17th U.S.-Japan-New Zealand Workshop on the Improvement of Structural Engineering and Resilience Rydges Lakeland Resort, Queenstown, New Zealand November 1-14, 18 RESILIECY EVALUATOIN OF REINFORCED CONCRETE BUILDINGS Sam Kono, Ryo Kuwabara, Fuhito Kitamura, Eko Yuniarsyia, Hidekazu Watanabe, Tomohisa Mukai, and David J. Mukai Tokyo Institute of Technology, Yokohama, Japan Building Research Institute, Tsukuba, Japan University of Wyoming, Laramie, USA
Ben Lomond
3 Lessons from 16 Kumamoto EQ Safety is still the most critical issue. People want to use their buildings continuously after EQ s without losing any building functions. Intermediate or severe damage to structural and non-structural elements cannot be accepted anymore.
Current design issues (Evolution of PBEE methodology) 4
Evaluation of minor/intermediate damages of RC buildings 5
Continual functionality using real scale five-story RC buildings The experiment was conducted by NILIM and BRI. Tokyo Tech was one of three universities who collaborated with them. 6 From Tokyo tech Mr. Eko Yuniarsyah Mr. F. Kitamura Prof. H. Watanabe Prof. S. Kono
Objectives set up by Tokyo Tech 7 Simulate the behavior of a 5-story building specimen with FE analysis. Simulate damages numbers/width/length of cracks area of cover spalling extent of concrete crushing extent of rebar yielding/bucking/fracturing
Specimen 8 6m6m 1m 1 m Reaction Wall The experiment was conducted by NILIM and BRI. Tokyo Tech was one of three universities who collaborated with them. (Papers in WCEE 17) Positive Master Jack Negative Loading Stub RF P 18.7m Slave Jack Reaction Wall 18.7m P Slave Jack Reaction Floor
9 5mm 5 Specimen 75 15 14 15 75 1 71 458 7mm 5mm T=mm 71 7mm 7mm 71.5 163.5 115 115 163.5 71.5 5 16 17 7 57 7 7 Beam section Corner column section beam beam 45 4 column column hanging wall column wall wing wing wall pier wall wall pier standing wall Typical story elevation in the longitudinal direction
Crack distributions 1 R=.5% R=.5% R=1%
Crack measurement 1m m 97m m Crack Crack scale card Crack Beam Center colum n Wing wall Grid Corner Colum n Page.6
Crack length ratio(%) 1 1 8 6 4 Summary of recorded cracks 1 crack length ratio (%) = Total Crack length(mm) Surface area mm. to 1.mm 1/16 1/8 1/4 1/ 1/1 (.63%) (.15%) (.5%) (.5%) (1.%) Roof drift Less than. mm Page.1
13 Numerical model using FEM Program FINAL Stress σ(n/mm) Stress σ(n/mm σc ) σ r B C=1. εb Strain Strain εcr Concrete(Comp.) Concrete (Tens.) Modified Ahmad Model) (Izumo Model) Stress Stress-Strain relations Strain Reinforcement (Modified Menegotto Pinto model)
Base shear 1F 層せん断力 force, Q(kN) Q (kn) 5 4 3 1-1 - -3-4 -5 FEM Results Base shear force Roof drift relation FEM 1F 層せん断力 - 代表変形角 Experiment 代表変形角 R(%) 実験解析 - -1.5-1 -.5.5 1 1.5 Roof drift (%) 14
Base shear force, Q (kn) 1F 層せん断力 Q(kN) FEM Results Member level 5 4 3 1-1 - -3-4 -5 北柱 部材回転角 θ(%) 実験解析柱主筋降伏 ( 実験 ) 柱主筋降伏 ( 解析 ) - -1.5-1 -.5.5 1 1.5 Member rotation (%) Base shear force, Q (kn) Base shear force, Q (kn) 1F 層せん断力 Q(kN) 1F 層せん断力 Q(kN) 5 4 3 1-1 - -3-4 -5 5 4 3 1-1 - -3-4 -5 北梁 部材回転角 θ(%) 実験解析梁主筋降伏 ( 実験 ) 梁主筋降伏 ( 解析 ) - -1.5-1 -.5.5 1 1.5 中柱北側袖壁 Member rotation (%) 部材回転角 θ(%) 解析実験開口補強筋降伏 ( 実験 ) 開口補強筋降伏 ( 解析 ) - -1.5-1 -.5.5 1 1.5 Member rotation (%) 15
16 Flexural crack simulation 1. Spacing (Number of cracks) CEB-FIP Model Code. Width Use axial strain of FEM 3. Length Flexural analysis based on FEM
17 Flexural crack simulation 1. Spacing Crack spacing formula (CEB-FIP 1978) s = c s 1 k k d p Crack Crack spacing Crack spacing (mm) srm=mean crack spacing cs=clear concrete cover Sy=maximum spacing between longitudinal bars, k1=factor that takes into account bond properties of reinforcing bar=.4 for deformed bars,k=factor that takes into account strain gradient, k=.5(ε1+ε)/ε1, ε1 and ε correspond to the largest and smallest concrete tensile strain, dby=longitudinal bar diameter, py=ratio of the area of reinforcement effectively bonded to the concrete to the cross-sectional 1 8 6 Cal.(189mm) Exp. (Average) 4 Corner column at 1/4 1/16 (.63%) 1/8 (.15%) 1/4 (.5%) Roof drift 1/ (.5%) 1/1 (1.%) Page.11
Flexural crack simulation. Width 18 S S The crack width of the i-the crack, w i, in a region (from h i to S rm +h i ) is expressed as: S S S S Assumption: axial strain is caused by cracks but not concrete (concrete does not deform).
1μ Flexural crack simulation 3μ. Width w = s rm ε dy w cr1 L(mm) 19 Accumulation crack width s rm w cr1 +w cr s rm w cr1 +w cr +w cr3 s rm s rm s rm w cr1 +w cr + +w crn Axial strain distribution ε Corner Column Crack spacing Σw cr (mm)
Crack Crack pattern at 1/4(.5%) Corner column (Exp.) Flexural crack simulation Crack width w cr1 (mm) w cr w cr3 w crn 8 4 w cr1 +w cr 16 w cr1 +w cr +w cr3 1 8 4 w cr1 +w cr + +w crn. Width 1 3 Total crack width 4 5 Peak 1/1(FEM) 1/(FEM) 1/4(FEM) 1/1(Exp.) 1/(Exp.) 1/4(Exp.) 6 7 1 Accumulation crack width (mm) Residual 1/1(FEM) 1/(FEM) 1/4(FEM) 3
Flexural crack simulation 3. Length 1 Wcr-visible: minimum visible crack with(=.1mm Xn Lmin Lcr Wcr:crack width Xn: neutral axis depth(mm) Lmin: invisible crack length(mm) Lcr: Visible crack length(mm)
Flexural crack simulation 3. Length α = L L α = L L (detouring&meandering) (horizontal to diagonal) L :Horizontal projection L :Real crack length L :Distance between two points
Flexural crack simulation S rm CEB-FIP 1978 1. Crack spacing S rm Procedure flow Nonlinear Finite Element Analysis Axial strain distribution S rm S rm S rm S rm S rm Izumo et al. Visible crack width W cr-visible L f1 Column Crac k L fn 3 W 1 W W n Exp.. Crack width(peak) Conversion factor α(exp.). Crack width(residual) 3. Horizontal crack length Correction factor 1, (exp.) 3. Curved&meandering crack length L 1 ~L n Exp. Residual Crack Summary ΣL fi for mm < W <.mm ΣL fi for.mm < W < 1mm ΣL fi for 1mm < W < mm
Crack length ratio(%) 1 1 8 6 4 Flexural crack simulation 3. Length crack length ratio (%) = Total Crack length(mm) Surface area Total crack length ratio(fem) mm Total crack length ratio(exp.) Crack width. to 1.mm(Exp.) Crack width under. mm (Exp.) Under. mm (FEM) 4. to 1.mm (FEM) Under. mm (FEM) 1/16 1/8 1/4 1/ 1/1 (.63%) (.15%) (.5%) (.5%) (1.%) Roof drift Page.1
Flexural crack simulation Final results 5 Residual crack length ratio Σ(Residual crack length) = 1 Surface area Crack length ratio(%) 残留ひび割れ率 Crack length ratio(%) Crack length ratio(%) 16. 14. 残留ひび割れ率 ( 中柱北側袖壁 ) Wall 1. FEM(Residual) EXP(Residual) 1. 8. 6. 4.. 加力サイクル (rad). 1/16 1/8 1/4 1/ 1/1 Roof drift 16. 16. 14. FEM(Residual) 残留ひび割れ率 ( 北柱 ) EXP(Residual) 14. 残留ひび割れ率 ( 北梁 ) 1. 1. FEM(Residual)_ 下端上端合計 1. Column 1. EXP(Residual) Beam 8. 8. 6. 6. 4. 4... 加力サイクル (rad) 加力サイクル (rad).. 1/16 1/8 1/4 1/ 1/1 1/16 1/8 1/4 1/ 1/1 残留ひび割れ率 ひび割れ率 Roof drift Roof drift
Coordinate conversion
Summary of Experiment and Simulation Flexural 合計曲げひび割れ幅 crack width (mm) W 14 1 1 8 6 4 Flexural crack Shear crack 合計曲げひび割れ幅 ( ピーク, 14 年度試験体 ) 北柱 (FEM) 北柱 (EXP) 中柱北側袖壁 (FEM) 中柱北側袖壁 (EXP) 北梁下端 (FEM) 北梁下端 (EXP) 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 Drift Wall Column 合計せん断ひび割れ幅 (mm) Shear crack width W Beam 8 7 6 5 4 3 合計せん断ひび割れ幅 ( ピーク, 14 年度試験体 ) 北柱 (FEM) 北柱 (EXP) 中柱北側袖壁 (FEM) 中柱北側袖壁 (EXP) 北梁上端 (FEM) 北梁上端 (EXP) 北梁下端 (FEM) 1 北梁下端 (EXP) 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 Drift Wall Column Beam
8 Summary of crack evaluation In order to assess damage states of reparability limit state, cracks were numerically simulated and compared to the test results for the five story RC building. Crack width and spacing were well simulated for peak points but not so for unloaded points. Crack length was simulated from FEM results by considering limit visible width. Finally, computed crack length ratio agreed with experimental results.
Design concept for safety limit state (1981 Design Standard) Lateral load Building response Collapse Target Strength 強度補強 dependent resistance Required performance Ductility dependent resistance 靭性補強 9 Low seismic performance Drift 崩壊補強前
3
Damage Evaluation of Reinforced Concrete Members with Nonlinear Finite Element Analysis ひび割れ幅の比較 ピーク時曲げひび割れ幅 残留曲げひび割れ幅 合計曲げひび割れ幅 合計曲げひび割れ幅 (mm) 14 1 1 8 6 4 3 FEM EXP 引張縁伸び 部材縁の伸び 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 FEM 解析値実験値 合計曲げひび割れ幅 (mm) 3 7 6 5 4 3 1 FEM EXP 引張縁伸び 実験値部材縁の伸び 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 FEM 解析値 最大曲げひび割れ幅 最大曲げひび割れ幅 (mm).5 1.5 1.5 EXP 実験値 解析値 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 最大曲げひび割れ幅 (mm).5 1.5 1.5 EXP 修復限界 Ⅱ 修復限界 Ⅰ 使用限界 実験値 解析値 代表変形角 (rad) -1/16-1/8-1/4-1/ -1/1 合計ひび割れ幅および最大ひび割れ幅の実験値と解析値の比較 (14 年度試験体北柱 )
Shear Crack Width and Shear Drift Component in RC Beams with High Strength Transverse Rebars Ricky Rinaldi, Advisor: Prof. Susumu Kono, Tokyo Institute of Technology Introduction Crack is an important factor in evaluating seismic damage on reinforced concrete (RC) structures. A simple model was proposed by AIJ Guidelines 4 to predict crack width from member s shear deformation. This paper evaluates the proposed model on six RC beam specimens. Measurement System Crack width (W ) and slip (W ) were measured using crack gauges in Fig. 1. The gauges were attached perpendicular to the cracks on the center line as shown on Fig.. Shear component of drift ( δ ) was measured using diagonal displacement gauges. The following equations were used to compare the horizontal crack component (W ) with shear drift component (δ ). W W = cos θ sin θ sin θ cos θ W W Slip (Y) Crack Width (X) Kumamoto Earthquake (BRI, 16) - Axis (a) Specimen #1 (b) Specimen Figure 1 Crack Gauges Figure # Crack Pattern δ = W Experimental Result Displacem ent Gauge Figure 3 Displacement Gauges Conclusion Y W According to AIJ Guidelines 4 Loading θ X W Figure 4 Relation between Crack Width and Shear Deformation The summation of horizontal component of cracks has good agreement with shear drift component. Compared to higher residual drift, the crack gauges picked up shear drift component better at lower residual drifts. Contribution to Society Y X δ W W W W Shoul d be same This study provides a better understanding of earthquake damage on RC structures, and contributes to the development of low damage structural system and resilient structures. θ θ θ θ W 9 7.5 Wh (mm) 6 4.5 3 1.5 R=1% R=1.5% R=% 1.5 3 s 4.5 (mm) 6 7.5 9 Wh (mm).5 1.5 Wh (mm) 1.5 3.5 3.5 1.5 1.5 Good Agreement Specimen #1 Good Agreement Specimen # R=1% R=1.5% R=% -.5 -.5.5 1 1.5.5 3 3.5 Good Agreement R=1% s (mm) Specimen #3 R=1.5% R=%.5 1 1.5.5 s (mm) Figure 5 Horizontal Crack Comp. ( W - Residual Shear Drift (δ )
Rocking system (Ductility with resiliency) LOAD-DRIFT RATIO RELATIONS 4-3 3 3 3 1 1 1-1-1-1 3-3 4 - - -1-1 4 1 1-4 NSW7 1 Residual Drift Angle (%) 3-4 4-3 - R(%) -4-3 - -1-1 D-1-1-1 1-3 -4 4 3 4 R(%) Rocking wall (With damper) ウェブ降伏点 フランジ降伏点 圧縮ひび割れ点 圧壊点 軸方向組立筋 降伏点 軸方向組立筋ひずみ 1. 到達点 PC鋼棒弾性限界点 最大耐力 D-3 (ダンパー大) -4 D-3 3 R(%) -3 D- 1 - Q(kN) - D- (With damper) RC.4 4 Q(kN) NSW7A.5 3 Rocking wall (No damper) -4 3-3 R(%) -3 3-1-1 1 - Q(kN) -.6-3 RC walls -4-3 -4 4 R(%) - -4 4 Q(kN) NSW7 Equivalent Damping Ratio (heq) (%) -4 4 Q(kN) 降伏はひずみゲージの値で判断 圧壊点 かぶりコンクリートの剥落 NSW7A D-1 D- D-3 16 ダンパー無 PCaPC.3..1 1 RC 8 ダンパー無 PCaPC 4 -.5-1.5 -.5.5 Drift Angle (R) (%) 1.5.5 残留変形角-経験最大部材変形角関係 No.33 No.33 No.33.5 1 Drift Angle (R) (%) 1.5 hｅｑ-経験最大部材変形角関係 18年度修 論 発表会
Kamo River, Kyoto
35 Damage to RC Structures at Kumamoto Earthquake, 15
Kumamoto 36
Uto municipal office 37
Kumamoto 38
Kumamoto 39
Kumamoto 4
41 New call from the society How to make a quick recovery after EQ s with losing no/minor loss of building functions.
FEM Results Member level (Q- relation) 4 Base 1F 層せん断力 shear force, Q(kN) Q (kn) 5 4 3 1-1 - -3-4 -5 北梁 部材回転角 Experiment θ(%) 実験解析梁主筋降伏 ( 実験 ) 梁主筋降伏 ( 解析 ) - -1.5-1 -.5.5 1 1.5 Member rotation (%) FEM
1 FEM Results Member level (deformation decomposition) Shear deformation Corner column 43 Wing wall 8 6 4 1 8 6 4 Flexural deformation FEM Exp. FEM Exp. North beam FEM Exp. Exp. FEM North beam Conner column Wing wall Center column Center column +1/16-1/16 +1/8-1/8 +1/4-1/4 +1/ -1/ +1/1-1/1 +1/16-1/16 +1/8-1/8 +1/4-1/4 +1/ -1/ +1/1-1/1 Deformation component(%) Roof Drift
Flexural crack simulation. Width 44 Relation between residual crack width (Wr) and peak crack width (Wp) Wr= Wp =.3(Column),.43(Wall,),.6(Beam)
Flexural crack simulation. Width 45 3 3.5 ひび割れ開閉率 ( 北柱 ).5 ひび割れ開閉率 ( 北梁 ) 残留ひび割れ幅 (mm) Wr(mm) 1.5 1.5 Wp (mm) y =.3 x R² =.57 ピーク時ひび割れ幅 (mm).5 1 1.5.5 3 残留ひび割れ幅 (mm) Wr(mm) 1.5 1.5 y =.6 x R² =.9 Wp (mm) ピーク時ひび割れ幅 (mm).5 1 1.5.5 3 3.5 ひび割れ開閉率 ( 中柱北側袖壁 ) 残留ひび割れ幅 (mm) Wr(mm) 1.5 1.5 Wp (mm) y =.43 x R² =.71 ピーク時ひび割れ幅 (mm).5 1 1.5.5 3
Height of column(mm) 8 4 16 1 Flexural crack simulation. Width Peak crack width multiplied α is residual crack width 1/1(FEM) 1/(FEM) 1/4(FEM) 1/1(FEM) 1/(FEM) 1/4(FEM) 1/1(Exp.) 1/(Exp.) 1/4(Exp.) 46 8 4 Peak Residual 4 6 Accumulation crack width (mm) 1 3
Flexural crack simulation 3. Length 47 La 1 8 6 4 α1( 北柱 ) y = 1.5 x R² =.99 La 1 8 6 4 α1( 中柱北側袖壁 ) y = 1.7 x R² =.96 La 1 8 6 4 α1( 北梁 ) y = 1.8 x R² =.98 Lv 4 6 8 1 Lv 4 6 8 1 Lv 4 6 8 1 Lv 1 8 6 α( 北柱 ) y = 1. x R² = 1. Lv 1. 8. 6. α( 中柱北側袖壁 ) y = 1.7 x R² =.98 Lv 1 8 6 α( 北梁 ) y = 1.6 x R² =.95 4 4. 4 4 6 8 1 Lh.. 4 6 8 1 Lh 4 6 8 1 Lh Crack length = L α α