# Experimental Research on Seismic Performance of Damaged Brick Walls Strengthened with Embedded Horizontal Steel Bars

Authors: Liu Tingbin; Jia Rubo; Pei Xianke; Zhang Jiawei; Zhao Jianchang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

Six brick masonry specimens (two unreinforced specimens, two reinforced specimens, and two specimens reinforced after being damaged), which have different aspect ratios, were tested under low-frequency cyclic loading. The seismic performances of these specimens, including failure characteristics, deformation capacity, carrying capacity, energy dissipation capacity, hysteresis characteristics, and stiffness degradation, were analyzed. The following results were obtained: the ductility of the damaged walls could be significantly improved after they were reinforced with embedded horizontal steel bars; the ultimate shear capacity of the damaged brick masonry walls with the aspect ratios of 1.8 and 0.5 was improved by 6.8% and 4.7%, respectively; the displacement corresponding to the ultimate bearing capacity was close to that of the unreinforced brick masonry wall; the hysteresis loop of the reinforced wall became plumper and encompassed a larger area; after the ultimate load was reached, a clear yielding platform appeared in the skeleton curve of the reinforced wall; the reinforced wall exhibited good ductility, after entering plastic stage; the energy dissipation capacity of the reinforced wall was significantly greater than that of the unreinforced wall. In conclusion, the seismic performance of the damaged brick masonry wall can be improved by embedding horizontal steel bars, and this reinforcing method can be applied in the postseismic reconstruction process.


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## Body

## 1. Introduction

The last two decades have witnessed mass casualties, heavy property loss, and severe damage to engineering structures caused by violent earthquakes. Seismic events in Chile [1], China [2], Haiti [3, 4], Nepal [5], Indonesia [6], Iran [7], and Europe [8] damaged or even demolished thousands of masonry structures. A main cause for casualties in the earthquakes is that a large number of unreinforced brick masonry structures (URM) still exist around the world. In the postdisaster recovery and reconstruction stage, economic and reliable restoration methods are generally needed to speed up the postdisaster reconstruction process.Various reinforcement methods are given in the design codes in different countries aiming at the reinforcement of damaged brick masonry structures [9–11], such as surface fiber reinforcement (FRP, BFRP, NSM-FRP, etc.) [12–14], joint reinforcement [15], steel reinforcement [16], and textile-mortar reinforcement [17]. For these reinforcement methods, a lot of research work has been carried out.In the area of masonry reinforcement, another interesting and relatively new technique used to repair brick or stone masonry is insertion of twisted stainless steel bars [18, 19] or CFRP strips [20] in horizontal joints, the purpose of which is to form enclosing loop to restrain the unreinforced masonry walls.For this type of technique, after slots (20–60 mm deep) are cut in the original joints, the steel bars or CFRP strips are inserted and then mortar is pasted. This allows preserving the fair-faced aspect of the masonry wall, without changing its original appearance, as the longitudinal bars are embedded with new mortar into the existing horizontal joints. Typically, longitudinal steel bars on both sides of the wall are tied by transverse steel bars. When the thickness of the walls is too large to bore and permit the transverse bars to pass through, the connection can be made with transverse bars, which run about 2/3 as long as the thickness of the wall and are anchored by injecting non-shrink high-strength mortar. Finally, a surface layer of new mortar, which completely covers the longitudinal bars, makes the reinforcement completely invisible and preserves the fair-faced aspect of the masonry.This retrofitting technique has been the subject of study of several researchers. The overall effectiveness of the method was studied by Ismail and Ingham [21], who find that through the reinforcing, not only the strength is increased about 434%, compared to the unreinforced walls, but also the ductility capacity of the walls is largely increased. Moreira et al. [22] tested the pull-out behaviour of twisted stainless steel bars in mortar joints, demonstrating the high bonding characteristics of the bars in mortar. Recently, Petersen et al. [23] proposed a method for a finite element modelling of unreinforced masonry walls strengthened with twisted steel bars, providing a valuable method for design purpose.In this paper, damaged brick masonry walls are chosen and hot-rolled plain steel bars are embedded in the walls, which is different from other researches. Experimental research on seismic performance of damaged brick walls strengthened with embedded horizontal steel bars was performed. The pseudostatic tests of six specimens of brick masonry walls, with different aspect ratios, were carried out under the action of low-frequency cyclic loading. The failure characteristics, carrying capacity, deformation capacity, energy dissipation capacity, hysteresis characteristics, and other seismic performances of unreinforced brick masonry walls, undamaged brick masonry walls reinforced by embedded bars, and damaged brick masonry walls reinforced by embedded bars were analyzed, respectively, and compared.


## 2. Testing Conditions

### 2.1. Specimen Design

The standard clay brick with a size of 240 mm × 115 mm × 53 mm was adopted, and its strength grade was MU7.5 (GB/T 2542-2012 [24]). M2.5 grade composite mortar was selected as the masonry mortar. The caulking material is YS-JGF (GB50728-2011 [25]), and it is produced by the Gansu Institute of Civil Engineering Science. The grade for the steel bars is HPB300 (GB1499.1-2008 [26]). The performance indexes of the caulking cement and steel bar are shown in Tables 1 and 2, respectively. According to GB/T50129-2011 [27], the measured shear strength fv0 and compressive strength f of the masonry were 0.19 MPa and 1.8 MPa, respectively.Table 1
Mechanical performance indexes of steel bar.
Specification
DiameterD (mm)
AreaAs (mm2)
Yield strengthfy (MPa)
Ultimate strengthft (MPa)
Elastic modulusEs (MPa)
HPB300
6.5
33.2
315
420
2.10 × 105Table 2
Performance indexes of caulking cement.
Specification
Compressive strength 28 d (MPa)
Flexural strength 28 d (MPa)
Bond strength 28 d (MPa)
Grip force (MPa)
YS-JGF
50
5.5
1.8
3.0Considering the loading capacity of testing equipment and the size of the wall piers between openings, the aspect ratios of specimens in the testing were chosen to be 1.8 and 0.5, respectively. The geometry size and reinforcement of the specimen are shown in Figure1. The brick walls were built on reinforced concrete base beams. The first layer of brick and the base beam were bonded with high-strength mortar to ensure that there was no sliding between the wall and the base beam during the horizontal loading process. The thickness of the mortar joint was controlled between 10 mm and 12 mm during the construction. After cured for 28 days, the wall, together with the base beam, was hoisted to the test platform and was fixed to the test platform by ground anchoring bolts. The specimens Q1 and Q2 were unreinforced brick masonry specimens; the specimens QA1 and QA2 were reinforced specimens before damaging; the specimens JQ1 and JQ2 were reinforced Q1 and Q2 specimens, which had undergone some damage, in advance, under the action of low-frequency cyclic loading. The basic parameters of the specimens and the vertical loading values are shown in Table 3.Figure 1
Geometry size and reinforcement of the specimens. (a) Geometry size and reinforcement of the specimen with aspect ratio of 1.80. (b) Geometry size and reinforcement of the specimen with aspect ratio of 0.50.
(a)
(b)Table 3
Basic parameters of specimens.
Test number
WidthB (mm)
HeightH (mm)
Aspect ratio (H/B)
Vertical pressureN (kN)
Compressive stressσ (MPa)
Reinforcement ratio (%)
Notes
Q1
1000
1800
1.80
240
1.00
0
URM
Q2
2000
1000
0.50
330
0.69
0
URM
QA1
1000
1800
1.80
240
1.00
0.061
Reinforced every 4 layers of brick
QA2
2000
1000
0.50
330
0.69
0.083
Reinforced every 4 layers of brick
JQ1
1000
1800
1.80
240
1.00
0.061
Reinforced every 4 layers of brick
JQ2
2000
1000
0.50
330
0.69
0.083
Reinforced every 4 layers of brick


### 2.2. Reinforcement Scheme

Horizontal slots, which are 30 mm deep and 12 mm wide, were cut, every 4 layers of brick and along the horizontal mortar joint, into the masonry, on every vertical plane of the specimen. The dust produced in the cutting process was cleaned, and the cut slots were moistened. The cement paste was painted, and the cement gum was embedded to half depth of the slots. Longitudinal steel bars were embedded in the slots and tied by transverse steel bars, with an interval of 300 mm along the specimen. Finally, the cement gum was pressed into mortar slots, and the pointing was completed.To ensure safety in the reinforcement process, 4 L20 × 4 steel angles and steel bars with a diameter of 16 mm were used to constrain the damaged specimen, as shown in Figure2(a). After the severely damaged bricks were removed, the caulking cement was injected into the cavity left, and some small cracks were sealed and repaired with 1 : 1 gluing cement paste. After the gluing cement became hardened, the temporary constraints of the specimen were removed. The specimen was strengthened according to the reinforcement method before damaged, as shown in Figures 2(b) and 2(c). The reinforced specimens were cured for 28 days.Figure 2
Reinforcing steps of damaged specimen. (a) Temporary constraints. (b) Slots on the specimen. (c) Embedding bar and pointing.
(a)
(b)
(c)


### 2.3. Loading Device of Tests

The specimens were tested according to the method described in JGJ101-2015 [28]. As shown in Figure 3, the vertical axial force was applied to the specimen by a hydraulic jack (with the maximum load being 3000 kN), with the steel frame beam as the reaction force support, and the vertical load kept constant throughout the testing process. As shown in Figure 4 (in the figure, Pcr is the test values of cracking load; Δcr is the displacement corresponding to cracking load), the horizontal force was applied by an hydraulic servo loading system (with the maximum load being 300 kN). A load-displacement double-control loading program was adopted. Load control was implemented before the specimen reached the estimated limit load, and the loading increment was reduced when close to the limit load. After the specimen reached the limit load, the displacement control was implemented. When the load on the specimen dropped to 85% of the limit load or a large crack appeared in the specimen, it was believed that the specimen could not be further loaded and the specimen had failed.Figure 3
Diagram and real photo of testing devices. 1, reaction force frame; 2, reaction wall; 3, jacking device; 4, displacement meter; 5, specimen; 6, cap beam; 7, actuator; 8, distribution beam; 9, base beam; 10, anchoring bolt.Figure 4
Horizontal loading method.


## 2.1. Specimen Design

The standard clay brick with a size of 240 mm × 115 mm × 53 mm was adopted, and its strength grade was MU7.5 (GB/T 2542-2012 [24]). M2.5 grade composite mortar was selected as the masonry mortar. The caulking material is YS-JGF (GB50728-2011 [25]), and it is produced by the Gansu Institute of Civil Engineering Science. The grade for the steel bars is HPB300 (GB1499.1-2008 [26]). The performance indexes of the caulking cement and steel bar are shown in Tables 1 and 2, respectively. According to GB/T50129-2011 [27], the measured shear strength fv0 and compressive strength f of the masonry were 0.19 MPa and 1.8 MPa, respectively.Table 1
Mechanical performance indexes of steel bar.
Specification
DiameterD (mm)
AreaAs (mm2)
Yield strengthfy (MPa)
Ultimate strengthft (MPa)
Elastic modulusEs (MPa)
HPB300
6.5
33.2
315
420
2.10 × 105Table 2
Performance indexes of caulking cement.
Specification
Compressive strength 28 d (MPa)
Flexural strength 28 d (MPa)
Bond strength 28 d (MPa)
Grip force (MPa)
YS-JGF
50
5.5
1.8
3.0Considering the loading capacity of testing equipment and the size of the wall piers between openings, the aspect ratios of specimens in the testing were chosen to be 1.8 and 0.5, respectively. The geometry size and reinforcement of the specimen are shown in Figure1. The brick walls were built on reinforced concrete base beams. The first layer of brick and the base beam were bonded with high-strength mortar to ensure that there was no sliding between the wall and the base beam during the horizontal loading process. The thickness of the mortar joint was controlled between 10 mm and 12 mm during the construction. After cured for 28 days, the wall, together with the base beam, was hoisted to the test platform and was fixed to the test platform by ground anchoring bolts. The specimens Q1 and Q2 were unreinforced brick masonry specimens; the specimens QA1 and QA2 were reinforced specimens before damaging; the specimens JQ1 and JQ2 were reinforced Q1 and Q2 specimens, which had undergone some damage, in advance, under the action of low-frequency cyclic loading. The basic parameters of the specimens and the vertical loading values are shown in Table 3.Figure 1
Geometry size and reinforcement of the specimens. (a) Geometry size and reinforcement of the specimen with aspect ratio of 1.80. (b) Geometry size and reinforcement of the specimen with aspect ratio of 0.50.
(a)
(b)Table 3
Basic parameters of specimens.
Test number
WidthB (mm)
HeightH (mm)
Aspect ratio (H/B)
Vertical pressureN (kN)
Compressive stressσ (MPa)
Reinforcement ratio (%)
Notes
Q1
1000
1800
1.80
240
1.00
0
URM
Q2
2000
1000
0.50
330
0.69
0
URM
QA1
1000
1800
1.80
240
1.00
0.061
Reinforced every 4 layers of brick
QA2
2000
1000
0.50
330
0.69
0.083
Reinforced every 4 layers of brick
JQ1
1000
1800
1.80
240
1.00
0.061
Reinforced every 4 layers of brick
JQ2
2000
1000
0.50
330
0.69
0.083
Reinforced every 4 layers of brick


## 2.2. Reinforcement Scheme

Horizontal slots, which are 30 mm deep and 12 mm wide, were cut, every 4 layers of brick and along the horizontal mortar joint, into the masonry, on every vertical plane of the specimen. The dust produced in the cutting process was cleaned, and the cut slots were moistened. The cement paste was painted, and the cement gum was embedded to half depth of the slots. Longitudinal steel bars were embedded in the slots and tied by transverse steel bars, with an interval of 300 mm along the specimen. Finally, the cement gum was pressed into mortar slots, and the pointing was completed.To ensure safety in the reinforcement process, 4 L20 × 4 steel angles and steel bars with a diameter of 16 mm were used to constrain the damaged specimen, as shown in Figure2(a). After the severely damaged bricks were removed, the caulking cement was injected into the cavity left, and some small cracks were sealed and repaired with 1 : 1 gluing cement paste. After the gluing cement became hardened, the temporary constraints of the specimen were removed. The specimen was strengthened according to the reinforcement method before damaged, as shown in Figures 2(b) and 2(c). The reinforced specimens were cured for 28 days.Figure 2
Reinforcing steps of damaged specimen. (a) Temporary constraints. (b) Slots on the specimen. (c) Embedding bar and pointing.
(a)
(b)
(c)


## 2.3. Loading Device of Tests

The specimens were tested according to the method described in JGJ101-2015 [28]. As shown in Figure 3, the vertical axial force was applied to the specimen by a hydraulic jack (with the maximum load being 3000 kN), with the steel frame beam as the reaction force support, and the vertical load kept constant throughout the testing process. As shown in Figure 4 (in the figure, Pcr is the test values of cracking load; Δcr is the displacement corresponding to cracking load), the horizontal force was applied by an hydraulic servo loading system (with the maximum load being 300 kN). A load-displacement double-control loading program was adopted. Load control was implemented before the specimen reached the estimated limit load, and the loading increment was reduced when close to the limit load. After the specimen reached the limit load, the displacement control was implemented. When the load on the specimen dropped to 85% of the limit load or a large crack appeared in the specimen, it was believed that the specimen could not be further loaded and the specimen had failed.Figure 3
Diagram and real photo of testing devices. 1, reaction force frame; 2, reaction wall; 3, jacking device; 4, displacement meter; 5, specimen; 6, cap beam; 7, actuator; 8, distribution beam; 9, base beam; 10, anchoring bolt.Figure 4
Horizontal loading method.


## 3. Experiment Results and Analyses

### 3.1. Failure Modes of Specimens

#### 3.1.1. Failure Modes of Unreinforced Specimens

For the specimen with the aspect ratio of 1.8, there were almost no indicating signs before cracks occurred. With the load reaching 82 kN, through cracks appeared promptly along the diagonal direction and developed rapidly. A large number of bricks in the diagonal direction were cut through, and the widest crack was located in the middle of the specimen, with the maximum width being about 13 mm. The failure mode is shown in Figure5(a).Figure 5
Failure modes of specimens. (a) Developing of cracks in Q1. (b) Morphology of Q1 after repairing (JQ1). (c) Developing of cracks in JQ1. (d) Developing of cracks in QA1. (e) Developing of cracks in Q2. (f) Morphology of Q2 after repairing (JQ2). (g) Developing of cracks in JQ2. (h) Developing of cracks in QA2.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)For the specimen with the aspect ratio of 0.5, when the load reached 143 kN, the crack occurred and a number of ladder-like cracks gradually developed along the mortar joint. When the load reached 180 kN, horizontal cracks appeared in the middle of the specimen, and all cracks in the corner of the specimen further extended. When the limit load was applied, the cracks in the corner and the middle of the specimen were basically connected, and some of the bricks were broken. The widest crack was located in the lower right corner of the specimen with the maximum width being about 15 mm, and the failure mode is shown in Figure5(e).


#### 3.1.2. Failure Modes of Undamaged Specimens Strengthened with Embedded Horizontal Steel Bars

For the specimen with the aspect ratio of 1.8, when the load reached 88 kN, subtle oblique cracks formed along the diagonal direction in the lower left corner and lower right corner. The cracks would further extended with the load increasing, accompanied by brittle sound during the loading process. At the same time, in other parts of the specimen, a number of oblique cracks appeared along directions parallel to the diagonal direction, and the cracks were narrow and densely distributed. When the limit load is reached, the oblique cracks along the diagonal direction developed into main through cracks, and the maximum crack width was about 4 mm. The failure mode is shown in Figure5(d).For the specimen with the aspect ratio of 0.5, when the load reached 152 kN, horizontal cracks appeared along the mortar joints in the lower part. When the load reached 190 kN, horizontal cracks appeared along the mortar joint in the middle part, and meanwhile, the ladder-like horizontal cracks appeared along the mortar joint in the lower right corner. When the load reached 200 kN, horizontal cracks appeared in the second mortar joint from top to bottom in the top right area. With the load increasing, new oblique cracks occurred along the diagonal direction, and the original oblique cracks continued to expand and were connected with the horizontal cracks in the middle part. Finally, oblique through cracks were formed, and some bricks near the oblique cracks were broken. The failure mode was shown in Figure5(h).


#### 3.1.3. Failure Modes of Damaged Specimens Strengthened with Embedded Horizontal Steel Bars

The damaged specimen Q1 was renumbered as JQ1 after it was reinforced. As shown in Figure5(b), in the initial loading process of JQ1, oblique cracks appeared immediately along the original cracking path (the diagonal direction), with the width being around 1 mm. In addition, there were almost no cracks produced in other parts. With the load increasing, cracks continued to expand slowly, and meanwhile, a number of narrow oblique cracks appeared in the direction parallel to the main crack in the middle of the specimen. The width of the main crack was about 5 mm when the specimen was failed, and the width of cracks in other parts was about 2 mm. The failure mode is shown in Figure 5(c).The damaged specimen Q2 was renumbered as JQ2 after it was reinforced. As shown in Figure5(f), a number of minor cracks appeared in the corner and middle of the specimen during the initial loading process. Then, many ladder-like cracks appeared on the right side of the specimen, and the original crack width increased slowly. Some of the repaired cracks on the upper right area and lower right area did not expand. The failure mode is shown in Figure 5(g).


### 3.2. Analysis of Failure Modes

It can be observed from the failure modes that the unreinforced specimen Q1 with the aspect ratio of 1.8 showed a typical brittle shear failure; the unreinforced specimen Q2 with the aspect ratio of 1.8 showed typical brittle shear-friction failure; the reinforced specimen QA1 with the aspect ratio of 1.8 showed typical ductile shear failure, and the reinforced specimen QA2 with the aspect ratio of 1.8 showed typical shear-friction failure with some ductility; although some cracks occurred along the original failure surface in the reinforced damaged specimens JQ1 and JQ2 during the initial loading stage, both of them still showed good ductility during the subsequent loading process. Because of the constraint effect of steel bars, all reinforced specimens exhibited a “crack but not collapse” characteristic under the ultimate load.


### 3.3. Load and Deformation

The shear bearing capacity and deformation of the specimens are shown in Table4. In the table, Pcr, Pu, and Pf are the test values of cracking load, limit load, and failure load, respectively; Δcr, Δu, and Δf are displacements corresponding to cracking load, limit load, and failure load, respectively; μ denotes the ductility coefficient and μ = Δu/Δcr; γc, γu, and γf represent the specimen rotation angle corresponding to cracking load, limit load, and failure load, respectively; Κcr and Κu are the increase values of the cracking load and ultimate load of reinforced specimen, respectively, compared with those of the unreinforced specimen with the same aspect ratio, respectively. δcr and δu are the increase values of cracking load and the displacement corresponding to the cracking load of embedded reinforced specimen, compared with those of the unreinforced specimen with the same aspect ratio, respectively.Table 4
Shear capacity of specimens and displacement of the top surface of specimen.
Test no.
P
cr (kN)
κ
cr (%)
Δcr (mm)
δ
cr (%)
γ
c
P
u (kN)
κ
u (%)
Δu (mm)
δ
u (%)
γ
u
P
f (kN)
Δf (mm)
γ
f
μ
Q1
81
—
1.91
—
1/942
88
—
3.45
—
1/521
88
3.45
1/521
1.81
QA1
88
8.6
1.95
2.1
1/923
103
17.1
5.30
53.6
1/339
78
16.68
1/108
2.72
JQ1
83
—
1.86
—
1/968
94
6.8
5.07
47.0
1/197
73
15.96
1/63
—
Q2
143
—
1.73
—
1/578
190
—
6.40
—
1/156
143
15.84
1/63
3.70
QA2
152
6.3
1.83
5.8
1/546
214
12.6
7.49
17.0
1/133
168
18.53
1/54
3.86
JQ2
155
—
1.81
—
1/552
199
4.7
6.33
—1.1
1/158
155
15.65
1/64
—For JQ1 and JQ2, even after repair and strengthening, there were still cracks in the wall, and thus the cracking load and the displacement were not included in the table. For specimen QA1 with the aspect ratio of 1.8, the cracking load and the ultimate load increased by 8.6% (Kcr) and 17.1% (Ku), respectively, compared with those of the unreinforced specimen Q1, while the displacements corresponding to the cracking load and the ultimate load increased by 2.1% (δcr) and 53.6%, respectively. The ultimate load and the corresponding displacement of specimen JQ1 increased by 6.8% and 47.0%, compared with those of specimen Q1. The ultimate load and the corresponding displacement of specimen QA1 were greater than those of specimen JQ1.For specimen QA2, the cracking load and ultimate load increased by 6.3% and 12.6%, compared with those of specimen Q2, respectively, while the displacements corresponding to cracking load and ultimate load increased by 5.8% and 17%, respectively. The ultimate load of specimen JQ2 increased by 4.7%, while the displacement corresponding to the ultimate load scarcely change compared with that of specimen Q2.


### 3.4. Hysteresis Curve and Skeleton Curve

The hysteresis curve and the skeleton curve of each specimen are shown in Figure6. It can be observed that: for specimen Q1 and Q2, the deformation was small during the initial loading stage, and the area encompassed by the hysteresis loop was also small. After cracking, specimen Q1 failed very soon, and the hysteresis loop terminated. For specimen Q2, with the cracks developing, the load increment became smaller, the hysteresis loop area increased gradually, the residual deformation started to increase, and the specimen stiffness began to degenerate. Finally, the hysteresis loop shifted to a horizontal axis, indicating the specimen stiffness decreased rapidly.Figure 6
Hysteresis curve and skeleton curve of specimen. (a) Hysteresis curve of specimen Q1. (b) Hysteresis curve of specimen Q2. (c) Hysteresis curve of specimen QA1. (d) Hysteresis curve of specimen JQ1. (e) Hysteresis curve of specimen QA2. (f) Hysteresis curve of specimen JQ2. (g) Skeleton curve of wall with the aspect ratio of 1.8. (g′) Magnification of the skeleton diagrams. (h) Skeleton curve of wall with the aspect ratio of 0.5. (h′) Magnification of the skeleton diagrams.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)For reinforced specimens QA1, QA2, JQ1, and JQ2, the hysteresis curves were similar to those of unreinforced specimens Q1 and Q2 during the initial loading process. After cracks occurred, the hysteresis loop of the reinforced specimens became plumper and encompassed a larger area. When the ultimate load was reached, the horizontal thrust of the actuator decreased, but the displacement still increased and its increment also increased. A significant descending section occurred in the hysteresis loop until the specimen failed. The hysteresis loops of specimens QA1 and QA2 were plumper and encompassed a larger area than specimens JQ1 and JQ2, respectively, during the stage from cracking to failure.It can be observed from the skeleton curves that the specimen was basically in the elastic stage before cracking, and the slope (elastic stiffness) of the skeleton curve of each specimen was almost the same in the elastic stage. The specimens QA1 and QA2 had a slightly larger slope, followed by the specimens Q1 and Q2, and the specimens JQ1 and JQ2 had the smallest slope. After cracking, both the masonry and the steel bars participated in bearing the load, and the ultimate bearing capacity of QA1, QA2, JQ1, and JQ2 were improved, compared with that of Q1 and Q2. After reaching the limit load, Q1 and Q2 exhibited significant brittleness and all the reinforced specimens demonstrated good ductility.


### 3.5. Stiffness Degeneration

The wall stiffness is defined asKn, which can be calculated according to formula (1).(1)Kn=+Pn+−Pn+Δn+−Δn,where Pn is the maximum load value of each loading cycle and Δn is the displacement value corresponding to the maximum load value. According to formula (1), the stiffness degradation curve of each specimen is shown in Figure 7.Figure 7
Stiffness degradation curves of specimens. (a) Stiffness degradation curve of wall with aspect ratio of 1.8. (b) Stiffness degradation curve of wall with aspect ratio of 0.5.
(a)
(b)It can be observed from Figure7 that the initial stiffness of specimen Q1 and QA1 was 130.4 kN/mm and 135.1 kN/mm, respectively, while the initial stiffness of Q2 and QA2 was 195.7 kN/mm and 200.5 kN/mm, respectively, which suggested that the reinforcement itself could not greatly improve the structural stiffness. Hence, the reinforcement would not result in a greater seismic load, which was favorable to the wall. The initial stiffness of JQ1 (125.3 kN/mm) is much close to that of Q1 (130.4 kN/mm), as is the case for JQ2 and Q2 (190.4 kN/mm and 195.7 kN/mm, respectively), which indicated that the initial stiffness of the damaged specimens could be improved by the reinforcement. However, the initial stiffness could not be fully restored, which mainly depended on physical and mechanical properties of the caulking cement and the construction technique.The stiffness degradation of all the specimens was similar. In the early loading stage, the stiffness degradation rate of the specimens was very large, but later on, it tended to be stable. For the specimens with the aspect ratio of 1.8, when the horizontal displacement reached 3.0 mm, the stiffness was reduced by 75% to 78%; for the specimens with the aspect ratio of 0.5, when the horizontal displacement reached 5.0 mm, the stiffness was reduced by 80%–83%.


### 3.6. Energy Dissipation Capacity

Energy dissipation value (E) [28] and equivalent viscous damping coefficient (he) were used to evaluate the energy dissipation capacity of the specimens, and the calculation formulas are shown in formulas (2) and (3), respectively. In addition, a calculating graph is shown in Figure 8. It is believed that a larger he represents a greater energy dissipation capacity. The equivalent viscosity coefficients at the moments of cracking and failure were calculated according to formulas (2) and (3) are listed in Table 5. where SABCD is the area encompassed by the hysteresis loop curve, while SOBE and SODF are the areas surrounded by two triangles, respectively.Figure 8
Calculating graph ofE and he.(2)
E
=
S
ABCD
,
(3)
h
e
=
1
2
π
⋅
S
OBE
+
S
ODF
S
ABCD
,Table 5
Energy dissipation capacity of specimens.
Specimen number
Cracking load
Ultimate load
E
c (mm2)
h
e,c
E
u (mm2)
h
e,u
Q1
634.61
0.083
670.04
0.089
QA1
687.18
0.091
2355.58
0.193
JQ1
—
—
2111.51
0.176
Q2
888.61
0.076
1294.31
0.081
QA2
1034.03
0.085
4520.28
0.174
JQ2
—
—
4064.25
0.152Before cracking, the energy dissipation capacity of the specimens was very small. For the specimens with the aspect ratio of 1.8, the energy dissipation of QA1 is just 8.3% greater than that of Q1, while for the specimens with the aspect ratio of 0.5, the energy dissipation of QA2 is 16.4% greater than that of Q2. After entering the elastoplastic stage, the energy dissipation ability of the specimens reinforced by embedded steel bars was improved, due to the participation of steel bars in bearing the load (QA1 increased by 252%, compared with Q1, while JQ1 increased by 215%, compared with Q1). Meanwhile, in this stage, with the number of cracks increasing sharply, the damage developed towards a more adequate extent. Besides, the cumulative energy dissipation capacity was also improved. Among the six specimens, the energy dissipation capacity of QA1 and QA2 were the largest, followed by that of JQ1 and JQ2. The energy dissipation capacity of Q1 and Q2 were the smallest. There was a similar law forhe and E.


## 3.1. Failure Modes of Specimens

### 3.1.1. Failure Modes of Unreinforced Specimens

For the specimen with the aspect ratio of 1.8, there were almost no indicating signs before cracks occurred. With the load reaching 82 kN, through cracks appeared promptly along the diagonal direction and developed rapidly. A large number of bricks in the diagonal direction were cut through, and the widest crack was located in the middle of the specimen, with the maximum width being about 13 mm. The failure mode is shown in Figure5(a).Figure 5
Failure modes of specimens. (a) Developing of cracks in Q1. (b) Morphology of Q1 after repairing (JQ1). (c) Developing of cracks in JQ1. (d) Developing of cracks in QA1. (e) Developing of cracks in Q2. (f) Morphology of Q2 after repairing (JQ2). (g) Developing of cracks in JQ2. (h) Developing of cracks in QA2.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)For the specimen with the aspect ratio of 0.5, when the load reached 143 kN, the crack occurred and a number of ladder-like cracks gradually developed along the mortar joint. When the load reached 180 kN, horizontal cracks appeared in the middle of the specimen, and all cracks in the corner of the specimen further extended. When the limit load was applied, the cracks in the corner and the middle of the specimen were basically connected, and some of the bricks were broken. The widest crack was located in the lower right corner of the specimen with the maximum width being about 15 mm, and the failure mode is shown in Figure5(e).


### 3.1.2. Failure Modes of Undamaged Specimens Strengthened with Embedded Horizontal Steel Bars

For the specimen with the aspect ratio of 1.8, when the load reached 88 kN, subtle oblique cracks formed along the diagonal direction in the lower left corner and lower right corner. The cracks would further extended with the load increasing, accompanied by brittle sound during the loading process. At the same time, in other parts of the specimen, a number of oblique cracks appeared along directions parallel to the diagonal direction, and the cracks were narrow and densely distributed. When the limit load is reached, the oblique cracks along the diagonal direction developed into main through cracks, and the maximum crack width was about 4 mm. The failure mode is shown in Figure5(d).For the specimen with the aspect ratio of 0.5, when the load reached 152 kN, horizontal cracks appeared along the mortar joints in the lower part. When the load reached 190 kN, horizontal cracks appeared along the mortar joint in the middle part, and meanwhile, the ladder-like horizontal cracks appeared along the mortar joint in the lower right corner. When the load reached 200 kN, horizontal cracks appeared in the second mortar joint from top to bottom in the top right area. With the load increasing, new oblique cracks occurred along the diagonal direction, and the original oblique cracks continued to expand and were connected with the horizontal cracks in the middle part. Finally, oblique through cracks were formed, and some bricks near the oblique cracks were broken. The failure mode was shown in Figure5(h).


### 3.1.3. Failure Modes of Damaged Specimens Strengthened with Embedded Horizontal Steel Bars

The damaged specimen Q1 was renumbered as JQ1 after it was reinforced. As shown in Figure5(b), in the initial loading process of JQ1, oblique cracks appeared immediately along the original cracking path (the diagonal direction), with the width being around 1 mm. In addition, there were almost no cracks produced in other parts. With the load increasing, cracks continued to expand slowly, and meanwhile, a number of narrow oblique cracks appeared in the direction parallel to the main crack in the middle of the specimen. The width of the main crack was about 5 mm when the specimen was failed, and the width of cracks in other parts was about 2 mm. The failure mode is shown in Figure 5(c).The damaged specimen Q2 was renumbered as JQ2 after it was reinforced. As shown in Figure5(f), a number of minor cracks appeared in the corner and middle of the specimen during the initial loading process. Then, many ladder-like cracks appeared on the right side of the specimen, and the original crack width increased slowly. Some of the repaired cracks on the upper right area and lower right area did not expand. The failure mode is shown in Figure 5(g).


## 3.1.1. Failure Modes of Unreinforced Specimens

For the specimen with the aspect ratio of 1.8, there were almost no indicating signs before cracks occurred. With the load reaching 82 kN, through cracks appeared promptly along the diagonal direction and developed rapidly. A large number of bricks in the diagonal direction were cut through, and the widest crack was located in the middle of the specimen, with the maximum width being about 13 mm. The failure mode is shown in Figure5(a).Figure 5
Failure modes of specimens. (a) Developing of cracks in Q1. (b) Morphology of Q1 after repairing (JQ1). (c) Developing of cracks in JQ1. (d) Developing of cracks in QA1. (e) Developing of cracks in Q2. (f) Morphology of Q2 after repairing (JQ2). (g) Developing of cracks in JQ2. (h) Developing of cracks in QA2.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)For the specimen with the aspect ratio of 0.5, when the load reached 143 kN, the crack occurred and a number of ladder-like cracks gradually developed along the mortar joint. When the load reached 180 kN, horizontal cracks appeared in the middle of the specimen, and all cracks in the corner of the specimen further extended. When the limit load was applied, the cracks in the corner and the middle of the specimen were basically connected, and some of the bricks were broken. The widest crack was located in the lower right corner of the specimen with the maximum width being about 15 mm, and the failure mode is shown in Figure5(e).


## 3.1.2. Failure Modes of Undamaged Specimens Strengthened with Embedded Horizontal Steel Bars

For the specimen with the aspect ratio of 1.8, when the load reached 88 kN, subtle oblique cracks formed along the diagonal direction in the lower left corner and lower right corner. The cracks would further extended with the load increasing, accompanied by brittle sound during the loading process. At the same time, in other parts of the specimen, a number of oblique cracks appeared along directions parallel to the diagonal direction, and the cracks were narrow and densely distributed. When the limit load is reached, the oblique cracks along the diagonal direction developed into main through cracks, and the maximum crack width was about 4 mm. The failure mode is shown in Figure5(d).For the specimen with the aspect ratio of 0.5, when the load reached 152 kN, horizontal cracks appeared along the mortar joints in the lower part. When the load reached 190 kN, horizontal cracks appeared along the mortar joint in the middle part, and meanwhile, the ladder-like horizontal cracks appeared along the mortar joint in the lower right corner. When the load reached 200 kN, horizontal cracks appeared in the second mortar joint from top to bottom in the top right area. With the load increasing, new oblique cracks occurred along the diagonal direction, and the original oblique cracks continued to expand and were connected with the horizontal cracks in the middle part. Finally, oblique through cracks were formed, and some bricks near the oblique cracks were broken. The failure mode was shown in Figure5(h).


## 3.1.3. Failure Modes of Damaged Specimens Strengthened with Embedded Horizontal Steel Bars

The damaged specimen Q1 was renumbered as JQ1 after it was reinforced. As shown in Figure5(b), in the initial loading process of JQ1, oblique cracks appeared immediately along the original cracking path (the diagonal direction), with the width being around 1 mm. In addition, there were almost no cracks produced in other parts. With the load increasing, cracks continued to expand slowly, and meanwhile, a number of narrow oblique cracks appeared in the direction parallel to the main crack in the middle of the specimen. The width of the main crack was about 5 mm when the specimen was failed, and the width of cracks in other parts was about 2 mm. The failure mode is shown in Figure 5(c).The damaged specimen Q2 was renumbered as JQ2 after it was reinforced. As shown in Figure5(f), a number of minor cracks appeared in the corner and middle of the specimen during the initial loading process. Then, many ladder-like cracks appeared on the right side of the specimen, and the original crack width increased slowly. Some of the repaired cracks on the upper right area and lower right area did not expand. The failure mode is shown in Figure 5(g).


## 3.2. Analysis of Failure Modes

It can be observed from the failure modes that the unreinforced specimen Q1 with the aspect ratio of 1.8 showed a typical brittle shear failure; the unreinforced specimen Q2 with the aspect ratio of 1.8 showed typical brittle shear-friction failure; the reinforced specimen QA1 with the aspect ratio of 1.8 showed typical ductile shear failure, and the reinforced specimen QA2 with the aspect ratio of 1.8 showed typical shear-friction failure with some ductility; although some cracks occurred along the original failure surface in the reinforced damaged specimens JQ1 and JQ2 during the initial loading stage, both of them still showed good ductility during the subsequent loading process. Because of the constraint effect of steel bars, all reinforced specimens exhibited a “crack but not collapse” characteristic under the ultimate load.


## 3.3. Load and Deformation

The shear bearing capacity and deformation of the specimens are shown in Table4. In the table, Pcr, Pu, and Pf are the test values of cracking load, limit load, and failure load, respectively; Δcr, Δu, and Δf are displacements corresponding to cracking load, limit load, and failure load, respectively; μ denotes the ductility coefficient and μ = Δu/Δcr; γc, γu, and γf represent the specimen rotation angle corresponding to cracking load, limit load, and failure load, respectively; Κcr and Κu are the increase values of the cracking load and ultimate load of reinforced specimen, respectively, compared with those of the unreinforced specimen with the same aspect ratio, respectively. δcr and δu are the increase values of cracking load and the displacement corresponding to the cracking load of embedded reinforced specimen, compared with those of the unreinforced specimen with the same aspect ratio, respectively.Table 4
Shear capacity of specimens and displacement of the top surface of specimen.
Test no.
P
cr (kN)
κ
cr (%)
Δcr (mm)
δ
cr (%)
γ
c
P
u (kN)
κ
u (%)
Δu (mm)
δ
u (%)
γ
u
P
f (kN)
Δf (mm)
γ
f
μ
Q1
81
—
1.91
—
1/942
88
—
3.45
—
1/521
88
3.45
1/521
1.81
QA1
88
8.6
1.95
2.1
1/923
103
17.1
5.30
53.6
1/339
78
16.68
1/108
2.72
JQ1
83
—
1.86
—
1/968
94
6.8
5.07
47.0
1/197
73
15.96
1/63
—
Q2
143
—
1.73
—
1/578
190
—
6.40
—
1/156
143
15.84
1/63
3.70
QA2
152
6.3
1.83
5.8
1/546
214
12.6
7.49
17.0
1/133
168
18.53
1/54
3.86
JQ2
155
—
1.81
—
1/552
199
4.7
6.33
—1.1
1/158
155
15.65
1/64
—For JQ1 and JQ2, even after repair and strengthening, there were still cracks in the wall, and thus the cracking load and the displacement were not included in the table. For specimen QA1 with the aspect ratio of 1.8, the cracking load and the ultimate load increased by 8.6% (Kcr) and 17.1% (Ku), respectively, compared with those of the unreinforced specimen Q1, while the displacements corresponding to the cracking load and the ultimate load increased by 2.1% (δcr) and 53.6%, respectively. The ultimate load and the corresponding displacement of specimen JQ1 increased by 6.8% and 47.0%, compared with those of specimen Q1. The ultimate load and the corresponding displacement of specimen QA1 were greater than those of specimen JQ1.For specimen QA2, the cracking load and ultimate load increased by 6.3% and 12.6%, compared with those of specimen Q2, respectively, while the displacements corresponding to cracking load and ultimate load increased by 5.8% and 17%, respectively. The ultimate load of specimen JQ2 increased by 4.7%, while the displacement corresponding to the ultimate load scarcely change compared with that of specimen Q2.


## 3.4. Hysteresis Curve and Skeleton Curve

The hysteresis curve and the skeleton curve of each specimen are shown in Figure6. It can be observed that: for specimen Q1 and Q2, the deformation was small during the initial loading stage, and the area encompassed by the hysteresis loop was also small. After cracking, specimen Q1 failed very soon, and the hysteresis loop terminated. For specimen Q2, with the cracks developing, the load increment became smaller, the hysteresis loop area increased gradually, the residual deformation started to increase, and the specimen stiffness began to degenerate. Finally, the hysteresis loop shifted to a horizontal axis, indicating the specimen stiffness decreased rapidly.Figure 6
Hysteresis curve and skeleton curve of specimen. (a) Hysteresis curve of specimen Q1. (b) Hysteresis curve of specimen Q2. (c) Hysteresis curve of specimen QA1. (d) Hysteresis curve of specimen JQ1. (e) Hysteresis curve of specimen QA2. (f) Hysteresis curve of specimen JQ2. (g) Skeleton curve of wall with the aspect ratio of 1.8. (g′) Magnification of the skeleton diagrams. (h) Skeleton curve of wall with the aspect ratio of 0.5. (h′) Magnification of the skeleton diagrams.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)For reinforced specimens QA1, QA2, JQ1, and JQ2, the hysteresis curves were similar to those of unreinforced specimens Q1 and Q2 during the initial loading process. After cracks occurred, the hysteresis loop of the reinforced specimens became plumper and encompassed a larger area. When the ultimate load was reached, the horizontal thrust of the actuator decreased, but the displacement still increased and its increment also increased. A significant descending section occurred in the hysteresis loop until the specimen failed. The hysteresis loops of specimens QA1 and QA2 were plumper and encompassed a larger area than specimens JQ1 and JQ2, respectively, during the stage from cracking to failure.It can be observed from the skeleton curves that the specimen was basically in the elastic stage before cracking, and the slope (elastic stiffness) of the skeleton curve of each specimen was almost the same in the elastic stage. The specimens QA1 and QA2 had a slightly larger slope, followed by the specimens Q1 and Q2, and the specimens JQ1 and JQ2 had the smallest slope. After cracking, both the masonry and the steel bars participated in bearing the load, and the ultimate bearing capacity of QA1, QA2, JQ1, and JQ2 were improved, compared with that of Q1 and Q2. After reaching the limit load, Q1 and Q2 exhibited significant brittleness and all the reinforced specimens demonstrated good ductility.


## 3.5. Stiffness Degeneration

The wall stiffness is defined asKn, which can be calculated according to formula (1).(1)Kn=+Pn+−Pn+Δn+−Δn,where Pn is the maximum load value of each loading cycle and Δn is the displacement value corresponding to the maximum load value. According to formula (1), the stiffness degradation curve of each specimen is shown in Figure 7.Figure 7
Stiffness degradation curves of specimens. (a) Stiffness degradation curve of wall with aspect ratio of 1.8. (b) Stiffness degradation curve of wall with aspect ratio of 0.5.
(a)
(b)It can be observed from Figure7 that the initial stiffness of specimen Q1 and QA1 was 130.4 kN/mm and 135.1 kN/mm, respectively, while the initial stiffness of Q2 and QA2 was 195.7 kN/mm and 200.5 kN/mm, respectively, which suggested that the reinforcement itself could not greatly improve the structural stiffness. Hence, the reinforcement would not result in a greater seismic load, which was favorable to the wall. The initial stiffness of JQ1 (125.3 kN/mm) is much close to that of Q1 (130.4 kN/mm), as is the case for JQ2 and Q2 (190.4 kN/mm and 195.7 kN/mm, respectively), which indicated that the initial stiffness of the damaged specimens could be improved by the reinforcement. However, the initial stiffness could not be fully restored, which mainly depended on physical and mechanical properties of the caulking cement and the construction technique.The stiffness degradation of all the specimens was similar. In the early loading stage, the stiffness degradation rate of the specimens was very large, but later on, it tended to be stable. For the specimens with the aspect ratio of 1.8, when the horizontal displacement reached 3.0 mm, the stiffness was reduced by 75% to 78%; for the specimens with the aspect ratio of 0.5, when the horizontal displacement reached 5.0 mm, the stiffness was reduced by 80%–83%.


## 3.6. Energy Dissipation Capacity

Energy dissipation value (E) [28] and equivalent viscous damping coefficient (he) were used to evaluate the energy dissipation capacity of the specimens, and the calculation formulas are shown in formulas (2) and (3), respectively. In addition, a calculating graph is shown in Figure 8. It is believed that a larger he represents a greater energy dissipation capacity. The equivalent viscosity coefficients at the moments of cracking and failure were calculated according to formulas (2) and (3) are listed in Table 5. where SABCD is the area encompassed by the hysteresis loop curve, while SOBE and SODF are the areas surrounded by two triangles, respectively.Figure 8
Calculating graph ofE and he.(2)
E
=
S
ABCD
,
(3)
h
e
=
1
2
π
⋅
S
OBE
+
S
ODF
S
ABCD
,Table 5
Energy dissipation capacity of specimens.
Specimen number
Cracking load
Ultimate load
E
c (mm2)
h
e,c
E
u (mm2)
h
e,u
Q1
634.61
0.083
670.04
0.089
QA1
687.18
0.091
2355.58
0.193
JQ1
—
—
2111.51
0.176
Q2
888.61
0.076
1294.31
0.081
QA2
1034.03
0.085
4520.28
0.174
JQ2
—
—
4064.25
0.152Before cracking, the energy dissipation capacity of the specimens was very small. For the specimens with the aspect ratio of 1.8, the energy dissipation of QA1 is just 8.3% greater than that of Q1, while for the specimens with the aspect ratio of 0.5, the energy dissipation of QA2 is 16.4% greater than that of Q2. After entering the elastoplastic stage, the energy dissipation ability of the specimens reinforced by embedded steel bars was improved, due to the participation of steel bars in bearing the load (QA1 increased by 252%, compared with Q1, while JQ1 increased by 215%, compared with Q1). Meanwhile, in this stage, with the number of cracks increasing sharply, the damage developed towards a more adequate extent. Besides, the cumulative energy dissipation capacity was also improved. Among the six specimens, the energy dissipation capacity of QA1 and QA2 were the largest, followed by that of JQ1 and JQ2. The energy dissipation capacity of Q1 and Q2 were the smallest. There was a similar law forhe and E.


## 4. Conclusions

This paper investigates the seismic performances of unreinforced brick masonry walls, reinforced brick masonry walls, and damaged brick masonry walls strengthened with embedded horizontal steel bars. Based on the analysis, the following findings are obtained:(1)
After the damaged brick masonry walls were reinforced with embedded horizontal steel bars, their ductility could be improved significantly. Because of the constraint of steel bars, these walls exhibited a “crack but not collapse” failure mode under the ultimate load.(2)
For the wall with aspect ratio of 1.8, the ultimate load and the corresponding displacement of specimen JQ1 (damaged and then strengthened) increased by 6.8% and 47.0%, respectively, compared with those of specimen Q1 (unreinforced). For the wall with aspect ratio of 0.5, the ultimate load of JQ2 (damaged and then strengthened) increased by 4.7% than that of specimen Q2 (unreinforced), while the displacement corresponding to the ultimate load scarcely increased.(3)
For the walls QA1, QA2 JQ1, and JQ2, their hysteresis curves were similar to those of unreinforced walls Q1 and Q2 during the initial loading process. After cracks occurred, the hysteresis loops of reinforced walls were plumper and encompassed a larger area. When the ultimate load was reached, the horizontal thrust of the actuator decreased, but the displacement still increased and its increment also increased. A significant descending section occurred in the hysteresis loop until the specimen failed. The hysteresis loops of specimens QA1 and QA2 were plumper and encompassed a larger area than specimens JQ1 and JQ2, respectively, during the stage from cracking to failure.(4)
After entering the elastoplastic stage, the energy dissipation capacities of reinforced walls QA1 and QA2 were the strongest, followed by those of QA1 and QA2 (damaged and then reinforced). The energy dissipation capacity of unreinforced walls Q1 and Q2 were the smallest, which was in good agreement with the failure modes of the walls.(5)
The method of embedding horizontal steel bars to reinforce damaged brick masonry walls can effectively improve their seismic performance. This method can be applied in the postseismic reconstruction process.



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*Source: 6520982-2020-02-10.xml*