Cyclic Behavior of Mortarless Brick Joints with Different ... - MDPI

materials Article

Cyclic Behavior of Mortarless Brick Joints with Different Interlocking Shapes Hongjun Liu 1 , Peng Liu 1 , Kun Lin 1, * and Sai Zhao 2 1

2

*

Shenzhen Engineering Lab for Wind Environment and Technology, Shenzhen Key Lab of Urban & Civil, Engineering Disaster Prevention & Reduction, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, China; [email protected] (H.L.); [email protected] (P.L.) Zhengzhou Architectural Design Institute, Zhengzhou 450052, China; [email protected] Correspondence: [email protected]; Tel.: +86-755-2603-4653

Academic Editor: Jung Ho Je Received: 26 January 2016; Accepted: 29 February 2016; Published: 4 March 2016

Abstract: The framed structure infilled with a mortarless brick (MB) panel exhibits considerable in-plane energy dissipation because of the relative sliding between bricks and good out-of-plane stability resulting from the use of interlocking mechanisms. The cyclic behaviors of MB are investigated experimentally in this study. Two different types of bricks, namely non-interlocking mortarless brick (N-IMB) and interlocking mortarless brick (IMB), are examined experimentally. The cyclic behavior of all of the joints (N-IMB and IMB) are investigated in consideration of the effects of interlocking shapes, loading compression stress levels and loading cycles. The hysteretic loops of N-IMB and IMB joints are obtained, according to which a mechanical model is developed. The Mohr–Coulomb failure criterion is employed to describe the shear failure modes of all of the investigated joints. A typical frictional behavior is observed for the N-IMB joints, and a significant stiffening effect is observed for the IMB joints during their sliding stage. The friction coefficients of all of the researched joints increase with the augmentation of the compression stress level and improvement of the smoothness of the interlocking surfaces. An increase in the loading cycle results in a decrease in the friction coefficients of all of the joints. The degradation rate (DR) of the friction coefficients increases with the reduction in the smoothness of the interlocking surface. Keywords: mortarless brick joints; interlocking shapes; cyclic loads; shear-compression behavior; experiment

1. Introduction Reinforced concrete (RC) frame structures with masonry panels are known for their economic feasibility and low technology requirement. However, their disadvantage in terms of seismic behavior is increasingly highlighted, especially in high seismic-prone regions [1–4]. To improve seismic behavior, a conceptually novel system for framed masonry panels was proposed in [5]. According to the concept, the frame was infilled with a mortarless brick (MB) panel. An MB panel can dissipate energy because of the relative sliding of each brick and avoid out-of-plane failure through the interlocking mechanism (see Figure 1). A series of experiments on an MB panel infilled frame was carried out by the authors, and the results indicated that the MB panel exhibits considerable energy dissipation during cyclic loading and can significantly improve the seismic behavior of the frame structure [5]. To evaluate the contribution of the energy dissipation and lateral resistance of the MB panel to the frame, an equivalent model was introduced in [6]; the authors found that the energy dissipation of the MB panel results from friction between bricks.

Materials 2016, 9, 166; doi:10.3390/ma9030166

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Materials 2016, 9, 166 Materials 2016, 9, 166

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Figure 1. Reinforcement concrete frame with a mortarless brick (MB) panel. Figure 1. Reinforcement concrete frame with a mortarless brick (MB) panel.

Improvement of the energy dissipation of the MB panel requires some knowledge of the Improvement of the energy dissipation of the MB panel requires some knowledge of the particular particular mechanical properties of the novel component. However, previous research mainly mechanical properties of the novel component. However, previous research mainly focused on the focused on the shear and compression behaviors of traditional masonry with mortared brick shear and compression behaviors of traditional masonry with mortared brick units [7–12]; their units [7–12]; their results are unsuitable for dry stack masonry. Studies on the MB panel became results are unsuitable for dry stack masonry. Studies on the MB panel became active only in the last active only in the last decade. However, these recent studies mainly focused on the cyclic behavior of decade. However, these recent studies mainly focused on the cyclic behavior of non-interlocking non‐interlocking mortarless brick (N‐IMB) joints. Lourenco et al. [13,14] applied the couplet test to mortarless brick (N-IMB) joints. Lourenco et al. [13,14] applied the couplet test to investigate the investigate the shear‐compression behavior of dry stack stone joints. According to their research, the shear-compression behavior of dry stack stone joints. According to their research, the Mohr–Coulomb Mohr–Coulomb failure criterion can describe the characteristics of dry stone joints under different failure criterion can describe the characteristics of dry stone joints under different compression stress compression stress levels; the friction coefficients of the dry stone joints were obtained levels; the friction coefficients of the dry stone joints were obtained experimentally, and the cohesion experimentally, and the cohesion for the investigated joints could be neglected. Zuccarello et al. [15] for the investigated joints could be neglected. Zuccarello et al. [15] applied the traditional triple test applied the traditional triple test and confirmed that the shear‐compression behaviors of N‐IMB and confirmed that the shear-compression behaviors of N-IMB joints represent the Coulomb friction joints represent the Coulomb friction law. Lin et al. [16,17] proposed a new modified loading device, law. Lin et al. [16,17] proposed a new modified loading device, which was improved through the which was improved through the traditional triple test, to study the cyclic behavior of N‐MIB joints. traditional triple test, to study the cyclic behavior of N-MIB joints. However, the new loading device However, the new loading device induced additional bending moments on the contact surface; the induced additional bending moments on the contact surface; the additional bending moments resulted additional bending moments resulted in a pinch phenomenon in the hysteretic loops. Therefore, the in a pinch phenomenon in the hysteretic loops. Therefore, the proposed loading device should be proposed loading device should be improved to avoid the additional moments. improved to avoid the additional moments. Different from the non‐interlocking mortarless brick (N‐IMB) panel, the interlocking mortarless Different from the non-interlocking mortarless brick (N-IMB) panel, the interlocking mortarless brick (IMB) panel exhibits different in‐plane/out‐of‐plane behaviors, damping ratios and energy brick (IMB) panel exhibits different in-plane/out-of-plane behaviors, damping ratios and energy dissipations [18–21]. Sturm et al. [22] and Rui et al. [23] studied the shear and compression behaviors dissipations [18–21]. Sturm et al. [22] and Rui et al. [23] studied the shear and compression behaviors of IMB experimentally. Their results indicated that the cohesion of IMB can be neglected, and of IMB experimentally. Their results indicated that the cohesion of IMB can be neglected, and pre‐compression level and interlocking shapes are both important to the shear‐compression pre-compression level and interlocking shapes are both important to the shear-compression behavior behavior of the researched interlocking blocks. The cyclic behavior of IMB wall was investigated by of the researched interlocking blocks. The cyclic behavior of IMB wall was investigated by Qu et al. [20]; Qu et al. [20]; severe damage was found at the bottom of the IMB walls because of large drift levels, severe damage was found at the bottom of the IMB walls because of large drift levels, which indicate which indicate that the interlocking shapes need to be improved. Thanoon et al. [24–26] studied the that the interlocking shapes need to be improved. Thanoon et al. [24–26] studied the effects of the effects of the interlocking shapes of blocks on the compressive and out‐of‐plane behaviors of interlocking shapes of blocks on the compressive and out-of-plane behaviors of mortarless block mortarless block masonry through numerical simulations and experimental tests; however, the masonry through numerical simulations and experimental tests; however, the influence on the in-plane influence on the in‐plane behavior was not investigated. behavior was not investigated. The mechanical behavior of the contact between the mortarless bricks, which is a nonlinear The mechanical behavior of the contact between the mortarless bricks, which is a nonlinear problem, can become highly sophisticated by considering the influence of interlocking shapes. Ensuring problem, can become highly sophisticated by considering the influence of interlocking shapes. Ensuring accuracy during the processing and installation of mortarless bricks in practical engineering is accuracy during the processing and installation of mortarless bricks in practical engineering is difficult difficult and causes a far less idealized contact between mortarless bricks under practical conditions and causes a far less idealized contact between mortarless bricks under practical conditions than than those under laboratory test conditions. Moreover, the use of interlocking bricks aggravates the those under laboratory test conditions. Moreover, the use of interlocking bricks aggravates the non‐idealized characteristics of the contact conditions for mortarless joints. Therefore, the frictional non-idealized characteristics of the contact conditions for mortarless joints. Therefore, the frictional parameters (mainly the friction coefficient) and shear force‐displacement hysteretic loops obtained parameters (mainly the friction coefficient) and shear force-displacement hysteretic loops obtained from from previously‐reported shear‐compression tests of N‐IMB joints are unsuitable for the characterization previously-reported shear-compression tests of N-IMB joints are unsuitable for the characterization of of IMB joints. Obtaining in‐depth insights into the shear‐compression characteristics of IMB joints by IMB joints. Obtaining in-depth insights into the shear-compression characteristics of IMB joints by considering the influence of different interlocking shapes is highly necessary. considering the influence of different interlocking shapes is highly necessary. A comprehensive experimental investigation of the behavior of IMB joints with four different interlocking shapes was carried out at Harbin Institute of Technology Shenzhen Graduate School. The present study aims to improve knowledge of the mortarless masonry structure under cyclic

Materials 2016, 9, 166

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A comprehensive experimental investigation of the behavior of IMB joints with four different interlocking shapes was carried out at Harbin Institute of Technology Shenzhen Graduate School. The present study aims to improve knowledge of the mortarless masonry structure under cyclic loading, which is of crucial importance in the evaluation of the energy dissipation of MB panels. Aside from those of interlocking shapes, the effects of compressive stress and loading cycles were also investigated and analyzed quantitatively. 2. Description of the Specimen 2.1. Design and Construction of the Brick Light aggregate concrete (LAC) bricks were selected for the cyclic test. According to the material standard for LAC [27], the mix proportion (cement:fly ash:ceramsite:sand) of LAC was determined to be 1:0.27:1.7:2.6, with a water cement ratio (w/c) of 0.42. Then, three specimens of different mix proportions were selected for minor adjustments. The corresponding apparent density and seven-day compressive strength for each specimen are listed in Table 1. The No. 3 mix proportion, which meets the provision of the strength standard, was selected for the LAC brick specimens investigated in the subsequent experiments. Table 1. Mix proportion design of bricks. w/c: Water cement ratio.

Specimen

Cement (kg/m3 )

Fly Ash (kg/m3 )

Ceramsite (kg/m3 )

Sand (kg/m3 )

Water-Reducing Admixture

w/c

14-Day Compressive Strength (MPa)

Apparent Density (kg/m3 )

1 2 3

300 300 280

50 50 70

430 500 560

780 650 600

1.2% 1.2% 1.2%

0.42 0.42 0.42

22.12 29.77 27.53

1843 1792 1700

As shown in Figure 2, the YAS-5000 compression-testing machine (Changchun Kexin Test Instrument Company, Changchun, China) was utilized to perform the uniaxial test to determine the compressive strength of LAC. The obtained 28-day compressive strength and material density for 18 LAC cubic specimens are listed in Table 2. The average density (ρ = 1746 kg/m3) and average Materials 2016, 9, 166 4 of 12 compressive strength (fc = 31.7 MPa) were obtained for LAC.

Figure 2. YAS-5000 compression-testing machine. Figure 2. YAS‐5000 compression‐testing machine.

2.2. Dimension and Interlocking Shapes of the Brick 2.2. Dimension and Interlocking Shapes of the Brick Although IMB IMB can can improve improve the the out‐of‐plane out-of-plane stability stability of of the the MB MB panel panel effectively, effectively, unsuitable Although unsuitable interlocking shapes dimensions would leadlead to significant stress stress concentration and potential damage interlocking shapes oror dimensions would to significant concentration and potential for the MB panel [28–30]. damage for the MB panel [28–30].

In this study, the shear‐compression characteristics of N‐IMB joints and IMB joints with three interlocking shapes, namely rectangular, trapezoidal and circular, were investigated through the cyclic loading tests. The designed bricks are shown in Figure 3. The length, width and height of the bricks for the upper and bottom portions are 80 mm × 115 mm × 80 mm and 375 mm × 115 mm × 80 mm, respectively, as shown in Figure 4. The interlocking height and width ratio of IMB have been confirmed to be 0.3 and 0.4 according to previous research [28,29]. The dimensions and profiles of


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Table 2. Density and compressive strength of bricks. Specimen


Density (kg/m3 )

28-Day Compressive Strength (MPa)

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4 of 12 1-1 1779 33.2 1-2 1730 35.5 1-3 1799 32.5 2-1 1750 30 2-2 1756 30.8 2-3 1735 32.9 3-1 1754 32.3 3-2 1743 31.3 3-3 1728 30.5 4-1 1698 27.6 4-2 1706 32.8 4-3 1742 33.6 5-1 1777 31 5-2 1793 32.3 5-3 1759 31.1 Figure 2. YAS‐5000 compression‐testing machine. 6-1 1796 33.3 Figure 2. YAS‐5000 compression‐testing machine. 6-2 1699 30.4 2.2. Dimension and Interlocking Shapes of the Brick 6-3 1687 29 2.2. Dimension and Interlocking Shapes of the Brick Average 1746 31.7 Although IMB can improve the out‐of‐plane stability of the MB panel effectively, unsuitable

Bottom Brick

Bottom Brick

115

Bottom Brick 115

115

115

46 Brick Bottom Bottom Brick 115

28 46 28 46 28 46

24 24

Bottom Brick

80 80

46

Upper Brick 23 4623 46 23 4623

46 Brick Bottom

56 56

46

56 56

46

24 24

115 Upper Brick 28Brick Upper

80 80

115

115 Upper Brick

80 80

115

115 Upper Brick 46Brick Upper 24 24

Upper Brick

115

24 24

Upper Brick

80 80

115

Bottom Brick 115 115

115

56 56

115

80 80

Although IMB can improve the would out‐of‐plane stability of the MB panel effectively, interlocking shapes or dimensions lead to significant stress concentration and unsuitable potential interlocking shapes or dimensions would lead to significant stress concentration potential damage for the MB panel [28–30]. In this study, the shear-compression characteristics of N-IMB joints and IMBand joints with three damage for the MB panel [28–30]. In this study, the shear‐compression characteristics of N‐IMB were joints investigated and IMB joints with three interlocking shapes, namely rectangular, trapezoidal and circular, through the cyclic In this study, the shear‐compression characteristics of circular, N‐IMB joints and IMB joints with three interlocking shapes, namely rectangular, trapezoidal and were investigated through the loading tests. The designed bricks are shown in Figure 3. The length, width and height of the bricks interlocking shapes, namely rectangular, trapezoidal and circular, were investigated through the cyclic loading tests. The designed bricks are shown in Figure 3. The length, width and height of the for the upper and bottom portions are 80 mm ˆ 115 mm ˆ 80 mm and 375 mm ˆ 115 mm ˆ 80 cyclic loading tests. The designed bricks are shown in Figure 3. The length, width and height of the mm, bricks for the upper and bottom portions are 80 mm × 115 mm × 80 mm and 375 mm × 115 mm × 80 mm, respectively, as shown in Figure 4. The interlocking height and width ratio of IMB have been confirmed bricks for the upper and bottom portions are 80 mm × 115 mm × 80 mm and 375 mm × 115 mm × 80 mm, respectively, as shown in Figure 4. The interlocking height and width ratio of IMB have been to be confirmed to be 0.3 and 0.4 according to previous research [28,29]. The dimensions and profiles of 0.3 and 0.4 according previous research [28,29]. The dimensions andratio profiles of the cross-section respectively, as shown toin Figure 4. The interlocking height and width of IMB have been for the non-interlocking and interlocking bricks are shown in Figure 3. Figure 4 shows photos of the confirmed to be 0.3 and 0.4 according to previous research [28,29]. The dimensions and profiles of the cross‐section for the non‐interlocking and interlocking bricks are shown in Figure 3. Figure 4 the cross‐section for the non‐interlocking and interlocking bricks are shown in Figure 3. Figure 4 test specimens of the bricks casted in-place in the laboratory. shows photos of the test specimens of the bricks casted in‐place in the laboratory. shows photos of the test specimens of the bricks casted in‐place in the laboratory.

Figure 3. Dimensions and profiles of the cross‐section for specimens of bricks with various Figure 3. Dimensions and profiles of the cross-section for specimens of bricks with various interlocking Figure 3. Dimensions profiles of the (b) cross‐section specimens (c) of circular bricks with various interlocking shapes: (a) and non‐interlocking; rectangular for interlocking; interlocking; shapes: (a) non-interlocking; (b) rectangular interlocking; (c) circular interlocking; (d) trapezoidal interlocking shapes: (a) non‐interlocking; (b) rectangular interlocking; (c) circular interlocking; (d) trapezoidal interlocking. (Units: mm). interlocking. (Units: mm). (d) trapezoidal interlocking. (Units: mm).

(a) (a)

(b) (b) Figure 4. Cont.


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(c)

(c)

(d)

(d)

Figure 4. Photos for specimens of the bricks with various interlocking shapes: (a) non‐interlocking;

Figure 4. Photos for specimens of the bricks with various interlocking shapes: (a) non-interlocking; Figure 4. Photos for specimens of the bricks with various interlocking shapes: (a) non‐interlocking; (b) rectangular interlocking; (c) circular interlocking; (d) trapezoidal interlocking. (b) rectangular interlocking; (c) circular interlocking; (d) trapezoidal interlocking. (b) rectangular interlocking; (c) circular interlocking; (d) trapezoidal interlocking.

3. Description of Testing Procedures

3. Description of Testing Procedures 3. Description of Testing Procedures

The test setup is shown in Figure 5. The upper brick is fixed in the steel clamping plate, which is

connected to the support frame through a rigid drive rod. The bottom brick is fixed in the steel slot, The test setup is shown in Figure 5. The upper brick is fixed in the steel clamping plate, which is The test setup is shown in Figure 5. The upper brick is fixed in the steel clamping plate, which is which is bolted on the sliding plate of the loading device. The counter weights, which are employed connected to the support frame through a rigid drive rod. The bottom brick is fixed in the steel slot, connected to the support frame through a rigid drive rod. The bottom brick is fixed in the steel slot, to apply different to the upper brick, are fixed on the top of are the employed steel which is bolted on thevertical slidingcompression plate of the levels loading device. The counter weights, which which is bolted on the sliding plate of the loading device. The counter weights, which are employed clamping plate through a steel rod. Both the support frame and loading device system are fixed on a to to the are fixed to apply apply different different vertical vertical compression compression levels levels to the upper upper brick, brick, are fixed on on the the top top of of the the steel steel steel platform. clamping plate through a steel rod. Both the support frame and loading device system are fixed on clamping plate through a steel rod. Both the support frame and loading device system are fixed on a asteel platform. steel platform.

(a)

(b)

Figure 5. Test setup: (a) entire view; (b) loading system.

(b) (a) A linear motor, which can achieve real‐time control and provide cyclic horizontal displacement with constant speed, was utilized as the loading equipment. The loading speed of the linear motor Figure 5. Test setup: (a) entire view; (b) loading system. Figure 5. Test setup: (a) entire view; (b) loading system. ranges from 1 to 500 mm/s, and the acceleration time is 0.1 s with a repositioning accuracy of 0.02 mm. The mass of each counter weight is 5.098 kg. The axial deformation of the linked drive rod A linear motor, which can achieve real‐time control and provide cyclic horizontal displacement A linear motor, which can achieve real-time control and provide cyclic horizontal displacement caused by the horizontal right/left sliding of the bottom brick was measured with four strain gauges with constant speed, was utilized as the loading equipment. The loading speed of the linear motor with symmetrically plastered on the surface of the drive rod to avoid the effects of out‐of‐plane bending. constant speed, was utilized as the loading equipment. The loading speed of the linear motor ranges from 1 to 500 mm/s, and the acceleration time is 0.1 s with a repositioning accuracy of 0.02 mm. The deformation (strain) was then converted to axial force the adrive rod, which is equal of to 0.02 the mm. ranges from 1 to 500 mm/s, and the acceleration time is 0.1 s of with repositioning accuracy The mass of each counter weight joint is 5.098 kg. upper The axial deformation of the linked drive rod shear force of the sliding mortarless between and bottom bricks. Lastly, the frictional The mass of each counter weight is 5.098 kg. The axial deformation of the linked drive rod caused by the horizontal right/left sliding of the bottom brick was measured with four strain gauges coefficients, which are equal to shear force divided by the area of the contact surface, were obtained. caused by the horizontal right/left sliding of the bottom brick was measured with four strain gauges symmetrically plastered on the surface of the drive rod to avoid the effects of out‐of‐plane bending. The resistance and sensitivity coefficients of the strain gauge are 120 ± 0.12 Ω and 2.12 ± 0.12, symmetrically plastered on the surface of the drive rod to avoid the effects of out-of-plane bending. respectively. The DH5929 data collection device (with a measuring range of −1000 to +1000 με and The deformation (strain) was then converted to axial force of the drive rod, which is equal to the The deformation (strain) was then converted to axial force of the drive rod, which is equal to the sampling frequency range of 1 Hz to 20,000 Hz) was utilized to collect the deformation (stain) data of shear force of the sliding mortarless joint between upper and bottom bricks. Lastly, the frictional shearthe linked rod. force of the sliding mortarless joint between upper and bottom bricks. Lastly, the frictional coefficients, which are equal to shear force divided by the area of the contact surface, were obtained. coefficients, which are equal to shear force divided by the area of the contact surface, were obtained. The Prior to the test, the devices shown in Figure 5 were assembled together as an entire loading The resistance and sensitivity coefficients of the strain gauge are 120 ± 0.12 Ω and 2.12 ± 0.12, resistance and sensitivity coefficients of the strain gauge are 120 ˘ 0.12 Ω and 2.12 ˘ 0.12, respectively. system. The leveling adjustment for all loading devices was enhanced during the assembling process respectively. The DH5929 data collection device (with a measuring range of −1000 to +1000 με and to ensure that the brick slides in the same horizontal level all of the time. During the test process, The DH5929 data collection device (with a measuring range of ´1000 to +1000 µε and sampling sampling frequency range of 1 Hz to 20,000 Hz) was utilized to collect the deformation (stain) data of leveling adjustment of the loading devices towas carried out with a dial indicator. Real‐time frequency range of 1 to 20,000 Hz) was utilized collect the deformation (stain) data of the linked rod. the linked rod. monitoring of the deformation of two supporting screw rods was employed to ensure the symmetry Prior to the test, the devices shown in Figure 5 were assembled together as an entire loading Prior to the test, the devices shown in Figure 5 were assembled together as an entire loading and level of the dial indicator. All of these measures guarantee the accuracy of the measured force. system. The leveling adjustment for all loading devices was enhanced during the assembling process system. The leveling adjustment for all loading devices was enhanced during the assembling process to ensure that the brick slides in the same horizontal level all of the time. During the test process, to ensure that the brick slides in the same horizontal level all of the time. During the test process, leveling adjustment of the loading devices was carried out with a dial indicator. Real-time monitoring leveling adjustment of the loading devices was carried out with a dial indicator. Real‐time monitoring of the deformation of two supporting screw rods was employed to ensure the symmetry and level of the dial indicator. All of these measures guarantee the accuracy of the measured force.


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This test involved 16 load cases. Four types of interlocking shapes (i.e., non‐interlocking, circular interlocking, trapezoidal interlocking and rectangular interlocking) and four compression stress levels (i.e., 0.017, 0.028, 0.039 and 0.05 MPa) were investigated. Four loading cycles with an Materials 2016, 9, 166 6 of 12 amplitude of 250 mm were applied to each loading case. The loading speed was set to 1 mm/s, which can be assumed as a quasi‐static test. of the deformation of two supporting screw rods was employed to ensure the symmetry and level of 4. Experimental Results and Discussion the dial indicator. All of these measures guarantee the accuracy of the measured force. This test involved 16 load cases. Four types of interlocking shapes (i.e., non-interlocking, circular 4.1. Hysteretic Loops interlocking, trapezoidal interlocking and rectangular interlocking) and four compression stress levels Figure 6 shows the typical hysteretic loops of the N‐IMB and IMB joints. A mechanical model (i.e., 0.017, 0.028, 0.039 and 0.05 MPa) were investigated. Four loading cycles with an amplitude of was established and is shown in Figure 7. The results indicate that the hysteretic loop can be divided 250 mm were applied to each loading case. The loading speed was set to 1 mm/s, which can be into four asstages, namely test. initial loading (Stage a), constant loading (Stage b and Stage d) and assumed a quasi-static unloading (Stage c). Compared to those of the N‐IMB joints, the initial and unloading stages of the 4. Experimental Results and Discussion IMB joints exhibit similar characteristics. However, for the constant stage, the N‐IMB and IMB joints exhibit a significant difference. 4.1. Hysteretic Loops Unlike that in the N‐IMB joints, the shear force of the IMB joints exhibits stiffness hardening behavior in 6the constant loading stage (Stages b and d); this and behavior varied the interlocking Figure shows the typical hysteretic loops of the N-IMB IMB joints. Aas mechanical model shape changed, shown as in Figure 6b–d. In consideration of the test process, it is concluded that the was established and is shown in Figure 7. The results indicate that the hysteretic loop can be divided stiffness hardening behavior was caused by the loading direction being not parallel to the longitudinal into four stages, namely initial loading (Stage a), constant loading (Stage b and Stage d) and unloading extension of the interlocking portion during the loading process. Therefore, additional compression (Stage c). Compared to those of the N-IMB joints, the initial and unloading stages of the IMB joints stress was generated; the shear force of for the joints stage, increased; and the hardening exhibit similar characteristics. However, theIMB constant the N-IMB andstiffness IMB joints exhibit behavior appeared. a significant difference.

(a)

(b)

(c)

(d)

Figure 6. Typical hysteretic loops for the non‐interlocking mortarless brick (N‐IMB) and IMB joints Figure 6. Typical hysteretic loops for the non-interlocking mortarless brick (N-IMB) and IMB joints under four cyclic cyclic experimental experimental tests: tests: (a) (a) non-interlocking; non‐interlocking; (b) circular interlocking; interlocking; (c) (c) trapezoidal trapezoidal under four (b) circular interlocking; (d) rectangular interlocking. interlocking; (d) rectangular interlocking.

Unlike that in the N-IMB joints, the shear force of the IMB joints exhibits stiffness hardening behavior in the constant loading stage (Stages b and d); this behavior varied as the interlocking shape changed, shown as in Figure 6b–d. In consideration of the test process, it is concluded that the stiffness hardening behavior was caused by the loading direction being not parallel to the longitudinal extension of the interlocking portion during the loading process. Therefore, additional compression stress was generated; the shear force of the IMB joints increased; and the stiffness hardening behavior appeared.


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IMB joints. Figure 7. Mechanical model of the hysteric loops for the N-IMB and Figure 7. Mechanical model of the hysteric loops for the N-IMB and IMB joints.

Figure 7. Mechanical model of the hysteric loops for the N‐IMB and IMB joints. 4.2. Mohr–Coulomb Failure Criterion

The average value of the constant stage was selected to calculate shear and compression stresses 4.2. Mohr–Coulomb Failure Criterion 4.2. Mohr–Coulomb Failure Criterion as follows: The average value of the constant stage was selected to calculate shear and compression stresses The average value of the constant stage was selected to calculate shear and compression stresses F N as follows: as follows: τ  F， σ  N (1) A τ “ ,σ “ A (1) FA NA τ  ， σ  (1) where τ is the shear stress, σ is the normal stress, shear force that is equal to the average force A F isFthe where τ is the shear stress, σ is the normal stress, isAthe shear force that is equal to the average of the constant loading stages, N is the normal force that is equal to the vertical applied force caused force of the constant loading stages, N is the normal force that is equal to the vertical applied force where τ is the shear stress, σ is the normal stress, F is the shear force that is equal to the average force by the gravity effects of the countered weights and A is the vertical projection contact area in caused by the gravity effects of the countered weights and A is the vertical projection contact area in of the constant loading stages, N is the normal force that is equal to the vertical applied force caused the experiment. the the experiment. by gravity effects of the countered stress weights A is the vertical projection loading contact isarea in The shear stress versus compression forand all specimens under four-cycle shown The shear stress versus compression stress for all specimens under four-cycle loading is shown in the experiment. in Figure 8. As indicated by the figure, the relationship between shear stress and compression stress Figure 8. As indicated by the figure, the relationship between shear stress and compression stress for The shear stress versus compression stress for all specimens under four‐cycle loading is shown for both N-IMB and IMB joints under all researched compression levels complies with the both N-IMB and IMB joints under all researched compression levels complies with the Mohr–Coulomb in Figure 8. As indicated by the figure, the relationship between shear stress and compression stress Mohr–Coulomb failure criterion, namely, failure criterion, for both N‐IMB namely, and IMB joints under all researched compression levels complies with the  μσ (2) µσ (2) Mohr–Coulomb failure criterion, namely, ττ“ cc00 ` where c00 denotes initial cohesion, which can be and τ assumed c0  μσ as zero for both N-IMB and IMB joints, (2) µ denotes the representation coefficient. The friction coefficients of both N-IMB and IMB joints with μ 0 denotes initial cohesion, which can be assumed as zero for both N‐IMB and IMB joints, and where c different in Table Table 3. 3. interlocking shapes are listed in μ denotes the representation coefficient. The friction coefficients of both N‐IMB and IMB joints with different interlocking shapes are listed in Table 3.

(a)

(b)

(a)

Figure 8. Cont.

(b)


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(c) (c)

(d)

(d)

Figure 8. Experimental failure criteria for N-IMB and IMB joints under different compression Figure 8. Experimental failure criteria for N‐IMB and IMB joints under different compression stress levels: stress levels: (a) non-interlocking; (b) circular interlocking; (c) trapezoidal interlocking; (a) non‐interlocking; (b) circular interlocking; (c) trapezoidal interlocking; (d) rectangular interlocking. Figure 8. Experimental failure criteria for N‐IMB and IMB joints under different compression stress levels: (d) rectangular interlocking. (a) non‐interlocking; (b) circular interlocking; (c) trapezoidal interlocking; (d) rectangular interlocking. Table 3. Effect of compression stress on the friction coefficient. Table 3. Effect of compression stress on the friction coefficient. Table 3. Effect of compression stress on the friction coefficient.

Compression Stress 0.017 MPa 0.028 MPa 0.039 MPa 0.05 MPa Compression Stress Compression Stress Interlocking Shape Interlocking Shape Non‐interlocking 0.55 MPa 0.592 0.622 0.638 0.017 0.028 MPa 0.039 MPa 0.05 MPa 0.017 MPa 0.028 MPa 0.039 MPa 0.05 MPa Non-interlocking 0.55 0.592 0.622 0.638 Circular 0.514 0.559 0.602 0.613 Non‐interlocking 0.55 0.592 0.622 0.638 Circular 0.514 0.559 0.602 0.613 Trapezoidal 0.512 0.535 0.568 0.581 Circular 0.514 0.559 0.602 0.613 Trapezoidal 0.512 0.535 0.568 0.581 Rectangular 0.502 0.55 0.562 0.576 Trapezoidal 0.512 0.535 0.568 0.581 Rectangular 0.502 0.55 0.562 0.576 Rectangular 0.502 0.55 0.576 role in the According to Figure 9 and Table 3, compression stress level 0.562 plays an important Interlocking Shape

friction coefficients of the and IMB joints. Regardless of the interlocking as the the According toto Figure 9 and Table 3, compression stress level level plays an important roleshapes, in the According Figure 9 N‐IMB and Table 3, compression stress plays an important role friction in compression stress increases, the friction coefficient increases by more than 12.5%, and the variation coefficients of the N-IMB and IMB joints. Regardless of the interlocking shapes, as the compression friction coefficients of the N‐IMB and IMB joints. Regardless of the interlocking shapes, as the decreases. The maximum increment in the friction coefficient was observed for IMB with a circular stress increases, the friction coefficient increases by more than 12.5%, and the variation decreases. compression stress increases, the friction coefficient increases by more than 12.5%, and the variation shape (18%), and the minimum increment was achieved for IMB with a rectangular shape (12.5%). The maximum increment in the friction coefficient was observed for IMB with a circular shape (18%), decreases. The maximum increment in the friction coefficient was observed for IMB with a circular The friction coefficient is insensitive to the interlocking shape. Under the same compression stress, and the minimum increment was achieved for IMB with a rectangular shape (12.5%). The friction shape (18%), and the minimum increment was achieved for IMB with a rectangular shape (12.5%). when the interlocking shape varies, the variation range of the friction coefficients is less than 10%. coefficient is insensitive to the interlocking shape. Under the same compression stress, when the The friction coefficient is insensitive to the interlocking shape. Under the same compression stress, interlocking shape varies, the variation range of the friction coefficients is less than 10%. when the interlocking shape varies, the variation range of the friction coefficients is less than 10%.

Figure 9. Effects of compression stress level on the friction coefficients. Figure 9. Effects of compression stress level on the friction coefficients.

Figure 9. Effects of compression stress level on the friction coefficients. The effect of compression stress on the friction coefficients is primarily caused by the contact degree between two bricks. The upper and bottom bricks do not have a tight contact, because of the The effect of compression stress on the friction coefficients is primarily caused by the contact The effect of compression onin the friction is primarily caused by contact existence of “micro burrs”, as stress shown Figure 10. coefficients The real contact area between the the upper and degree between two bricks. The upper and bottom bricks do not have a tight contact, because of the degree between two bricks. The upper and bottom bricks do not have a tight contact, because of the bottom bricks varies as the compression changes. As the compression stress increases, more micro existence of “micro burrs”, as shown in Figure 10. The real contact area between the upper and existence ofinto “micro burrs”, as shown Figuresurface, 10. The resulting real contact between the upper area and bottom burrs bite one another on the in contact in area an additional contact and an bottom bricks varies as the compression changes. As the compression stress increases, more micro bricks varies as the compression changes. As the compression stress increases, more micro burrs bite increment in the shear force of the mortarless joints. Furthermore, with the increase in compression burrs bite into one another on the contact surface, resulting in an additional contact area and an stress, the bite force is overcome during sliding, which also contributes to the increment in shear force. increment in the shear force of the mortarless joints. Furthermore, with the increase in compression

stress, the bite force is overcome during sliding, which also contributes to the increment in shear force.


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into one another on the contact surface, resulting in an additional contact area and an increment in the shear force of the mortarless joints. Furthermore, with the increase in compression stress, the bite force Materials 2016, 9, 166 9 of 12 is overcome during sliding, which also contributes to the increment in shear force.

Cyclic displacement

Upper Brick

Bottom Brick

Figure 10. Sketch of the contact status for the MBs. Figure 10. Sketch of the contact status for the MBs.

4.3. Effect of Loading Cycles 4.3. Effect of Loading Cycles The effects effects of of loading loading cycles cycles on on the the MB MB joints’ joints’ behavior behavior were were investigated investigated by by comparing comparing the the The experimental results after four and 36 cycles. Both the friction coefficient and wear condition on the experimental results after four and 36 cycles. Both the friction coefficient and wear condition on the contact surface were investigated, and a constant compression stress level (0.05 MPa) was selected. contact surface were investigated, and a constant compression stress level (0.05 MPa) was selected. The friction coefficients for N‐IMB and IMB joints under different loading cycles are listed in Table 4. The friction coefficients for N-IMB and IMB joints under different loading cycles are listed in Table 4. Table 4. Effects of loading cycles on the friction coefficients. Table 4. Effects of loading cycles on the friction coefficients.

Interlocking Shape Interlocking Shape

Non‐interlocking Non-interlocking Circular Circular Trapezoidal Trapezoidal Rectangular Rectangular

Loading Cycles Loading Cycles 4 Cycles 36 Cycles 4 Cycles 36 Cycles 0.638 0.502 0.638 0.502 0.613 0.497 0.613 0.497 0.581 0.405 0.581 0.405 0.576 0.369 0.576 0.369

Degradation Rate (DR) (%) Degradation Rate (DR) (%)

21% 21% 19% 19% 30% 30% 36% 36%

The degradation rate (DR) of the friction coefficients was introduced to analyze the influence of The degradation rate (DR) of the friction coefficients was introduced to analyze the influence of the loading cycles quantitatively. DR can be calculated as: the loading cycles quantitatively. DR can be calculated as: ˇ μ μ ˇ DR ˇ µ 36´ µ 4ˇ  100% DR “ ˇˇ 36 μ 4 ˇˇ ˆ 100% µ44

(3) (3)

where μ and μ where µ44and µ3636 are the friction coefficients obtained after four and 36 cycles, respectively. The DR are the friction coefficients obtained after four and 36 cycles, respectively. The DR for for IMB with a circular interlocking shape has the minimum value (19%), which is close to the value IMB with a circular interlocking shape has the minimum value (19%), which is close to the value of the of the joints N‐IMB joints Meanwhile, (21%). Meanwhile, the DRs for IMB with rectangular and interlocking trapezoidal N-IMB (21%). the DRs for IMB joints with joints rectangular and trapezoidal interlocking shapes are much larger (with an average of 33%). The results indicate that DR increases shapes are much larger (with an average of 33%). The results indicate that DR increases with the with the decrease in the smoothness of the interlocking surface. decrease in the smoothness of the interlocking surface. The wear conditions of the MB joints after four and 36 cycles are marked in Figure 11. For the The wear conditions of the MB joints after four and 36 cycles are marked in Figure 11. For the specimens of N‐IMB, the wear area was almost all around the contact surface (see Figure 11a) after specimens of N-IMB, the wear area was almost all around the contact surface (see Figure 11a) after performing four four cycles cycles of of loading; loading; only only aa slight slight increase increase in in wear wear was was observed observed after after 36 36 cycles cycles of of performing loading, as shown in Figure 11b. For the specimens of IMB, as shown in Figure 11c–h, almost no loading, as shown in Figure 11b. For the specimens of IMB, as shown in Figure 11c–h, almost no wear was observed on the interlocking portion after four cycles of loading. However, as the loading wear was observed on the interlocking portion after four cycles of loading. However, as the loading cycles increased from four cycles to 36 cycles, more wear occurred. Compared to the research on DR, cycles increased from four cycles to 36 cycles, more wear occurred. Compared to the research on DR, the newly‐produced wear has a positive correlation with the DR of the friction coefficient, namely, the newly-produced wear has a positive correlation with the DR of the friction coefficient, namely, when more wear occurs, a larger degradation ratio is obtained. when more wear occurs, a larger degradation ratio is obtained.

(a)

(b)

performing four cycles of loading; only a slight increase in wear was observed after 36 cycles of loading, as shown in Figure 11b. For the specimens of IMB, as shown in Figure 11c–h, almost no wear was observed on the interlocking portion after four cycles of loading. However, as the loading cycles increased from four cycles to 36 cycles, more wear occurred. Compared to the research on DR, the newly‐produced wear has a positive correlation with the DR of the friction coefficient, namely, Materials 2016, 9, 166 10 of 12 when more wear occurs, a larger degradation ratio is obtained.


(a)

(b)

(c)

(d)

(e)

(f)

(g) 4‐cycles

(h) 36‐cycles

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Figure 11. Photos Photos wear condition for N‐IMBs and IMBs after loading different loading cycles. Figure 11. of of thethe wear condition for N-IMBs and IMBs after different cycles. (a) N-IMBs (a) N‐IMBs after four cycles; (b) N‐IMBs after 36 cycles; (c) circular IMBs after four cycles; (d) circular after four cycles; (b) N-IMBs after 36 cycles; (c) circular IMBs after four cycles; (d) circular IMBs after trapezoidal IMBs after 36 cycles; IMBs after cycles; (e) IMBs trapezoidal IMBs after (f)four cycles; (f) 36 cycles; (e)36 trapezoidal after four cycles; trapezoidal IMBs after 36 cycles; (g) rectangular (g) rectangular IMBs after four cycles; (h) rectangular IMBs after 36 cycles. IMBs after four cycles; (h) rectangular IMBs after 36 cycles.

5. Conclusions 5. Conclusions (1) A series of cyclic tests was carried out to investigate the compression‐shear behavior of MB (1) A series of cyclic tests was carried out to investigate the compression-shear behavior of MB joints. In these tests, four different interlocking shapes, four compression stress levels and two joints. In these tests, four different interlocking shapes, four compression stress levels and two loading loading cycles were investigated. A novel loading test methodology, which is convenient and cycles were investigated. A novel loading test methodology, which is convenient and accurate for accurate for cyclic tests, was applied. cyclic tests, was applied. (2) The hysteretic loops of the N‐IMB and IMB joints under the shear‐compression cyclic tests (2) The hysteretic loops of the N-IMB and IMB joints under the shear-compression cyclic tests were were obtained. A typical Mohr–Coulomb frictional behavior was observed in the N‐IMB joints. obtained. A typical Mohr–Coulomb frictional behavior was observed in the N-IMB joints. A significant A significant stiffness hardening effect was found for the IMB joints; the effect was mainly caused by stiffness hardening effect was found for the IMB joints; the effect was mainly caused by the loading the loading direction being not parallel to the longitudinal extension of the interlocking portion direction being not parallel to the longitudinal extension of the interlocking portion during loading. during loading. (3) Compression stress level plays an important role in the friction coefficients of the N-IMB and (3) Compression stress level plays an important role in the friction coefficients of the N‐IMB and IMB joints. Regardless of the interlocking shapes, as the compression stress increases, the friction IMB joints. Regardless of the interlocking shapes, as the compression stress increases, the friction coefficient increases by more than 12.5%, and the variation decreases. The friction coefficients are coefficient increases by more than 12.5%, and the variation decreases. The friction coefficients are insensitive to the interlocking shapes. Under the same compression stress, when the interlocking shape insensitive to the interlocking shapes. Under the same compression stress, when the interlocking varies, the variation range of the friction coefficients is less than 10%. The influence of compression shape varies, the variation range of the friction coefficients is less than 10%. The influence of compression stress on the friction coefficients is primarily caused by the contact degree between two bricks. stress on the friction coefficients is primarily caused by the contact degree between two bricks. (4) The influence of loading cycles was examined by comparing the experimental results after (4) The influence of loading cycles was examined by comparing the experimental results after four and 36 cycles. The wear condition was studied, and the degradation rate of the friction coefficient four and 36 cycles. The wear condition was studied, and the degradation rate of the friction coefficient was defined. The results showed that as the loading cycle increases, the wear becomes increasingly severe. Wear condition has a positive correlation with the DR of the friction coefficient, which means that when more wear occurs, a larger DR is obtained. (5) The circular IMB is the preferred choice for the MB panels. Firstly, the circular IMBs can be constructed easily in the engineering application; secondly, the circular IMB joints can absorb more


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was defined. The results showed that as the loading cycle increases, the wear becomes increasingly severe. Wear condition has a positive correlation with the DR of the friction coefficient, which means that when more wear occurs, a larger DR is obtained. (5) The circular IMB is the preferred choice for the MB panels. Firstly, the circular IMBs can be constructed easily in the engineering application; secondly, the circular IMB joints can absorb more in-plane energy dissipation and exhibit better out-of-plane behavior during the seismic action compared to the rectangular and trapezoidal IMB joints because of the maximum friction coefficient and the minimum DR of the friction coefficient due to the increase of loading cycles are obtained. Acknowledgments: The authors are grateful for the financial support from the National Natural Science Foundation of China (NSFC-51178153), the China Postdoctoral Science Foundation (2013M541387) and the Shenzhen Technology Innovation Program-Technology Development Projects (Grant No. CXZZ20140904154839135). Author Contributions: Hongjun Liu, Kun Lin and Peng Liu conceived of and designed the experiments. Hongjun Liu provided the research references and suggestions. Kun Lin, Sai Zhao and Peng Liu performed the experiments. Kun Lin and Sai Zhao analyzed the data. Hongjun Liu wrote the paper. Kun Lin polished the paper and improved the logic. Conflicts of Interest: The authors declare no conflict of interest.

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