difference between the absolute horizontal acceleration measured on the mass and the table acceleration. The oscillation of the mass reflected the wall behavior; therefore the fundamental frequency was defined as the location of the peak Fourier amplitude between 1 and 5 Hz for each test run. The lower bound, of this range, avoided low frequency disturbances appearing from measurements and numerical imprecision. The upper bound, of this range, avoided high frequency disturbances appearing from hydraulic jack. As shown in Fig. 17 several Fourier amplitude peaks at similar locations appeared in the investigated frequency. From a test run to the following test run, the relative amplitudes of the peaks rather than their location were modified. This feature is a characteristic of a nonlinear behavior. As a consequence, the fundamental frequency did not change gradually with increasing the test runs but rather dropped suddenly from a peak to another after staying constant at the same peak for several test runs. For slender retrofitted specimens, the retrofitting did not change the fundamental frequency it remained at approximately 3.3 Hz at the beginning of the test; at the test end, the fundamental frequencies were ranging from 2. to 2.54 Hz. For squat specimens, full surface retrofitting change a little the fundamental frequency from 4.49 to approximately 4.76 Hz. In addition, using diagonal retrofitting for squat specimen approximately recovered its fundamental frequency. 4. Design approaches 4.1. Shear design Limited design proposals exist for URM-WRC. Comparisons between these models can be found in [14]. For squat specimens S2-WRAP-G-F and S2-WRAP-A-F two models were used to calculate their shear strengths. The first model developed by Triantafillou and Antonopoulos [15] hereinafter called TA model. The second model is adopted by AC125 [16] hereinafter called AC125 model. These models calculate the shear strength as follows F Z F m CF FRP (1) where F m is the shear strength of URM wall, which can be determined according to existing codes. In this research F m was determined as 56 kn according to EC6 [17]. F FRP, contribution of FRP to the shear strength of URM wall.

13 16 M.A. ElGawady et al. / Composites: Part B 37 (26) The main difference between TA model and AC125 model is how to calculate F FRP. According to TA model, F FRP can be calculated as follows F FRP Z r h E FRP 3 eff tl (2) f 2=3 :56 c 3 eff Z :65 ðdebondingþ (3a) r h E FRP f 2=3 :3 c 3 eff Z :17 3 r h E FRP for CFRP and FRP fc 2=3 :47 :48 3 r h E FRP for AFRP ðruptureþ FRP (3b) where r h is the reinforcement ratio of FRP in the horizontal direction; E FRP, modulus of elasticity of FRP; t, thickness of masonry wall; L, length of masonry wall; 3 eff, effective strain of FRP at failure; f c, masonry characteristic compressive strength. Eqs. (3a) and (3b) represent failure due to debonding and FRP rupture, respectively. To transfer the mean value of 3 eff to a characteristic value the expressions in Eqs. (3a) and (3b) should be multiplied by a reduction factor of.8. In addition, the characteristic value of 3 eff has an upper limit of.5. According to AC125 model, F FRP can be calculated as follows F FRP Z :75r h f j tl (4a) Table 5 Comparisons between F estimated according to the existing models as well as the experimental results F total, (Experimental) F total (AC125 Model) Ratio (%) 1 58 F total (TA Model) Ratio (%) The AC125 model does not take into considerations the effects of reinforcement ratio on FRP s axial strain. For the FRPs used in this research, the first part of Eq. (4b) dominated the stresses in FRP and then the stresses in FRPs are proportional to their modulus of elasticity. The difference between these two models is small for small reinforcement ratio; however, the difference increased with increasing the reinforcement ratio [14]. The resistances F of the specimens are presented in Table 5. Also, the experimental lateral forces of the test specimens are presented in the same table. The prediction according to each model was followed by a row containing values called ratio. The ratio is defined as the ratio between the experimental lateral force and the predicted F. As shown in the table, S1-WRAP-G-F was very close to failure and S2-WRAP-A-F was approximately at 6% of its ultimate strength. In the experimental tests, both specimens did not reach its ultimate strength. However, at the test end of S1- WRAP-G-F very limited delamination appeared in the FRP layer. f j Z :4E FRP %:75f FRP;u (4b) 4.2. Flexural design where f j is the axial force in FRP; f FRP,u, ultimate tensile strength of FRP. Table 4 presents F FRP calculated according to these models. As shown in the table, the AC125 prediction is lower than TA model prediction in case of S1-WRAP-G-F. By increasing the specimen s reinforcement ratio and the modulus of elasticity of the retrofitting material (i.e. for specimen S2-WRAP-A-F), the AC125 prediction became higher than TA model prediction. This is because TA model used effective strains in the FRP inversely proportional to the reinforcement ratio and the modulus of elasticity. Table 4 Comparisons between F FRP estimated according to the existing models Parameters S1-WRAP-G-F S2-WRAP-A-F r (%) E (GPa) 7 1 f t (MPa) (%) eff (K) f 28 4 F FRP (kn), AC Model F FRP (kn), TA Model A common method to calculate the flexural capacity of structural elements is the use of linear elastic approach. It is an easy method and intended to incorporate a realistic behavior of a structural element by assuming that it behaves linearly up to failure. In case of URM-WRC, this assumption is justified by the observed behavior of the tested specimens. The derivation of the mathematical equations is given in this section; the derivation is based on the following assumptions: Plane section remains plane before and after deformations and only rocking mode of failure is considered. Full composite action between composite material and the brick surface is assumed. Debonding of the composite material is avoided by choosing appropriate dimensions for composite and good anchorage system. Tensile strength in brick and adhesive is neglected; this means that all tensile stresses in the wall section are resisted by composite materials only. Masonry ultimate compressive strain (3 m ) is.35, while the ultimate tensile strain in glass fiber is.3 for fabric glass,.4 for grid glass, and.28 for aramid woven.

14 M.A. ElGawady et al. / Composites: Part B 37 (26) L ε m x l ε ε f Strains f k f t Stresses a=.8 x Internal Forces C T Mu External Forces N Table 6 Summary of flexural assessment of URM-WRC Parameters S1-WRAP- G-F S2-WRAP- A-F L1-WRAP- G-F L2-GRID- G-F r (%) u (K) h (K) K.6 K.76 K.1399 K.98 x (mm) M u (kn m) F (kn) F (measured) 74.1 a 72. a (kn) Ratio (%) 91% a 63% a 126% 136% a Earthquake simulator maximum force capacity. Fig. 18. Strain, stresses, internal, and external forces in retrofitted masonry specimen. The effect of the thickness of the composite material has been ignored to simplify the design equations. The compressive force in the masonry C is determined from Whitney s equivalent stress block. According to the notation in Fig. 18, the following equation was derived :5ðr f ltþe f 3Kf k ta ZKN (5) where T is the tension force in the fiber; f k, compressive strength; 3, axial tensile strain in the fiber at the specimen edge computed based on linear variation of strains in the cross-section; E f Zfiber tensile modulus of elasticity; r f Z A f /A; A f is the fiber cross-sectional area; A, cross-sectional area of the specimen; x, compression zone length; l, cracking length. By dividing by specimen cross-sectional area and masonry characteristic compressive strength, this yields :5u l l K:8 x Z h (6) x L L where x, compression zone length; u, mechanical reinforcement ratiozr f E f 3 m /f k ; n, normalized compressive strengthzn/f k A; N, normal force. Solving Eq. (6) for x yields: p Kðh CuÞ C ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hðh C2:uÞ C1:6u x Z L (7) ð1:6kuþ The ultimate moment of resistance M u is given by: M u f k A Z :8x :5K:4 x L C:5u ðlkxþ2 :5K LKx (8) x 3L This method is used to calculate the lateral resistances of the full surface retrofitted specimens (i.e. S1-WRAP-G-F, S2-WRAP-A-F, L1-WRAP-G-F, and L2-GRID-G-F). The calculations were made based on FRP nominal material characteristics. Table 6 shows the predicted versus experimental lateral strengths. The predicted values were approximately 76% of the measured lateral resistance. The authors believe that this difference is mainly due to the difference between the nominal and real characteristics of the FRPs. 5. Findings and conclusions Five half-scale URM walls were built using half-scale brick units. These five walls were dynamically tested as reference specimens. Then, these reference specimens were retrofitted using composites and retested. As a consequence, a total of 11 specimens were tested on the earthquake simulator of ETHZ. This experimental research led to the following findings: The FRP retrofitting technique is effective in significantly increasing the in-plane strength, stiffness, and deformability of URM walls. The maximum axial strains measured in FRPs were approximately 5% of its nominal ultimate strains. For slender specimens, the vertical strain distributions along the specimens cross-sections were approximately linear even at failure. The retrofitting materials did not change the fundamental frequencies and the initial stiffness of the specimens. Simple linear elastic design approach predicted flexural strengths of the slender specimens on average 24% lower than their experimental strengths. Existing shear models predicted shear strengths ranging from 1 to 17% of the measured lateral strengths of the squat specimens. However, these specimens did no reach their ultimate strengths due to test set-up limitations. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:1.116/j.compositesb

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