1. A new assessment method for masonry arch bridges (SMART) Clive Melbourne, Adrienn Tomor School of Computing, Science and Engineering, University of Salford

2. Masonry arch bridge assessment methods
but …
Semi-empirical Methods: MEXE
Experience needed
No analytical input
Limit Analysis Methods
Only considers ULS
No indication of SLS or residual life
Solid Mechanics Methods
Highly dependent on parameters and boundary conditions that are difficult to quantify
Careful validation is essential.

3. ULS and SLS definitions
The ultimate limit state (ULS) for masonry arch bridges can be defined as the condition at which a collapse mechanism forms in the structure or its supports.
The serviceability limit state (SLS) for masonry arch bridges can be defined as the condition at which there is a loss of structural integrity which will measurably affect the ability of the bridge to carry its working loads for the expected life of the bridge.

4. New assessment method: Sustainable Masonry Arch Resistance Technique (SMART)
Determining the residual life of the bridge
Taking the effects of historical damage and repair methods into account on the long-term performance of the bridge

5. SMART method
Prior to reaching the ULS, the structure will achieve a statically determinate state.
Endurance limit states can be determined for at least the statically determined state with the help of interactive S-N curves
S-N curves are proposed

6. Fundamental fatigue properties
Endurance of a structural element may be defined as the number of cycles to failure in every component of the structure.
From that accumulated damage, its effects and the residual strength can be determined.
1/m
Linear regression through mean of experimental data
Log S
Log N

7. (Permissible Limit State)
Limit states
ULS
SLS (Serviceability Limit State)
FLS (Fatigue Limit State)
DLS (Durability Limit State)
PLS
(Permissible Limit State)

8. SMART assessment - Procedure
1) Geometry, construction
(Incl. Foundations, backfill)
2) Traffic loading
with dynamic effects
3) Materials
Masonry: Strong / Medium / Weak
4) Structural analysis
Statically determinate or indeterminate structure
5) Limits states
Failure mode
ULS
PLS
Determined by
Mechanism
ULS-M
PLS-M
Tensile strength of radial mortar joint
Ring separation
ULS-R
PLS-R
Longitudinal shear strength of inter-ring mortar joint
Crushing
ULS-C
PLS-C
Compressive strength of masonry
Sliding
ULS-S
PLS-S
Shear strength of radial mortar joint
Others …
Log N
ΔS Smax
(Sult)2
1/2
ULS
for all possible failure modes
7) PLS
For all possible failure modes
8) LIFE EXPECTANCY (e.g. application of Miner’s rule)

9. SMART assessment - Example
Geometry, construction
Loading
Materials
Span = 5000mm
Rise = 1250mm
Ring thickness = 330mm
Arch width = 675mm
Number of rings = 3
Span:rise ratio = 4:1
Shape = Semi-circular
Dead load: 2 x 22.5kN at ¼ and ¾ span
Live load: ¼ span.
Compressive strength
(N/mm2)
Shear strength
(kg/m3)
Density
Class ‘A’ Engineering brick
154
N/A
2370
Brickwork 25
0.3
2180
Mortar 1:2:9 cement:lime:sand
1.7
1550

10. Structural Analysis SLS ULS Conclusions
Compressive stress limit => 30 kN
Ring separation => 10 kN
Punching shear => very low
ULS
4-hinge mechanism => 35 kN
Ring separation => 30 kN
Conclusions
Long-term load capacity = 10 kN
(Compare: ½ x ULS = 15 kN)
=> Arch can carry 15 kN only for 50,000 cycles (based on load tests)

11. Conclusions
Current masonry arch bridge assessment methods do not take long-term behaviour and residual life into account.
New SMART method offers a methodology for the assessment of long-term behaviour and residual life.