Seismic assessment of existing masonry buildings

Transcription

1 Erlenbach, September 12 th, 2013 Seismic assessment of existing masonry buildings Andrea Penna Department of Civil Engineering and Architecture University of Pavia, Italy Masonry Bricks Roman squared stones Rubble stone Column cross section 1

2 Different masonry types Use of different stones, with different workability: stones from quarries, fieldstones, pebbles, etc. Dry stone masonry or use of mortar with different characteristics and mechanical properties Different strength and stiffness characteristics Different in-plane displacement capacity limit states Different out-of-plane behaviour for different types of cross section (multiple leaves) Stone masonry typologies 2

3 Different types of stone masonry layout (Mannoni, 2005) Variability of mechanical properties Masonry typology Rubble stone masonry (pebbles, fieldstones, irregular stones) Undressed stone masonry with facing walls of limited thickness and infill core (sacco) Partially dressed stone masonry with good bonding (usually double leaf) f m 0 E G [MPa] [MPa] [MPa] [MPa] Soft stone masonry (tuff, limestone, etc.) Dressed rectangular stone masonry Plausible ranges of variation for the mechanical properties of some common stone masonry typologies (from Commentary to the Italian Building Code, 2009) 3

4 Seismic response of masonry buildings Global behaviour and local mechanisms Earthquake damage to masonry buildings (L Aquila 2009, Italy) 4

5 Messina 1908 M7.2 Friuli, 1976 M6.4 L Aquila, 2009 M6.3 Earthquake damage to masonry buildings (Christchurch, New Zealand, 2011) (Kashmir, Pakistan, 2005) 5

6 Out-of-plane vulnerability is the most important cause of earthquake damage to existing masonry buildings 6

7 0 50 0cm cm Masonry cross sections Masonry cross sections (Binda et al. 1999, 2003) 7

8 Out-of-plane response Equilibrium limit analysis Static collapse multiplier (Sahlin, 1971) Kinematic analysis of out-of-plane (local) failure modes Identification of possible mechanisms (kinematic chain of rigid bodies): geometry, constraints and acting loads Use of the Principle of Virtual Works to determine the horizontal load multiplier, o, that activates the mechanism (linear analysis) and its evolution for increasing displacements (nonlinear analysis) Conversion of the D curve in A* D* curves for an equivalent SDOF system Determination of the expected performance from a comparison of displacement capacity and displacement demand, considering the motion amplification along the building height and the dynamic interaction between building and subsystem responses (D Ayala & Speranza, 2002) 8

9 Kinematic analysis of out of plane (local) failure modes A YIELDING OF TIE-ROD OVERTURNING WITH TIE-ROD FAILURE OF TIE-ROD OR ANCHORAGE 3-HINGE OVERTURNING MECHANISM SIMPLE OVERTURNING W/O TIE-ROD LOSS OF EQUILIBRIUM LOSS OF EQUILIBRIUM (Magenes and Penna, 2011) D Kinematic analysis of out of plane (local) failure modes This approach is based on a number of literature works (e.g. Heyman 1969, Psycharis and Jennigs 1983, Giuffrè 1993, Giuffrè and Carocci 1996, de Felice and Giannini 2001, Doherty et al. 2002, Griffith et al. 2003, Lagomarsino 2006, Sorrentino et al. 2008, Lagomarsino and Resemini 2009, Vaculik et al. 2012) supported by some experimental data (e.g. Griffith et al. 2004, Al Shawa et al. 2011, Restrepo-Vélez et al, 2012). Commentay to the Italian Building Code 2009 (first introduced in OPCM 3431, 2005) Will Eurocode 8 part 3 include this or any other method for assessing local/out-of-plane failure modes in existing masonry buildings? 9

10 Importance of good connections Global response governed by in-plane behaviour of masonry structural members (L Aquila, 2009) Connections between orthogonal walls 10

11 In-plane response: piers and lintels In-plane failure modes (a) (b) (c) Flexural-rocking Shearsliding Sheardiagonal cracking 11

12 Assessment of existing buildings Local mechanisms (kinematic approach) Global response (in-plane frame-type analysis; non-linear pushover analysis) Structural knowledge Performance-based assessment STRUCTURAL SURVEY GEOMETRICAL SURVEY STRUCTURAL DETAILS HISTORY OF THE BUILDING: - SEISMIC HISTORY -PREVIOUS DAMAGE 12

13 Structural modifications: Structural modifications: 13

14 Structural modifications: Previous damages and deformations 14

15 Role of in-situ non-destructive testing IN-SITU SHEAR TESTS (Sheppard, 1985) 15

16 Modelling Strategies Limit analysis POR Method Finite Elements Como & Grimaldi Tomaževič Gambarotta & Lagomarsino, Anthoine, Maier et al., Lourenço Macro-elements fascia maschio nodo MAS3D Braga, Liberatore, Spera PEFV D Asdia e Viskovic SAM Magenes, Della Fontana, Bolognini TREMURI Lagomarsino, Penna, Galasco Pushover Analysis 16

17 Capacity Curve and Displacement Limit States Fb [kn] SLD SLU Curva modello SLD 600 Curva modello SLU 400 Stati limite d [cm] Capacity Curve TB Non-linear static analysis steps SA DTOP SD SA SA SD SD 17

18 18 In-plane floor stiffness Membrane elements ˆ G m me m E m m E m m E D k j i x y e e e ii ij ik e e jj jk e kk e k k k K k k k As e T ij i j k B DB j k k j k j j k y y x x A x x y y B i i y x j k l j i l k j l k i = ½ + DR R D T In plane floor stiffness Orthotropic membrane elements cls cls trave s E E E is A E E 2 1 G 12 =G cls s E.g.: Steel beams, clay tiles and r.c. topping Homogenized equivalent membrane element (orthotropic)

19 Timber floors: equivalent membrane stiffness In-plane floor stiffness (Valluzzi et al., 2007) 19

20 Vault structures equivalent diaphragm stiffness (Cattari, Lagomarsino & Resemini, 2008) Issues in pushover analysis of existing masonry buildings Buildings with flexible diaphragms Different foundation levels Interaction between adjacent buildings Mixed masonry-r.c. buildings 20

21 Modal analysis P3 P3 P4 P5 P2 P4 P5 P2 P1 Inf. Rigid diaphragms (no inplane distortion) P1 Flexible diaphragms (inplane distortion) P3 P3 Inf. flexible diaphragm P4 P5 P2 P4 P5 P2 (single wall modes) P1 P1 Very flexible diaphragms 21

22 Pushover analysis of complex buildings Mixed masonry-r.c. buildings Lumped plasticity models for RC members Failure modes: shear (brittle) simple compression/tension bending (ductile) M M N N Ultimate rotation u f 1 yw ,35 sx V f c 100 d el max(0,01; ' ) 0,016 (0,3 ) fc max(0,01; ) L h 25 (1,25 ) 22

23 Mixed masonry-r.c. buildings Lumped plasticity models for RC members Beam Column Wall cracked stiffness ratio (Paulay e Priestley 1992) Comparison with fiber models plicazione 2D Frame LP model F model: SEISMOSTRUCT Damage comparison F model LP model Shear failure Plastic hinge Bending failure (ultimate rotation 23

24 Mixed masonry-r.c. buildings B: presence of ring beams C: internal r.c. frame (gravity load design) D: r.c. shear walls E: Added storey (r.c. frame) B C D E (C) P4 P5 Y Parete 4 Parete 5 24

25 Base Shear/Weight 0,35 0,30 0,25 0,20 0,15 0,10 0,05 0,00 Phase I Phase I Phase II Phase III (collapse) Average displacement of 3 th floor [mm] Phase II P5 Phase III (E) Damage pattern (modal distribution) 25

26 Adjacent buildings (modelling options) Adjacent buildings (modelling options) Struts : (J=0) compressive strength Null tensile strength 26

27 Adjacent buildings (modelling options) Multi-level foundations MODAL DISTRIBUTION 27

28 Conclusions Role of structural knowlegde and uncertainties Analysis methods and tools for local and global response assessment Mixed RC masonry structures Issues in pushover analysis of existing buildings Issues in nonlinear analysis (see morning presentation!) Strengthening and retrofitting THANK YOU FOR YOUR ATTENTION! 28