Experimental and numerical evaluation of confined masonry walls retrofitted with engineered cementitious composites

Engineering Structures 207 (2020) 110249

Contents lists available at ScienceDirect

Engineering Structures journal homepage: www.elsevier.com/locate/engstruct

Experimental and numerical evaluation of confined masonry walls retrofitted with engineered cementitious composites Mingke Deng, Shuo Yang

T

⁎

School of Civil Engineering, Xi'an University of Architecture and Technology, Xi'an 710055, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Confined masonry walls Engineered cementitious composite (ECC) Retrofitting Cyclic loading Finite element analysis

This study presents experimental and numerical research on the in-plane behavior of unreinforced confined masonry walls retrofitted using engineered cementitious composite (ECC) coatings. The experimental results, obtained from cyclic loading tests, demonstrated that this retrofitting technique effectively increased the lateral strength of the walls and changed the failure modes under specific conditions. Simplified micro finite element models were established, in which non-thickness cohesive elements were used to represent the mortar joints, and the material model of the mortar was implemented in a subroutine and linked with ABAQUS finite element software using the VUMAT interface. The mechanical behaviors of the ECC were simulated using the concrete damaged plasticity model. The predictive capacity of the numerical models was verified through a comparable study between the simulation results and experimental data. The models, which were applied under monotonic loading, could adequately reproduce the main behavior of the experimental specimens. Subsequently, a numerical sensitivity analysis was conducted, the results of which suggested that the in-plane behavior of the retrofitted walls were significantly affected by the tensile properties of the ECC, and that all walls were affected by the mortar strength mainly in terms of the cracking load and stiffness.

1. Introduction Traditional unreinforced masonry structures are characterized by an inadequate seismic performance, which has been verified by a considerable number of earthquake disaster investigations. This poor behavior is generally attributed to the inappropriate properties exhibited by the masonry under tensile stress. In this context, unreinforced masonry structures can be combined with vertically and horizontally reinforced concrete elements (confining elements) to form the confined masonry (CM) structures, which have the benefit of providing efficient confinement for masonry walls and improving the deformation capability of the structures [1–3]. Nevertheless, CM walls can also suffer from serious damage when the spacing of the tie columns (vertical elements) is excessively large or the masonry panel confined by the tie elements is fabricated using a low-strength mortar [4–6]. On the other hand, unreinforced CM structures may also be vulnerable during rare earthquake events. For these reasons, particularly with older constructions, retrofitting approaches should be applied to enhance the performance of confined masonry structures. During the last decades, extensive retrofitting techniques have been proposed for masonry structures and validated experimentally. With these retrofitting approaches, the use of externally bonded composite ⁎

layers, fabric embedded in the inorganic matrices, and ferrocement or fiber-reinforced cementitious coatings as the strengthening systems has recently received increased attention. In [7], four full-scale initially damaged brick masonry walls were repaired using externally bonded carbon fiber reinforced polymer (FRP) strips and tested under in-plane cyclic loading up to failure. In [8], three hollow clay brick masonry walls were first tested to predefined degree of damage and then retrofitted using FRPs, and one wall was directly upgraded with FRP after construction. These experimental results exhibited that the load bearing and deformation capacity of the repaired/strengthened walls were similar or better than that of the original ones. Türkmen et al. [9] performed an experimental campaign in which the retrofitted clay brick masonry wallettes were subjected to the diagonal compression to assess the effectiveness of the single-sided fabric-reinforced cementitious matrix (FRCM) overlay on the in-plane behavior of the walls. Cyclic inplane loading tests on the FRCM strengthened non-ductile RC frames with masonry infill have been presented in [10], where the effects of the different FRCM configurations on the lateral strengths and deformation capacity of the retrofitted infilled frames were assessed. The results of the cyclic loading tests on CM walls retrofitted with ferrocement and GFRP were presented in [11], where the transformation of the failure mode of the walls after strengthening was emphasized. In [12],

Corresponding author. E-mail address: [email protected] (S. Yang).

https://doi.org/10.1016/j.engstruct.2020.110249 Received 5 July 2019; Received in revised form 15 December 2019; Accepted 15 January 2020 0141-0296/ © 2020 Elsevier Ltd. All rights reserved.

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

matrix, a smeared crack approach can be used with a softening under tension and plasticity during compression, whereas the linear elastic behavior up to a fracture without a compressive strength is applied for the composite grid material. During the past few years, the modeling approaches of fiber reinforced concrete used as the strengthening material have also been investigated and validated. S. Dehghan et al. [17,27] conducted numerical studies on the in-plane shear behavior of both solid and perforated masonry walls retrofitted with SFRC through 3D finite element modeling. In these studies, based on the fact that the constitutive model of the FRC is similar to that of concrete, the concrete damage plasticity (CDP) model inserted into ABAQUS [28], which is commonly adopted to simulate brittle or quasi-brittle materials, such as concrete, was used to reproduce the nonlinear behavior of the FRC. The engineered cementitous composite (ECC) is characterized by the pseudo strain hardening performance induced from multiple cracking under tension [29,30]. In addition, the multiple cracking of this material that occurs under shearing can be exhibited through an Ohno shear test [31] and an Iosipescu shear [32]. Based on these advantages, the ECC has already been proposed as an externally bonded material for the retrofitting of masonry elements [33–36]. The test results demonstrate that the shear resistance, the lateral stiffness, and the structural ductility of the retrofitted structural elements are significantly improved. In addition, the numerical models of the ECCretrofitted masonry elements proposed by some researchers have been validated and have provided insight into the enhanced performance of the structural elements retrofitted by this material. To reproduce the nonlinear behavior of the ECC as a strengthening layer to enhance the out-of-plane behavior of the masonry, S. Pourfalah et al. [37] employed a multi-linear plastic material model, of which the tensile behavior is represented by the tri-linear stress–strain curve. In [38], precast ECC plates for retrofitting the masonry beam on the tension and/or compression side were simulated using the CDP model with ABAQUS, where the plastic parameters used for the ECC were obtained through a sensitivity analysis or were set as the default values of ordinary concrete. The smeared rotating crack material model [39] and multi-surface Rankine-Rankine plasticity-based model [40] have also been adopted for the material model of the ECC. These material models were validated based on the results of the in-plane monotonic or cyclic loaded retrofitted masonry elements. In these numerical models of the ECC-retrofitted masonry members mentioned above, several approaches were adopted to account for the ECC-masonry interface, including the establishment of nonlinear interface elements between the ECC and the masonry elements, allowing a Coulomb-friction behavior with tensile debonding, and a coupling of the nodes of the ECC and masonry elements when assuming a full bond between them. In this study, the structural efficiency of the retrofitting technique using ECC coatings applied to the CM walls, the investigations of which are still rare in the literature, is assessed through in-plane cyclic lateral loading tests conducted on 12 test specimens. A numerical investigation of all experimental specimens as a validation of the numerical models developed for the ECC-retrofitted CM walls under in-plane monotonic loading was carried out, in which the simplified micro model and the CDP model (ABAQUS/Explicit [28]) were adopted to simulate the mechanical behavior of the masonry and the ECC. A good agreement between the load-displacement curves obtained from the experimental tests and the simulation, and the consistency of the failure modes, was observed. Finally, the numerical sensitivity analyses were implemented to investigate the effects of the ECC with different tensile constitutive laws and the variation in the mortar strength on the in-plane behavior of unretrofitted and retrofitted CM walls. The corresponding findings, which should be further verified by extended experiences, may contribute to the knowledge of the practical design for retrofitting of the CM walls using the ECC.

the masonry walls produced from aerated concrete and hollow brick retrofitted with steel fiber reinforced concrete (SFRC) panels were tested under the diagonal compression, and the strengths and energy capacity of these strengthened walls were discussed. From the results of the above tests on the retrofitted structural elements using cementitious composites, it can be concluded that the application of such approaches can improve the stiffness, lateral strength, and energy dissipation of the masonry members. In addition, a numerical analysis of these techniques for a seismic retrofitting of the masonry structures has been emphasized and applied for many years [13–17]. Regarding a finite element (FE) modeling of the retrofitted masonry members, one aspect of this subject is the establishment of a numerical model of the masonry. A modeling of the masonry structural elements can be categorized into the detailed micro-, simplified micro-, and macro-numerical models [13,17–19]. With a detailed micro modeling approach, the masonry units, the mortar and the brick-mortar interface are modeled in detail with distinct properties, generally using continuum elements accompanied with discontinuous elements or contacts. Consequently, despite the capacity to capture the complex cracking patterns of the masonry, considerably high computational costs are required, and the method is generally used to simulate relatively small masonry elements to determine all possible realistic crack patterns. In this context, a simplified micro modeling approach has been proposed and implemented [20,21]. With this approach, the mortar and the adjacent brick-mortar interface are lumped into a zero-thickness interface element, in which the tensile, shear, and/ or crushing failures of the masonry can be regarded. The units are expanded by half the mortar joint thickness to keep the geometry of the specimen unchanged. For the macro models, the continuum elements, homogenized by the nonlinearity of the masonry, are used to establish the integration of all components in the masonry. The material of the masonry in this type of the model is generally assumed by the softening anisotropic elastic-plastic model with a Rankine-type criterion under tension following a smeared crack approach [16,22]. This approach is commonly used for practical purposes where the general behavior of the components is the main subject of interest [23] and is particularly effective for an investigation of the average responses of the masonry elements from the viewpoint of computational efficiency. Another important aspect is the appropriate modeling of strengthening overlays and of the interface between the masonry substrates and overlays. In the literature, simulations of the masonry panels retrofitted with FRP have been extensively investigated and applied. In terms of modeling the FRP strips or grids for strengthening, the element type, the material model, and the interface between the FRP and the masonry substrate have been areas of focus in numerous studies. In [24], the FRP strips are directly tied to the masonry substrate, assuming a full bond between the surface of the masonry and the FRP. The constitutive material models selected for the FRP are characterized by the elastic behavior of the lamina without fracture and delamination failures. Singh et al. [25] adopted an orthotropic plasticity model developed from the Hill-type yield criterion to simulate the anisotropic nature of the FRP. Plane-stress quadrilateral elements were used to establish the model of the FRP strips, the nodes of which are directly connected to the nodes of the units in the masonry. Considering the debonding failure of the strips, the tensile properties of the FRP were calibrated to reflect the nonlinearity of the FRP-masonry interface. To model the behavior of composite materials consisting of fabrics embedded into a cementitious matrix, which is generally called textile reinforced mortar (TRM), some researchers have used a micro-modeling approach, by which the matrix and the fiber mesh are modeled separately, to establish additional elements representing the strengthening material and to tie the masonry substrate elements when assuming a perfect bond between them [15,16,26]. The quadrilateral plane stress elements or shell elements are usually adopted for the matrix model, in which the model of the reinforcement grid based on an equivalent smeared distribution of the fibers is embedded. For the material model of the 2

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

2. Experimental investigation

vertical confining elements were 240 (width) × 120 (depth) mm. On the top surface of the bottom beam, a groove 35 mm thick was applied to anchor the half thickness of the lowest course of the masonry panel to prevent the premature sliding between the wall and bottom beam. The tie elements have four Φ 12 (12 mm diameter) longitudinal bars with a yield strength of 372 MPa and an ultimate tensile strength of 405 MPa, and Φ 6 (6.5 mm diameter) stirrups with a yield strength of 338 MPa and an ultimate tensile strength of 405 MPa. The stirrups were intensively spaced at both ends of the tie elements and equally spaced at other parts of them. The details of the reinforcement in the confining elements are shown in Fig. 1b. The longitudinal reinforcement ratio of the tie columns was chosen to improve the bending capacity of the walls and make it more likely that the walls will exhibit a diagonal tension failure under shear-compression loading. To guarantee the connection between the masonry panel and tie columns, the masonry infill was fabricated prior to the casting of the concrete for the tie elements. In addition, three Φ 4 (4 mm diameters) steel wire meshes of 400 mm in length were used for the connection between the RC columns and the masonry wall, equally spaced across the toothed interface between them at each end of the wall. Table 1 summarizes the characteristics of all test walls. In each group of wall specimens, masonry panels constructed using a cementlime mortar of different strengths, containing an average cube compressive strength of 1.89 and 9.29 MPa, are included. A compression

The main objective of the experimental campaign is to assess the effectiveness of the retrofitting techniques for CM walls using externally troweled ECC coatings. First, the mechanical properties of the ECC for strengthening were quantified through the cubic compression test, the uniaxial compression test, and the uniaxial tension test. Subsequently, 12 test walls, which were designed to be approximately 1/2 reducedscale models, were tested under a combination of a constant vertical load and an in-plane reversed cyclic loading, and the obtained behavior of the ECC-retrofitted walls including different strengthening schemes (single-sided troweling and double-sided troweling) were assessed though the lateral strength, the failure mode and the deformation capacity. In the next section, the corresponding primary results of the experimental campaign are addressed.

2.1. Specimen configurations and material properties According to the common configurations of load bearing masonry walls in typical low- to medium-rise masonry buildings, all specimens were designed to be 2300 mm long, 1370 mm high, and 240 mm thick (two-leaf), resulting in a height to length aspect ratio of 0.6, as shown in Fig. 1a. The reduced-scale models were adopted considering the limitation of the test setup. The sectional dimensions of the horizontal and

1250

1250

120

120

1

3 (4)

2

3 (4)

350

2300

1

400

400

2

350

350

2300

350

6@200

2 12

Sec (2-2)

Filled groove

2 12

2 12 2 20

15

6@200 8@200

2 12

Filled groove 2 20

Sec (1-1)

ECC coating (full coverage)

Sec (3-3)

2 12 6@200

2 12 2 12 15

440

2 12

2 12

Filled groove

ECC coating (on single side)

240 50

2 12

2 12

2 12

240 50

2 12

6@200

240 50

(a)

2 12

Sec (4-4)

(b) Fig. 1. Configurations and dimensions of the specimens (mm): (a) facades of unreinforced and retrofitted CM walls, and (b) details of the retrofitting schemes and reinforcement of the confining elements. 3

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Table 1 Design of the tested specimens. Specimen

Wall state

Retrofitting pattern

Compressive strength of the mortar

Vertical stress (MPa)

Unretrofitted group CW-1-1 CW-1-2 CW-2-1 CW-2-2

Unretrofitted Unretrofitted Unretrofitted Unretrofitted

— — — —

1.89 1.89 9.29 9.29

0.3 0.5 0.3 0.5

Single-sided group SCW-1-1 SCW-1-2 SCW-2-1 SCW-2-2

ECC-retrofitted ECC-retrofitted ECC-retrofitted ECC-retrofitted

Covering Covering Covering Covering

wall wall wall wall

1.89 1.89 9.29 9.29

0.3 0.5 0.3 0.5

Double-sided group DCW-1-1 DCW-1-2 DCW-2-1 DCW-2-2

ECC-retrofitted ECC-retrofitted ECC-retrofitted ECC-retrofitted

Full Full Full Full

coatings coatings coatings coatings

1.89 1.89 9.29 9.29

0.5 0.6 0.3 0.5

one one one one

coverage coverage coverage coverage

side side side side of of of of

of of of of

the the the the

the the the the

variable differential transformers (LVDTs) were installed to measure the horizontal, vertical, and diagonal in-plane displacements of the walls. One LVDT, installed at the tie beam level and the center of the walls (on the retrofitted side for single-sided retrofitted walls), measured the horizontal displacement of the specimens relative to the strong floor of the laboratory (LVDT-1). Two LVDTs were diagonally attached to the walls (on the unretrofitted side for the single-sided retrofitted walls) to record the diagonal deformations (LVDT-2, LVDT-3). Two LVDTs were installed near the left and right ends of the wall to measure the vertical deformations induced by the bending or rocking of the walls (LVDT-4, LVDT-5). Finally, LVDT-6 was installed at the end of the bottom beam to monitor the probable sliding of the specimen with respect to the strong floor. In addition, some strain gauges were attached to the longitudinal and transverse reinforcement at the key locations to record the amount of strain at different loading stages. During the tests, the lateral load of the walls was continuously controlled and monitored by a load cell, and the cracking patterns were detected and marked at each loading stage. The loading procedure consisted of two phases, namely, forced- and displacement-controlled cycles. Prior to the cracking, which was detected through a visual inspection during the tests, the applied lateral load was gradually increased in 40-kN load increments. Next, the loading scheme changed to the displacement-controlled stage with drift increments of 0.15%. The loading stopped during the failure state of the walls, during which the lateral load decreased to lower than 85% of the maximum lateral load recorded during the test or a collapse of the walls possibly occurred. The loading scheme is shown in Fig. 4.

test for the mortar of each mortar strength level was carried out on twenty four 70.7 mm cubes. All masonry walls were constructed using solid clay bricks with nominal dimensions of 240 × 115 × 53 mm (length × width × height) using a bond in which the stretchers and headers alternate in every course resulting in a discontinuity of the head joints. The average compressive strength of the brick is 13 MPa. The thickness of the head and bed mortar joints is approximately 10 mm. The confining elements were fabricated using concrete with an average cubic compressive strength of 35.1 MPa. A compression test of the concrete was conducted on nine 100-mm cubes. For the retrofitted walls, four walls were retrofitted with an ECC coating on one side, and another four walls were retrofitted on both sides. To reduce the possibility of a delamination between the ECC coating and the wall, 15 mm thick overlays were troweled from the front (back) surface to the left and right ends of the wall successively. To obtain an adequate bond between the coatings and wall surfaces, the masonry panels were prewetted, and the surfaces of the confining elements were chiseled prior to strengthening. The bottom of the ECC coatings was also anchored to the groove of the bottom beams to exploit the shear performance of the material as much as possible. Details of the retrofitting schemes are shown in Fig. 1b. The ECC used for strengthening in this study was prepared using a 1.7% volume fraction of polyvinyl alcohol (PVA) fibers. According to the tensile stress–strain curves obtained from the uniaxial tensile tests, the average tensile strength with initial cracking σcr and the average ultimate tensile strength σtu of the ECC coatings can be determined to be 5.38 and 6.00 MPa, respectively. The ultimate tensile strain can reach 0.3%. The details of the test setup, configuration of the specimen, loading procedure for the uniaxial tensile test of the ECC are the same as those in [36]. The average cube and uniaxial compressive strength of the ECC coatings are 66.5 and 57.4 MPa, respectively, which were obtained from the compression tests in accordance with JGJ/T 70-2009 [41].

2.3. Discussion of the test results 2.3.1. Unretrofitted walls From the cracking process of the unretrofitted CM walls treated as the control specimens, some common characteristics can be seen. The walls showed a practically linear behavior until some fine stepped shear cracks formed in the central part or at the top corner of the walls. Next, the lateral load continued to increase until the peak load was reached, accompanied by a propagation of the existing cracks. As the displacement increased, some other cracks occurred resulting in the formation of a network of shear cracks, in addition, two appropriately diagonal primary shear cracks completely formed, predominately moving through the bed and head joints. From the hysteretic response of the unretrofitted walls, as shown in Fig. 5, it can be seen that at the larger displacement during the phase in which the lateral strength degraded, the lateral resistance and the stiffness of the wall did not clearly decrease, indicating the efficient confinement effect provided by the tie elements on the masonry panel. The average maximum resistances of the unretrofitted walls CW-1-1, CW-1-2, CW-2-1 and CW-2-2 obtained

2.2. Test setup and loading protocol The overall view of the test setup and the layout of the specimen are shown in Fig. 2. The test walls were subjected to the in-plane cyclic loading using a double-hinged servo-controlled hydraulic actuator reacting against the reaction wall. A pre-compression was applied to the wall using a vertical jack connected to the steel frame. The top of the wall was free to rotate, and the bottom was fixed to the floor of the laboratory. Constant vertical stresses of 0.3 MPa, 0.5 MPa, and 0.6 MPa were chosen to represent the overburden loads of the walls on the first floor of common multi-storey masonry buildings. A steel beam connected to the vertical jack was placed on the top of the wall to distribute the vertical load. The layout of the test instruments is depicted in Fig. 3. Six linear 4

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 2. Test setup.

Drift (%)

from the tests are 161.7, 191.2, 220.2, and 232.0 kN, respectively. It is indicated that the peak lateral strength of the unretrofitted walls increased with an increase in the mortar strength level or the vertical stress level. The displacements of the walls at a state of failure were large, indicating that the tie elements can considerably improve the deformation capacity of the masonry walls, as reported previously [42–44]. During the last cycles of the test, the primary shear cracks widened and a crushing of the masonry at the top corner of the wall occurred. In general, the failure modes of all unretrofitted walls were characterized by diagonal tension cracking. In addition, for the unretrofitted walls constructed using high strength mortar, more splitting cracks appeared on the bricks near the tie columns. The failure modes of all unretrofitted walls are shown in Fig. 6. 2.3.2. Retrofitted walls For the single-sided retrofitted CM walls, the behavior was nearly linear elastic until the initial cracking occurred. The first visible cracks initiated on the unretrofitted face of the walls, and the cracks initiated on the coatings appeared practically at the same time. As the damage pattern of the walls during the initial cracking phase, minor fine cracks appeared on the coatings and the stepped cracks went through the mortar joints, propagating from the upper corner to the central part of the walls. As the displacement increased, some inclined cracks formed on the strengthening coatings and appeared on the unretrofitted face of the walls, predominately going through the mortar joints. The hysteretic behavior of the single-sided retrofitted walls is shown in Fig. 5. From the hysteretic response curves, it can be seen that the shape of the loops was more widened compared with that of the unretrofitted walls

1.05 0.90 0.75 0.60 0.45 0.30 0.15 −0.15 −0.30 −0.45 −0.60 −0.75 −0.90 −1.05

First cracking Force control

1 cycle for each force level

Displacement control

3 cycles for each displacement level

Time Fig. 4. Loading protocol.

characterized by an obvious pinching phenomenon. It can be seen that the average lateral loads corresponding to the initial cracking are approximately 318 kN, 380 kN, 360 kN, and 440 kN for the specimens SCW-1-1, SCW-1-2, SCW-2-1, and SCW-2-2, respectively, and their maximum increase is approximately 166% compared to that of unretrofitted walls. As the maximum lateral load was reached, the displacements of the walls were reduced compared with those of unretrofitted walls. The average lateral resistances of specimens SCW-1-1, SCW-1-2, SCW-2-1, and SCW-2-2 are 318, 412, 389, and 449 kN, obtaining peak strength increases of 96%, 116%, 77%, and 94%,

Fig. 3. Instrumentation scheme illustrated by the single-sided retrofitted specimen: elevation views of (a) retrofitted side and (b) unretrofitted side. 5

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 5. Hysteretic responses of all specimens under cyclic loading.

coating from the wall, indicating the effective confinement for the walls provided by the strengthening coating. In addition, the lateral displacements of the single-sided retrofitted walls at the end of the test are considerably reduced compared with those of the unretrofitted walls. Nevertheless, the resistances of the former at failure are higher than or close to those of the latter. The behavior of the double-sided retrofitted walls was similar to that of the single-sided retrofitted walls before cracking, where the initial cracking loads of the former increased by 235%, 102%, 99%, and 100% compared to the corresponding values of unretrofitted walls. The initial fine cracks were detected at the bottom of the strengthening coatings for all double-sided retrofitted walls, after which the hysteretic loops exhibited a slight degradation in the lateral stiffness, as shown in Fig. 5. As the displacement increased, some discontinuous fine cracks initiated and propagated from the top corner of the walls to the midpoint of the bottom on the surface of the strengthening coatings for specimens DCW-1-1 and DCW-1-2. When the maximum lateral load was reached, minor fine cracks completely formed along the approximately diagonal direction on the surfaces of the coatings. The strengthening coatings exhibited a multi-cracking phenomenon during the pre-peak process of the loading. As shown in Fig. 5, the average lateral

compared with that of their unretrofitted counterparts, respectively. It can be concluded that the lateral strength of the single-sided retrofitted walls increased with an increase in the mortar strength level or the vertical stress level, which is similar to that obtained from the experimental results of unretrofitted walls. For all single-sided retrofitted walls, the crossed primary shear cracks formed completely on both sides of the wall at a displacement of 4–6 mm. The primary stepped cracks continued to widen and some other fine cracks formed and propagated across the previously formed primary shear cracks. This resulted in that the central part of the strengthening coatings, enclosed by shear cracks intersecting each other, detached from the masonry substrate and the lateral strength of the walls gradually deteriorated. At a displacement level of 10 mm for all single-sided retrofitted walls, at the intersection of the diagonal cracks, the cracked part of the strengthening coating buckled or nearly delaminated, ripping off a thin layer of the masonry substrate, and the test ended. In general, approximately diagonal tension cracks occurred on the retrofitted side of the walls, whereas stepped cracks propagating through the mortar joints dominated the crack pattern of the unretrofitted side, as shown in Fig. 7. Nevertheless, it can be observed that the stepped cracks did not extend to the retrofitted side of the wall by removing the strengthening 6

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 5. (continued)

the maximum lateral resistance. Owing to the occurrence of a premature failure within the local region of the groove used to anchor the bottom of the wall, the average lateral strength of specimen DCW-2-1 reached only 390 kN, which is almost the same as that of specimen SCW-2-1. The average maximum lateral resistance of the specimen DCW-2-2 is 603 kN obtaining an increase of 160% compared to that of the unretrofitted wall. During the subsequent process of loading, it can be seen that the tensile cracks almost extended over the entire length of the wall bottom with no obvious reduction in the lateral strength for specimen DCW-2-1, indicating that the wall exhibited a rocking failure mode at the end of the test. For specimen DCW-2-2, the lateral strength degraded gradually after the peak load. During the last cycles of the test, a slight toe crushing and spalling of the coatings at the bottom corner of the wall occurred, accompanied by a local medium fracture of the groove at the bottom of the wall. As shown in Fig. 5, the hysteretic response curves of specimens DCW-2-1 and DCW-2-2 have inverse “s” shaped loops characterized with high residual displacements, suggesting a feature of sliding included in the failure modes of these walls. In the case of sliding, the ultimate displacement of the specimen DCW2-1 will be substantially higher than the experimental value if the wall is continued to be loaded, as discussed in [45]. Since the vertical load applied to the specimen DCW-2-2 increased, the toe crushing occurred

resistances of specimens DCW-1-1 and DCW-1-2 are 562 and 571 kN, achieving strength increases of 247% and 199% compared with that of unretrofitted walls, respectively. It is indicated that the lateral strengths of the double-sided retrofitted walls, in which a diagonal-tension failure occurred, are almost the same even though the walls were subjected to the vertical loads of different levels. In the post-peak loading phase, some discontinuous inclined cracks formed near the primary shear cracks, and the cracked parts of the coatings, located in the central position of the walls on one side, gradually detached from the masonry substrate. The displacements of the two retrofitted walls under different vertical loads at failure are significantly decreased compared with those of the unretrofitted walls. From the hysteretic response of the specimens DCW-1-1 and DCW-1-2, it can be observed that the loops have a less obvious pinching phenomenon and are more widened when compared with those of the unretrofitted walls. The failure modes of specimens DCW-1-1 and DCW-1-2 are shown in Fig. 8. By removing the cracked coatings, it can be seen that the approximately diagonal cracks propagated through the brick and mortar along a practically identical path of the cracks formed on the coatings. For specimens DCW-2-1 and DCW-2-2, the tensile cracks continued to propagate toward the center of the bottom of the wall after the initial cracking. The lateral stiffness evidently decreased and the lateral strength increased slightly to reach 7

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 6. Failure modes of specimens (a) CW-1-1, (b) CW-1-2, (c) CW-2-1, and (d) CW-2-2.

3.1. Mesh and boundary conditions

resulting in a limited deformation capacity of this wall. The failure patterns of specimens DCW-2-1 and DCW-2-2 are shown in Fig. 8.

In these 3D finite element models, bricks (expanded units) and mortar joints are modeled separately according to the simplified micro modeling approach, as described in the previous section. The model employed (1) the zero-thickness cohesive elements (COH3D8) to represent the mortar joints and potential cracks to capture the fracturing of bricks, (2) the first-order, reduced integration hexahedral continuum elements (C3D8R) with an hourglass control for the bricks and concrete of the confining elements constructed around the masonry panel, (3) the 8-node linear hexahedral continuum elements (C3D8) for the ECC coatings, considering that the hourglass modes, appearing in the coatings modeled with C3D8R, can be avoided absolutely in this way founded through trial and error, (4) the Timoshenko beam elements (B31) for the steel wires used for connecting the tie columns and the masonry panel, and linear 2-node 3D-truss elements (T3D2) for the longitudinal steel rebars and stirrups. As observed in the experimental results, no separation occurred at the toothed interface between the tie columns and the masonry panel throughout the entire test process, and thus the interface between them was modeled with a tie constraint. For the model of the retrofitted walls, because the experimental results showed that the debonding failure of the strengthening layers does not occur until the failure state of the wall is approached, in which the debonding effects can be considered in the model by modifying the softening branch of the tensile constitutive law for the ECC, the coating models were assumed to be tied to the masonry elements in the numerical models. The reinforcement was embedded inside the concrete material, which assumes full compatibility between the reinforcement and the concrete. Based on the results of the mesh convergence study, a solid element with a width and length of 20 mm and a thickness of 30 mm was used for the expended units and the confining elements; meanwhile, a solid element of 15 mm in the thickness direction with the same geometry as the substrate masonry elements was used for the ECC coatings. The details of the mesh convergence study are described in the following sections. A typical numerical model and the corresponding meshed components are shown in Fig. 9. In terms of boundary conditions, the base and both ends of the bottom beam were assumed to be constrained in all directions of the

3. Numerical modeling Because of the expensive and time-consuming process of experimental testing, the finite element method can usually be used to thoroughly understand the behavior of unreinforced and retrofitted masonry walls under in-plane loading. Moreover, numerical modeling can be considered to conduct a parametric analysis investigating the effects of different parameters, such as various strengthening schemes and a wide range of conditions the walls are subjected to, on the response of the walls. In this study, the general purpose finite element package ABAQUS was used to establish three-dimensional finite element models, in which the simplified micro modeling approach was adopted for reproducing the behavior of the test walls and relevant expanded analyses, considering its acceptable computational costs (10–20 h of CPU time was used for all models in this study) and the capacity of reproducing the actual crack patterns of the masonry. To establish the FE models of the masonry infill, a solid panel was first modeled with the same geometry as its prototype, and cohesive elements were then inserted into the position of the mortar joints and replaced in the middle of the bricks to form potential cracks via a code complied using the Python script. In this way, the time-consuming process of generating the meshed models was avoided, and a correct sequencing of the number of nodes for the interface elements was easily guaranteed. In addition, the cohesive elements intersect with voids and share the nodes of adjacent elements to allow a co-ordination of the deformation, which was previously verified to be reliable [24]. Regarding the analysis technique applied, an explicit analysis procedure was adopted for the current problem because of the highly nonlinear behaviors of the masonry and the strengthening coating. The deterioration of these materials often results in convergence difficulties in an implicit analysis algorithm, whereas an explicit analysis is capable of adequately processing such degradation. In addition, for a quasi-static analysis, the selected loading rate must be controlled to ensure a small ratio of the kinetic energy to the internal energy of the entire model. 8

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 7. Cracking patterns of single-sided retrofitted walls at a displacement of 8 mm: (a) unretrofitted and (b) retrofitted surfaces of SCW-1-1 in the push loading direction; (c) unretrofitted and (d) retrofitted surfaces of SCW-1-2 in the pull loading direction; (e) unretrofitted and (f) retrofitted surfaces of SCW-2-1 in the pull loading direction; and (g) unretrofitted and (h) retrofitted surfaces of SCW-2-2 in the push loading direction.

acceptable accuracy and smaller computation costs compared with the cyclic displacement loading, as indicated in previous studies [13,46–48].

translational degrees of freedom. The constant vertical pressure was uniformly applied to the top of the cap beam, and a linearly incremental monotonic displacement load was applied to the end nodes of the upper bond beam elements, as shown in Fig. 10. For the models of the retrofitted CM walls, it should be noted that the lateral displacement load was not applied to the strengthening coatings tied on the front and back sides of the walls, and the vertical pressure was not applied to the coatings, which is the same as in the experiments conducted. The monotonic horizontal displacement protocol was adopted based on the

3.2. Material models used in the numerical analysis The concrete damage plasticity (CDP) model, as mentioned in the section above, was adopted to simulate the nonlinear mechanical behavior of the ECC. The CDP model considers both tensile cracking and 9

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 8. Failure modes of specimens (a) DCW-1-1, (b) DCW-1-2, (c) DCW-2-1, and (d) DCW-2-2.

commonly combined with the damage index in the loading and unloading regimes, as depicted in Fig. 11. The uniaxial stress–strain relation of the ECC under compression is represented by the curve proposed by Sargin [51], in which the compressive strain corresponding to the peak strength is set to 0.4%, as dipicted in Fig. 12a. The uniaxial tensile stress–strain curve is simplified through a tri-linear model, including linear elastic, strain hardening, and strain softening stages,

compressive crushing, which is usually characterized through an isotropic scalar damage evaluation. The yield function proposed by Lubliner et al. [49] and developed by Lee and Fenves [50] is adopted in this model and is represented by the surface of the effective stress space, the evaluation of which is accomplished through the strain softening (stiffening) law of the material under tension and the strain hardening followed by the strain softening law during compression, which are

Fig. 9. The FE model of the single-sided retrofitted specimen: (a) meshed model of the retrofitted CM wall, (b) meshed part of the ECC coating, (c) meshed model of reinforcement, and (d) models of the mortar and potential cracks. 10

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

its asymptote, is set to the default value of 0.1.

• Parameter K , which is involved in the yield function and used to c

define the shape of the failure surface in the deviatoric plane, is set to the default value of 0.667. The ratio fb0/fc0, which is one of the parameters used to define the yield function, can be obtained through an input parameter identification approach proposed in the available literature [53,54]. As demonstrated in these studies, the path of the stress can significantly influence the optimum values of the input parameters of the CDP model. Therefore, four standard tests, namely, the uniaxial compression test, the uniaxial tensile test, the four-point bending test, and the Iosipescu shear test, were simulated to calibrate the parameter fb0/fc0. It was found that the numerical results match the experimental or theoretical results with a minimum average error as the fb0/fc0 were set as 1.05. More detailed descriptions of these experimental tests are provided in the literature [32,55]. The dilation angle ψ, which is involved in the non-associated potential and measured in the p-q plane at a high confining pressure, is set as 36°, which is also based on the parameter identification approach mentioned above [53,54].

•

Fig. 10. The boundary conditions of the numerical model.

•

σt σ t0 wt = 0

wt = 1 (1 − d c ) E0

A comparison between the experimental and theoretical results and the numerical results obtained from the models with fb0/fc0 = 1.05 and ψ = 36° is shown in Fig. 13. It is worth noting that, because the minimum average error was used for identification of the parameters, the curves numerically obtained are not exactly coincident with the corresponding curves derived experimentally or empirically. In addition to the ECC coating, the CDP model was also used to simulate the nonlinear behavior of the extended units and the concrete, as implemented in previous studies [56–58]. The values of ψ, ε, fb0/fc0, and Kc for both materials were set to 30°, 0.1, 1.16, and 0.667, respectively, which were found to be appropriate to match the numerical results with the experimental results. To simulate the crushing of the masonry under compression, the uniaxial compressive stress–strain curve proposed by Kaushik et al. [59] was used to represent the uniaxial compressive behavior of the expanded units. Considering that the tensile behavior of the brick is mainly dependent on the localized cracks, the linear elastic behavior in the pre-cracking stage followed by a bilinear softening stress-crack displacement curve [60] was used to define the tensile model of the units, where the area under the post-peak curve represents the tensile fracture energy of the material, contributing to the mesh objectivity of the numerical results. The constitutive model for the units under compression and that of the post-peak phase under tension are shown in Fig. 14. The compressive behavior model proposed by Sargin was also used to represent the compressive behavior of the concrete, where the compressive strain corresponding to the peak strength can be calculated using the mechanical parameters of the concrete according to the Chinese code GB 50010-2010 [61]. The

E0 (1 − d t ) E0

(1 − d t )(1 − d c ) E0

wc = 0

ε

wc = 1

E0

Fig. 11. The uniaxial load cycle combined with the damage indexes and stiffness recovery factors.

where the tensile strain at failure can take into account the tensile fracture energy, which is independent of the mesh size [52] (Fig. 12b). In addition, the Drucker Prager hyperbolic function is used for the nonassociated potential. There are five plasticity parameters used to define the CDP model, namely, the dilation angle (ψ), eccentricity parameter (ε), ratio of the biaxial compressive strength to the uniaxial compressive strength (fb0/fc0), ratio of the second invariant of the deviatoric stress tensor in tensile meridians to that in compressive meridians (Kc), and viscosity parameter. Because the simulations were conducted by an explicit solver, the viscosity parameter was set to zero. Another four parameters, required to completely define the yield surface as well as the non-associated potential, are as follows:

• The eccentricity ε, which controls the deviation of the potential from

σtu σcr

50 40 30 20 10 0 0.0

GfI : Mode I fracture energy lch : Characteristic length of the element 2GfI ε f = εtu + σ tu lch

Tensile stress (MPa)

Compressive stress (MPa)

60

0.2

0.4

0.6

0.8

GfI lch

εcr

1.0

εtu

εf

Tensile strain (%)

Compressive strain (%)

(a)

(b)

Fig. 12. The constitutive laws used for the ECC under (a) uniaxial compression and (b) uniaxial tension. 11

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 13. Comparison of load-displacement or stress–strain curves and cracking patterns obtained from tests or an empirical equation and numerical analysis for (a) ECC dog-bone specimen under uniaxial tension [55], (b) ECC beam under four-point bending [55], (c) ECC Iosipescu specimen under a constant shear load acting on the center of the specimen [32], and (d) ECC prismatic model under uniaxial compression.

as indicated in [58]. Based on the fact that the monotonic displacement load was applied to the numerical models, it can be appropriately assumed that the deterioration of the material is not primarily dominated by the damage parameters. Therefore, no damage variables were considered in all models applied in this study. The material constitutive model of the longitudinal reinforcement averaged in the cracked and non-cracked regions of the concrete, the

average tensile stress-strain curve between cracked and non-cracked concrete was used to define the tensile behavior of the concrete, accounting for the tension stiffening effect after cracking [62]. In the CDP model, the degradation of the material stiffness can be considered based on the damage indexes in tension and compression regimes, as shown in Fig. 11. The hysteretic response of the structural elements can be substantially affected by the input damage parameters, 12

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 14. The constitutive laws used for the units under (a) uniaxial compression and (b) uniaxial tension.

experimental results in [65]. The selection of values for αb was carried out by matching the ascending branch of the load-displacement curves obtained from the analysis, using the models of unretrofitted specimens, to that of the experimental tests with generally consistent slopes. Meanwhile, the values of αh for the head joints are set slightly smaller than the values of αb for the bed joints, considering the effect of the non-fully filled mortar used in the former. The relationship of the two factors was assumed to be αh = 0.7 αb in this case, based on the fact that the lateral strength of the unretrofitted walls obtained from the analysis will severely decrease if the values of the factors selected for the bed and head joints are too small. The final values selected, which are also adopted for the models of all retrofitted walls, are listed in Table 2; τx and τy are the shear stresses in the in-plane and out-of-plane directions, respectively, and τcr is the cracking shear strength which can be calculated based on the tensile strength ft and the normal stress σn [65]. The post peak behavior of the mortar joints and the potential cracks are defined using the 3D multi-surface yield function, isotropic softening, and the associated and non-associated flow rules. This yield function, which has been assessed and developed by numerous researchers [20,21,69], generally involves three components, namely, the tension cut-off for the tension failure, the Mohr-Coulomb criterion for the shear failure, and the compression cap for the compressive failure of the masonry. The associated flow rules are used for the evolution of the tensile strength, whereas the non-associated flow rules are considered

equations of which can be found in [63], was adopted to account for the bond-slip effect in the modeling of the reinforcement embedded in the concrete elements. Nevertheless, for simplicity, the ideal elastic-plastic model was used for the tensile stress–strain relationship of the stirrups and steel wires. For the pre-peak behavior of the interface elements, the bond stress–slip relationship behaves non-linearly up to the peak strength, as indicated in other studies [64,65]. Accordingly, the bilinear shear stiffness is adopted in the pre-peak phase of the shear regime, and the stiffness of the interfacial components in the models can be determined as follows:

kn =

1 Em Eb h m Eb − Em

e = ⎧ k sx,y

1 Gm Gb , hm G b − G m

⎨ k cr = α k e , b,h sx,y ⎩ sx,y τcr = ft 1 +

(1)

τx2 + τy2 ⩽ τcr τx2 + τy2 > τcr

(2)

σn ft

(3) e k sx,y

where kn is the normal stiffness and is the elastic shear stiffness in the in-plane and out-of-plane directions, respectively. The calculation method of these three parameters is the same as that of [18]; in addition, Em and Gm are the equivalent elastic normal and shear modulus of the mortar joints, respectively, which can be calculated as follows by referring to [66]:

HEb Em Ew = nhb Em + (n − 1) h m Eb

Table 2 Summary of the interface parameters.

(4)

Symbol

where Ew is the elastic modulus of the masonry, which can be determined using Ew = 550 fm [59]; fm = the prism compression strength of the masonry which can be calculated through the relationship fm = 0.78f10.5 (1 + 0.07f2 ) , in which f1 and f2 are the average compressive strength of the brick and mortar, respectively [67]; H, hb, hm, and n are the height of the masonry assemblage, thickness of the bricks, thickness of the mortar joints, and stacking amounts, respectively; and Eb and Gb are the elastic normal and shear modulus of the bricks, respectively. The value of Eb can be calculated based on the relationship Eb = 4467f10.22 in accordance with [68], and the value of Gb can be obtained from G b = Eb [2(1 + v b)], where the Poisson’s ratio vb is cr adopted in accordance with [20]. In addition, k sx,y is the post-cracking shear stiffness in the in-plane and out-of-plane directions, respectively. Because there is no accurate estimation of the experimental shear deformation corresponding to the peak shear strength, which can be used cr cr to calculate k sx,y , as described in [65], the value of k sx,y can be dee termined by multiplying k sx,y with different constant factors (αb,h) for the bed and head joints, and the values should be set differently between the low- and high-strength mortar joints, with reference to the

Tension regime

kn (N/ mm3) ft/MPa GfI (N/

Bed joints

Head joints

Potential cracks

High strength

Low strength

High strength

Low strength

56.58

33.11

30.51

28.72

900

0.27 0.068

0.12 0.022

0.09 0.04

0.04 0.018

0.6 0.075

mm) Shear regime

13

e k sx,y

24.60

14.40

13.26

12.48

900

(N/ mm3) c0/MPa cr/MPa tanφ0 tanφr tanψ GfII (N/

0.38 0.02 0.75 0.65 0.0 0.68

0.17 0.01 0.75 0.65 0.0 0.22

0.12 0.007 0.75 0.65 0.0 0.40

0.06 0.004 0.75 0.65 0.0 0.18

1.3 0.08 0.70 0.65 0.0 0.70

mm) αb αh

0.11 –

0.18 –

– 0.08

– 0.13

– –

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

τs

Shear regime

c Tension regime

σn

ft

(a)

(b)

Fig. 15. Yield surface without the cap mode for (a) 2D and (b) 3D models. Table 3 Mechanical parameters of ECC, bricks, and concrete. Material

ECC Brick Concrete

Elastic

(8)

c σs (usp) = cr + (c0 − cr ) exp ⎜⎛− 0II usp ⎞⎟ ⎠ ⎝ Gf

(9)

Non-linear

E/MPa

ν

fcm/MPa

fcr/MPa

ftu/MPa

εtu(%)

Gf (N/mm)

17,182 7854 29,400

0.15 0.15 0.20

57.40 3.18 (4.64) 22.33

5.38 – –

6.00 0.60 2.23

0.30 – –

2.0 0.15 –

and for the non-associated plastic potential,

g2 =

Note: The value in the bracket represents the parameters for specimens of high mortar strength.

for the evolution of the shear strength and the compressive strength. Because the compressive failure of the masonry was simulated through the softening behavior of the expended units under compression, the elastic behavior was assumed for the cohesive elements under compression in this simulation, and the yield surfaces without the cap mode (Fig. 15) were employed herein. The user subroutine written in Fortran and the interface of VUMAT were used to implement these material models. The formulations of the yield surfaces are as follows: For the tension cut-off,

f1 (σ , u np) = σt − σtu (u np)

(5)

f σtu = ft exp ⎛⎜− tI u np ⎞⎟ G f ⎠ ⎝

(6)

whereas for the shear failure criterion,

τx2 + τy2 + σn tan φ − σs (usp)

τx2 + τy2 + σn tan ψ − c0

(10)

where σt, u np , and GfI are the normal tensile stress, normal plastic displacement, and mode-Ⅰ fracture energy, respectively; φ0, φr, c0, cr, usp , and GfII are the initial and residual friction angle, initial and residual cohesion, shear plastic displacement, and mode-Ⅱ fracture energy, respectively; and ψ is the dilatancy angle, which controls the uplift upon shearing. The values of the aforementioned input parameters in the interface elements are summarized in Table 2. The value of c0 for the bed joints can be calculated based on the relationship c0 = 0.125 f2 according to the masonry structure code of China (GB 50003–2011) [67]. Considering the fact that the head joints are not completely filled, the cohesion is assumed to be less than that of the bed joints. The ratio of the value of c0 for the head joints to that for the bed joints is assumed to be 1/3, which is determined through a calibration and based on the appropriate accordance of the cracking patterns of the numerical models and the tested walls. The elastic normal and shear stiffness of the head joints can then be derived using Eqs. (1) and (2). The value of c0 for the potential cracks is selected with reference to the literature [21,66] and combined with some adjustments. The values of the residual cohesion for the mortar joints and the potential cracks are calculated based on the relationship cr = 0.06c0 with reference to previous studies [65,70]. The tensile strength for the mortar joints is determined by the relationship ft = c0/1.4 with reference to [20]. The initial and residual friction angles for the mortar joints and the potential cracks can be obtained from the values explicitly mentioned in previous studies [20,70]. The values of the mode-Ⅰ and mode-ⅠI fracture energies for the mortar joints and the potential cracks can be determined based on the available studies [21,66,71] and the relative stable descending branch of the load-displacement curves obtained from the analysis. The mechanical properties of the ECC, bricks, and concrete are summarized in Table 3, where E and ν are the elastic modulus and Poisson’s ratio; fcm and ftu are the uniaxial compressive strength and the ultimate tensile strength; and fcr and εtu are the initial cracking strength and the ultimate tensile strain of the ECC coatings, respectively; and Gf is the tensile fracture energy of the ECC or the bricks. For the ECC, the value of E can be derived from the elastic stage of the experimental tensile stress–strain curves. The value adopted for the Poisson’s ratio follows the value used in [37]. The value of the tensile fracture energy is selected in accordance with that proposed in [52]. The remaining

Fig. 16. Effect of mesh density on load-displacement curves.

f2 (σ , usp) =

c tan φ = tan φ0 + (tan φr − tan φ0) ⎛⎜1 − exp ⎛⎜− 0II usp ⎞⎟ ⎞⎟ ⎝ Gf ⎠⎠ ⎝

(7) 14

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 17. Comparison between lateral load-displacement curves obtained from the FE analysis and envelope curves in the push direction extracted from the experimental results.

parameters can be determined through the aforementioned mechanical tests of the ECC. For the bricks, the value of E is set equal to that of Eb and the value of v is set equal to vb, which can be obtained through the aforementioned approaches. The value of fcm is set equal to the prism compression strength of the masonry calculated using the previously provided relationship. The values of ftu and Gf can be selected with reference to the available literature [60,72], and finally through an extensive calibration processes against the test results. For concrete, the values of all parameters can be determined by the recommended values or the relevant empirical equations provided by the concrete structure code of China (GB 50010–2010) [61].

u ̇ (i +

1 2

) = u̇(i - 12 ) +

Δt (i + 1) + Δt (i) (i) u¨ 2

u(i + 1) = u(i) + Δt (i + 1) u̇(

i+ 1 2

(11)

)

(12)

where u̇ and u¨ are the velocity and acceleration vector respectively, corresponding to the equations of motion. The superscript i refers to the 1 1 increment number, meanwhile i − 2 and i + 2 refer to the mid increment values. This method generally uses a large number of small time increments to ensure the accuracy of the analysis. In addition, the time increment should be less than the stability limit calculated by the element-element estimation as follows:

(

Le Cd

)

(

)

3.3. Analysis algorithm

Δtmax ⩽

ABAQUS/EXPLICIT, which has been validated and employed as the solver for the quasi-static analysis of the masonry [21,56], was chosen for the numerical analysis in this study. The explicit analysis procedure uses the central difference method (CDM) to integrate the equations of the motion for the nonlinear problem. Because no iterations are needed to find the displacements to satisfy the equations, this procedure has been mostly used to solve the dynamic or quasi-static problems involving complicated nonlinear constitutive laws, and is particularly effective for the prediction of the post-peak deterioration of the materials. The explicit central difference integration rules are as follows [28]:

where Le is the smallest element characteristic length in the model and Cd = E ρ is the current effective wave velocity, of which E and ρ are the modulus of elasticity and the density of the element respectively.

(13)

4. Validation of the model 4.1. Convergence study A mesh convergence study was first conducted on the aforementioned numerical models. The analysis for the model of the specimen 15

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 17. (continued) Table 4 Comparison of stiffness, lateral strength, and displacement of the experimental and FE results. Specimen

Pmax,EXP (kN)

Pmax,FE (kN)

Pmax,EXP/Pmax,FE

Δu,EXP (mm)

Δu,FE (mm)

Δu,EXP/Δu,EF

CW-1-1 CW-1-2 CW-2-1 CW-2-2 SCW-1-1 SCW-1-2 SCW-2-1 SCW-2-2 DCW-1-1 DCW-1-2 DCW-2-1 DCW-2-2 Avg C.O.V (%)

163.4 190.7 217.8 243.6 317.9 436.8 417.9 441.4 588.9 577.6 416.1 635.0

163.1 199.8 234.1 263.9 327.9 414.5 414.0 447.6 586.4 584.3 433.8 596.1

1.00 0.95 0.93 0.92 0.97 1.05 1.01 0.99 1.00 0.99 0.96 1.07 0.99 0.05

12.0 17.0 10.0 20.0 4.0 6.0 6.0 7.0 6.0 7.0 6.3a 7.9

23.6 19.1 11.3 16.6 7.4 7.0 4.7 5.5 6.6 7.0 6.7a 8.5

0.51 0.89 0.88 1.20 0.54 0.86 1.28 1.27 0.91 1.00 0.94 0.93 0.93 0.26

Note: Pmax,EXP and Pmax,FE are the experimental peak load in the push direction and the numerical peak load, respectively, and Δu,EXP and Δu,FE are the experimental displacement in the push direction at failure and the numerical displacement at failure, respectively. a The value is the maximum displacement where a 20% reduction in the lateral resistance was not reached.

(length × width × height), respectively. A comparison of the numerical load-displacement curves and the experimental envelope curve of the specimen in the push direction are shown in Fig. 16. The former can be extracted from the reaction force of the tie-beam end and the

CW-1-1 under monotonic loading was used as an example. The expended units and the concrete component of the confining elements were discretized by the solid elements of 60 × 30 × 30 mm, 30 × 30 × 30 mm, 20 × 20 × 30 mm, and 20 × 20 × 20 mm 16

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

(a) CW-1-1

(b) CW-1-2

(c) CW-2-1

(d) CW-2-2

(e) SCW-1-1

(f) SCW-1-2 Fig. 18. Crack patterns of the numerical models at failure for unretrofitted specimens and double-sided retrofitted specimens, and at a displacement of 8 mm for single-sided retrofitted specimens.

accuracy of the results, a mesh size of 20 × 20 × 30 mm was adopted for the units and confining elements.

displacement of the unique node in the center of the tie beam, which is the same with the experimental tests. The latter was obtained from aforementioned hysteretic curves for the first loading cycle of each load/displacement level in the push direction. It can be seen that the differences between these cases are not remarkable except for that of 60 × 30 × 30 mm. To balance the computational costs and the

4.2. Numerical-experimental comparison The experimental envelope curves in the push direction and the 17

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

(g) SCW-2-1

(h) SCW-2-2

(i) DCW-1-1

(j) DCW-1-2

(k) DCW-2-1

(l) DCW-2-2 Fig. 18. (continued)

was assumed for the bottom of the coating models to make the numerical result to be generally consistent with that of the experiment. In addition, considering the scattering of the material properties, an appropriate adjustment of the tensile properties of the ECC coatings was conducted on the numerical model of the specimen DCW-2-2 to achieve a good matching of the failure modes for the simulation and experimental test. Finally, a tensile strength of 6.5 MPa and a reduced tensile fracture energy are adopted, based indirectly on a trial and error

numerical load-displacement curves are presented in Fig. 17. This figure illustrates the curves extracted from the analysis are capable of capturing the primary features and match the variation trend of the experimental load-displacement curves. Because the anchored region of the specimen DCW-2-1 was prematurely damaged, as mentioned above, the peak load is largely overestimated by the numerical model without adjustments to the material parameters input as compared with the experimental results. Therefore, a lower performance of the material 18

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

σt0

performance of the retrofitted walls changes by controlling the tensile properties of the ECC coatings, the uniaxial tensile models with different ultimate tensile strengths and ultimate tensile strains are applied for a parametric analysis. As observed from previous experimental results [73], for a normal mixture proportion of PVA-ECC, the ECC material generally contains a high ultimate tensile strength accompanied with a low ultimate tensile strain, and vice versa. Thus, three different constitutive laws of the ECC under tension (Fig. 19), given according to the nature of the material mentioned above, are used in the numerical model of the strengthening coatings, where the initial cracking strengths are both set to 80% of the ultimate tensile strengths and the mode-I fracture energy that represents the area under the descending branch of the stress–strain curve is set as 2.0 N mm for all constitutive laws. In addition, the uniaxial compressive strength of case 1 is set to 60 MPa and the uniaxial compressive strengths of cases 2 and 3 are both set to 50 MPa. The elastic modulus of case 1 is set to 15 GPa, while the modulus of cases 2 and 3 are both set to 13 GPa corresponding to the lower compressive strength. In addition, to extensively investigate the influence of the mortar strength level on the in-plane behavior of the CM walls and the effectiveness of this retrofitting technique, which can be considered an auxiliary device for the experimental tests on the retrofitted walls of different mortar strengths, the parameters defining the shape of the yield surface of brick-mortar interfaces, including the tensile strength and the cohesion combined with the fracture energy, are also used as the variables of another group of the sensitivity analyses. Table 5 summarizes the values of the parameters for the material model of mortar joints used in the sensitivity analysis. The compressive strengths of the bed joints were selected to represent the weak mortar, intermediate mortar, and strong mortar, respectively. The fracture energy of the mortar joints selected was reliable because the values fall within the range of variation for this parameter, as reported in a previous study [71]. The values of the factor αb,h for the weak mortar and intermediate mortar were set equal to those of the experimental specimens of a low mortar strength, and the values of αb,h were set equal to those specimens of a high mortar strength. The remaining parameters can be derived from the compressive strength of the bed joints through the relationships mentioned in Section 3.2. The numerical models of single- and double-sided retrofitted walls subjected to the vertical stress of 0.5 MPa, whose dimensions and material properties for confined masonry walls are the same as those of the specimen CW-1-2, were used for a sensitivity analysis of the variation in the ECC tensile properties. In addition, the numerical models of singleand double-sided retrofitted walls with the same mechanical properties as the ECC model reported in Table 3, subjected to a vertical stress of 0.5 MPa, were used for the analysis of unretrofitted and retrofitted walls with a variation of the mortar joint parameters. The mechanical properties of the brick units and tie columns are set to the same values as those of the experimental specimens. The objective of using a masonry substrate model constructed with a low strength mortar in the former analysis and applying the vertical stress of 0.5 MPa to the top of all models is to make it even more possible for the retrofitted wall models to exhibit a diagonal tension failure.

σ t0 = 5 MPa

Case 1

ε tu = 0.5%

Case 2

0.8σt0

Case 3

0.6σt0

εtu

3ε

tu

5ε

tu

Fig. 19. Tensile stress-strain relationships used for the sensitivity analysis.

calibration. Table 4 summarizes the comparison between the FE and test results in terms of the maximum resistance and the displacement corresponding to a failure state in which the lateral load reduced to 80% of the peak lateral strength of the specimens. The average value of Pu,EXP/Pu,FE is 0.99 with a C.O.V. of 0.05, and the average value of Δu,EXP/Δu,FE is 0.93 with a C.O.V. of 0.26. This indicates that the FE models are capable of estimating the maximum resistance with an acceptable accuracy, although accompanied with a relative high variation in the comparison of the displacement during a failure state. The crack patterns combined with a contour plot of the tensile equivalent plastic strain (PEEQT) at failure, or with specific displacement levels obtained from the FE analysis, are shown in Fig. 18 for all specimens. Because a monotonic displacement load was implemented, only the cracks in the push direction are detected in the numerical models. As indicated from this figure, the failure mode is dominated by the diagonal cracking for the FE models of unretrofitted CM walls, which is similar to that of the tested specimens. For the models of all single-sided retrofitted walls and double-sided retrofitted walls of a low mortar strength, the diagonal cracking of the strengthening coatings are satisfactorily captured. For the models of double-sided retrofitted walls of high mortar strength, the crack band is localized at the bottom of the wall, indicating that the rocking and sliding failure modes can also be captured well with these numerical models. A more ductile behavior without significant reduction in the lateral strength is obtained from some of the FE analyses for the retrofitted walls, which is associated with the fact that the tie connection between the strengthening coating model and the masonry substrate model inappropriately captures the premature debonding failure of the strengthening coatings, even if the properties of the strengthening coatings were equivalently modified when accounting for the delamination effects. 5. Sensitivity analysis results and discussion To investigate the influence of the variation in the input material parameters on the behavior of the retrofitted walls, the sensitivity of certain parameters in the material models was investigated through a numerical analysis. Based on the fact that it remains uncertain how the Table 5 Summary of the mortar joint parameters used in the sensitivity analysis. Type of the mortar

Position

Cube compressive strength f2 (MPa)

Tensile strength ft (MPa)

Initial cohesion c0 (MPa)

Residual cohesion cr (MPa)

Fracture Energy (N/mm)

GfI

GfII

Weak

Bed joints Head joints

2.5 0.28

0.14 0.047

0.20 0.066

0.012 0.004

0.028 0.023

0.28 0.23

Intermediate

Bed joints Head joints

5.0 0.56

0.20 0.067

0.28 0.093

0.017 0.006

0.060 0.028

0.60 0.28

Strong

Bed joints Head joints

7.5 0.75

0.24 0.079

0.34 0.11

0.020 0.007

0.068 0.03

0.68 0.3

19

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Fig. 20. Sensitivity analysis when varying the tensile properties of the ECC coatings for (a) single- and (b) double-sided retrofitted walls.

Table 6 Lateral strengths obtained from the experimental tests and sensitivity analysis when varying the constitutive law of the ECC under tension. Specimen/model

Retrofitting scheme

Tensile behavior of ECC

Pmax (kN)

ΔPC∗− C3 Pmax - REF

ΔPC∗ - C2 Pmax - REF

ΔPC∗ - C1 Pmax - REF

SCW-1-2 (REF) SCW-C1 SCW-C2 SCW-C3 DCW-1-1 (REF) DCW-C1 DCW-C2 DCW-C3 CW-1-2

Single-sided retrofitting

Reported in Table 3 Case-1 Case-2 Case-3 Reported in Table 3 Case-1 Case-2 Case-3 —

436.8 (push direction) 363.2 329.8 307.2 588.9 (push direction) 509.7 448.0 393.7 190.7 (push direction)

68.0% 29.4% 11.9% — 102.4% 60.8% 28.5% — —

56.1% 17.5% — — 73.9% 32.4% — — —

38.6% — — — 41.5% — — — —

Double-sided retrofitting

Unretrofitted

Note: Pmax is the experimental or numerical peak load; ΔPC∗− C1, ΔPC∗− C2 , and ΔPC∗− C3 are the differences in the peak loads between an experimental and numerical model and the retrofitted walls using the ECC of cases 1-3, respectively; Pmax-REF represents the peak load of the reference specimen CW-1-2. Table 7 Displacements at failure obtained from the experimental tests and sensitivity analysis when varying the constitutive law of the ECC under tension. Specimen/model

Retrofitting scheme

Tensile behavior of ECC

δmax (mm)

ΔδC∗ - EXP δmax - REF

ΔδC∗ - C1 δmax - REF

ΔδC∗ - C2 δmax - REF

SCW-1-2 (REF) SCW-C1 SCW-C2 SCW-C3 DCW-1-1 (REF) DCW-C1 DCW-C2 DCW-C3 CW-1-2

Single-sided retrofitting

Reported in Table 3 Case-1 Case-2 Case-3 Reported in Table 3 Case-1 Case-2 Case-3 —

6.0 (push direction) 8.2 16.1 17.2 6.0 (push direction) 9.9 12.4 14.2 17.0 (push direction)

— 12.9% 59.4% 65.9% — 22.9% 37.6% 48.2% —

— — 46.5% 52.9% — — 14.7% 25.3% —

— — — 6.5% — — — 10.6% —

Double-sided retrofitting

Unretrofitted

Note: δmax is the experimental or numerical displacement at failure corresponding to a decrease in the lateral strength of the walls to 80% of the maximum resistance previously recorded; ΔδC∗ - EXP , ΔδC∗ - C1, and ΔδC∗ - C2 are the differences in the displacements at failure between a numerical model and the retrofitted walls using the ECC employed in the experiments and the ECC of cases 1 and 2, respectively; δmax-REF represents the displacement of the reference specimen CW-1-2 at failure.

Fig. 22. Cracking and peak loads of unretrofitted and retrofitted wall models for the sensitivity analysis.

The lateral load-displacement curves obtained from the numerical sensitivity analysis varying the ECC properties are shown in Fig. 20. Accordingly, the peak strengths of the walls and the displacements at failure in the sensitivity analysis are summarized in Tables 6 and 7. From the analysis results, it can be seen that the properties of the ECC can significantly influence the lateral resistance of the retrofitted walls. The increases in resistances of the double-sided retrofitted walls when

Fig. 21. Sensitivity analysis when varying the properties of the mortar joints.

20

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

strength of 9.29 MPa differs from that of the model for the specimen DCW-2-2 used in the section 4.2 because no adjustment of the ECC tensile properties is carried out for the former to make a diagonal tension failure occur. It can be seen that the increase in the lateral strengths for all wall models decreases with an increase in the mortar strength. When the mortar strength of the wall is greater than 5.0 MPa, the increments of the lateral strengths for retrofitted walls owing to the increase in the mortar strength are insignificant. 6. Conclusions An experimental study was carried out to assess the efficiency of the retrofitting technique using ECC coatings applied to unreinforced confined masonry (CM) walls, in which four unretrofitted walls and eight ECC-retrofitted walls were tested under in-plane cyclic loads. To extend the analysis of the experimental tests, three-dimensional micro finite element models of the experimental specimens were established and calibrated based on the test results, and a numerical sensitivity analysis for the effect of the ECC tensile properties and the strength degree of the mortar on the in-plane response of the walls was then carried out using the proposed modeling approaches. Some conclusions drawn from the experimental and numerical analyses are as follows:

Fig. 23. Influence of the compressive strength of mortar on the lateral strengths for unretrofitted and retrofitted walls.

varying the tensile constitutive models of the ECC from cases 1–3 are more obvious than that of the single-sided retrofitted walls. Regarding the influence of the ECC on the deformation capacity of the retrofitted walls, it is worth noting that the displacements of the retrofitted walls at failure are not increased compared with those of unretrofitted walls, as both the experimental and numerical results demonstrate. Nevertheless, it can be seen from the numerical load-displacement curves that the residual lateral strengths of the retrofitted walls in the state where the lateral load decreases to 85% of the maximum resistance are considerably higher than the lateral strength of the unretrofitted walls, which is similar to that exhibited by the experimental results, indicating that the damage are mostly localized in the local region of the retrofitted walls, and thus the masonry panel confined by tie elements and the strengthening coatings still holds a considerable bearing capacity. When the ultimate tensile strain of the ECC exceeds 0.5%, the ultimate displacements can be clearly improved, particularly for single-sided retrofitted walls. The lateral load-displacement curves obtained from the sensitivity analysis of the variation in the cube compressive strength of the mortar joints are shown in Fig. 21. The cracking loads of all models, at which the initial diagonal cracking occurs, and the peak loads of all models are shown in Fig. 22. In these figures, U indicates unretrofitted walls, S shows single-sided retrofitted walls, D represents for double-sided retrofitted walls, W indicates a weak mortar, I is an intermediate mortar, and H is a strong mortar. The failure patterns of all models in the sensitivity analysis are a diagonal tension failure. From these curves obtained from the analysis, it can be seen that the strength of the mortar slightly influences the response curves of the retrofitted wall models before cracking. The effects of the mortar strength on the cracking load and the post-cracking lateral stiffness of all wall models are non-negligible. The cracking stiffness of the wall models containing the strongmortar elements considerably increased compared with that of the remaining wall models. For unretrofitted wall models and retrofitted models containing the elements of weak and intermediate mortar joints, the ascending region of the load-displacement curves between the cracking and peak is more apparent compared with that of the retrofitted models containing strong-mortar elements. As shown in Fig. 22, the cracking loads differ between the models of different mortar strengths. The variation in the cracking loads of the retrofitted walls is less than that of the unretrofitted walls. The ratios of the cracking load to the peak load fall within the range of 0.92–0.97 for unretrofitted wall models and retrofitted models containing the elements of weak and intermediate mortar joints. However, the cracking loads almost coincide with the peak loads for the retrofitted models of strong mortar. In addition, the lateral strengths of all models of the sensitivity analysis and of the models for the experimental specimens subjected to a vertical stress of 0.5 MPa are shown in Fig. 23. It should be noted that the lateral strength of the double-sided retrofitted wall model with a mortar

(1) Applying an ECC coating on one or both sides of a CM walls is an effective retrofitting technique for improving its in-plane performance. An ECC coating toweled on one side and on both sides of the wall can increase the lateral strengths within the range of 94–116% and 77–247%, respectively. (2) As indicated in the experimental and numerical analysis results, the displacement of retrofitted walls at failure is moderately less than that of unretrofitted walls. On the other hand, the residual lateral strengths of retrofitted walls at failure are substantially higher than the maximum lateral strengths of unretrofitted walls. (3) The proposed finite element models are capable of reproducing the in-plane response of the retrofitted CM walls with an acceptable accuracy, although some deviation can be detected from comparing the ultimate displacements of the experimental walls with those of their numerical counterparts. The crack patterns of all test CM walls and the change in failure mechanisms of the walls owing to a retrofitting are captured well by the numerical models. It can also be concluded from the numerical results that the concrete damage plasticity (CDP) model in ABAQUS, combined with the calibration of the input plasticity parameters, can be used to simulate the inplane behavior of the ECC under a monotonic shear-compression load. (4) With regard to the sensitivity of the numerical results to various tensile constitutive laws of the ECC, it is suggested that the ultimate tensile strength of the ECC can significantly influence the maximum resistance of the retrofitted walls. The ultimate tensile strain of the ECC has a considerable effect on the deformation capacity of the retrofitted walls. Furthermore, the results obtained from a numerical sensitivity analysis of the variation in the mortar strength indicate that the increase in the lateral strengths for all walls decreases with an increase of the mortar strength. The influence of the mortar strength on the cracking load and cracking stiffness of the retrofitted walls is not negligible. If the compressive strength of the mortar used for the walls is greater than 5.0 MPa, the increments in the lateral strengths induced by the increase in the mortar strength are negligible for the retrofitted walls when using the ECC coatings, as characterized by a tensile strength of 6.0 MPa. CRediT authorship contribution statement Mingke Deng: Conceptualization, Methodology, Resources, Supervision, Project administration, Funding acquisition. Shuo Yang: Conceptualization, Methodology, Validation, Formal analysis, 21

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

Investigation, Resources, Writing - original draft, Writing - review & editing, Project administration.

Conference on Natural Hazards & Infrastructure, Chania, Greece; 2016. [26] Garofano A, Ceroni F, Pecce M. Modelling of the in-plane behaviour of masonry walls strengthened with polymeric grids embedded in cementitious mortar layers. Compos B Eng 2016;85:243–58. [27] Dehghan SM, Najafgholipour MA, Kamrava AR, Khajepour M. Application of ordinary fiber-reinforced concrete layer for in-plane retrofitting of unreinforced masonry walls: test and modelling. Sci Iran 2018;25. [28] Simulia DS. ABAQUS 6.13 user’s manual, providence, RI, USA: DS SIMULIA Corp; 2013. [29] Li VC, Leung CK. Steady-state and multiple cracking of short random fiber composites. J Eng Mech ASCE 1992;118(11):246–2264. [30] Pan ZF, Wu C, Liu JZ, Wang W, Liu JW. Study on mechanical properties of costeffective polyvinyl alcohol engineered cementitious composites (PVA-ECC). Constr Build Mater 2015;78:397–404. [31] Li VC, Mishra DK, Naaman AE, Wight JK, LaFave JM, Wu HC, et al. On the shear behavior of engineered cementitious composites. Adv Cem based Mater 1994;1(3):142–9. [32] GPAG, Van Zijl. Improved mechanical performance: shear behaviour of strainhardening cement-based composites (SHCC). Cem Concr Res 2007;37(8):1241–7. [33] Kyriakides MA, Billington SL. Cyclic response of nonductile reinforced concrete frames with unreinforced masonry infills retrofitted with engineered cementitious composites. J Struct Eng ASCE 2013;2:04013046. [34] Lin YW, Wotherspoon L, Scott A, Ingham JM. In-plane strengthening of clay brick unreinforced masonry wallettes using ECC shotcrete. Eng Struct 2014;66:57–65. [35] Dehghani A, Nateghi-Alahi F, Fischer G. Engineered cementitious composites for strengthening masonry infilled reinforced concrete frames. Eng Struct 2015;105:197–208. [36] Deng MK, Yang S. Cyclic testing of unreinforced masonry walls retrofitted with engineered cementitious composites. Constr Build Mater 2018;177:395–408. [37] Pourfalah S, Cotsovos DM, Suryanto B. Modelling the out-of-plane behaviour of masonry walls retrofitted with engineered cementitious composites. Comput Struct 2018;201:58–79. [38] Singh SB, Patil R, Munjal P. Study of flexural response of engineered cementitious composite faced masonry structures. Eng Struct 2017;150:786–802. [39] Koutromanos I, Shing PB. Numerical study of masonry-infilled RC frames retrofitted with ECC overlays. J Struct Eng ASCE 2014;140(7):04014045. [40] GPAG, Van Zijl, de Jager DJA. Improved ductility of SHCC retrofitted unreinforced load bearing masonry via a strip-debonded approach. J Build Eng 2019;24:100722. [41] JGJ/T 70-2009. Standard for test method of basic properties of construction mortar. Beijing (CN); 2009. [42] Tomaževič M, Klemenc I. Seismic behaviour of confined masonry walls. Earthq Eng Struct Dyn 1997;26(10):1059–71. [43] Pourazin K, Eshghi S. In-plane behavior of a confined masonry wall. TMS J 2009;27:21–34. [44] Tomaževič M. Earthquake-resistant design of masonry buildings. Innovations in structures and construction. London; 1999. [45] Magenes G, Calvi GM. In-plane seismic response of brick masonry walls. Earthq Eng Struct Dyn 1997;26(11):1091–112. [46] Gattesco N, Amadio C, Bedon C. Experimental and numerical study on the shear behavior of stone masonry walls strengthened with GFRP reinforced mortar coating and steel-cord reinforced repointing. Eng Struct 2015;90:143–57. [47] Medeiros P, Vasconcelos G, Lourenço PB, Gouveia J. Numerical modelling of nonconfined and confined masonry walls. Constr Build Mater 2013;41:968–76. [48] Wang GJ, Li YM, Zheng NN, Ingham JM. Testing and modeling the in-plane seismic response of clay brick masonry walls with boundary columns made of precast concrete interlocking blocks. Eng Struct 2017;131:513–29. [49] Lubliner J, Oliver J, Oller S, Onate E. A plastic-damage model for concrete. Int J Solids Struct 1989;25(3):299–326. [50] Lee J, Fenves GL. Plastic-damage model for cyclic loading of concrete structures. J Eng Mech ASCE 1998;124(8):892–900. [51] Sargin M. Stress-Strain relationships for concrete and analysis of structural concrete sections. Canada: Ontario; 1971. [52] Zhang YX, Ueda N, Nakamura H, Kunieda M. Behavior investigation of reinforced concrete members with flexural strengthening using strain-hardening cementitious composite. ACI Struct J 2017;114(2):417. [53] Labibzadeh M. Damaged-plasticity concrete model identification for prediction the effects of CFRPs on strengthening the weakened RC two-way slabs with central, lateral and corner openings. Int J Struct Eng 2015;6(3):240–68. [54] Labibzadeh M, Zakeri M, Shoaib AA. A new method for CDP input parameter identification of the ABAQUS software guaranteeing uniqueness and precision. Int. J. Struct. Integr 2017;8(2):264–84. [55] Dai J. Experimental study on the mechanical behavior of HDC and shear performance of HDC beams. PhD thesis. Xi’an University of Architecture and Technology, Xi’an; 2017. [56] Dhanasekar M, Haider W. Explicit finite element analysis of lightly reinforced masonry shear walls. Comput Struct 2008;86(1–2):15–26. [57] Agnihotri P, Singhal V, Rai DC. Effect of in-plane damage on out-of-plane strength of unreinforced masonry walls. Eng Struct 2013;57:1–11. [58] Minaie E, Moon FL, Hamid AA. Nonlinear finite element modeling of reinforced masonry shear walls for bidirectional loading response. Finite Elem Anal Des 2014;84:44–53. [59] Kaushik HB, Rai DC, Jain SK. Stress-strain characteristics of clay brick masonry under uniaxial compression. J Mater Civil Eng 2007;19(9):728–39. [60] Park K, Paulino GH, Roesler JR. Determination of the kink point in the bilinear softening model for concrete. Eng Fract Mech 2008;75(13):3806–18. [61] GB 50010-2010. Code for design of concrete structures. Beijing (CN): 2010.

Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements The authors wish to acknowledge the funding support provided from National Natural Science Foundation of China (Grant No. 51878545). References [1] Liu XH, Zhang HX, Liu JW, Liu LQ. The seismic behavior of the brick masonry buildings strengthened with reinforced concrete structural columns. J Build Struct 1981;6:47–55. [2] Tomaževič M, Klemenc I. Verification of seismic resistance of confined masonry buildings. Earthq Eng Struct Dyn 1997;26(10):1073–88. [3] Riahi Z, Elwood KJ, Alcocer SM. Backbone model for confined masonry walls for performance-based seismic design. J Struct Eng ASCE 2009;135(6):644–54. [4] Wu H. Study on seismic performance and earthquake damage mechanism control of masonry school buildings PhD thesis Chengdu: Southwest Jiaotong University; 2013. [5] Cai GC, Su QW, Tsavdaridis KD, Degée H. Simplified density indexes of walls and tie-columns for confined masonry buildings in seismic zones. J Earthq Eng 2018:1–23. [6] Yekrangnia M, Bakhshi A, Ghannad MA. Force-displacement model for solid confined masonry walls with shear-dominated failure mode. Earthq Eng Struct Dyn 2017;46(13):2209–34. [7] Santa-Maria H, Alcaino P. Repair of in-plane shear damaged masonry walls with external FRP. Constr Build Mater 2011;25(3):1172–80. [8] ElGawady MA, Lestuzzi P, Badoux M. Static cyclic response of masonry walls retrofitted with fiber-reinforced polymers. J Compos Constr ASCE 2007;1(50):50–61. [9] Türkmen ÖS, De Vries BT, Wijte SNM, Vermeltfoort AT. In-plane behaviour of clay brick masonry wallettes retrofitted with single-sided fabric-reinforced cementitious matrix and deep mounted carbon fibre strips. Bull Earthq Eng 2019:1–41. [10] Ismail N, El-Maaddawy T, Khattak N. Quasi-static in-plane testing of FRCM strengthened non-ductile reinforced concrete frames with masonry infills. Constr Build Mater 2018;186:1286–98. [11] El-Diasity M, Okail H, Kamal O, Said M. Structural performance of confined masonry walls retrofitted using ferrocement and GFRP under in-plane cyclic loading. Eng Struct 2015;94:54–69. [12] Buyukkaragoz A. Shear behavior of aerated concrete and hollow brick walls strengthened with steel fiber-reinforced concrete panels. Mech Adv Mater Struct 2019:1–9. [13] Shakib H, Dardaei S, Mousavi M, Rezaei MK. Experimental and analytical evaluation of confined masonry walls retrofitted with CFRP strips and mesh-reinforced PF shotcrete. J Perform Constr Fac ASCE 2016;30(6):04016039. [14] Mantawy IM, Okail H, Abdelrahman A. In-plane lateral load behaviour of confined masonry walls retrofitted using carbon-fibre-reinforced polymers. Int J Mason Res Innov 2017;2(1):61–82. [15] Lignola GP, Prota A, Manfredi G. Nonlinear analyses of tuff masonry walls strengthened with cementitious matrix-grid composites. J Compos Constr ASCE 2009;13(4):243–51. [16] Wang X, Ghiassi B, Oliveira DV, Lam CC. Modelling the nonlinear behaviour of masonry walls strengthened with textile reinforced mortars. Eng Struct 2017;134:11–24. [17] Najafgholipour MA, Dehghan SM, Kamrava AR. In-plane shear behavior of masonry walls strengthened with steel fiber-reinforced concrete overlay. Asian J Civ Eng 2018;19(5):553–70. [18] Lourenço PB, Rots JG. Multisurface interface model for analysis of masonry structures. J Eng Mech ASCE 1997;123(7):660–8. [19] D'Altri AM, de Miranda S, Castellazzi G. Sarhosis V. A 3D detailed micro-model for the in-plane and out-of-plane numerical analysis of masonry panels. Comput Struct 2018;206:18–30. [20] Lourenco PB. Computational Strategies for masonry structures. PhD thesis. Delft; 1996. [21] Aref AJ, Dolatshahi KM. A three-dimensional cyclic meso-scale numerical procedure for simulation of unreinforced masonry structures. Comput Struct 2013;120:9–23. [22] Grande E, Imbimbo M, Sacco E. Finite element analysis of masonry panels strengthened with FRPs. Compos B Eng 2013;45(1):1296–309. [23] Lourenço PB, Rots JG, Blaauwendraad J. Continuum model for masonry: parameter estimation and validation. J Struct Eng 1998;124(6):642–52. [24] Zhang S, Yang DM, Sheng Y, Garrity SW, Xu LH. Numerical modelling of FRPreinforced masonry walls under in-plane seismic loading. Constr Build Mater 2017;134:649–63. [25] Singh M, Stavridis A. Nonlinear Analysis of Unreinforced Masonry Structures Strengthened with FRP Strips under In-Plane Lateral Loads. 1th International

22

Engineering Structures 207 (2020) 110249

M. Deng and S. Yang

[68] Liu GQ. The research on the basic mechanical behavior of masonry structure. PhD thesis. Hunan University, Changsha; 2005. [69] Lotfi HR, Shing PB. Interface model applied to fracture of masonry structures. J Struct Eng ASCE 1994;120(1):63–80. [70] Atkinson RH, Amadei BP, Saeb S, Sture S. Response of masonry bed joints in direct shear. J Struct Eng ASCE 1989;115(9):2276–96. [71] Stavridis A, Shing PB. Finite element modeling of nonlinear behavior of masonryinfilled RC frames. J Struct Eng ASCE 2010;136(3):2285–96. [72] Angelillo M, Lourenço PB, Milani G. Masonry behaviour and modelling. In: Angelillo M, editor. Mechanics of masonry structures. Vienna: Springer; 2014, p. 1–26. [73] Li VC, Wang SX, Wu C. Tensile strain-hardening behavior of polyvinyl alcohol engineered cementitious composite (PVA-ECC). ACI Mater J 2001;98(6):483–92.

[62] Maekawa K, Pimanmasn A, Okamura H. Non-linear mechanics of reinforced concrete; 2014. [63] Dehestani M, Mousavi SS. Modified steel bar model incorporating bond-slip effects for embedded element method. Constr Build Mater 2015;81:284–90. [64] Rahman Ataur, Ueda T. Experimental investigation and numerical modeling of peak shear stress of brick masonry mortar joint under compression. J Mater Civil Eng 2013;26(9):04014061. [65] Rahgozar A, Hosseini A. Experimental and numerical assessment of in-plane monotonic response of ancient mortar brick masonry. Constr Build Mater 2017;155:892–909. [66] Abdulla KF, Cunningham LS, Gillie M. Simulating masonry wall behaviour using a simplified micro-model approach. Eng Struct 2017;151:349–65. [67] GB 50003-2011. Code for design of masonry structures. Beijing (CN); 2012.

23