Multi-scale Modeling for Life-Cycle Management of Concrete Structures

Transcription

1 Multi-scale Modeling for Life-Cycle Management of Concrete Structures Underground space fatigue failure of RC bridge deck Building management against earthquake and aging (1) Summary of multi-scale platform (2) Seismic response of multi-story RC building and impact of drying (weak coupling) (3) Long-term deformation of underground RC culverts and durability over 30 years (weak coupling) (4) Fatigue life assessment of bridge decks (strong coupling) (5) PDCA cycle for asset management Koichi Maekawa T. Ishida Y. Hiratsuka X. Zhu

2 Multi-scale modeling and simulation with regard to the space and the time domains km Construction Curing In service Deterioration Long-term Durability m Size Reinforced Concrete Shear failure of column Time (Days) cm Concrete mm Aggregate, cement paste matrix, interfacial transition zone Fatigue of RC slab Carbonation, Chloride Rebar Corrosion µm Capillary water, C-S-H hydrate Shrinkage & Thermal cracking nm Gel pores, water molecule, C-S- H layer structure Long-term deflection of PC bridge Nuclear waste barrier facility (Ultra long-term stability)

3 10-9 m nano space model scanning microscope image Unhydrated cement Hydrate product (C-S-H grain) Low hydration After few hours Interlayer (2.8A thick) Inner hydrate Outer hydrate Gel pore I (~1.6nm) Gel pore II (1.6nm~) Pore inside gel grain Pore among gel grain Capillary pore Free space for hydrate Mature Integration dv/dlnr Gel pore 7days 28days Capillary pore 1day 3days log(r[m]) 10-9 m 10-6 m space structures micro-pores Model assumptions Liquid Transport K L gel dv/d log r S r c log r Vapor φρv Do ( ) ( ) Transport KV = [ 1 S K h ][ Mh ρl RT] r 2 Knudsen diffusion factor φ ρ c l = rdv History dependent liquid viscosity 50η m 10-6 m pore moisture state and motion

4 dv/dlnr Gel pore 7days 28days Capillary pore 1day 3days log(r[m]) micro-pores Model assumptions Liquid Transport K L gel dv/d log r S r c log r Vapor φρv Do ( ) ( ) Transport KV = [ 1 S K h ][ Mh ρl RT] r 2 Knudsen diffusion factor φ ρ c l = rdv History dependent liquid viscosity 50η m 10-6 m space structures 10-9 m 10-6 m pore moisture state and motion Integration F= ( ρ φs ) l t div { J( P, P, T )} Q = 0 l hyd 10-6 m 10-3 m scale potential flux term sink term concrete composite section

5 10-9 m nano space model scanning microscope image Unhydrated cement Hydrate product (C-S-H grain) Low hydration After few hours Interlayer (2.8A thick) Inner hydrate Outer hydrate Gel pore I (~1.6nm) Gel pore II (1.6nm~) Pore inside gel grain Pore among gel grain Capillary pore Free space for hydrate Mature Integration Micro-pores Time Solidifying cluster of cement paste Seepage of water 10-9 m 10-6 m cement + moisture system

6 Micro-pores Time Solidifying cluster of cement paste Seepage of water 10-9 m 10-6 m cement + moisture binder system V ag V cp Cement Paste Aggregate Integration G i = σ ii ε kk,p,,s j + f x i + ρu i = 0 j 10-6 m 10-3 m stress gradient gravity acceeration term

7 F= ( ρ φs ) l t div { J( P, P, T )} Q = 0 l hyd 10-6 m 10-3 m scale potential flux term sink term concrete composite section Integration F(x,y,z) W 1 (x,y,z)dv = 0 F(x,y,z) W 2 (x,y,z)dv = Weighted residual Function method F(x,y,z) W k (x,y,z)dv = m scale integral over the structural element 3 p = E w w i + ε x ii i i=1 /n

8 G i = σ ii ε kk,p,,s j + f i + ρu i = 0 x j 10-6 m 10-3 m stress gradient gravity acceeration term Integration G i (x,y,z) W 1 (x,y,z)dv = 0 G i (x,y,z) W 2 (x,y,z)dv = G i (x,y,z) W k (x,y,z)dv = 0 B T σ dd =F m scale integral over the structural element with crack stress transfer concrete composite section 3 p = E w w i + ε x ii i i=1 /n

9 F W 1 (x,y,z)dv=0 F W 2 (x,y,z)dv=0.... F W k (x,y,z)dv=0 G i (σ) W 1 (x,y,z)dv=0 G i (σ) W 2 (x,y,z)dv= G i (σ) W k (x,y,z)dv=0 Integration= assembly of elements over 10 +1~+2 m Reinforcement Local strain of steel Crack location Mean strain Yield level Mean stress Local stress of steel Mean stress of steel coupling Local response Averaged response of steel in concrete Mean strain of steel RC Local strain of concrete Nonlinear dynamic structural analysis Cracked concrete Multi-system Crack location Mean stress Damage zone Shear stress transferred Shear slip along a crack Comp. strength reduction 1.0 Crack width LOCAL RESPONSE Shear stress transferred Comp. strength reduction Average tensile strain Mean shear strain 1.0 Mean normal strain in x-dir. Comp. strength Comp. strain MEAN RESPONSE

10 weak coupling

11 Seismic full 3D analysis : disp. At the 2 nd floor experiment analysis In consideration of drying Z X Y Magnification of displacement=5

12 Effect of drying shrinkage on seismic performance Ducom-COM3 link analysis 3nd floor (X Y)displacement 7~28 days drying ~28 days sealed 10% 25% [mm mm] 100% 50% E-defense initial shrinkage cracking

13 Cracking and Drying (weak coupling): Experiment by Kim and Bažant 1987 Bažant et al carried out experiment on the effect of cracking on diffusivity of concrete. X-direction strain contour

14 Research object:shallow underground RC culvert Cable Electric 国土交通省中部整備局 Wire Water supply Role keeping lifelines underground Status of development Gas sewer Many RC culverts constructed in urban areas Number of cracks Background mm After a few decades, Long-term excessive deformations at the top slab are reported Top slab Crack condition 30 years 15 years Distance from center(mm) 国土交通省関東整備局 Deflection excess 3~4times Crack width(mm) of prediction Displacement(mm) Actual crack picture White line: chalked cracks Deflection shape of top slab (30years after completion) Expected in design Unknown cause deformation Future behavior is concerned about Measured

15 2D: Long-time excessive deformation analysis 640 Model mesh 4 Contrast cases 35 C.L RC Backfilled sand Based on actual structure and material data 1 Design 2 RH:99.99% 3 RH: 99.99% RH: 99.99% Surrounding soil settlement Differences reflect each effects RH: 99.99% Drying shrinkage, creep RH: 60% RH: 99% 4 Soil settlement + drying shrinkage,creep RH: 60% RH: 99% Deflection(mm) Deflection at the center of top slab 27.4years Soil settlement Case II,III simply added Measured Design soil settlement Elapsed time after curing(day) Dry (27.4years) Mid-span deflection(mm) Mid-span tension steel strain Dry + soil settlement Soil settlement Measured Analytical soil pressure could reflect the real soil pressure Time (day) Design Analytical results considering interacting behavior of structures and soil and Drying shrinkage show that long-term excessive deformation. Dry It shows that soil pressure is the main factor effecting steel tension strain.

16 Destructive test: drilling and scanning inside shear crack roughness level>flexure crack roughness shear path of inclined crack Core part Scan inside Shear crack Crack Coarse aggregate Steel rebar Crack Relative deformation Relative deformation Scan photos Flexur e crack Crack Coarse aggregate Crack Steel rebar Flat Opening (2)Use light to check the shadow Haunch 1-2mm raised Light Haunch

17 Life-Cycle Assessment and Inspection Data Assimilation for Concrete Bridge Deck Management flexure Punching failure after repetition of moving traffics strong coupling In design: fatigue life prediction In maintenance: remaining fatigue life with and without damage

18 Seismic Fatigue Numbers of cycles, strain levels, reversed/single sided cyclic FATIGUE EARTHQUAKE cycles, lower stress level cycles, much high strain level single sided, years reversed cyclic, sec

19 Extended to High cycle Fatigue Simulation In the case of normal RC beams without any web reinforcement V c /V co V log V r = V c co min / = *(1 r r ) log N V max FE analysis cm log N 240cm time integration : t logarithmic time integration : t (log t) evolution term: dk=fdt + Gdε Ftd(logt)+ Gdε

20 Moving load 2~3 order reduced life stagnant water 1~2 order Normalized amplitude Cyclic moving point shear by FE analysis fixed point cyclic shear by FE analysis moving experiment by Matsui, et al. fixed pulsating by Perdikalis, et al Number of cycles and passages (log N) Perdikalis, et al. S-P/Po Dry experimental results Submerged experimental results Cycle

21 Aggregation (erosion) of concrete on bridge deck slab Aggregation on Highway bridge deck Wheel loading test of RC slab specimen East Nippon Expressway Co., Ltd Nihon University VTR (Inspection) Aggregation lead the failure of specimen East Nippon Expressway Co., Ltd CL Nihon University Sawn specimen after loading test

22 Erosion (disintegration) at the top surface of the slab Closure Pressure (MPa) Time (sec) (Yokoyama et al. 2012) Positive pressure Opening Negative pressure Driving action of Erosion (disintegration, freeze-thaw)

23 Erosion at the top surface of the slab Dry Moist Submerged Fatigue As above and Water compression and Reduction of Shear Transfer As above and Erosion Influence of water Influence of erosion N=1 N=1000 N=30000

24 Migration of gel into cracks Anisotropic pore pressure σ ij = σ ij + δ ij l i p l i ; unit vector normal to crack plane 3 p = E w w i + ε x ii i i=1 /n Gel production swelling ASR-gel SiO2 nsio2 + 2 NaOH Na2O nsio2 + H 2O Na2O nsio2 + mh 2O Na2O nsio2 mh 2O Na 2 O K 2 O Absorption of water Crack!! 骨材 Adsorption of gel into micro-pores Isotropy of liquid action Anisotropy of gel as a part of solid ゲルの液体性に関するパラメータ 0.0<βx<0.90 は時間と共に増大 (β x = β x_prev + K *(P i -P a )) Gel migration takes time due to the viscosity Washburn Eq.: r=-2πcosθ/p r: 空隙半径 θ: 接触角 p: 圧力 Pore distribution Pressure dependent adsorption into the micro-pore Rate of reaction Gel generation R R ASR _ Na + = k C + F Gra 1.0E Na water Linked with cement hydration and micro-pore formation model ( ( 1. RH ) ) R + + = exp 0 ASR _ Na Gel Solid Na + Na _ ASR R = = 2.0 Gel ASR _ Na Na + ρ + ρ t M Dependent on alkalinity, moisture, and active silica Consumed alkalinity Consumed water gel gel gel 1.0E + 6 W 6 M Na _ ASR = 8.4 Gel + ρ Na gel 1.0E + gel ASR _ Na M gel By Micheal et al C & CR, 2013

25 DuCOM-COM3 ASR reaction and expansion modeling verified Uniaxial confinement test Axial expansion (analysis) Axial expansion (exp) YY 方向ひずみ分布 10cm 10cm 40cm prism Confined by plates Cracking along steel bar Confined expansion of ASR 30cm 45cm 60cm 試験体 Mockup of footing Beam model 10cm 18cm 170cm ZZ 方向表面ひずみ分布 XX ひずみ [μ] YY ひずみ [μ] D6 Space-discretization 1/4 D13 D10 Cracking according to the rebar arrangement Cracking along ties Cracking at corners Cracking along main bars

26 DuCOM-COM3 Corrosion and expansion modeling verified Strain, Micron Experiment S2-C2 ; Experiment S2-C3 ; Experiment S2-C4 ; Experiment S2-C5 ; Analysis S2-C2 Analysis S2-C3 Analysis S2-C4 Analysis S2-C5 Interface deformation (µm) Node_1 Node_2 Node_3 Node_4 Node_5 Node_6 Node_7 Node_ Time (days) Corrosion % S2-C3 S2-C5 S2-C4 Experiment by Oh et al Experiment by Micheal et al. 2013

27 Corroded bridge decks in lab. by Prof. Iwaki of Nihon Univ. 塩水の入替 Deflection for live load (mm) E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 Equivalent repeated cycles 載荷荷重せん断強度比 (P/Psx) Normalized shear force 1 S-N 曲線 浸漬 内在 散布 健全 健全 ( 参考値 1) 健全 ( 参考値 2) E+05 1.E+06 1.E+07 1.E+08 等価繰返し走行回数 Equivalent number of cycle strong coupling

28 Deflection (mm) Corroded bridge decks by analysis (Iwaki, Tsuchiya, Maekawa) Data assimilation in terms of corrosion degree strong coupling Corrosion rate (%) a)3 億 7800 万回 b)27 億 8000 万回 a)112 万回 b)2760 万回 Main ref Distribution ref Chloride concentration Ion concentration (kg/m3)

29 Wheel type moving Loads by Prof. Iwaki, Nihon University Live load deflection (mm) 活荷重たわみ (mm) 3 床版 No acceleration Ⅰ 2.5 床版 ASR Ⅱ 床版 ASR Ⅲ( + water 水張り ) 2 健全供試体 No reactive aggregate ( 参考 ) E+00 1.E+02 1.E+04 1.E E+08 0 等価繰返し走行回数 Number of load cycle No ASR ASR + Water ひずみ量 (μ) ASR Expansion in each axis Vertical : μ 床版 Ⅱ-x 床版 Ⅱ-y 床版 Ⅱ-z 床版 Ⅲ-x 床版 Ⅲ-y 床版 Ⅲ-z 材齢 ( 日 )

30 Fatigue analysis of ASR damaged decks (ASR+Force+water) 1800μ of free expansion

31 FABriS software (2015 version) based on DuCOM-COM3 Cracks, water, NDT data, ambient states future life (fatigue failure)

32 Graphics switch Digitalized crack location and the width can be a part of database for maintenance of RC decks Crack information is converted to digit dataset.

33 Pseudo-Cracking Method Crack maps by inspection Converted field of Pseudocracking strain Conversion of current cracking to strain field

34 Influence of water (Analysis of moving load) The influence of water RC Slab Load : 160kN It has sufficient fatigue life at the design load level Dry Wet No water in crack With water in crack Fatigue life is reduced by 2-3 order under the influence of water. We cannot describe the cave-in of the strengthened slab.

35 Re-deterioration of Strengthened Slabs (Debonding, Cave-in) Source : Steel Plate Bonding Method Steel plate bonding method has been applied in numerous bridges. Re-deterioration of strengthened slabs has been reported. Neither experiments nor analysis have systematically been made concerning the re-deterioration mechanism. Make clear the process of re-deterioration and residual life

36 S-N curve of corrosion of the strengthened slab Case Corrosion Condition Dry 0% Dry Wet 0% Wet Corr 50mg 1.60% Dry Corr 20mg 0.64% Dry Effects of corrosion Corrosion occur, rebar expand -> Concrete failed in layers -> Slab turned into a built-up beam -> Fatigue life deteriorated. Numerical analysis showed fatigue life deteriorated because of corrosion of the strengthened slab.

37 S-N curve of strengthened damaged decks -Damaged concrete is not removed- Steel plate bonded 気中 水中 Additional beam

38 S-N curve of strengthened damaged decks -Damaged concrete is not removed- Overlaid upper face Overlaid bottom face

39 Remaining fatigue life assessment of existing RC bridge decks coupled with multi-scale platform users Advice etc. Knowledge of engineers Pseudo-cracking method Compile & link computational platform site inspection simple measurement 数値解析による推定寿命 簡易計測結果 Max. stress/comp.strength Compressive Stress (MPa) Compressive Strain specified S-N diagram for design 0.01Hz analysis rate of loading = 1.0Hz Clear output =S-N diagrams Log N Knowledge of engineers Combination of site inspection data and simulation platform

40 Thank you for your kind attention. U-Tokyo 2015