1 Introduction
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Masonry with poor mortar strength
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Masonry with poor unit strength
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Masonry with poor unit and mortar strength
Sample | Type of test | Parameters | Numerical (experimental) outcome | References |
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Tuff masonry panel | Diagonal compression | Shear stress | 0.39 MPa (0.38 MPa) | [14] |
Adobe wall panel | Diagonal compression | Shear stress | 0.15 MPa (0.14 MPa) | [1] |
Hollow concrete block | Compression | Peak load | 550 kN (600 kN) | [8] |
Hollow clay units | Cyclic shear load | Shear capacity | 215 kN (222 kN) | [15] |
2 Modelling Methodology
2.1 Geometry
Combinations | Model symbol |
---|---|
Block-only unplastered | M1—(U) |
8-mm-thick plain-plastered column | M2—(P,8,N) |
20-mm-thick plain-plastered column | M3—(P,20,N) |
8-mm-thick rice-straw-plastered column | M4—(P,R,8) |
20-mm-thick rice-straw-plastered column | M5—(P,R,20) |
8-mm-thick sisal-plastered column | M6—(P,S,8) |
20-mm-thick sisal-plastered column | M7—(P,S,20) |
Model | Block elements no | Block interface elements No | Plaster interface elements no | Plaster elements no |
---|---|---|---|---|
M1—(U) | 2400 | 520 | – | – |
M2—(P,8,N) | 2400 | 520 | 640 | 1480 |
M3—(P,20,N) | 2400 | 520 | 640 | 3700 |
M4—(P,R,8) | 2400 | 520 | 640 | 1480 |
M5—(P,R,20) | 2400 | 520 | 640 | 3700 |
M6—(P,S,8) | 2400 | 520 | 640 | 1480 |
M7—(P,S,20) | 2400 | 520 | 640 | 3700 |
2.2 Material and Interface Properties
2.2.1 Block Properties
Material | Modulus of elasticity E (MPa) | Poison’s ratio n | Compressive strength fc (MPa) | Tensile strength ft (MPa)* | Fracture energy Gf (N/mm) |
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Block | 201 | 0.15 | 0.83 | 0.080 | 0.0441 |
2.2.2 Block Interface Properties
Model | Df11 (N/mm3) | Df22 (N/mm3) | µ | S1 (MPa) | F1 (mm) | S2 (MPa) | F2 (mm) |
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M1—(U) | 0.02 | 0.20 | 0.1 | 0 | 0 | 3.488E−07 | 150 |
M2—(P,8,N) | 0.02 | 0.20 | 0.1 | 0 | 0 | 0.0001744 | 150 |
M3—(P,20,N) | 0.01 | 0.1 | 0.1 | 0 | 0 | 0.0001744 | 150 |
M4—(P,R,8) | 0.0021 | 0.021 | 0.1 | 0 | 0 | 0.0001744 | 150 |
M5—(P,R,20) | 0.0015 | 0.015 | 0.1 | 0 | 0 | 0.0001744 | 150 |
M6—(P,S,8) | 0.0021 | 0.021 | 0.1 | 0 | 0 | 0.0001744 | 150 |
M7—(P,S,20) | 0.00035 | 0.0035 | 0.1 | 0 | 0 | 0.0001744 | 150 |
2.2.3 Plaster Properties
Material | Modulus of elasticity E (MPa) | Poison’s ratio n | Compressive strength fc (MPa) | Tensile strength ft (MPa)* | Fracture energy Gf (N/mm) |
---|---|---|---|---|---|
Plain plaster | 2990 | 0.15 | 19.33 | 1.933 | 0.065 |
Rice straw plaster | 2483 | 0.15 | 8.67 | 0.867 | 0.053 |
Sisal plaster | 7175 | 0.15 | 19.88 | 1.988 | 0.657 |
2.2.4 Properties of the Interface Between Block and Plaster
Model | Df11 (N/mm3) | Df22 (N/mm3) | τpeak (N/mm2) | Speak (mm) | Su (mm) | Gfi (N/mm) |
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M1—(U) | – | – | – | – | – | – |
M2—(P,8,N) | 157.8 | 1577.9 | 3.590 | 0.164 | 0.031 | 0.295 |
M3—(P,20,N) | 157.8 | 1577.9 | 3.590 | 0.164 | 0.031 | 0.295 |
M4—(P,R,8) | 157.8 | 1577.9 | 3.082 | 0.141 | 2.66E−02 | 0.218 |
M5—(P,R,20) | 157.8 | 1577.9 | 3.082 | 0.141 | 2.66E−02 | 0.218 |
M6—(P,S,8) | 157.8 | 1577.9 | 3.609 | 0.165 | 0.031 | 0.299 |
M7—(P,S,20) | 157.8 | 1577.9 | 3.609 | 0.165 | 0.031 | 0.299 |
2.3 Loading Applied
2.4 Constraint Condition
2.5 Solution Method
Model | Size (step) mm | Tolerance mm | Nonlinear analysis method | Max no. of Iterations | Convergence critical mm |
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M1—(U) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.05 |
M2—(P,8,N) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.2 |
M3—(P,20,N) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.2 |
M4—(P,R,8) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.9 |
M5—(P,R,20) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.9 |
M6—(P,S,8) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.9 |
M7—(P,S,20) | 0.1 (20) | 1.00E−6 | Secant | 1,000,000 | 0.9 |
3 Results and Validation
3.1 Maximum Load
Model | Experimental lateral peak/failure load (Fexp) (N) | TNO DIANA lateral peak/failure load (FDIANA) (N) | Ratio Fexp/FDIANA | Average |
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M1—(U) | 15 | 14.8 | 1.01 | 1.01 |
M2—(P,8,N) | 48 | 42.2 | 1.13 | 1.07 |
M3—(P,20,N) | 75 | 74.57 | 1.00 | |
M4—(P,R,8) | 238 | 242.5 | 0.98 | 1.00 |
M5—(P,R,20) | 256 | 247.9 | 1.03 | |
M6—(P,S,8) | 242 | 232.2 | 1.04 | 1.04 |
M7—(P,S,20) | 312 | 289.3 | 1.04 |
3.2 Load–Displacement Curves
3.3 Crack Pattern
3.4 Sensitivity Analysis
3.4.1 Effect of Mesh Size
3.4.2 Tensile Strength Effect
4 Parametric Study
4.1 Strength of Block
4.2 Strength of Plaster
4.3 Thickness of Plaster
5 Cost Analysis and Practical Application
5.1 Sensitivity Analysis and Results
Model | Fz (N) with 150-mm block thickness | Fz (N) with reduced block thickness | Reduced thickness of block |
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A—Unmortared unplastered (Datum) | 27.36 | – | – |
B—Unmortared plain-plastered | 137.54 | 35.8 | 25 mm + 8 mm plaster |
C—Unmortared fibrous-plastered | 167.7 | 45.4 | 25 mm + 8 mm plaster |
D—Unplastered but Mortared | 208 | – | – |
5.2 Cost Comparison
Type | A—Datum | B—thickness 25 mm | C—thickness 25 mm | D—150 mm thickness |
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Cost ($)/m2 | 3.52 | 1.15 | 1.16 | 5.90 |
Normalized to unmortared unplastered wall (A) | 1.00 | 0.33 | 0.33 | 1.68 |
6 Conclusion
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Lateral failure loads from FE models were in fair agreement with the experimental results. The average experimental and FE failure lateral load ratios obtained were 1.0, 1.07, 1.00 and 1.04 for unplastered, plain-plastered, rice-straw-reinforced plaster and sisal-plastered columns, respectively. This has validated the FE models and can be used for further analysis.
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The load–displacement curves showed that the stiffness of the FE model was markedly higher than the experimental results for the first stage of crack formation. This could be due to assumptions for constraint conditions being fixed in FE model. Once the crack forms, the failure load was comparable between the FE values and experimental results, because of the rotational smeared crack model.
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The FE models crack patterns have a good agreement with the crack patterns observed in the experimental tests, e.g. the opening of joints for unplastered columns and cracking in the interface between plaster and block for plastered ones. This showed most emphasis is required to increase the strength of interface for an overall increase in lateral resistance.
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Parametric study of block strength has shown that the failure load is directly proportional to the compressive strength of masonry blocks. Failure of blocks was not found to be a governing failure mode in experimental work.
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Parametric studies suggest that increasing the strength of plaster does not change the failure load. This is because failure is initiated by cracks in the interface between plaster and block. Also plaster contribution is expected in the tensile zone rather than compressive.
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Parametric study for thickness of plaster showed that increase in thickness of plaster resulted in the increase in failure load, but this increase is not linear with the increase in thickness of plaster, e.g. a 150% increase in thickness of plaster only resulted in 28% increase in failure load.
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Column thickness can be reduced to 25 mm of blocks with 8 mm of plaster and yet exceed the lateral strength of a 150-mm-thick unplastered column.
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Cost comparison showed that fibrous-plastered with 25 mm thickness gave equivalent performance to the 150-mm-thick unplastered column with 67% cost saving.