CYCLIC LOAD CAPACITY AND ENDURANCE LIMIT OF MULTI-RING MASONRY ARCHES Clive Melbourne, Adrienn Tomor Jinyan Wang School of Computing, Science and Engineering, University of Salford

Background and context 40% of all European bridges is masonry 60% of masonry bridges are over 100 years old

Background and context Due to the increasing traffic loading the life expectancy, capacity and fatigue performance of arch bridges needs to be better understood. Most experimental work so far has been carried out under static loading. Ring separation failure under cyclic loading is one of the main sources of concerns as it can significantly reduce the capacity of multiring brickwork arches.

Test series 3m span arches 5m span arches

A series of 3m span arches (2 rings)

and a series of 5m span arches under static and cyclic loading. (3 rings) under static and cyclic loading.

Loading Dead load Live load Static loading Cyclic loading

TEST RESULTS

STATIC LOADING 3M SPAN Four – hinge mechanism

STATIC LOADING 5M SPAN Ring separation

TEST RESULTS

CYCLIC LOADING 3M SPAN Ring separation

CYCLIC LOADING 3M SPAN COLLAPSE: By hinging

CYCLIC LOADING 5M SPAN Ring separation

Small increase in the load level can cause rapid failure. (% of static load) Number of cycles Small increase in the load level can cause rapid failure. Failure occurred within a relatively few number of cycles (400,000) once endurance limit was reached. Endurance limit was reached around 37-57% of the static load capacity of fully bonded arches. Typical failure mode was ring separation. 100 75 50 25 100,000 200,000 300,000 400,000 57% 37% Endurance limit (5m arch) Endurance limit (3m arch)

Endurance limit (3m arch) Endurance limit (5m arch) 100 75 50 25 100,000 200,000 300,000 400,000 Load (% of static load) Number of cycles Endurance limit (3m arch) Endurance limit (5m arch) 57% 37% Mortar bond (%)

Endurance limit (5m arch) Load (% of static load) 100 75 50 25 100,000 200,000 300,000 400,000 Endurance limit (5m arch) 50 25 50% 0% Endurance limit (3m arch) Endurance limit Mortar bond (%) Number of cycles

Interactive S-N curve Interactive S-N CURVE Ring separation 4-hinge mechanism Number of cycles (Log) Stress (Log) An Interactive S-N (ISN) curve can be developed for each mode of failure for every arch. Endurance limit (E) can be expressed for each mode of failure from the Interactive S-N curve as a function of the load range (R), slope (m) and intersection (H): E = 10H R–m 3m test data Slope (m) H Number of cycles (Log) Load (Log) 3M TEST DATA As a practical tool an Interactive S-N (ISN) curve can be developed for each mode of failure for every arch.

Shear capacity of the mortar-brick bond was also investigated Shear testing Shear capacity of the mortar-brick bond was also investigated Small-scale: Triplet tests Large-scale: Arch sections

Triplet tests Mortar bond in arches is rarely perfect (100%). Shear capacity with various extent of mortar bond was tested under static and cyclic loading.

Trendline for static tests Shear testing summary Shear testing summary Trendline for static tests Exponential relationship between shear strength and the extent of mortar bond was indicated under static loading. Significant reduction in the static shear capacity was observed for <90% bonded surface area. Large-scale arch sections show significantly greater shear capacity compared to triplets. Cyclic shear capacity seems to be significantly smaller than the static load capacity.

Conclusions Cyclic load capacity of arches is significantly lower (up to 60%) than static load capacity. Under cyclic loading multiring arches failed by ring separation at significantly lower loads than that associated with a four-hinge mechanism. A model for an Interactive S-N curve for the various modes of failures was proposed for assessment of residual life and fatigue performance. Shear capacity of the mortar bond showed strong relationship to the extent of mortar bond.

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Finite elements analysis

FE analysis Longitudinal shear stresses DL + LL DL 1st crack

Finite elements analysis Currently there is not enough data available for calibrating and modelling arches under cyclic loading. Convenient for modelling arches as a continuum, but ring separation and other modes of failures need to be investigated specifically. Under static loading FE showed that radial cracks can locally increase the longitudinal shear stresses that can cause ring separation at a significantly lower load associated with formation of hinges.