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**Dipartimento di Ingegneria Civile – Università degli Studi di Salerno**

Dottorato di Ricerca in Ingegneria delle Strutture e del recupero edilizio e urbano - IX ciclo N. S. Presentazione del lavoro di tesi Analisi non lineare di pareti murarie sotto azioni orizzontali: modellazione a telaio equivalente Fisciano, 6 Maggio 2011 Dottorando: Ing. Riccardo Sabatino Tutor: Prof. Vincenzo Piluso Co-Tutor: Prof. Gianvittorio Rizzano

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

All exact science is dominated by the idea of approximation Bertrand Russell Science is organized knowledge Herbert Spencer R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Introduction Fresco found in Rekhamara’s Tomb (1500 b.C. – Egypt) First Stone Dwellings (8350 b.C. – Jericho, Tell-es-Sultan) Djoser Pyramid (2600 b.C. – Egypt) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Introduction Performance-based Earthquake Engineering Non-linear static procedures (NLP) Non-linear Static Analysis R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Introduction Strategies for Modelling Masonry Buildings FEM models VS Simplified models √ Very accurate prediction √ Any kind of structure may be analysed X Time-consuming X Amount of input data X High Analytical Skills required √ Suitable for professional purposes √ Quick analyses X Regular geometry needed X Simplifications need to evaluated R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Accurate Modelling: mesoscale model Blocks are modelled using continuum elements, while mortar and brick-mortar interfaces are modelled by means of nonlinear interface elements (Lourenço & Rots, 1996). Solid and interface elements account for large displacements, while only interface elements represent cracks in mortar and bricks. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 9

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

A novel 2D nonlinear interface element Material model Multi-surface nonassociated plasticity Elastic response Yield functions F1 - F2 Elastic stiffness Plastic potentials Q1 - Q2 Mortar joints R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 10

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

A novel 2D nonlinear interface element Material model Nonassociated plasticity Elastic response Yield function F1 Elastic stiffness penalty factor Brick interface Plastic potential Q1 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 11

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

A novel 2D nonlinear interface element Material properties s sC - compressive strength s st st - tensile strength GC - crushing energy Gf,I - mode I fracture energy Gf,I s s s uz sc t s Gc C - cohesion s<0 t s uz Gf,II - mode II fracture energy c stanf t Gf,II f - friction angle s ux(y) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 12

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**A novel 2D nonlinear interface element**

PhD Dissertation Talk – Fisciano, 6th May 2011 A novel 2D nonlinear interface element Work-softening plasticity Evolution of the material parameters Evolution of the surfaces with Wpl1 - plastic work related to F1 Wpl2 - plastic work related to F2 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 13

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**PhD Dissertation Talk – Fisciano, 6th May 2011 shear cyclic behaviour**

A novel 2D nonlinear interface element Traction deformation response shear tension shear cyclic behaviour tension-compression cyclic behaviour R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 14

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) mortar interface brick interface pv=0.3 MPa J4D J5D R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 15

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) Wpl1 Wpl2 Wpl1 Wpl1 Wpl1 pv=0.3 MPa pv=2.12 MPa pv=0.3 MPa J4D J5D dynamic analysis R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 16

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

In-plane behaviour Mesh assessment Mesh refinement Number of integration points over the interface R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 17

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

In-plane behaviour Vermeltfoort AT, Raijmakers TMJ (1993) Wpl1 Wpl2 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling 18

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Influence of spandrels Numerical Modelling (STRAUS7): 144 panels Panels have been obtained by assembling a reference module whose geometry (piers, spandrels) has been properly varied. The parameter l, ratio between the shear stiffness of piers and spandrels, has been used to take into account the panels geometry. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Influence of spandrels Panels have been modelled by assuming two limit schemes: infinite stiffness spandrels and “unreinforced” spandrels. The parameter represents the expected improvement of relative shear strength achievable by means of spandrels retrofitting. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Influence of spandrels The comparison shows a significant improvement in the field l<1.5, i.e. for weak spandrels. In such field the average strength improvement can be estimated as: R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting Then the panels 1-1 and 4-4 have been extensively investigated by considering the retrofitting approach suggested in Italian Building Code. For each panel, the weak spandrel (l=0.70) and the strong spandrel (l=5.35) schemes have been analysed. Three different kinds of reinforcements have been taken into account: Injection Grouts; Reinforced plasters; Ring beams / Jack Arch. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting The shear resistance of the panels has been evaluated by means of a non-linear static analysis. Both the unreinforced and the reinforced wall have been analyzed. The improvement deriving from the reinforcement has been summarized into the parameter where T is the reinforced wall resistance, Tnc the unreinforced wall resistance. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Wall 1-1 For weak spandrels walls, the spandrel improvement gives the same results of injection grouts/reinforced plasters. For strong spandrels walls, best improvements have been achieved with injection grouts/reinforced plasters. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Wall 4-4 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting The expected improvement gets the same order of magnitude of data available in literature [Modena et al.] R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Retrofitting: Parete 4-4 For the wall 4-4, further numerical simulations have been performed, by assuming the reinforcement (reinforced plaster/injection ) applied to 1 to 4 storeys. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Simplified Models R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Description of the model Equivalent Frame Model Spandrels Piers (Heff after Dolce, 1991) Main features 1. Displacement Control approach NLP 2. Global and local equilibrium 3. Spread plasticity approach 4. Quick Analysis and Easy Post-processing Rigid Offsets R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Piers - Constitutive Laws Generalized Uniaxial Compressive Stress-Strain Relationship A=2, B=-1, C=2 [Hendry, 1998] A=6.4, B=-5.4, C=1.17 [Turnšek-Čačovič, 1980] [After Tomaževič, 1999] Accurate Moment-Curvature R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Piers - Flexural Behaviour Cross-section Equilibrium Equations x normalised neutral axis normalised axial force m normalised bending moment R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**Moment-Curvature relationship workflow**

PhD Dissertation Talk – Fisciano, 6th May 2011 Moment-Curvature relationship workflow D, t, c, n cu NO c < cu END YES ccr x M R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Piers - Shear Behaviour Experimental Behaviour Model [After Anthoine, Magenes, Magonette, 1994] Ultimate drift du = 0.4% Heff [Italian Building Code] R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Piers - Shear Behaviour R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**Shear-strain relationship workflow**

PhD Dissertation Talk – Fisciano, 6th May 2011 Shear-strain relationship workflow min Vu gi=Vi/Ki gel=Vu/Kel YES gi < gel Ki+1=Kel NO Ki+1=Ki *Vu/Vi R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**Shear-strain relationship workflow**

PhD Dissertation Talk – Fisciano, 6th May 2011 Shear-strain relationship workflow Collapse condition when the desired value of drift (set by the user) is attained (Italian Building Code suggets d = for shear collapse) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Spandrels - Shear Behaviour Experimental Behaviour Model Residual Strength a = 0.25 [Magenes and Della Fontana, 1998] R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Spandrels - Flexural Behaviour Experimental Behaviour Model [After Calderoni et al., 2008] R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Spandrels - Flexural Behaviour Proposed formulations for Mu – [Italian Building Code, 2008] Stress-block approach (same equation of piers) 2. If no tensile-resistant element is present Mu=0 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Spandrels - Flexural Behaviour Proposed formulations for Mu [Schubert & Weschke, 1986] a) Take into account an “equivalent strut” provided with a tensile strength ftu ftu is the minimum between two collapse mechanisms: a) bricks failure b) bed joints failure b) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Spandrels - Flexural Behaviour Spandrels M-N Limit Domain [Cattari and Lagomarsino, 2008] Constitutive Law Improvement of rocking resistance, also with low (or zero) values of N. h = ratio between tensile strength ftu and compressive strength R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Outline Chapter 1: Introduction Chapter 2: FEM modelling Chapter 3: Masonry Buildings Modelling Strategies Chapter 4: Mechanical Behaviour of masonry panels Chapter 5: Matrix Analysis of structures Chapter 6: The FREMA code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Masonry Panels – Anthoine, Magonette and Magenes (1998) Cross-Section: 100 x 25 cm2 Low panel high: 135 cm High panel high: 200 cm Normal Load: 150 kN Low Panel High Panel R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Pavia Door Wall – Calvi and Magenes (1994) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Pavia Door Wall – Calvi and Magenes (1994) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Pavia Door Wall – Calvi and Magenes (1994) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Catania Project - Investigation on the seismic response of two masonry buildings (2000) “Via Martoglio” 2D Wall Equivalent Frame model: 128 elements, 81 nodes, 219 DOF R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Martoglio” 2D Wall Model 1: Masonry, NO R.C. Ring Beams R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Martoglio” 2D Wall Model 2: Masonry, Elastic R.C. Ring Beams (E=20,000 MPa) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Martoglio” 2D Wall Model 3: Masonry, Elastic R.C. Ring Beams (E=4,000 MPa) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Preliminary validation of the model Catania Project - Investigation on the seismic response of two masonry buildings (2000) “Via Verdi” Building Wall 1 Wall 2 Wall 3 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Verdi” – Wall 1 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Verdi” – Wall 2 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code “Via Verdi” – Wall 3 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Mallardo et al. (2008) – Palazzo Renata di Francia R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Mallardo et al. (2008) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Salonikios et al. (2003) Two-storey, 7-bay masonry wall Two lateral load distributions considered: Uniform (ACC) F= {1.00; 0.59} Inverse Triangular (LOAD) F= {1.00; 1.19} R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Salonikios et al. (2003) – 7B_Uniform Discrete FEM model Proposed Model SAP 2000 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

The FREMA Code Salonikios et al. (2003) – 7B_Inverse Triangular Discrete FEM model Proposed Model SAP 2000 R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Mesh Refinement Salonikios et al. (2003) b=Log(Nc/Dx) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Mesh Refinement Salonikios et al. (2003) – 7B_Inverse Triangular R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Mesh Refinement Salonikios et al. (2003) – 7B_Uniform R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Time-cost Analysis Salonikios et al. (2003) b=Log(Nc/Dx) R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Time-cost Analysis R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Conclusions This dissertation deals with the seismic behaviour of masonry structures; The first part of the work is aimed at understanding the potentialities of very accurate FEM model in predicting masonry panels seismic response; the panels simulated by means of ADAPTIC showed a very good prediction of the experimental results, both in terms of force-displacement curve and in terms of cracks path. A further application of simplified (homogeneous) FEM models has been performed on masonry panels, aiming at evaluating the influence of spandrels reinforcement on the overall resistance; in the same application some reinforcement techniques have been applied considering the Italian Building Code approach; R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Conclusions In the second part of the dissertation, a novel equivalent frame model has been developed. The main features of the model have been discussed, by highlighting the main features of the proposed model (displacement control approach, accurate moment-curvature for piers behaviour, spandrels behaviour); A validation and application of the model has been carried out comparison with experimental tests and accurate numerical simulations The comparison showed a good agreement between the proposed model and both experimental and numerical results, showing that FREMA code is a reliable tool for performing the non-linear static analysis of masonry panels. R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**PhD Dissertation Talk – Fisciano, 6th May 2011**

Thank you very much! R. Sabatino – Non-linear analysis of masonry walls under horizontal loads: equivalent frame modelling

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**Dipartimento di Ingegneria Civile – Università degli Studi di Salerno**

Dottorato di Ricerca in Ingegneria delle Strutture e del recupero edilizio e urbano - IX ciclo N. S. Presentazione del lavoro di tesi Analisi non lineare di pareti murarie sotto azioni orizzontali: modellazione a telaio equivalente Fisciano, 6 Maggio 2011 Dottorando: Ing. Riccardo Sabatino Tutor: Prof. Vincenzo Piluso Co-Tutor: Prof. Gianvittorio Rizzano

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