1. N ONLINEAR A NALYSIS OF M ASONRY A RCH B RIDGES U SING M ESOSCALE P ARTITIONED M ODELLING Y ANYANG Z HANG, L ORENZO M ACORINI AND B ASSAM A. I ZZUDDIN C OMPUTATIONAL S TRUCTURAL M ECHANISM G ROUP (CSM) D EPARTMENTAL OF C IVIL AND E NVIRONMENTAL E NGINEERING I MPERIAL C OLLEGE L ONDON 22 ND ACME C ONFERENCE ON C OMPUTATIONAL M ECHANICS, 2-4 A PRIL, E XETER, UK

2. O UTLINE M ASONRY A RCH B RIDGES M ESOSCALE P ARTITIONED M ODELLING N UMERICAL D ESCRIPTION OF A RCH - FILL I NTERACTION 3D M ESOSCALE M ODELS C ONCLUSIONS AND F UTURE W ORK 2 3 4 5 1

3. M ASONRY ARCH BRIDGE Play a crucial role in public transportation systems Belong to the engineering and architectural heritage Fill

4. 3D M ESOSCALE D ESCRIPTION FOR M ASONRY S TRUCTURES Macorini L and Izzuddin B.A.(2011) Brick elements 2D nonlinear interfaces C

5. 3D M ESOSCALE D ESCRIPTION OF S KEW A RCH 1 2 3 4 Block N c Block i

6. M ESOSCALE P ARTITIONED M ODELLING FOR M ASONRY A RCHES Brick-masonry arch Parent structure modelling with super-elements 1 2 3 4 Tow-way communication partition-parent structure Parent structure corresponding to partitioned boundary Partition 1 Partition 2 Partition 3 Partition 4

7. M ESOSCALE P ARTITIONED M ODELLING FOR A RCH -B ACKFILL I NTERACTION Communication partition-parent structure Parent structure corresponding to partitioned boundary Partition 1 Brick-masonry arch 15-noded prisms Continuum domain Partition 2 The backfill 20-noded brick elements+ 16-noded interface elements Discontinued domain

8. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH Dead Load F + Live Load PDead load F mortar interfaces mortar interfaces brick interfaces mortar interfaces Wang J. (2004) F=10kN / P=1kN F=10kN 20-noded brick elements 20-noded brick elements

9. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH ¾ span ¼ span FE mesh in ADAPTIC Countour of plastic work of the interface elementsLoad-deflection curve

10. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH ¾ span ¼ span FE mesh in ADAPTIC Countour of plastic work of the interface elementsLoad-deflection curve

11. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH Wang J. (2004) ¾ span ¼ span FE mesh in ADAPTIC Countour of plastic work of the interface elements Load-deflection curve

12. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH Wang J. (2004) ¾ span ¼ span FE mesh in ADAPTIC Countour of plastic work of the interface elements Load-deflection curve

13. 3D M ESOSCALE M ODEL ------ M ASONRY S QUARE A RCH Wang J. (2004) ¾ span ¼ span FE mesh in ADAPTIC Countour of plastic work of the interface elements Load-deflection curve

14. 3D M ESOSCALE M ODEL ------ M ASONRY S KEW A RCH Wang J. (2004) Vertical load P T9 T3

15. 3D Mesoscale Model ------ Arch-Backfill Interaction Model FE mesh in ADAPTIC 15-noded wedge elements for the backfill 20-noded Brick elements for brick units Continuum domain with no interface elements Vertical Line load P ADAPTIC mesoscale FE mesh (interfaces) 16-noded interface elements For mortar joints 16-noded interface elements for the interface between arch barrel and the backfill

16. 3D M ESOSCALE M ODEL ------ A RCH -B ACKFILL I NTERACTION M ODEL Deformed FE mesh in ADAPTIC Countour of plastic deformation of the backfill Contour of plastic work W cr1 at interface elements of masonry arch

17. Full 3D model of masonry arch bridges accounted for spandrel walls will be presented in the future. Full 3D model of masonry arch bridges accounted for spandrel walls will be presented in the future. In comparison with simplified modelling approach, detailed modeling approach present more precise result. In comparison with simplified modelling approach, detailed modeling approach present more precise result. When using 3D mesoscale description incorporated with the domain partitioning approach, computational efficiency is preserved. When using 3D mesoscale description incorporated with the domain partitioning approach, computational efficiency is preserved. 3D mesoscale representation provides accurate description for masonry Arches bridges taken into account for the real texture of masonry. 3D mesoscale representation provides accurate description for masonry Arches bridges taken into account for the real texture of masonry. 1 1 2 2 3 3 4 4 C ONCLUSIONS

18. N ONLINEAR A NALYSIS OF M ASONRY A RCHES AND B RIDGES U SING M ESOSCALE P ARTITIONED M ODELLING THANK YOU !