Nonlinear Analysis of Reinforced Concrete Structures in Design and Structural Assessment

1 Nonlinear Analysis of Reinforced Concrete Structures in Design and Structural Assessment Jan Cervenka Červenka Consulting, Prague, Czech Republic Outline: Červenka Consulting - Computer simulation (virtual testing) of concrete structures Finite element system ATENA theoretical background, structure, practical applications

Contents 1. What is simulation? 1. Numerical models for the simulation of reinforced concrete: 1. Nonlinear finite element analysis 2. Material models, fracture-plastic, microplane 3. Special FE for reinforced concrete modeling Validation: Tension stiffening Round robin predictions Full scale structural tests Applications: Bridges Tunnels Nuclear containment 2

Why nonlinear simulation of structures? Supports expert engineering knowledge 3

í in Nonlinear při provozním simulation zatížení of reinforced concrete structures E 2 E 3 E 10 E 15 E 18 E 27 low strength high strength 4

ATENA: reinforcement modeling realistic crack display run-time visualization 5

Nonlinear Finite Element Analysis 6 ATENA analysis

7 Nonlinear constitutive models in ATENA variety of nonlinear material models: for concrete plain reinforced pre-stressed fibre reinforced other quasi-brittle materials masonry rock soil metals

Material Models for Concrete Plasticity Damage mechanics Microplane models Uniaxial law Bi-axial criterion 3D failure surface Kupfer 1969 Menetrey Willam, ACI 1995 8

9 Program ATENA Crack band method correct energy dissipation during the fracturing process concrete in tension tensile cracks post-peak behavior fracture energy crack band method

Demonstration Examples mesh objectivity Importance of Fracture mechanics x Stress-strain laws 10

Support Reaction [MN] Support Reaction [MN] Exponential Model Fracture mech.: 1,60E-03 1,40E-03 1,20E-03 1,00E-03 8,00E-04 Coarse Mesh (80x16.7mm) Fine Mesh (26.7x16.7mm) Finest Mesh (15.4x16.7mm) Theory of Elasticity Experiment 6,00E-04 4,00E-04 2,00E-04 0,00E+00 0,00E+00 1,00E-04 2,00E-04 3,00E-04 4,00E-04 5,00E-04 6,00E-04 7,00E-04 8,00E-04 Local model: Deformation [m] 1,60E-03 1,40E-03 1,20E-03 1,00E-03 Local Strain Model Coarse Mesh (80x16.7mm) Fine Mesh (26.7x16.7mm) Finest Mesh (15.4x16.7mm) Theory of Elasticity Experiment 8,00E-04 6,00E-04 4,00E-04 2,00E-04 0,00E+00 0,00E+00 1,00E-04 2,00E-04 3,00E-04 4,00E-04 5,00E-04 6,00E-04 7,00E-04 8,00E-04 Deformation [m] 11

12 Program ATENA Numerical core - nonlinear material models concrete in tension tensile cracks post-peak behavior crack band method fracture energy Crack band size: L e = w L fixed or rotated cracks crack localization deterministic size-effect is captured

Special elements for reinforced concrete analysis 13

Reinforcement bond model 14

VALIDATION: Simulation of laboratory experiments Reality Simulation 15

Validation and Reliability Blind Predictions Toronto Panel (Collins, Melhorn) 1986 competition results (Panel C). a) Variations in predicted shear strength b) Variations in predicted load-deformation response winner Vladimir Cervenka 16

Validation: Round Robin Competition, Marti 2005 ATENA predictions 17

Validation: Field Test Örnsköldsvik, Sweden 18

Validation: Field Test Örnsköldsvik, Sweden Final failure Step 40, Cracks: in elements, <5.000E-03;...), openning: <-4.092E-04;4.226E-02>[m], Sigma_n: <-1.912E+01;2.009E+00>[MPa], Sigma_T: <-2.535E+00;2.151E+00>[MPa] ATENA analysis Field test 19

Load [MN] Örnsköldsvik Bridge shear strength comparison, experiment, ATENA calculation Analysis with stirrups 14 12 10 8 6 4 2 0 Exper. side 1 Exper. side 2 Initial ATENA w/o CFRP Initial ATENA w. CFRP Eurocode 2 ATENA final 0 20 40 60 80 100 120 140 Deflection [mm] Stirrups not modelled in the initial analyses 20

Load [MN] 3D analysis by LTU 12 11.5 11 10.5 10 9.5 9 8.5 8 7.5 7 6.5 6 5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 West beam mid-span displacement East beam mid-span displacement ATENA 10 30 50 70 90 0 20 40 60 80 100 Displacement [mm] 21

Foundation slab cracks due to underground water pressure forensic investigation crack 22

ATENA numerical simulation 23

Foundation slab Measured cracks FE analysis Results due to water pressure 24

Foundation slab Measured cracks FE analysis Conclusion: Cracks not due to shrinkage but due to water pressure Results due to shrinkage Constant shrinkage based on EC2 25

Measured deflections Analyzed deflections 26

Construction 514, bridge crossing river Berounky near Prague, Czech Rep., design Novák & Partner, Ing. M. Šístek Global verification of safety during construcion stages 27

Double console Pier n. 39 R = 750 m 112 m 50 m 50 m 1,4 m 35 m 28

Prestressing cables 29

Special continuum 3D layered shell elements, concrete C35/45 výztuž 30

Loading Cases ZS16 vertical wind pressures ZS17 concreting vehicle ZS18 longitudinal wind ZS19 cross-wind 31

Relative load [%] 32 Structural capacity 180 160 140 120 100 80 60 40 20 0 0.20 0.00-0.20-0.40-0.60-0.80-1.00 Maximal deflection [m]

33 Optimization of precast structures precast prestressed hollow core slabs without shear reinforcement shear failure test in laboratory and in nonlinear computer simulation (crack widths) V1 L1 0.000866 0.000812 0.000758 0.000704 0.00065 0.000596 0.000541 0.000487 0.000433 0.000379 0.000325 0.000271 0.000217 0.000162 0.000108 0.0000541 Output Set: Load Step ID 40 Contour: C:COD CRACK_ATTRIBUTES -3.02E-12

34 ATENA applications plain concrete lining railway tunnel in Prague typical cross section outer diameter 6 m

New Railway Connection in Prague 35

New Railway Connection in Prague tunnels under the Vítkov Hill 36

37 Nonlinear analysis of the tunnel profile finite element model 5000 elements 1 m longitudinal section plane stress state supported by nonlinear springs reflect soil properties variants: various upper vault thickness plain or reinforced with or without bottom vault

38 Nonlinear analysis of the tunnel profile finite element model 1 m longitudinal section plane stress state supported by nonlinear springs reflect soil properties Drucker-Prager ground variants: various upper vault thickness plain or reinforced with or without bottom vault

39 Step 26, NSf-UZL - nevyztuzene osteni 300, MSU, zima, liniove pruzne ulozeni Scalars:iso-areas, Basic material, in nodes, Principal Stress, Max., <-5.027E-01;9.964E-01>[MPa] Results from NLA Iso-areas of principal stress maximal (tensile) -5.027E-01-4.500E-01-3.000E-01-1.500E-01 0.000E+00 1.500E-01 3.000E-01 4.500E-01 6.000E-01 7.500E-01 9.000E-01 9.964E-01 unreinforced ultimate limit state dead load creep shrinkage temperature in winter

1.784E-02-5.099E-04 1.081E-04-5.037E-04 1.252E-04 Results from NLA Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E-16;5.182E -4.236E-02-4.766E-02-4.427E-02 normal forces bending moments -6.749E-02-6.697E-02 5.324E-03-8.330E-03-1.006E-03 unreinforced ultimate limit state -2.763E-02-2.745E-02 dead load creep shrinkage temperature in winter -1.258E-01 1.752E-02 8.516E-03-1.248E-01 8.076E-03 40

41 Results from NLA Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E-16;5.182E Crack pattern unreinforced ultimate limit state dead load creep shrinkage temperature in winter

42 Results from NLA Step 26, NSf-UZL - nevyztuzene osteni 300, MSP, zima, liniove pruzne ulozeni Cracks: in elements, <2.000E-04;...), openning: <-1.544E-04;1.592E-03>[m], Sigma_n: <-1.237E+00;9.998E-01>[MPa], Sigma_T: <1.017E- Main crack description of crack width max. 1.6 mm 4.493E-04 7.423E-04 unreinforced 9.772E-04 1.269E-03 ultimate limit state dead load creep shrinkage temperature in winter 1.592E-03

BARC, Indie, Containment Pressure Test Model 1:4 43

3D model 44

ATENA 3D shell element geometry layers reinforcement 45

3D Analysis 3.00 design pressure, P = 0.4239 MPa 46

Internal Pressure [MPa] 47 2D - 3D Analysis Comparison 4 3.5 3 2.5 3.2 3.5 P d 2 1.5 1 0.5 Design Pressure 0.1413 MPa 0-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Radial Displacement [m] Axi-symmetric 3D old 3D new

New 3D Model based on BARCOM 2009 workshop corrected cover of openings 48

Safety formats for non-linear analysis - 4 methods Example: bending shear - deep beam bridge pier geometric nonlin. railway tunnel Comparative study of different safety formats 49

Safety Formats for Nonlinear Analysis R x - is the structural resistance obtained by nonlinear analysis E d R x R g R - is the global safety factor of the structural resistance E d - is the factorized load effect as in the case of partial safety factor method 50

Safety Format (1), PSF Method Partial safety factors Action Resistance E ( ) R ( ) d G, i d d, j M ed < M rd f f cd yd Rd Ed 1.0 Use design value of material parameter to calculate R d : design val.= characteristic val. partial safety factor f cd fck 30 1.5 c 20 MPa 51

Safety Format (2), EN1992-2 Global safety factor E ( ) R / d G, i m R All failure modes: R 1.27 Adjusted mean values of material parameters: f cm 0.85 f f 1.1 f ck ym yk 1.1 x 1.15/1.5 52

Safety Format (3), ECOV Estimate of Coefficient of Variation Coefficient of variation, assuming lognormal distribution of resistance Global resistance factor we need 2 analyses R R exp( 1.65 V ) k m R R R exp( V ) d m R R V R 1 R ln m 1.65 Rk 4.7 R 0.8 m exp( V ) R R R Reliability index Resistance sensitivity 53

Safety Format (4), Probabilistic Analysis Probability of failure: P( E R) (1) (2) Reliability index: Z E R P( Z 0) ( Z) ~ 10-6 ~ 4.7 EN 1990: Basis of structural design, 2002 54

Safety and Reliability Factors Safety factors scatter not considered Probabilistic approach scatter - considered mz Z 55

Results probabilistic, SARA+ATENA 120 samples 56

Bending Beam 5f14 300 6000 (t=1000 mm) 300 300 M 77.9 knm M 93 knm Ed Rd 57

Example: Deep beam Tested by: Melvin Asin, Delft University, 1999 Nonlinear, probabilistic analysis by: ATENA, 2006 58

Deep beam 59

Reinforced Concrete Bridge Pier Load factor PSF Mean Charact. Horizontal deflection [mm] 60 Interaction diagram PSF Mean EN 1992-2 Characteristic w/o geom. nonlin.

Safety Formats Comparison 61

Internal Pressure [MPa] Types of Nonlinear Analysis Ultimate Limit State max load (ULS) 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 Radial displ @ z=23 m 0.4 0.2 Radial displ @ z=10 m 0.0-100 0 100 200 300 400 500 600 Radial Displacement [mm] Service Limit State deflection (SLS) crack width Seismic Assessment (SA) pushover accelerogram 62

Types of Nonlinear Analysis Structural details reinforcement detailing special details problems with boundary conditions Overall structural behaviour redistribution due to cracking ULS, SLS, SA bending OK shear or other local effects not modelled?? 63

Modelling Issues for nonlinear analyses of RC Columns bending failure expected Use beam elements with fibres Bending failure expected Use shell elements Shear + bending failure Use solid elements 64

Conclusions Simulation by nonlinear analysis is used as a standard tool in design practice or for the evaluation of existing structures Removes inconsistency in standard design process between linear analysis and non-linear cross-section check Provides insight into the structural behavior Helps to discover critical locations and failure modes May discover additional load-carrying capacity Ideal tool for checking reinforcement detailing in complicated D-regions State of art: Complexity -> old myth from the 20 th century Available in many commercial finite element codes Computationally more demanding than linear analysis Supplement standard design based on linear analysis and section design 65

Thank you for your attention 66