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

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.

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.

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

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

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

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

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)

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

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)

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.