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2D Nonlinear Finite Element Analysis of Masonry Bedjoint

by Osvald, Andrej


Page 31

CALCULATION WITH CRUSHED BRICK PARTICLES 31

The samples differs from each other in the bedjoint thickness, shape and quality of
crushed brick particles and each sample configuration is subjected to both, shear
displacement and shear combined with compression by the prescribed pressure.
Many combinations of these variables have been tested. To avoid confusion the
following codes of specimens are sorted in Tab. 6.1.
The quality of crushed bricked particles and material properties of bricks and
mortar are summarized in Tab. 6.2 and Tab. 6.3. These values are based on experience,
literature study and our own measurements.

Quality of crushed
bricks particles
Young’s modulus Fracture energy Tensile strength

E [GPa] Gf [J.m-2] ft [MPa]

high 12 12 3
low 5 3 1

Tab. 6.2: Quality of crushed brick particles

Young’s modulus Fracture energy Tensile strength
E [GPa] Gf [J.m-2] ft [MPa]

mortar 7 3,9 1,3
bricks 12 12 3

Tab. 6.3: Material properties of bricks and mortar


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CALCULATION WITH CRUSHED BRICK PARTICLES 32

5.1 Pure Shear

Fig. 6.2: Load-displacement of bedjoints having a various thickness and loaded by shear displacement

It can be seen in Fig. 6.2 that the load-displacement diagrams of specimens
having a various joint thickness and without any addition of crushed bricks within
the joints exhibit the same failure mode. The higher joint thickness contributes
neither to higher strength nor ductility. Assuming the mortar to be “weaker”
material characteristics than bricks (Tab. 6.3), it seems that the joint of lower thickness
slightly better resists shear loads.

Fig. 6.3: Plain bedjoint of 40 mm thickness loaded by pure shear


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CALCULATION WITH CRUSHED BRICK PARTICLES 33

After reaching a peak load a rapid failure arrives in the same way damage is
localized at the boundary between mortar and brick.

Fig. 6.4: Comparison of plain joint of 20 mm and 40 mm thick bedjoints containing crushed brick
particles loaded by shear displacement

The crushed brick particles were placed in 40 mm thick bedjoints and have
been compared with plain 20 mm thick bedjoint. Mortar with fine crushed particles
exhibits higher ductility.

Fig. 6.5: 40 mm thick bedjoint contains fine crushed brick particles of low quality loaded by pure shear


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CALCULATION WITH CRUSHED BRICK PARTICLES 34

In Fig. 6.5 we can see that if the fine crushed bricks are of a lower quality than mortar,
the cracks are slightly smeared and do not localise into a single major crack.

Fig. 6.6: 40 mm thick bedjoint contains fine crushed brick particles of high quality loaded by pure
shear

The addition of fine crushed bricks of higher quality than mortar (Fig. 6.6) means that
the damage is more localized at the boundary between bricks and mortar.

Fig. 6.7: 40 mm thick bedjoint contains coarse crushed brick particles of low quality loaded by pure
shear

Fig. 6.8: 40 mm thick bedjoint contains coarse crushed brick particles of high quality loaded by pure
shear


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CALCULATION WITH CRUSHED BRICK PARTICLES 35

According to Fig. 6.7 and Fig. 6.8 we can assume that coarse crushed brick particles do
not contribute to smearing of cracks if the specimen is loaded by pure shear
displacement.

5.2 Shear and Compression

Fig. 6.9: Load-displacement of precompressed bedjoints having various thickness and loaded by shear
displacement

It is shown in Fig. 6.9 that the load-displacement diagrams of specimens having
various joint thickness and without any addition of crushed bricks within the joints
are exposed to the same failure mode. Again, as in pure shear case (Fig. 6.2), the
higher joint thickness contributes neither to higher strength nor ductility. Assuming
the mortar being “weaker” material than bricks (Tab. 6.3), it seems that the joint of
lower thickness slightly better resists shear loads.


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CALCULATION WITH CRUSHED BRICK PARTICLES 36

Fig. 6.10: Plain bedjoint of 40 mm thickness loaded by shear and displacement

If a moderate compressive force (pressure) is applied, the crack penetrates to the
brick under the bedjoint (Fig. 6.10).

Fig. 6.11: Comparison of precompressed plain joint od thickness 20 mm and precompressed 40 mm
thick bedjoints containing crushed brick particles loaded by shear displacement

In Fig. 6.11 the comparison between precompressed 40 mm thick bedjoints
containing crushed brick particles and plain precompressed 20 mm thick bedjoint
can be seen. The bedjoints with brick particles behave more relaxed during failure


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CALCULATION WITH CRUSHED BRICK PARTICLES 37

and damage is not so immediate. The results are more obvious from next figures
showing the failure mode.

Fig. 6.12: 40 mm thick bedjoint contains fine crushed brick particles of low quality loaded by shear and
displacement

The presence of fine crushed brick particles of lower quality significantly contributes
to the formation of smeared cracks over the joint (Fig. 6.12). Fine particles participate
in the stress distribution over the bedjoint.

Fig. 6.13: 40 mm thick bedjoint contains fine crushed brick particles of high quality loaded by shear
and displacement

Fine crushed bricks of higher quality do not contribute so efficiently to the formation
of smeared cracks and more localized damage can be observed (Fig. 6.13).


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CALCULATION WITH CRUSHED BRICK PARTICLES 38

Fig. 6.14: 40 mm thick bedjoint contains coarse crushed brick particles of low quality loaded by shear
and displacement

The presence of bigger crushed brick particles of lower quality (Fig. 6.14) contributes
to a similar effect as the fine brick particles, just the localization into major cracks is
more pronounced.

Fig. 6.15: 40 mm thick bedjoint contains coarse crushed brick particles of high quality loaded by shear
and displacement

The addition of crushed brick particles of a bigger diameter does not contribute to
the smearing of cracks (Fig. 6.15). A major localized crack forms as if there were no
crushed brick particles added into the bedjoint this complies with Fig. 6.10.


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CONCLUSION 39

Conclusion

Based on the plane stress finite element analysis utilizing an anisotropic
damage model, it can be conclude that for a pure shear and shear loading combined
with compression it is advantageous to make the bedjoints of lower thickness and
containing fine crushed brick particles.
The assumption of crushed brick particles contribution is confirmed, particles
improve behaviour under shear loading by smearing of cracks, especially in the case
of combined shear and compression.
Mortar with fine crushed particles also improves the bedjoint ductility. Quite
surprisingly the crushed brick particles of lower strength and stiffness contribute
better to the crack smearing over the joint, which results in a better energy
dissipation and slower softening of the bedjoint, especially in case of pure shear
loading.
The results of this paper cannot be considered exact because there were made
some simplifications in calculations and the 2D plane stress analysis is not as
accurate as full 3D model. Despite the above mentioned simplifications, the model
should provide valuable information about the formation of cracks in bedjoints, their
localization and generally enhance knowledge about the masonry behaviour.


Page 40

REFERENCES 40

References

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[3] NIKISHKOV G.P., Introduction to the Finite Element Method, Lecture Notes, UCLA
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[4] VASANI P.C., Criteria for selection of FEM models, Lecture Notes, L. D. College of
Engineering, Ahmedabad

[5] IVANČO V., Nonlinear Finite element analyses, Script of lectures, Faculty of
Mechanical Engineering, Technical University of Košice, Slovakia 2001

[6] KÖNKE H.C., Advanced Finite element methods, Handouts, Fakultät für
Bauingenieurwesen, Bauhaus-Universität Weimar

[7] TIMOSHENKO S., GOODIER J.N., Theory of Elasticity, Standford University 1951

[8] NARASAIAH G.L., Finite Element Analysis, MLR Institute of Technology 2008

[9] PATZÁK B., Material Model Library Manual, Department of Structural Mechanics,
Faculty of Civil Engineering, Czech Technical University 2011

[10] JIRÁSEK M., ZEMAN J., Přetváření a porušování materiálů, Faculty of Civil
Engineering, Czech Technical University 2008

[10] LOURENCO P.B., Experimental and numerical issues in the modelling of the
mechanical behaviour of masonry, Department of Civil Engineering, University of
Minho

Fig. 1.1 - http://www.vki.com/htdocs/mesh_gen.gif
Fig. 1.5 - https://upload.wikimedia.org/wikipedia/commons/7/75/FEM_car_crash1.jpg
Fig. 1.6 - [5]
Fig. 1.7 - [5]

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