1. “COMPRESSIVE
BEHAVIOUR OF
MASONRY PRISMS”
Prepared by: Mina GayedApril 19th, 2010
CIVIL ENGINEERING: AN INTRODUCTION TO
FINITE ELEMENT ANALYSIS

2. 1. Goals
 Construct a micro-simulation finite element model
on Abaqus/CAE that closely represents a
standard test prism
 Conduct a parametric analysis to investigate the
effect of mortar joint thickness as well as stiffness
strength on the behaviour of masonry prisms
 Briefly compare results with those published in
literature

3. 2. Background
 Masonry compressive strength permeates all
design equations
 Prism testing is regarded as the standard
method to determine the compressive strength
 The results of prism testing are highly
susceptible to such factors as:
 Mortar joint thickness
 Mortar properties
 Block strength
 Prism geometry (h/t ratio)

4. 3. Analytical Program
Prism
5 mm
Joint
Eb/Em =
0.5
Eb/Em =
1.0
Eb/Em =
2.0
10 mm
Joint
Eb/Em =
0.5
Eb/Em =
1.0
Eb/Em =
2.0
15 mm
Joint
Eb/Em =
0.5
Eb/Em =
1.0
Eb/Em =
2.0
Note: Eb/Em is the modular ratio of block to
mortar

5. 4. Finite Element Model -
Assumptions
 Geometry assumptions taken:
 fillets at web to face shell connections were given a radius
of 8mm for lack of a better reference in the literature
 joint interfaces between the blocks and mortar are assumed
to be rigid since frictional forces created by compression
prevent slipping
 tapering of face shells and webs were eliminated
 Material is assumed linear elastic with loading at
less than 50% of failure
 Material is taken as homogeneous and isotropic

6. 5. Finite Element Model -
Creation
 Total of 8828
elements
 Block and mortar are
a 3D deformable
solid extrusion
 Block is
190x390x190
 Mortar is 32mm wide
times various
 Blocks: linear 8 node
brick elements –
meshed at 20 mm with
10 mm surface mesh
top&bottom
 Mortar joint: quadratic
20 node 3D brick with
10 mm mesh
Geometry Mesh
Creation 1 Creation 2 Creation 3

7. Meshing Details

8. 5. Finite Element Model -
Creation
Creation 1 Creation 2 Creation 3
 All materials are
homo-geneous and
isotropic
 Block:
 E = 21660 MPa
 ν = 0.2
 Mortar:
 E = Varies as 0.5 to 2 of
block’s modulus
 ν = 0.18
Material Assembly
 Prior to assembly 6
surfaces were
assigned
 2 for each mortar
layer
 1 for each interface
block layer
 4 instances total
were imported
 2 blocks
 2 mortar joint layers

9. Assembly Detail

10. 5. Finite Element Model -
Creation
 Tied all 6 surfaces
together  Mortar
joint “binds” the
interface and the
compressive forces
create additional
frictional resistance
 One step was
required
 Boundary conditions
taken as fixed
(encastre) at the
bottom
 Loading is top surface
pressure of 8 MPa
(approx. 50% of failure)
Surface Interaction Steps
Creation 1 Creation 2 Creation 3

11. B.C.’s and Loading Detail

12. 6. Results – General Trends
Minimum Principal Stresses
[10M2E]
Maximum Principal Stresses
[10M2E]
General Trends 1 General Trends 2 Parameter Variation 1 Parameter Variation 2
High compressive
stresses
Almost zero
compression
High tensile stress
concentrations

13. 6. Results – General Trends
Minimum Principal Stresses
[10M2E]
Maximum Principal Stresses
[10M2E]
Block face shell
in compression
High compression concentrations in
mortar
No tension in face
shells
Tension in mortar
at intersections
General Trends 1 General Trends 2 Parameter Variation 1 Parameter Variation 2

14. 6. Results – Parameter
Variation
-12
-11
-10
-9
-8
-7
-6
0 0.5 1 1.5 2 2.5
MinimumPrincipalStress[MPa]
Eb/Em Ratio
Minimum Principal Stresses in Hollow Concrete Prisms
5 mm Joint - Block Stress
5 mm Joint - Mortar Stress
10 mm Joint - Block Stress
10 mm Joint - Mortar Stress
15 mm Joint - Block Stress
15 mm Joint - Mortar Stress
Compressive stresses increased in
mortar with THICKER joints and
No distinction in block compressive
stresses with variation of joint thickness or
properties
General Trends 1 General Trends 2 Parameter Variation 1 Parameter Variation 2

15. 6. Results – Parameter
Variation
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.5 1 1.5 2 2.5
MaximumPrincipalStress[MPa]
Eb/Em Ratio
Maximum Principal Stresses in Hollow Concrete Prisms
5 mm Joint - Block Stress
5 mm Joint - Mortar Stress
10 mm Joint - Block Stress
10 mm Joint - Mortar Stress
15 mm Joint - Block Stress
15 mm Joint - Mortar Stress
For an Eb/Em ratio less than 1 mortar is in
compression but in tension for a ratio greater
than 1!
Higher stresses in general for THINNER joints
Block: less tensile stress with a
decrease in joint thickness and
softer mortar ( increasing Eb/Em
ratio)
General Trends 1 General Trends 2 Parameter Variation 1 Parameter Variation 2

16. 7. Future Work
 Study the nonlinear behaviour of prisms at a
load close to failure
 Determine whether or not the parameter
variation in this study will actually influence the
ultimate compressive strength of the prism
 Study the influence of prism geometry on the
compressive strength – vary h/t ratio
 Elaborate on the cause of
tension/compression variation of mortar as a
function of Eb/Em ratio
 Simulate an entire wall wythe and compare
results with those obtained from prisms

17. 8. Conclusion
 Finite element modeling is a very useful,
practical, and economical method to study the
cause and effect of parameter variation for
physical problems
 The model simulated is in good agreement with
prism tests found in the literature
 Varying mortar joint thickness and properties
has minimal effect on block stress propagation
 Less compressive stresses are observed in
mortar with thinner joints and higher Eb/Em
ratios
 Very interesting results observed for maximum

18. QUESTIONS ?
Compressive Behaviour of Masonry Prisms