applied sciences

Article

Experimental and Numerical Analysis of theCompressive and Shear Behavior for a New Typeof Self-Insulating Concrete Masonry System

Abu-Bakre Abdelmoneim Elamin Mohamad and Zhongfan Chen *

Key Laboratory of RC & PC Structures of Ministry of Education, Southeast University, Nanjing 210096, China;abubakre55@yahoo.com* Correspondence: 101003944@seu.edu.cn; Tel.: +86-139-5101-8486

Academic Editor: Stefano InvernizziReceived: 21 June 2016; Accepted: 19 August 2016; Published: 30 August 2016

Abstract: The developed study aimed at investigating the mechanical behavior of a new type ofself-insulating concrete masonry unit (SCMU). A total of 12 full-grouted wall assemblages wereprepared and tested for compression and shear strength. In addition, different axial stress ratioswere used in shear tests. Furthermore, numerical models were developed to predict the behaviorof grouted specimens using simplified micro-modeling technique. The mortar joints were modeledwith zero thickness and their behavior was applied using the traction–separation model of thecohesive element. The experimental results revealed that the shear resistance increases as the levelof precompression increases. A good agreement between the experimental results and numericalmodels was observed. It was concluded that the proposed models can be used to deduct the generalbehavior of grouted specimens.

Keywords: self-insulating concrete masonry units; masonry assemblage; compression test; shear test;micro modeling; cohesive surface-based behavior; full grouted masonry

1. Introduction

Masonry has been used as a common building material worldwide for many centuries. Masonry isa composite of block units bonded together with mortar. The most effective use of masonry buildingcan be found in load-bearing structures. The manufacturing of masonry units consumes significantamounts of resources and energy. This has added considerable pressure on the construction industryto reduce energy consumption associated with masonry production. Accordingly, many developedcountries applied the energy conservation concept in the building technology. This concept can beachieved by introducing alternative building materials that have a low impact on the environment.The use of thermal insulation materials in the production of masonry is one of the most effective waysfor green building technology [1,2].

A number of studies were carried out in this area, and it is thought that there are many parameterswhich influence the thickness of an insulator, such as building type, shape, construction materials,insulation materials, and costs [3–6]. In general, external insulation methods are common practicearound the world. However, use of insulation blocks composed of expanded polystyrene (EPS)foam, which are used to replace the external insulation of buildings, becomes more popular with theintention of thermal insulation. EPS is composed of small, white, and interconnected beads and offerssuperior engineering properties such as being lightweight, versatile, energy-efficient, and cost effective.Therefore, it is used as insulation material in buildings and it can be molded into many shapes to fitthe required purpose [7].

Appl. Sci. 2016, 6, 245; doi:10.3390/app6090245 www.mdpi.com/journal/applsci

Appl. Sci. 2016, 6, 245 2 of 14

Most of the previous researches focus on lightweight concrete masonry units as good thermalinsulation materials in buildings. This is because they have a lower thermal conductivity comparedwith normal-weight concrete. Unfortunately, masonry units made from lightweight concrete have lowmechanical properties compared with normal-weight concrete [8–12]. Inserting insulation materialsuch as EPS into normal-weight concrete with a special configuration of concrete masonry units (CMUs)leads to an increase in their thermal resistance without affecting their mechanical performance [13].Recently, a new type of unreinforced masonry system was developed in Europe for use in theconstruction of small houses. The developed system has an energy-efficiency enclosure withoutconcern for thermal bridges. This type of unreinforced masonry system offers significant contributionregarding the design and construction of cost-effective buildings in seismic regions [14].

In this research, a new type of concrete masonry unit has been developed with a self-insulatingfeature. The developed type of self-insulating concrete masonry unit (SCMU) would be applicable forboth low and medium height residential buildings in seismic area zones. The main objective of thisstudy was to investigate the mechanical properties, namely, compression strength and shear strength,of the proposed SCMUs. The second objective of this study was to develop numerical models to predictthe behavior of grouted specimens using a simplified micro-modeling technique. The successful use ofSCMUs in the construction industry can have a potentially significant impact on the sustainability ofmasonry structures.

2. Experimental Program

A comprehensive testing program was carried out to determine the compressive strength andshear strength of masonry wall assemblages. A total of 12 full-grouted wall assemblages wereconstructed with a new type of SCMU. Six specimens (Nanjing Shihao Co., Ltd., Nanjing, China) weretested for compression strength, whereas the remaining specimens were tested for shear strength(triplet test). It should be highlighted that all specimens were prepared with the same SCMUs, mortar,and grout properties.

2.1. Materials

The general dimensions of the new type of self-insulating concrete masonry unit used in this studyare 390 mm length, 190 mm height, and 240 mm width for block units and 190 mm length with thesame height and width for half-block units as shown in Figure 1. The SCMU has one core with circularvoids at the ends and two chambers: (1) an outer chamber with thickness of 20 mm to accommodateinsulation, and (2) an inner chamber with thickness of 160 mm to accommodate reinforcing steel withthe filling grouting concrete. The face and web shell thickness is 30 mm. After blocks were produced,the insulation material (EPS) with thickness 20 mm was inserted in chamber (1). Table 1 shows themechanical and thermal properties of EPS used in this study.

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Most of the previous researches focus on lightweight concrete masonry units as good thermal 43 insulation materials in buildings. This is because they have a lower thermal conductivity compared 44 with normal‐weight concrete. Unfortunately, masonry units made from  lightweight concrete have 45 low  mechanical  properties  compared  with  normal‐weight  concrete  [8–12].  Inserting  insulation 46 material such as EPS into normal‐weight concrete with a special configuration of concrete masonry 47 units  (CMUs)  leads  to  an  increase  in  their  thermal  resistance without  affecting  their mechanical 48 performance [13]. Recently, a new type of unreinforced masonry system was developed in Europe 49 for use in the construction of small houses. The developed system has an energy‐efficiency enclosure 50 without concern  for  thermal bridges. This  type of unreinforced masonry system offers significant 51 contribution regarding the design and construction of cost‐effective buildings in seismic regions [14]. 52

In this research, a new type of concrete masonry unit has been developed with a self‐insulating 53 feature. The developed type of self‐insulating concrete masonry unit (SCMU) would be applicable 54 for both low and medium height residential buildings in seismic area zones. The main objective of 55 this study was  to  investigate  the mechanical properties, namely, compression strength and shear 56 strength,  of  the proposed  SCMUs. The  second  objective  of  this  study was  to develop numerical 57 models to predict the behavior of grouted specimens using a simplified micro‐modeling technique. 58 The successful use of SCMUs in the construction industry can have a potentially significant impact 59 on the sustainability of masonry structures. 60

2. Experimental Program 61

A comprehensive testing program was carried out to determine the compressive strength and 62 shear  strength  of masonry wall  assemblages. A  total  of  12  full‐grouted wall  assemblages were 63 constructed with a new  type of SCMU. Six specimens  (Nanjing Shihao Co., Ltd., Nanjing, China) 64 were  tested  for  compression  strength, whereas  the  remaining  specimens were  tested  for  shear 65 strength  (triplet  test).  It  should  be  highlighted  that  all  specimens were  prepared with  the  same 66 SCMUs, mortar, and grout properties. 67

2.1. Materials   68

The general dimensions of the new type of self‐insulating concrete masonry unit used  in this 69 study are 390 mm length, 190 mm height, and 240 mm width for block units and 190 mm length with 70 the same height and width for half‐block units as shown in Figure 1. The SCMU has one core with 71 circular voids  at  the  ends  and  two  chambers:  (1)  an  outer  chamber with  thickness  of  20 mm  to 72 accommodate  insulation,  and  (2)  an  inner  chamber with  thickness  of  160 mm  to  accommodate 73 reinforcing steel with the filling grouting concrete. The face and web shell thickness is 30 mm. After 74 blocks were produced, the insulation material (EPS) with thickness 20 mm was inserted in chamber 75 (1). Table 1 shows the mechanical and thermal properties of EPS used in this study. 76

 (a)  (b)

Figure 1. Self‐insulating concrete masonry unit (SCMU) configurations: (a) block; and (b) half‐block 77 units. 78 Figure 1. Self-insulating concrete masonry unit (SCMU) configurations: (a) block; and (b) half-block units.

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Table 1. The mechanical and thermal properties of expanded polystyrene (EPS).

Density(kg/m3)

Thermal Conductivity(w/m·K)

Specific HeatCapacity (J/kg·◦C)

Young Modulus(kN/mm2)

Yield Strength(N/mm2)

30 0.04 1300 3.6 0.46

The compressive strength of SCMUs was determined in accordance with The American Society forTesting and Materials (ASTM) C140 [15] and ASTM C90 [16]. The test was conducted using universalmachine (Jinan Time Shijin Instruments Co., Ltd., Jinan, China) with load capacity of 2000 kN and loadrating of 0.05 ± 0.01 N/mm2/sec. The average compressive strength value of SCMUs was 6.7 N/mm2.Also, the weights of SCMUs were measured which have an average density value of 1850 kg/m3.The typical mode of failure with face-shell separation was observed during the test for all SCMUspecimens as shown in Figure 2. No cracks were observed during loading of the SCMUs, and thefailure was brittle without warning.

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Table 1. The mechanical and thermal properties of expanded polystyrene (EPS). 79

Density 

(kg/m3) 

Thermal Conductivity 

(w/m∙K) 

Specific Heat 

Capacity (J/kg∙°C)

Young Modulus 

(kN/mm2) 

Yield Strength 

(N/mm2) 

30  0.04  1300  3.6  0.46 

The compressive strength of SCMUs was determined in accordance with The American Society 80 for Testing  and Materials  (ASTM) C140  [15]  and ASTM C90  [16]. The  test was  conducted using 81 universal machine (Jinan Time Shijin Instruments Co., Ltd., Jinan, China) with load capacity of 2000 82 kN and load rating of 0.05 ± 0.01 N/mm2/sec. The average compressive strength value of SCMUs was 83 6.7 N/mm2. Also, the weights of SCMUs were measured which have an average density value of 1850 84 kg/m3. The  typical mode of  failure with  face‐shell separation was observed during  the  test  for all 85 SCMU specimens as shown in Figure 2. No cracks were observed during loading of the SCMUs, and 86 the failure was brittle without warning.   87

Figure 2. SCMU under compression test machine. 88

Mortar used in this study was Mb15 (GB50003‐2010) [17]. Mortar was composed of cement, sand, 89 lime, and water. The mortar mixtures were prepared according to JGJ/T98‐2011 [18]. Three cubes of 90 70.7 × 70.7 × 70.7 mm3 were casted and tested at 28 days of curing time to determine the compressive 91 strength of mortar. The average compressive strength value of the three specimens of mortar was 92 14.7 N/mm2. 93

The grout was used to fill the cores, increasing the effective cross‐sectional area of the masonry 94 for load resistance, and permitting the bonding of reinforcing bars to the concrete masonry blocks. 95 Three cubes of 100 × 100 × 100 mm3 were casted and tested at 28 days of curing time to determine the 96 compressive strength of grout. The grout specimens were  tested  in accordance with  the ordinary 97 concrete  mechanical  performance  test  method  (GBJ50081‐2002)  [19].  The  value  of  the  average 98 compressive strength of the three specimens of grout was 24.7 N/mm2. 99

2.2. Compressive Strength Test 100

Six prisms of SCMUs wall assemblages  (denoted by PC1–PC6) as  illustrated  in Table 2 were 101 prepared  according  to  the  procedure  specified  by  the  Chinese Masonry  Code  for  compressive 102 strength  test  [17].  The  compressive  strength  test  of masonry  prism was  conducted  on  units  of 103 dimensions of 590 mm length, 240 mm width, and 790 mm height, as shown in Figure 3. The masonry 104 prisms were constructed with four courses in running bond pattern. The prisms were fully grouted 105 and wooden forms were used to ensure the proper finishing of the grout at the end of the face‐shells. 106 The prisms were cured in standard conditions (22 ± 3 °C and 95% RH) for 28 days. Before testing, the 107 prisms were capped with a 10 mm thick cement mortar to have a uniform bearing surface. 108

Figure 2. SCMU under compression test machine.

Mortar used in this study was Mb15 (GB50003-2010) [17]. Mortar was composed of cement, sand,lime, and water. The mortar mixtures were prepared according to JGJ/T98-2011 [18]. Three cubesof 70.7 × 70.7 × 70.7 mm3 were casted and tested at 28 days of curing time to determine thecompressive strength of mortar. The average compressive strength value of the three specimensof mortar was 14.7 N/mm2.

The grout was used to fill the cores, increasing the effective cross-sectional area of the masonryfor load resistance, and permitting the bonding of reinforcing bars to the concrete masonry blocks.Three cubes of 100 × 100 × 100 mm3 were casted and tested at 28 days of curing time to determinethe compressive strength of grout. The grout specimens were tested in accordance with the ordinaryconcrete mechanical performance test method (GBJ50081-2002) [19]. The value of the averagecompressive strength of the three specimens of grout was 24.7 N/mm2.

2.2. Compressive Strength Test

Six prisms of SCMUs wall assemblages (denoted by PC1–PC6) as illustrated in Table 2 wereprepared according to the procedure specified by the Chinese Masonry Code for compressive strengthtest [17]. The compressive strength test of masonry prism was conducted on units of dimensionsof 590 mm length, 240 mm width, and 790 mm height, as shown in Figure 3. The masonry prisms wereconstructed with four courses in running bond pattern. The prisms were fully grouted and woodenforms were used to ensure the proper finishing of the grout at the end of the face-shells. The prismswere cured in standard conditions (22 ± 3 ◦C and 95% RH) for 28 days. Before testing, the prisms werecapped with a 10 mm thick cement mortar to have a uniform bearing surface.

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Figure 3. Masonry prism for compressive strength test (units in mm). 109

The  compressive  strength  test was performed using  a universal machine  (Jinan Time  Shijin 110 Instruments  Co.,  Ltd.,  Jinan,  China) with  capacity  of  5000  kN  and  loading  rate  of  0.05  ±  0.01 111 N/mm2/sec. The prism was placed in the lower plate and then both centroidal axes of the prism and 112 the center of  thrust of  the machine were aligned. Test setup of compressive strength  is shown  in 113 Figure 4. 114

 115

Figure 4. Compressive strength test setup. 116

Table 2 shows the results of compressive strength test of masonry prisms. The results revealed 117 that the average compressive strength and the standard deviation of tested prisms were 9.21 N/mm2 118 and 0.4 N/mm2, respectively. The typical failure pattern observed during the compressive strength 119 test is shown in Figure 5. It was observed that the prisms failed due to the development of vertical 120 cracks  along  their  height. Apparently,  the  lateral  expansion  of  the mortar  induced  high  tensile 121 stresses in the blocks, causing them to crack and eventually fail. Generally, the pattern of failure is 122 influenced by the modulus of elasticity of the different materials that made up the masonry system 123 [20].   124

Table 2. Compressive strength results of masonry prisms. 125

Specimen No. Compressive Strength (N/mm2) 

PC1  9.79 

PC2  9.58 

PC3  9.27 

PC4  8.85 

PC5  9.08 

PC6  8.71 

Average Compressive strength of prisms 9.21 

Figure 3. Masonry prism for compressive strength test (units in mm).

The compressive strength test was performed using a universal machine (Jinan TimeShijin Instruments Co., Ltd., Jinan, China) with capacity of 5000 kN and loading rate of0.05 ± 0.01 N/mm2/sec. The prism was placed in the lower plate and then both centroidal axesof the prism and the center of thrust of the machine were aligned. Test setup of compressive strengthis shown in Figure 4.

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Figure 3. Masonry prism for compressive strength test (units in mm). 109

The  compressive  strength  test was performed using  a universal machine  (Jinan Time  Shijin 110 Instruments  Co.,  Ltd.,  Jinan,  China) with  capacity  of  5000  kN  and  loading  rate  of  0.05  ±  0.01 111 N/mm2/sec. The prism was placed in the lower plate and then both centroidal axes of the prism and 112 the center of  thrust of  the machine were aligned. Test setup of compressive strength  is shown  in 113 Figure 4. 114

 115

Figure 4. Compressive strength test setup. 116

Table 2 shows the results of compressive strength test of masonry prisms. The results revealed 117 that the average compressive strength and the standard deviation of tested prisms were 9.21 N/mm2 118 and 0.4 N/mm2, respectively. The typical failure pattern observed during the compressive strength 119 test is shown in Figure 5. It was observed that the prisms failed due to the development of vertical 120 cracks  along  their  height. Apparently,  the  lateral  expansion  of  the mortar  induced  high  tensile 121 stresses in the blocks, causing them to crack and eventually fail. Generally, the pattern of failure is 122 influenced by the modulus of elasticity of the different materials that made up the masonry system 123 [20].   124

Table 2. Compressive strength results of masonry prisms. 125

Specimen No. Compressive Strength (N/mm2) 

PC1  9.79 

PC2  9.58 

PC3  9.27 

PC4  8.85 

PC5  9.08 

PC6  8.71 

Average Compressive strength of prisms 9.21 

Figure 4. Compressive strength test setup.

Table 2 shows the results of compressive strength test of masonry prisms. The results revealedthat the average compressive strength and the standard deviation of tested prisms were 9.21 N/mm2

and 0.4 N/mm2, respectively. The typical failure pattern observed during the compressive strengthtest is shown in Figure 5. It was observed that the prisms failed due to the development of verticalcracks along their height. Apparently, the lateral expansion of the mortar induced high tensile stressesin the blocks, causing them to crack and eventually fail. Generally, the pattern of failure is influencedby the modulus of elasticity of the different materials that made up the masonry system [20].

Table 2. Compressive strength results of masonry prisms.

Specimen No. Compressive Strength (N/mm2)

PC1 9.79PC2 9.58PC3 9.27PC4 8.85PC5 9.08PC6 8.71

Average Compressive strength of prisms 9.21

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Figure 5. Typical failure mode of prism. 126

2.3. Shear Strength Test   127

Six masonry prisms of SCMU assemblages (denoted by PS1–PS6), as presented in Table 3, were 128 prepared according to the procedure specified by the Chinese Masonry Code for shear strength test 129 [17]. The masonry prism of shear test was 390 mm in length, 240 mm in width, and 590 mm in height, 130 as shown in Figure 6. The shear prisms were constructed with three courses in running bond pattern. 131 All shear prisms were cured in the standard conditions (22 ± 3 °C and 95% RH) for 28 days. Before 132 testing, the prisms were capped with a 10 mm thick cement mortar to have a uniform bearing surface. 133

Shear strength test was performed using two load cells. One load cell (Shanghai Huali Sensor 134 Technology Co., Ltd., Shanghai, China) was used to apply a constant vertical precompression load 135 while the second load cell (Shanghai Huali Sensor Technology Co., Ltd., Shanghai, China) was used 136 to apply an increasing horizontal load. Steel plates were installed to ensure a uniform distribution of 137 load and to control the location of supporting points. 138

Prisms PS1, PS2, and PS3 were tested under precompression of 0.1 N/mm2, whereas prisms PS4, 139 PS5, and PS6 were tested under precompression of 0.3 N/mm2. Then the pressures were kept constant 140 while  the  shear  load was  applied until  the  failure of  the prism occurred  [21,22]. Shear  load was 141 increased at a rate of 0.1 N/mm2 per minute. 142

Figure 6. Masonry prism for shear test (units in mm). 143

Four potentiometers (Liyang Instruments Co., Ltd., Liyang, China) (i.e., two at each side) were 144 placed to monitor the slip between the outer and middle units. All measuring devices were connected 145 to a  computer  (ASUSTeK® Computer  Inc., Taibei, China), which processed  the data  in  real  time. 146 Figure 7 shows the shear strength test setup. 147

Figure 5. Typical failure mode of prism.

2.3. Shear Strength Test

Six masonry prisms of SCMU assemblages (denoted by PS1–PS6), as presented in Table 3, wereprepared according to the procedure specified by the Chinese Masonry Code for shear strengthtest [17]. The masonry prism of shear test was 390 mm in length, 240 mm in width, and 590 mmin height, as shown in Figure 6. The shear prisms were constructed with three courses in runningbond pattern. All shear prisms were cured in the standard conditions (22 ± 3 ◦C and 95% RH)for 28 days. Before testing, the prisms were capped with a 10 mm thick cement mortar to have auniform bearing surface.

Shear strength test was performed using two load cells. One load cell (Shanghai Huali SensorTechnology Co., Ltd., Shanghai, China) was used to apply a constant vertical precompression loadwhile the second load cell (Shanghai Huali Sensor Technology Co., Ltd., Shanghai, China) was used toapply an increasing horizontal load. Steel plates were installed to ensure a uniform distribution ofload and to control the location of supporting points.

Prisms PS1, PS2, and PS3 were tested under precompression of 0.1 N/mm2, whereas prismsPS4, PS5, and PS6 were tested under precompression of 0.3 N/mm2. Then the pressures were keptconstant while the shear load was applied until the failure of the prism occurred [21,22]. Shear loadwas increased at a rate of 0.1 N/mm2 per minute.

Appl. Sci. 2016, 6, 245  5 of 14 

 

Figure 5. Typical failure mode of prism. 126

2.3. Shear Strength Test   127

Six masonry prisms of SCMU assemblages (denoted by PS1–PS6), as presented in Table 3, were 128 prepared according to the procedure specified by the Chinese Masonry Code for shear strength test 129 [17]. The masonry prism of shear test was 390 mm in length, 240 mm in width, and 590 mm in height, 130 as shown in Figure 6. The shear prisms were constructed with three courses in running bond pattern. 131 All shear prisms were cured in the standard conditions (22 ± 3 °C and 95% RH) for 28 days. Before 132 testing, the prisms were capped with a 10 mm thick cement mortar to have a uniform bearing surface. 133

Shear strength test was performed using two load cells. One load cell (Shanghai Huali Sensor 134 Technology Co., Ltd., Shanghai, China) was used to apply a constant vertical precompression load 135 while the second load cell (Shanghai Huali Sensor Technology Co., Ltd., Shanghai, China) was used 136 to apply an increasing horizontal load. Steel plates were installed to ensure a uniform distribution of 137 load and to control the location of supporting points. 138

Prisms PS1, PS2, and PS3 were tested under precompression of 0.1 N/mm2, whereas prisms PS4, 139 PS5, and PS6 were tested under precompression of 0.3 N/mm2. Then the pressures were kept constant 140 while  the  shear  load was  applied until  the  failure of  the prism occurred  [21,22]. Shear  load was 141 increased at a rate of 0.1 N/mm2 per minute. 142

Figure 6. Masonry prism for shear test (units in mm). 143

Four potentiometers (Liyang Instruments Co., Ltd., Liyang, China) (i.e., two at each side) were 144 placed to monitor the slip between the outer and middle units. All measuring devices were connected 145 to a  computer  (ASUSTeK® Computer  Inc., Taibei, China), which processed  the data  in  real  time. 146 Figure 7 shows the shear strength test setup. 147

Figure 6. Masonry prism for shear test (units in mm).

Four potentiometers (Liyang Instruments Co., Ltd., Liyang, China) (i.e., two at each side) wereplaced to monitor the slip between the outer and middle units. All measuring devices were connectedto a computer (ASUSTeK® Computer Inc., Taibei, China), which processed the data in real time.Figure 7 shows the shear strength test setup.

Appl. Sci. 2016, 6, 245 6 of 14

Appl. Sci. 2016, 6, 245  6 of 14 

Figure 7. Shear test general setup. 148

Table 3 shows the results of shear strength test. The influence of the applied level of the pre‐149 compression is clearly visible from Table 3. The results revealed that the shear resistance increases 150 when increasing the level of pre‐compression. The failure occurred at the bed joint for all specimens, 151 as shown in Figure 8. The failure patterns observed during the tests can be characterized as sliding 152 failure mode. Sliding failure of the prism can be described by the classical Mohr‐Coulomb’s failure 153 criterion equation:   154

τ σc tan   (1)

Where, c denotes the cohesion, φ is the angle of internal friction, σ is the normal stress. 155

Table 3. Shear strength results of masonry prisms. 156

Specimen 

No. 

Precompression 

Load Fpi (kN) 

Maximum Shear 

Load Fimax (kN) 

Precompression 

Stress σi (N/mm2)

Shear Stress τi 

(N/mm2) 

PS1  8.7  103.0  0.10  0.60 

PS2  8.5  106.7  0.10  0.62 

PS3  8.4  105.1  0.10  0.61 

PS4  26.0  126.8  0.30  0.74 

PS5  25.0  124.5  0.29  0.73 

PS6  27.0  130.3  0.31  0.76 

σpi = Fpi/Ai  and  τi= Fimax/2Ai,  (Ai)  is  the  cross‐sectional  area of  a  specimen parallel  to  the bed  joints,  in  square 157 millimeters (mm2). 158

 159

Figure 8. Typical mode of failure for masonry shear prism. 160

Based on  the  test  results presented  in Table 3,  the  friction coefficient  in  the bed  joint can be 161 calculated based on the levels of compression and shear in the joint once sliding has occurred [22]. 162 The resulting shear‐stress‐normal‐stress graph is shown in Figure 9, which has been obtained from a 163 linear regression of points. The average cohesion and friction angle in the bed  joints of the SCMU 164 prisms are, respectively, 0.5433 N/mm2 and 33.7°. 165

Figure 7. Shear test general setup.

Table 3 shows the results of shear strength test. The influence of the applied level of thepre-compression is clearly visible from Table 3. The results revealed that the shear resistance increaseswhen increasing the level of pre-compression. The failure occurred at the bed joint for all specimens,as shown in Figure 8. The failure patterns observed during the tests can be characterized as slidingfailure mode. Sliding failure of the prism can be described by the classical Mohr-Coulomb’s failurecriterion equation:

τ = c + σtanφ (1)

where, c denotes the cohesion, φ is the angle of internal friction, σ is the normal stress.

Table 3. Shear strength results of masonry prisms.

SpecimenNo.

PrecompressionLoad Fpi (kN)

Maximum ShearLoad Fimax (kN)

PrecompressionStress σi (N/mm2)

Shear Stress τi(N/mm2)

PS1 8.7 103.0 0.10 0.60PS2 8.5 106.7 0.10 0.62PS3 8.4 105.1 0.10 0.61PS4 26.0 126.8 0.30 0.74PS5 25.0 124.5 0.29 0.73PS6 27.0 130.3 0.31 0.76

σpi = Fpi/Ai and τi = Fimax/2Ai, (Ai) is the cross-sectional area of a specimen parallel to the bed joints, in squaremillimeters (mm2).

Appl. Sci. 2016, 6, 245  6 of 14 

Figure 7. Shear test general setup. 148

Table 3 shows the results of shear strength test. The influence of the applied level of the pre‐149 compression is clearly visible from Table 3. The results revealed that the shear resistance increases 150 when increasing the level of pre‐compression. The failure occurred at the bed joint for all specimens, 151 as shown in Figure 8. The failure patterns observed during the tests can be characterized as sliding 152 failure mode. Sliding failure of the prism can be described by the classical Mohr‐Coulomb’s failure 153 criterion equation:   154

τ σc tan   (1)

Where, c denotes the cohesion, φ is the angle of internal friction, σ is the normal stress. 155

Table 3. Shear strength results of masonry prisms. 156

Specimen 

No. 

Precompression 

Load Fpi (kN) 

Maximum Shear 

Load Fimax (kN) 

Precompression 

Stress σi (N/mm2)

Shear Stress τi 

(N/mm2) 

PS1  8.7  103.0  0.10  0.60 

PS2  8.5  106.7  0.10  0.62 

PS3  8.4  105.1  0.10  0.61 

PS4  26.0  126.8  0.30  0.74 

PS5  25.0  124.5  0.29  0.73 

PS6  27.0  130.3  0.31  0.76 

σpi = Fpi/Ai  and  τi= Fimax/2Ai,  (Ai)  is  the  cross‐sectional  area of  a  specimen parallel  to  the bed  joints,  in  square 157 millimeters (mm2). 158

 159

Figure 8. Typical mode of failure for masonry shear prism. 160

Based on  the  test  results presented  in Table 3,  the  friction coefficient  in  the bed  joint can be 161 calculated based on the levels of compression and shear in the joint once sliding has occurred [22]. 162 The resulting shear‐stress‐normal‐stress graph is shown in Figure 9, which has been obtained from a 163 linear regression of points. The average cohesion and friction angle in the bed  joints of the SCMU 164 prisms are, respectively, 0.5433 N/mm2 and 33.7°. 165

Figure 8. Typical mode of failure for masonry shear prism.

Based on the test results presented in Table 3, the friction coefficient in the bed joint can becalculated based on the levels of compression and shear in the joint once sliding has occurred [22].The resulting shear-stress-normal-stress graph is shown in Figure 9, which has been obtained froma linear regression of points. The average cohesion and friction angle in the bed joints of the SCMUprisms are, respectively, 0.5433 N/mm2 and 33.7◦.

Appl. Sci. 2016, 6, 245 7 of 14Appl. Sci. 2016, 6, 245  7 of 14 

 166

Figure 9. The resulting shear‐stress–normal‐stress graph. 167

3. Finite Element Modeling   168

The finite element method (FEM) is one of the powerful tools for modeling a structure with very 169 complicated geometry and materials. There are many strategies, as shown in Figure 10, to model a 170 masonry structure with FEM, which includes macro‐ and micro‐modeling. The macro‐model is based 171 on the assumption of homogenous materials, and the mortar joints and units can be smeared into one 172 isotropic or anisotropic material. This procedure may be preferred for the analysis of large masonry 173 structures  due  to  the  reduced  time  and memory  requirements  as well  as  a  user‐friendly mesh 174 generation. In addition, this type of modeling is most valuable when a compromise between accuracy 175 and efficiency is needed [23,24]. 176

 177

Figure 10. Modeling strategies  for block masonry.  (a) Typical masonry sample;  (b) Detailed micro 178 modeling; (c) Simplified micro modeling; (d) Macro modeling. 179

More  accurate  response  of  a masonry  assembly  can  be  deducted  by  using micro‐modeling 180 techniques. In this method, the units and the mortar and unit/mortar  interface are represented by 181 continuum and discontinuous elements, respectively. Different properties for both units and mortar 182 were  separately applied, and  this  leads  to a  realistic  response of a masonry assembly with more 183 accurate prediction of its local behavior. Despite these advantages, this approach is uneconomic and 184 inefficient in terms of computational time. To overcome this problem, simplified micro‐modeling has 185 been used and, according to pervious research, it can give accurate results with a simple modeling 186 procedure. In this type of modeling, the mortar joints are clamped into the unit/mortar interface as a 187 discontinuous element. Expanded units—up to half of the mortar thickness in horizontal and vertical 188 directions—were simulated to continuum elements. This procedure can successfully predict the shear 189 behavior and crack pattern [25–28]. 190

3.1. Constitutive Models 191

(a) Concrete Damage Plasticity (CDP) 192

Figure 9. The resulting shear-stress–normal-stress graph.

3. Finite Element Modeling

The finite element method (FEM) is one of the powerful tools for modeling a structure with verycomplicated geometry and materials. There are many strategies, as shown in Figure 10, to modela masonry structure with FEM, which includes macro- and micro-modeling. The macro-model isbased on the assumption of homogenous materials, and the mortar joints and units can be smearedinto one isotropic or anisotropic material. This procedure may be preferred for the analysis of largemasonry structures due to the reduced time and memory requirements as well as a user-friendly meshgeneration. In addition, this type of modeling is most valuable when a compromise between accuracyand efficiency is needed [23,24].

Appl. Sci. 2016, 6, 245  7 of 14 

 166

Figure 9. The resulting shear‐stress–normal‐stress graph. 167

3. Finite Element Modeling   168

The finite element method (FEM) is one of the powerful tools for modeling a structure with very 169 complicated geometry and materials. There are many strategies, as shown in Figure 10, to model a 170 masonry structure with FEM, which includes macro‐ and micro‐modeling. The macro‐model is based 171 on the assumption of homogenous materials, and the mortar joints and units can be smeared into one 172 isotropic or anisotropic material. This procedure may be preferred for the analysis of large masonry 173 structures  due  to  the  reduced  time  and memory  requirements  as well  as  a  user‐friendly mesh 174 generation. In addition, this type of modeling is most valuable when a compromise between accuracy 175 and efficiency is needed [23,24]. 176

 177

Figure 10. Modeling strategies  for block masonry.  (a) Typical masonry sample;  (b) Detailed micro 178 modeling; (c) Simplified micro modeling; (d) Macro modeling. 179

More  accurate  response  of  a masonry  assembly  can  be  deducted  by  using micro‐modeling 180 techniques. In this method, the units and the mortar and unit/mortar  interface are represented by 181 continuum and discontinuous elements, respectively. Different properties for both units and mortar 182 were  separately applied, and  this  leads  to a  realistic  response of a masonry assembly with more 183 accurate prediction of its local behavior. Despite these advantages, this approach is uneconomic and 184 inefficient in terms of computational time. To overcome this problem, simplified micro‐modeling has 185 been used and, according to pervious research, it can give accurate results with a simple modeling 186 procedure. In this type of modeling, the mortar joints are clamped into the unit/mortar interface as a 187 discontinuous element. Expanded units—up to half of the mortar thickness in horizontal and vertical 188 directions—were simulated to continuum elements. This procedure can successfully predict the shear 189 behavior and crack pattern [25–28]. 190

3.1. Constitutive Models 191

(a) Concrete Damage Plasticity (CDP) 192

Figure 10. Modeling strategies for block masonry. (a) Typical masonry sample; (b) Detailed micromodeling; (c) Simplified micro modeling; (d) Macro modeling.

More accurate response of a masonry assembly can be deducted by using micro-modelingtechniques. In this method, the units and the mortar and unit/mortar interface are represented bycontinuum and discontinuous elements, respectively. Different properties for both units and mortarwere separately applied, and this leads to a realistic response of a masonry assembly with moreaccurate prediction of its local behavior. Despite these advantages, this approach is uneconomic andinefficient in terms of computational time. To overcome this problem, simplified micro-modeling hasbeen used and, according to pervious research, it can give accurate results with a simple modelingprocedure. In this type of modeling, the mortar joints are clamped into the unit/mortar interface as adiscontinuous element. Expanded units—up to half of the mortar thickness in horizontal and verticaldirections—were simulated to continuum elements. This procedure can successfully predict the shearbehavior and crack pattern [25–28].

Appl. Sci. 2016, 6, 245 8 of 14

3.1. Constitutive Models

(a) Concrete Damage Plasticity (CDP)

The nonlinear behavior of the masonry can be simulated in Abaqus using the CDP model, whichcan be used for concrete and other brittle materials [29]. The failure modes of this model are cracksin tension or crushing in compression. The stress–strain relationship and corresponding damageparameters for the validation models used in this study were based on primary models proposed byLubliner et al. [30] and Lee and Fenves [31]. The uniaxial compressive and tensile response of concreteis described by damage plasticity as shown in Figure 11.

Appl. Sci. 2016, 6, 245  8 of 14 

The nonlinear behavior of the masonry can be simulated in Abaqus using the CDP model, which 193 can be used for concrete and other brittle materials [29]. The failure modes of this model are cracks 194 in  tension or  crushing  in  compression. The  stress–strain  relationship  and  corresponding damage 195 parameters for the validation models used in this study were based on primary models proposed by 196 Lubliner et al. [30] and Lee and Fenves [31]. The uniaxial compressive and tensile response of concrete 197 is described by damage plasticity as shown in Figure 11. 198

 199

Figure 11. Response of concrete to uniaxial loading according to the Abaqus theory manual [29]. 200

(b) Cohesive Surface‐Based Element 201

The cohesive interaction is defined as a function of displacement separation between the edges 202 of  potential  cracks  [32].  Furthermore,  pervious  researches  have  been  conducted  to  study  the 203 parameters  that  affect  the  cohesive  interaction  performance  for  brittle  materials.  These  have 204 concluded that the mechanical behavior of cohesive elements can be defined by three methods: (1) 205 uniaxial  stress‐based,  (2)  continuum‐based  and  (3)  traction–separation  constitutive  model.  The 206 traction–separation model represents the corresponding initial separation caused by pure normal, in 207 plane, and out plane  shear  stress as  shown  in Figure 12. This  study  takes  into  consideration  the 208 damage  evolution  which  can  be  specified  by  either  using  the  post‐damage‐initiation  effective 209 separation at failure or the total fracture energy. Furthermore, Coulomb frictional contact behavior 210 was  applied  to  the  current models  by  introducing  a  coefficient  of  friction  ( ) which  prevents 211 components’ penetration after forming the contact as shown in Figure 13, especially for the normal 212 behavior  of  contacts.  For  this  study,  surface‐to‐surface  contact  was  chosen  and  the  contacting 213 properties for the tangential and normal behavior were specified. This type of contact is generally 214 used to describe the behavior of two deformable surfaces connecting together. Also the slip‐rate data 215 were specified to define the coefficient of friction [29,33]. 216

(a)  (b)

Figure 12. Typical traction–separation behavior and fracture modes. (a) Traction‐separation response; 217 (b) Fracture modes [29]. 218

Figure 11. Response of concrete to uniaxial loading according to the Abaqus theory manual [29].

(b) Cohesive Surface-Based Element

The cohesive interaction is defined as a function of displacement separation between the edges ofpotential cracks [32]. Furthermore, pervious researches have been conducted to study the parametersthat affect the cohesive interaction performance for brittle materials. These have concluded that themechanical behavior of cohesive elements can be defined by three methods: (1) uniaxial stress-based,(2) continuum-based and (3) traction–separation constitutive model. The traction–separation modelrepresents the corresponding initial separation caused by pure normal, in plane, and out plane shearstress as shown in Figure 12. This study takes into consideration the damage evolution which canbe specified by either using the post-damage-initiation effective separation at failure or the totalfracture energy. Furthermore, Coulomb frictional contact behavior was applied to the current modelsby introducing a coefficient of friction (µ) which prevents components’ penetration after formingthe contact as shown in Figure 13, especially for the normal behavior of contacts. For this study,surface-to-surface contact was chosen and the contacting properties for the tangential and normalbehavior were specified. This type of contact is generally used to describe the behavior of twodeformable surfaces connecting together. Also the slip-rate data were specified to define the coefficientof friction [29,33].

Appl. Sci. 2016, 6, 245  8 of 14 

The nonlinear behavior of the masonry can be simulated in Abaqus using the CDP model, which 193 can be used for concrete and other brittle materials [29]. The failure modes of this model are cracks 194 in  tension or  crushing  in  compression. The  stress–strain  relationship  and  corresponding damage 195 parameters for the validation models used in this study were based on primary models proposed by 196 Lubliner et al. [30] and Lee and Fenves [31]. The uniaxial compressive and tensile response of concrete 197 is described by damage plasticity as shown in Figure 11. 198

 199

Figure 11. Response of concrete to uniaxial loading according to the Abaqus theory manual [29]. 200

(b) Cohesive Surface‐Based Element 201

The cohesive interaction is defined as a function of displacement separation between the edges 202 of  potential  cracks  [32].  Furthermore,  pervious  researches  have  been  conducted  to  study  the 203 parameters  that  affect  the  cohesive  interaction  performance  for  brittle  materials.  These  have 204 concluded that the mechanical behavior of cohesive elements can be defined by three methods: (1) 205 uniaxial  stress‐based,  (2)  continuum‐based  and  (3)  traction–separation  constitutive  model.  The 206 traction–separation model represents the corresponding initial separation caused by pure normal, in 207 plane, and out plane  shear  stress as  shown  in Figure 12. This  study  takes  into  consideration  the 208 damage  evolution  which  can  be  specified  by  either  using  the  post‐damage‐initiation  effective 209 separation at failure or the total fracture energy. Furthermore, Coulomb frictional contact behavior 210 was  applied  to  the  current models  by  introducing  a  coefficient  of  friction  ( ) which  prevents 211 components’ penetration after forming the contact as shown in Figure 13, especially for the normal 212 behavior  of  contacts.  For  this  study,  surface‐to‐surface  contact  was  chosen  and  the  contacting 213 properties for the tangential and normal behavior were specified. This type of contact is generally 214 used to describe the behavior of two deformable surfaces connecting together. Also the slip‐rate data 215 were specified to define the coefficient of friction [29,33]. 216

(a)  (b)

Figure 12. Typical traction–separation behavior and fracture modes. (a) Traction‐separation response; 217 (b) Fracture modes [29]. 218

Figure 12. Typical traction–separation behavior and fracture modes. (a) Traction-separation response;(b) Fracture modes [29].

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 219

Figure 13. Frictional behavior [29]. 220

3.2. FE Model, Results, and Discussion 221

Three models—compression prism and shear prisms with precompression stress of 0.10 N/mm2 222 and 0.30 N/mm2—were generated using Abaqus software to simulate the experiments.   223

3.2.1. Model Inputs 224

(a) Concrete Damage Plasticity Parameters 225

The masonry assemblages were modeled according to the materials’ properties in Table 4. The 226 compression behavior of CDP model was extracted from compression test data for masonry prism. 227

Table 5 shows the stress–strain and the damage data applied to the models in this study, which 228 were calculated based on set of equations provided by Sinha et al [34]. 229

Table 4. The mechanical properties of masonry assemblages. 230

Sample 

Mass 

Density 

(kg/m3) 

Elasticity Plasticity 

Young’s 

Modulus 

(kN/mm2) 

Poisson’s 

Ratio 

Dilation 

Angle ΨEccentricity fbo/fco  K 

Viscosity 

Parameter

Compression 

and shear 

prism 

2672  15.2  0.2  34  0.1  1.16  0.67  0.001 

where,  Ψ  is  the dilation  angle  (degrees),  fbo  is  bidirectional  compressive  strength  of masonry  (N/mm2),  fco  is 231 unidirectional compressive strength of masonry (N/mm2), K is the ratio of the second stress invariant on the tensile 232 meridian, and Viscosity parameter is used for the viscoplastic regularization of the concrete constitutive equations 233 in Abaqus/Standard analyses (seconds). 234

Table 5. Compressive and tensile behavior of the model. 235

Concrete Damage Plasticity 

Compression and Shear Prism 

Compressive Behavior  Tensile Behavior 

Yield Stress (N/mm2)  Inelastic Strain  Yield Stress (N/mm2) Cracking Strain 

3.68  0  1.06  0 

5.95  0.00021  0.80  0.00013 

8.77  0.00082  0.65  0.00025 

9.16  0.00120  0.48  0.00052 

9.20  0.00140  0.43  0.00064 

9.13  0.00230  ‐  ‐ 

8.14  0.00746  ‐  ‐ 

(b) Joints Cohesive Behavior Parameters 236

The most common friction coefficient (μ) of concrete masonry is in the range of 0.6–0.8 [33]. The 237 best fit was obtained when using 0.80 in this study. Cohesive behavior of the bed and vertical joints 238

Figure 13. Frictional behavior [29].

3.2. FE Model, Results, and Discussion

Three models—compression prism and shear prisms with precompression stress of 0.10 N/mm2

and 0.30 N/mm2—were generated using Abaqus software to simulate the experiments.

3.2.1. Model Inputs

(a) Concrete Damage Plasticity Parameters

The masonry assemblages were modeled according to the materials’ properties in Table 4.The compression behavior of CDP model was extracted from compression test data for masonry prism.

Table 5 shows the stress–strain and the damage data applied to the models in this study, whichwere calculated based on set of equations provided by Sinha et al [34].

Table 4. The mechanical properties of masonry assemblages.

SampleMass

Density(kg/m3)

Elasticity PlasticityYoung’s

Modulus(kN/mm2)

Poisson’sRatio

DilationAngle Ψ

Eccentricity f bo/f co K ViscosityParameter

Compressionand shear

prism2672 15.2 0.2 34 0.1 1.16 0.67 0.001

where, Ψ is the dilation angle (degrees), f bo is bidirectional compressive strength of masonry (N/mm2), f co isunidirectional compressive strength of masonry (N/mm2), K is the ratio of the second stress invariant on thetensile meridian, and Viscosity parameter is used for the viscoplastic regularization of the concrete constitutiveequations in Abaqus/Standard analyses (seconds).

Table 5. Compressive and tensile behavior of the model.

Concrete Damage Plasticity

Compression and Shear PrismCompressive Behavior Tensile Behavior

Yield Stress (N/mm2) Inelastic Strain Yield Stress (N/mm2) Cracking Strain3.68 0 1.06 05.95 0.00021 0.80 0.000138.77 0.00082 0.65 0.000259.16 0.00120 0.48 0.000529.20 0.00140 0.43 0.000649.13 0.00230 - -8.14 0.00746 - -

(b) Joints Cohesive Behavior Parameters

The most common friction coefficient (µ) of concrete masonry is in the range of 0.6–0.8 [33].The best fit was obtained when using 0.80 in this study. Cohesive behavior of the bed and vertical

Appl. Sci. 2016, 6, 245 10 of 14

joints were defined as shown in Table 6. However, the average compressive strength of masonry prismof 9.2 N/mm2 was employed in order to model the normal damage initiation [33]. Shear (I) presentsthe in-plane shear, which was determined according to Equation (1) (Figure 9). It is well known thatthe shear strength for masonry depends on the mechanical properties of masonry assemblage and theamount of the applied vertical load. This leads to different values of shear strength for the three modelsas presented in Table 6. The last parameter of traction–separation model is shear (II) that definesthe out-of-plane shear, which was set to zero for all models. Furthermore, the maximum separationand stiffness coefficient specified for shear models only were 1.25 mm and 26 MN/m, respectively.These values were obtained indirectly by trial and error in the calibration process. More testedspecimens are needed to specify more accurate values for the maximum separation and stiffnesscoefficient. The contact was assumed to have a thickness of zero, therefore hard contact was assignedfor normal behavior of contact. It is supposed that “hard” contact prevents the penetration of surfaceswhich can occur in the models.

Table 6. Cohesive behavior of joints.

Sample

Contact

TangentialBehavior Normal

Behavior

Cohesive BehaviorTraction-Separation Behavior

Damage Initiation (N/mm2) EvolutionStiffness Coefficients (MN/m)

FricationCoefficient Knn Kss Ku Normal Shear I Shear II

PlasticDisplacement

(mm)Compression

prism 0.8Hard

contact - - - 9.2 0 0 -

Shear prism (1) 26 26 0 9.2 0.61 1.25Shear prism (2) 0.74

Knn, Kss, and Ku represent the stiffness coefficients in normal and two shear directions, MN/m.

The finite element mesh, boundary conditions, and loading of masonry assemblages are shown inFigure 14. All the nodes at the bottom of the compression prism were restrained in the three directions(x, y, and z axes) to simulate the friction test condition as shown in Figure 14a. While in the shearmodels, the bottom of the prism and the right sides (for bottom and top units) were restrained in thedirections against the loading as shown in Figure 14b.

Appl. Sci. 2016, 6, 245  10 of 14 

were defined as shown in Table 6. However, the average compressive strength of masonry prism of 239 9.2 N/mm2 was employed in order to model the normal damage initiation [33]. Shear (I) presents the 240 in‐plane shear, which was determined according to Equation (1) (Figure 9). It is well known that the 241 shear strength for masonry depends on the mechanical properties of masonry assemblage and the 242 amount of  the applied vertical  load. This  leads  to different values of shear strength  for  the  three 243 models as presented  in Table 6. The  last parameter of  traction–separation model  is shear  (II)  that 244 defines  the out‐of‐plane shear, which was set  to zero  for all models. Furthermore,  the maximum 245 separation and stiffness coefficient specified  for shear models only were 1.25 mm and 26 MN/m, 246 respectively. These values were obtained indirectly by trial and error in the calibration process. More 247 tested  specimens  are  needed  to  specify more  accurate  values  for  the maximum  separation  and 248 stiffness coefficient. The contact was assumed to have a thickness of zero, therefore hard contact was 249 assigned for normal behavior of contact. It is supposed that “hard” contact prevents the penetration 250 of surfaces which can occur in the models. 251

Table 6. Cohesive behavior of joints. 252

Knn, Kss, and Ku represent the stiffness coefficients in normal and two shear directions, MN/m. 253

The finite element mesh, boundary conditions, and loading of masonry assemblages are shown 254 in Figure  14. All  the nodes at  the bottom of  the  compression prism were  restrained  in  the  three 255 directions (x, y, and z axes) to simulate the friction test condition as shown in Figure 14a. While in the 256 shear models, the bottom of the prism and the right sides (for bottom and top units) were restrained 257 in the directions against the loading as shown in Figure 14b. 258

(a)  (b)

Figure 14. Geometry of assemblages,  finite element  (F.E.) mesh, boundary conditions and surface‐259 based interaction of units. (a) Compression prism; (b) Shear prism. 260

An eight‐node 3D stress linear brick (C3D8R) was used for modeling the masonry assemblages 261 to reduce the computation time without losing the results accuracy [33]. The geometry of assemblages 262

Sample 

Contact 

Tangential 

Behavior Normal 

Behavior 

Cohesive Behavior 

Traction‐Separation 

Behavior Damage Initiation (N/mm2)  Evolution 

Stiffness 

Coefficients (MN/m)

Frication 

CoefficientKnn Kss Ku  Normal Shear I Shear II 

Plastic 

Displacement 

(mm) 

Compression 

prism 0.8 

Hard 

contact ‐  ‐  ‐  9.2  0  0  ‐ 

Shear prism (1)      26  26 0  9.2  0.61    1.25 

Shear prism (2)              0.74     

Figure 14. Geometry of assemblages, finite element (F.E.) mesh, boundary conditions and surface-basedinteraction of units. (a) Compression prism; (b) Shear prism.

An eight-node 3D stress linear brick (C3D8R) was used for modeling the masonry assemblages toreduce the computation time without losing the results accuracy [33]. The geometry of assemblagesand defined interaction surfaces between units are shown in Figure 14. The size of units are390 × 220 × 195 mm and 195 × 220 × 195 mm with zero thickness of mortar.

Appl. Sci. 2016, 6, 245 11 of 14

3.2.2. Model Outputs

Figure 15 shows the final von Mises and maximum principal stress and strains for compressionprism. As can be seen, the maximum stress occurred at the bottom edges of prism, while the maximumstrain is located at the middle of the prism. Obviously, this leads to the initiation of vertical tensilesplitting cracks at the middle of the prism and spreading to the top and bottom units, which issimilar to what was found experimentally. The maximum stress obtained from the numerical modelwas 8.67 N/mm2 with a difference of 6% compared with that recorded from experimental results.

Appl. Sci. 2016, 6, 245  11 of 14 

and defined interaction surfaces between units are shown in Figure 14. The size of units are 390 × 220 263 × 195 mm and 195 × 220 × 195 mm with zero thickness of mortar. 264

3.2.2. Model Outputs 265

Figure 15 shows the final von Mises and maximum principal stress and strains for compression 266 prism. As  can  be  seen,  the maximum  stress  occurred  at  the  bottom  edges  of  prism, while  the 267 maximum strain is located at the middle of the prism. Obviously, this leads to the initiation of vertical 268 tensile splitting cracks at the middle of the prism and spreading to the top and bottom units, which 269 is  similar  to what was  found  experimentally. The maximum  stress obtained  from  the numerical 270 model was 8.67 N/mm2 with a difference of 6% compared with  that  recorded  from experimental 271 results. 272

(a)  (b) 

(c)

Figure 15. Compression prism F.E. results: (a) Principal stresses; (b) Strains; (c) Von Mises stresses. 273

Figure 16 shows the numerical results for the two shear models. Figure 16a presents the von 274 Mises and principal stresses and  strains  for shear prism with 0.1 N/mm2 axial constant  stress.  In 275 addition,  the  load  displacement  curve was  obtained  and  compared with  the  experimental  one. 276 Furthermore, Figure 16b describes the same output with different axial constant stress of 0.3 N/mm2. 277 Displacement for model (b) (with an axial constant stress of 0.3 N/mm2) is much higher than model 278 (a) (with an axial constant stress of 0.1 N/mm2), which is mainly due to increasing the constant axial 279 stress.   280

Figure 15. Compression prism F.E. results: (a) Principal stresses; (b) Strains; (c) Von Mises stresses.

Figure 16 shows the numerical results for the two shear models. Figure 16a presents the von Misesand principal stresses and strains for shear prism with 0.1 N/mm2 axial constant stress. In addition,the load displacement curve was obtained and compared with the experimental one. Furthermore,Figure 16b describes the same output with different axial constant stress of 0.3 N/mm2. Displacementfor model (b) (with an axial constant stress of 0.3 N/mm2) is much higher than model (a) (with anaxial constant stress of 0.1 N/mm2), which is mainly due to increasing the constant axial stress.

Appl. Sci. 2016, 6, 245  11 of 14 

and defined interaction surfaces between units are shown in Figure 14. The size of units are 390 × 220 263 × 195 mm and 195 × 220 × 195 mm with zero thickness of mortar. 264

3.2.2. Model Outputs 265

Figure 15 shows the final von Mises and maximum principal stress and strains for compression 266 prism. As  can  be  seen,  the maximum  stress  occurred  at  the  bottom  edges  of  prism, while  the 267 maximum strain is located at the middle of the prism. Obviously, this leads to the initiation of vertical 268 tensile splitting cracks at the middle of the prism and spreading to the top and bottom units, which 269 is  similar  to what was  found  experimentally. The maximum  stress obtained  from  the numerical 270 model was 8.67 N/mm2 with a difference of 6% compared with  that  recorded  from experimental 271 results. 272

(a)  (b) 

(c)

Figure 15. Compression prism F.E. results: (a) Principal stresses; (b) Strains; (c) Von Mises stresses. 273

Figure 16 shows the numerical results for the two shear models. Figure 16a presents the von 274 Mises and principal stresses and  strains  for shear prism with 0.1 N/mm2 axial constant  stress.  In 275 addition,  the  load  displacement  curve was  obtained  and  compared with  the  experimental  one. 276 Furthermore, Figure 16b describes the same output with different axial constant stress of 0.3 N/mm2. 277 Displacement for model (b) (with an axial constant stress of 0.3 N/mm2) is much higher than model 278 (a) (with an axial constant stress of 0.1 N/mm2), which is mainly due to increasing the constant axial 279 stress.   280

Figure 16. Cont.

Appl. Sci. 2016, 6, 245 12 of 14

Appl. Sci. 2016, 6, 245  12 of 14 

 

(a)

 (b)

Figure 16. Shear prisms; load displacement curves, principal, and von Mises stress and strain contours: 281 (a) Model with precompression stress 0.1 N/mm2; (b) Model with precompression stress 0.3 N/mm2. 282

The maximum horizontal loads obtained numerically for the two models were 94.4 kN and 119.9 283 kN for model (a) (with an axial constant stress of 0.1 N/mm2) and model (b) (with an axial constant 284 stress  of  0.3 N/mm2),  respectively. Moreover,  the  horizontal  displacement  corresponding  to  the 285 maximum horizontal loads was 0.074 mm and 0.13 mm, respectively. These results show a difference 286 not more than 10% compared with the experimental one. The stepped shape for the experimental 287 load‐displacement curves took place due to the fact that the load was manually applied with force 288 control. Furthermore, Figure 16 shows the maximum von Mises stress that occurred at the location 289 of applying the shear loading. The maximum strain is located in the horizontal joints for both models 290 which agreed with  the  experimental  results as  shown  in Figure 8. The amount of  the horizontal 291 displacement  (slip)  at  the  location  of  bed  joint  is  relatively  small,  indicating  a  high  degree  of 292 brittleness for the materials. Failure modes and load‐displacement curves for the numerical models 293 showed good agreement with the experimental results. 294

4. Conclusions   295

This paper presents an experimental and analytical study for masonry assemblages which were 296 built from a new type of self‐insulating concrete masonry unit (SCMU), and subjected to compression 297 and  shear  loadings.  Based  on  the  results  from  experimental  and  numerical  analysis,  it  can  be 298 concluded that: 299

(1) The special configuration of SCMUs has advantages in both structural and thermal properties. 300 The structural advantage is providing stronger bonds than the ordinary concrete masonry units by 301

Figure 16. Shear prisms; load displacement curves, principal, and von Mises stress and strain contours:(a) Model with precompression stress 0.1 N/mm2; (b) Model with precompression stress 0.3 N/mm2.

The maximum horizontal loads obtained numerically for the two models were 94.4 kN and119.9 kN for model (a) (with an axial constant stress of 0.1 N/mm2) and model (b) (with an axialconstant stress of 0.3 N/mm2), respectively. Moreover, the horizontal displacement correspondingto the maximum horizontal loads was 0.074 mm and 0.13 mm, respectively. These results showa difference not more than 10% compared with the experimental one. The stepped shape for theexperimental load-displacement curves took place due to the fact that the load was manually appliedwith force control. Furthermore, Figure 16 shows the maximum von Mises stress that occurred at thelocation of applying the shear loading. The maximum strain is located in the horizontal joints for bothmodels which agreed with the experimental results as shown in Figure 8. The amount of the horizontaldisplacement (slip) at the location of bed joint is relatively small, indicating a high degree of brittlenessfor the materials. Failure modes and load-displacement curves for the numerical models showed goodagreement with the experimental results.

4. Conclusions

This paper presents an experimental and analytical study for masonry assemblages which werebuilt from a new type of self-insulating concrete masonry unit (SCMU), and subjected to compressionand shear loadings. Based on the results from experimental and numerical analysis, it can beconcluded that:

Appl. Sci. 2016, 6, 245 13 of 14

(1) The special configuration of SCMUs has advantages in both structural and thermal properties.The structural advantage is providing stronger bonds than the ordinary concrete masonry units byfacilitating the grout between the units, both vertically and horizontally. On the other hand, the thermaladvantage is reducing the thermal bridges by using continuous insulation materials.

(2) The shear resistance of SCMUs’ assemblages increased as the level of precompressionincreased. The shear stress increased from approximately 0.61 N/mm2 to 0.74 N/mm2 as theprecompression stress increased from 0.1 N/mm2 to 0.3 N/mm2. A similar trend was obtainedfrom the numerical analysis.

(3) Using a simplified micro-modeling strategy for grouted masonry assemblages gave accurateresults with a simple model procedure. Furthermore, the mortar joints were modeled withzero thickness and their behavior was simulated using the traction–separation model of thecohesive element.

(4) The applications of Mohr–Coulomb’s failure criterion and the compressive strength of masonryprism in the traction–separation model displayed an acceptable procedure to deduce the generalbehavior of grouted masonry assemblages. An average cohesive stress of 0.54 N/mm2 and frictionangle of 33.7◦ for SCMUs’ prism were obtained from a linear regression model (R2 = 0.99).

(5) The crack patterns observed experimentally were in good agreement with those predicted bythe F.E. models. Also, excellent correlations between the numerical and experimental results of failureloads, displacement, and stress distribution were recorded. The predicted values of failure load andstress presented not more than 10% error.

Acknowledgments: This research was conducted with the financial support of the National “Twelfth Five-Year”Research Project in the National Science & Technology Pillar Program (Grant No. 2015BAL03B02).

Author Contributions: Abu-Bakre Abdelmoneim Elamin Mohamad wrote the manuscript; Abu-BakreAbdelmoneim Elamin Mohamad and Zhongfan Chen designed the experiments. Abu-Bakre AbdelmoneimElamin Mohamad and Zhongfan Chen modified the final paper.

Conflicts of Interest: The authors declare no conflict of interest.

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