CC2013: Analysis, Modelling and Design of Masonry Structures

1. CC2013: Analysis, Modelling and Design of Masonry Structures Mesoscale Modelling of Masonry Structures Accounting for Brick-Mortar Interaction Francisco B. Xavier, Lorenzo Macorini, Bassam A. Izzuddin Project Funding Department of Civil & Environmental Engineering, Imperial College London

2. Outline • Introduction • - Standard Mesoscacle Modelling • - Importance of Brick-Mortar Interaction Enhanced Meoscale Modelling - Interface FE Formulation Verification Examples under Uniaxial Compression - Elastic Analysis of Single Prism - Crack Initiation on Masonry Wall Closure - Ongoing Work

3. Numerical Analysis of Masonry Panels Bed Joint Brick Unit Head Joint

4. Numerical Analysis of Masonry Panels a) Micro-Model b) Simplified Micro-Model – Mesoscale Model Increasing Computational Expense c) Homogenised Macro-Model

5. Mesoscale Modelling 20-Noded Solid Element Elastic Material • Brick Units • Brick-Mortar Interfaces 16-Noded Interface Element Material Nonlinearity, Mix-Mode Cohesive Cracking, Crushing, Damage • “Brick-Brick” Interfaces

6. Mesoscale Modelling - Drawback • Brick Mortar Interaction Leading to Unit Cracking e.g.: Masonry Prism – Uniform Compression Tension assuming Eb> Em Compression

7. Mesoscale Modelling - Drawback Brick Mortar Interaction Leading to Unit Cracking e.g.: Masonry Prism – Uniform Compression assuming Eb> Em However, with standard interface modelling there is no coupling between in-plane and normal deformations: Approximate Solution at Interface Material Level Tension & Shear “Crushing” Failure Surface No Lateral Tension Develops in the Units

8. Enhanced Mesoscale Modelling Brick-Mortar Interaction - Typically Captured with Refined Micro-Models a) Micro-Model Modified Interface Element Kinematics b) Simplified Micro-Model – Mesoscale Model

9. Enhanced Mesoscale Modelling Considering interface finite elements representing an actual volume, in which one of the dimensions is considerable smaller than the other two – in this case the mortar joint thickness h It is possible to introduce triaxial stresses and deformations into a zero-thickness interface, while maintaining its capabilities for cohesive crack modelling

10. Enhanced Mesoscale Modelling • Assuming displacements inside the mortar layer as linear function of top and bottom surfaces: • A representative average strain vector is obtained as: • Introducing a further simplification with regards to shear strain definition in the x-z and z-y planes:

11. Enhanced Mesoscale Modelling • Assuming displacements inside the mortar layer as linear function of top and bottom surfaces: • A representative average strain vector is obtained as: • Assemble matrix L as:

12. Enhanced Mesoscale Modelling The strain vector for the enhanced interface element yields: Considering the conjugate stress vector: Average of top and bottom surface engineering strain The local elastic constitutive relationship is: with: Typical Interface displacement discontinuities uniformly smeared over the height of the mortar layer

13. Enhanced Mesoscale Modelling 3D Constitutive matrix: Directly obtained with shear test Coupling between interface opening and normal strains at mid-surface Interface stiffness to sliding In-plane shear stiffness at mid-surface

14. Enhanced Mesoscale Modelling Co-rotational Framework • Large Displacements Out-of-Plane Response under Extreme Loading

15. Enhanced Mesoscale Modelling Mortar joints detailed with solid FE Comparison between full continuum and enhanced interface elastic response at detailed level Masonry prism under uniform compression Symmetry Boundary Conditions Mortar joints lumped into zero-thickness enhanced interfaces • 10 mm thick mortar joints • 250x120x55 mm3 units • Eb>Em

16. Enhanced Mesoscale Modelling • Lateral Tensile Stresses in Brick Units Full Continuum With Interfaces Z X Good Match especially in the region where tensile cracks are expected to develop • Lateral Stresses in Mortar Joint Similar Pattern in Z-Y Plane Importance of 3D Modelling Continuum Mortar Joint Interface Mortar Joint

17. Enhanced Mesoscale Modelling Brick-Mortar Interface Enhanced Formulation Full Continuum Detailed with Interfaces Mesoscale a) Symmetry Boundary Conditions Brick-Brick Interface Standard Formulation Brick-Brick Interface Brick-Mortar Interface

18. Enhanced Mesoscale Modelling Full Continuum Detailed with Interfaces Mesoscale a) Mesoscale b) Mesoscale c) Lateral tensile Stresses in the Brick Units

19. Enhanced Mesoscale Modelling Comparison in terms of global stiffness Response obtained with standard interfaces No lateral stresses Computational Cost

20. Enhanced Mesoscale Modelling Unreinforced Masonry Wall – Uniaxial Compression test Mesoscale a) Mesoscale b) • Head and Bed mortar joints 10 mm thick Symmetry Boundary Conditions • Mesocale Model a) – 1 solid element along the height of brick units • Mesocale Model b) – 2 solid elements along the height of brick units • Head Mortar Joints Modelled with standard interfaces

21. Enhanced Mesoscale Modelling Enhanced Mesoscacle Elastic Initiation of cohesive cracking in the Mesoscale model Onset of cracking recorded experimentally Experimental Brick Cracking Activated

22. Closure Further Improvements on the enhanced interface element: • Adapt previous cohesive model (Macorini & Izzuddin, 2011) to accommodate new stress components in the new interface, i.e., allow mix-mode fracture (Tension & Shear) in brick-mortar interfaces (bed joints) • Introduce failure surface at interface level, accounting for triaxial stress state in order to capture the actual failure of confined mortar material • Non-linear response of masonry prisms by the knowledge of individual components properties, as opposed to composite properties dependent on the prism characteristics

23. Closure • Despite mechanically sound, full potential of this enhanced mesoscale modelling strategy is only achieved if realistic material properties for both mortar and brick units are available • Current published research underlines mortar material properties when part of a masonry assemblage or taken from single specimen to be markedly different • There is the need to establish procedures to assess the actual mortar material properties, thus enabling the composite behaviour o masonry panels to be characterized by its individual constituents properties

24. Thank You! Questions?