camus iii international benchmark

CAMUS III International Benchmark

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Organized by Commissariat à l'Energie Atomique , Electricité de France, INSA Lyon and ENS Cachan

CAMUS III INTERNATIONAL BENCHMARK

With the Financial Support of the European Networks TMR-ECOEST 2 and ICONS

Post-FraMCoS-4 Workshop “Seismic loading effects on structural walls”

under the auspices of the AFPS, ACI and JCI

1st June 2001, Cachan, France

Synthesis of the participant reports


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This document has been prepared by the Seismic Mechanic Study Laboratory of CEA Saclay and the CAMUS 3 Benchmark Working Group composed by :

Didier COMBESCURE and Pierre SOLLOGOUB

Seismic Mechanic Study Laboratory (EMSI)

Commissariat à l’Energie Atomique

CEA Saclay

DEN – DM2S - SEMT

F-91191 GIF Sur YVETTE

Nicolae ILE and Jean-Marie REYNOUARD

INSA Lyon

URGC, Bât 34

2, Rue Albert Einstein

F-69621 VILLEURBANNE Cedex

Jacky MAZARS

Laboratoire Sols, Solides, Structures

Domaine Universitaire

BP 53

F-38041 GRENOBLE Cedex 9

Pierre-Alain NAZE

Electricité de France, SEPTEN

12-14, Av. Dutriévoz

F-69628 VILLEURBANNE Cedex

The benchmark has been organised with the support of the European Networks ECOEST 2 (European Consortium of Earthquake Shaking Tables) and ICONS (Innovative Concepts for New and Existing Structures) of the Training and Mobility of Researchers Programme of the European Commission.

The experimental part of the CAMUS III project has been financially fully supported by the ECOEST 2 network while the design and the analysis have been performed within the ICONS project.

The workshop is held under the auspices of AFPS (French Association of Earthquake Engineering) ACI (American Concrete Institute) and JCI (Japan Concrete Institute).


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CAMUS III INTERNATIONAL BENCHMARK

Since the beginning of the 90’s, several experimental campaigns on reinforced concrete bearing walls under seismic loading have taken place in France in the framework of French and European research programmes. The seismic tests have been performed on the major Azalee shaking table of Commissariat à l’Energie Atomique (CEA) in the Saclay Nuclear Center. Between 1996 and 1999, four 1/3rd scaled specimens named CAMUS I to IV made of two RC walls and 6 floors with different steel reinforcement and boundary conditions have been tested under in-plane seismic loading. A new programme ,CAMUS 2000, studying 3D effects is in progress.

To draw some conclusions for the model behaviour requires experimental testing program but also many parametric studies using numerical modelling. A first benchmark was organised on the base of the CAMUS I experiment (walls with a low ratio of reinforcement designed in accordance with the French code PS92 and fully fixed to the shaking table). The results have been presented at a workshop organised during the XIth European Conference on Earthquake Engineering, Paris, September 1998.

As it was done in the first CAMUS Benchmark, the CAMUS III International Benchmark aimed at comparing and validating the numerical tools commonly used for RC load bearing walls. It concerned the CAMUS III specimen which was designed in accordance with EUROCODE 8 provisions. Participants had access to the experimental results after having performed a first series of blind computations (knowing only the real motions of the shaking table and the initial natural frequency). In the second stage of the Benchmark, they could modify their numerical modelling in order to improve the agreement between numerical and experimental results.

The present document shows the CAMUS I, II and III experimental programmes, the main results obtained during the testing campaign, the numerical models used by the participants of the CAMUS III Benchmark and their main numerical results.

In the first part, the characteristics of the CAMUS I, II and III specimens, their instrumentations and the main experimental results are reminded.

The second part of the report makes a synthesis of the blind calculations reports sent by the participants to the benchmark organisers. The numerical models used by the participants and the main numerical results are described. These results have been compared with the experimental ones for the high level tests.

The list and affiliation of the participants are given at the beginning of the second part and a list of references corresponding to works performed by the members of the CAMUS programme has been included in the following pages. Obviously they could not take part in the benchmark.

The organisers would like to thanks all the benchmark participants for the quality of the impressive work they have performed without any financial support from the Benchmark organisation.

Didier Combescure Jacky Mazars Pierre-Alain Nazé Jean-Marie Reynouard

CEA Saclay ENS Cachan EDF – SEPTEN INSA Lyon


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The French and European CAMUS Experimental Programmes


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1. Introduction

Reinforced concrete bearing walls with limited reinforcement ratio are commonly used in France for the building structures. In order to show their seismic performance and validate the provisions of both French PS92 and Eurocode 8 design codes, a series of seismic tests on 4 large scale models have been performed on the largest shaking table of the Commissariat à l’Energie Atomique (CEA) in Saclay, France. The tests on the 2 first specimens has been supported by the CAMUS French national research project while the third and fourth specimens have been tested in the framework of the TMR (Training and Mobility of Researchers) programme of the European Commission.

Four specimens with different reinforcement ratios and boundary conditions have been built. The 1/3rd specimens are composed of two parallel 5-floor R/C walls without opening linked by 6 square floors and have a total mass of 36 tons. The 2 first specimens have been designed according to French constructions. The first model CAMUS I is slightly reinforced while the second one CAMUS II has almost no reinforcement. For CAMUS I, the reinforcement ratio changes between two storeys in order to obtain steel yielding at several storeys. The tests have been performed up to obtain significant damage. Wide crack opening and extensive yielding and failure of the steel bars have been observed during the tests. The design of the third specimen CAMUS III follows the EC8 requirements. Although the ultimate bending moment at the base is the same one than the first specimen, its design aimed at concentrating damage at the base in a unique plastic hinge and not spread it on the height on the structure. The last specimen CAMUS IV has similar geometry and reinforcement than CAMUS I but its boundary conditions are very different since it is not anchored to the shaking table and stands only on 2 superficial foundations on a 40 cm deep sand layer. These tests aimed at investigating the effect of uplift on the overall response of the RC wall structures and are not considered in this report.

The first part of the document presents the main experimental results of the CAMUS I, II and III specimens. This presentation separates global results (diasplacements, internal forces, etc…) and local ones (crack opening, strain, etc…).


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2. Main characteristics of the Camus Specimens

Three specimens with different reinforcement ratios have been built in the framework of both the French CAMUS research programme and the ECOEST II European programme (Fig 1). The 1/3rd scaled specimens are composed of two parallel 5-floor R/C walls without opening linked by 6 square floors (including the floor connected to the footing). A heavily reinforced concrete footing allows the anchorage to the shaking table.

The total height of each model is 5.10 m and the total mass is estimated at 36 tons. Each wall is 1.70 m long and 6 cm thick. Each part of the structures (walls, floors and basements) is cast separately. The walls are cast in two parts in order to reproduce the construction joint at the level of each floor. The different parts of the specimen are assembled on the shaking table. The value of the additional masses fixed to each floor was chosen to obtain a vertical stress commonly found in such structures under the vertical static loading (1.6MPa in this case).

The 2 first specimens were designed according to French constructions. The first model CAMUS I was slightly reinforced while the second one has almost no reinforcement. 4.5, 5.0, 6.0 and 8.0 mm diameter steel bars have been used. Table 1 gives the steel rebars at each storey for the specimens CAMUS I and III. The steel reinforcement of CAMUS 1 was composed by vertical reinforcement concentrated in the 2 boundaries and the center of the section. The reinforcement ratio changes between two storeys in order to obtain steel yielding at several storeys and not a concentrated plastic hinge in the lower part of the wall. The CAMUS I and II specimens had no horizontal shear reinforcement.

The last specimen CAMUS III was designed according Eurocode 8 but with the same ultimate bending moment at the base than CAMUS I. The drawings of the steel reinforcement of CAMUS III are given Fig 2. The differences in reinforcement between CAMUS I and III concern mainly the construction details (spacing between the flexural vertical bars, for example), the shear reinforcement and the design of the upper storeys. A comparison between the longitudinal reinforcement of CAMUS I and III is given in table 1.

Table 1: Longitudinal reinforcement of the CAMUS I and III specimens

Boundaries (each) –

CAMUS I and IV

Boundaries (each) –

CAMUS III

Central reinforcement –

CAMUS I

Central reinforcement-

CAMUS III

5th storey 1φ4.5=15.9 mm2 2φ8+2φ4.5=132 mm2 4φ5=78.4 mm2 2x5φ4.5/200=159 mm2

4th storey 1φ6=28.2 mm2 4φ8+2φ4.5=233 mm2 4φ5=78.4 mm2 2x5φ4.5/200=159 mm2

3rd storey 1φ6+1φ8+1φ4.5=94.4 mm2 4φ8+2φ4.5=233 mm2 4φ5+2φ4.5=110 mm2 2x5φ4.5/200=159 mm2

2nd storey 2φ6+2φ8+2φ4.5=189 mm2 4φ8+2φ6+2φ4.5=289 mm2 4φ5+2φ4.5+φ6=138 mm2 2x5φ4.5/200=159 mm2

1st storey 4φ8+2φ6+2φ4.5=289 mm2 4φ8+2φ6+2φ4.5=289 mm2 4φ5+2φ4.5+φ6=138 mm2 2x5φ4.5/200=159 mm2


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Fig 1 – View of a CAMUS specimen

690

210

690

210

690

210

690

210

690

210

600

2100

Stirrups φ3/20

Stirrups φ3/40

Stirrups φ3/40

Stirrups φ3/20

2HA6 l=2100

2HA4.5/175

2HA4.5/175

2HA8 l=3700

2X7HA4.5 l=4900

2HA8 l=4900

2HA4.5/190

2HA4.5/190

50

200

Footing

2X7HA4.5

2HA8

1700

225

60

15 210200 200 200 200 210 225 15

Sections at 1s t and 2 nd floors

Section at 5th floor

Sections at 3rd and 4th floors

2X7HA4.5

4HA8

1700

150

60

75 15 210 200200 200200210 150 15 75

2X5HA4.5 2HA6 2HA8

2HA4.5 2HA8

1700

75 75

60

75 15 210 200200 200 20021075 75 75 15

Fig 2 – Steel reinforcement of CAMUS III specimen


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3. Description of the testing programme

3.1. Loading program

The seismic tests have been performed on the AZALEE shaking table of the CEA at Saclay. This 6 m X 6 m biaxial shaking table has a maximum payload of 100 tons and is the largest in capacity in Europe. Monoaxial time excitations with increasing levels were applied to the specimens. A second series of tests on the first specimen were performed after its retrofitting with fibre carbon material by the TFC© Group. The main parts of the seismic tests – the high levels tests included - have been performed with the 10s long artificial signal Nice whose response spectra fit the French Design Code design spectra. Two recorded signals named San Francisco (Fig 3) and Melendy Ranch (Fig 4) have also been used for intermediate tests on the specimens CAMUS I and III. These signals are characteristics of near-field moderate earthquakes (important acceleration but short duration and different frequency content, [Sollogoub et al, 1998]). The theorical signals and their corresponding response spectra are given Fig 4 and 5. The following tests have been performed:

CAMUS I : Nice 0.24g, San Francisco 1.11g, Nice 0.24g, Nice 0.40g, Nice 0.71g

CAMUS II : Nice 0.10g, Nice 0.23g, Nice 0.52g, Nice 0.51g

CAMUS III : Nice 0.22g, Melendy Ranch 1.35g, Nice 0.64g, Nice 1.0g

San Francisco signal (amax=1.5*0.25g)

Response spectra (5% damping)

Nice signal (amax=0.25g)

Acceleration (g)

0 2 4 6 8 10 -0,3

-0,2

-0,1

0,0

0,1

0,2

0,3

Time (s) Time (s) -0,4

-0,3

-0,2

-0,1

Acceleration (g)

0 5 10 15

0,0

0,1 0,2

0,3

0,4

10 20 30 40 50 0,00

0,25

0,50

0,75

1,00

1,25

1,50 Pseudo acceleration (g)

Frequency (Hz)

San Francisco (1.5*0.25g)

Nice (0.25g)

Fig 3 – Artificial Nice signal and San Francisco record


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2,0 0,0 0,5 1,0 1,5 0,0

2,0

4,0

6,0

8,0

10,0 Displacement (cm)

Period (s)

Melendy Ranch 1.5*0.25g

Taft 0.25g

Displacement response spectra Acceleration response spectra

0 10 20 30 40 50 -0,3

-0,2

-0,1

0,0

0,1

0,2

0,3 Acceleration (g)

Time (s)

Signal Taft (0.25g) 0 2 4 6 8 10

-0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4

Acceleration (g)

Time (s)

Signal Melendy Ranch (1.5*0.25g)

0 5 10 15 20 25 0,0

0,2

0,4

0,6

0,8

1,0

1,2

Pseudo acceleration (g)

Frequency (Hz)

Melendy Ranch 1.5*0.25g

Taft 0.25g

Fig 4 –Melendy Ranch record compared to Taft record

3.2. Instrumentation

Up to 64 measurement channels were recorded during each test. The instrumental set-up was designed in order to give information on the motion of the shaking table, the global and the local behaviour of the specimen. Horizontal displacement, horizontal and vertical accelerations were measured at each floor (Fig 5). The internal forces have been deduced directly from the accelerations (Fig 6). Strain gages were fixed on the steel bars and external transducers measuring the crack openings have been placed where damage were expected: at the construction joints of the 4 lower storeys for CAMUS I and II and at plastic hinges for CAMUS III.

AX2G

AX3G

AX4G

AX5G

AX6G

DX1

DX2

DX3

DX4

DX5

DX6AY6G

Référencebeam

AZ5G

AZ4G

AZ2G

AZ3G

AZ2TABAZ1TAB AXTAB

Displacement (horizontal)

Accelerometer (horizontal)

Accelerometer (out of plane)

Accelerometer (vertical)

AZ6G

Ox

Oz

Strain gages

Transducers

DZ3G2

DZ2G2

DZ1G2

JF2A** JF2A**

DZ3G1

DZ2G1 DT1G2 DT1G1

DZ1G3

DZ0G1

DZ1G1

DT2G2 DT2G1

DT3G2 DT3G1

JF1A** JF1A**

JF3A** JF3A**

DZ0G2

Ox

Oz

Fig 5 –Global and local instrumentations for CAMUS III (left wall)


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DX1

DX2

DX3

DX4

DX5

DX6

Storey 1

Storey 2

Storey 3

Storey 4

Storey 5

Level 5

Level 2

Level 1

Level 3

Level 4

Level 6

Nz1

My1 Tx1

Nz2

My2 Tx2

Nz3

My3 Tx3

Nz4

My4 Tx4

Nz5

My5 Tx5

Nz6

My6 Tx6

Fig 6 –Definition of the internal forces


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4. Main experimental results

The experimental results are divided in global results (motion of the shaking table, global displacements and internal forces) and local results (crack opening, strains in the steel bars).

4.1. Motion of the shaking table

The horizontal accelerometer fixed in the centre of the table has been used for the control of the experiment. During the first tests, the imposed signal was not exactly the reference signal since the specimen behavior was strongly non-linear. But for the high intensity tests, the difference between the reference and the obtained signals remained small. Two vertical accelerometers were fixed at the two extremities in order to check if rocking or vertical motion occurred during the tests. The analysis of the signals in the frequency domain has been performed computing their response spectrum (with 2% damping). Rocking seems to be neglectable since the difference of the signal given by the two accelerometers has a high frequency content which does not correspond to any bending mode of the specimens. For CAMUS I, the shaking table had a vertical motion which has reached a 0.43g amplitude with a frequency of about 20Hz. This value corresponds to the frequency of the 1st vertical eigenmode of the system table+specimen. A model of shaking table (mass and stiffness) has been given to the participants of both the CAMUS I and CAMUS III Numerical Benchmarks.

4.2. Global behaviour of the specimens

Motion of the specimens

The horizontal top displacement is computed relatively to the base of the first storey. The maximum values are given table 2. One may remark the maximum values of top displacement correspond to 1% drift for the 2 specimens. For such drift, extensive damage was obtained without loss of stability of the structural system. The analysis of the top displacement time history shows the specimens responded mainly on its first natural frequency (Fig 7 and 8). The decrease of natural frequency due to specimen damage can be estimated using :

- the transfert function computed by applying random excitations to the specimens between each test

- the response spectra with 2% damping of the top displacement time-histories which gives an apparent natural frequency

With the first method – it means at low level of excitation -, the fundamental frequency varies from 7.24 Hz to 6.60 Hz for CAMUS I, from 6.4 Hz to 6.05 Hz for CAMUS II and from 6.88 Hz to 4.30 Hz for CAMUS III: this decrease of frequency remains limited – except for CAMUS III specimen- due to the importance, for such type of structure, of the vertical load which closes the cracks. At the opposite, with the second method – it means when the cracks are opened -, the frequency of the motion decreases down to 2 Hz for CAMUS II and 2.3 HZ for CAMUS III. This great difference shows the difficulty to know the state of the structure (cracked, failure of steel bars …) with only the knowledge of the dynamic characteristics at low level of excitation.


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Relative displacement (mm)

6 8 10 12 14 16

-40

-20

0

20

40

Time (s)

Fig 7- Evolution of top displacement for the last test of CAMUS II (Nice 0.51g)

3 4 5 6 7 8 9 10

-30

-20

-10

0

10

20

30

5th Storey –Melendy Ranch 1,35 g

Relative displacement (mm)

Time (s)

Fig 8- Evolution of displacement at 5th storey for CAMUS III (Melendy Ranch 1.35g)

Analysis of the internal forces

The inertial forces and so the bending moments, the shear forces and the axial forces can be computed with the horizontal absolute acceleration given by the accelerometers and the estimation of the masses of each floor. The maximal values at the base of the first storey are given in the table 2. The difference of reinforcement ratio explains the large difference of the measured bending moment between the 2 specimens. The importance of the variations of axial forces has to be highlighted. For CAMUS I Nice 0.51g test, the amplitude of the variation of dynamic axial force is similar to the vertical static loading. This phenomenon can be explained by the mechanism of reinforced concrete. The variation of neutral axis due to concrete cracking induces a vertical motion of the floors. Compression force increases strongly when concrete recovers its stiffness at the crack closure, it means when the curvature and displacement are about zero. These shocks excite the first vertical mode of the system shaking table+specimen whose frequency is about 20Hz. Fig 10 and 11 show the interaction between bending moment and axial force for the last test on CAMUS II: the variation of axial force may induce important variation of bending moment when the plateau corresponding to steel yielding is reached. Similar phenomena has been observed during the CAMUS III-Melendy Ranch 1.35g test (Fig 9, 10 and 11). For CAMUS III, two different values are given for the dynamic variation of axial force (Table 2). The first


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value has been computed with the 5 vertical accelerometers of the left wall while the second value has taken into account the 2 accelerometers fixed on the right wall.

Bending moment (kN.m) Displacement (mm) Axial force (kN)

13,0 13,2 13,4 13,6 13,8 14,0 14,2 14,4 14,6 14,8 15,0

-200

-150

-100

-50

0

50

100

150

200

Time (s)

Fig 9 – Evolution of axial force and bending moment for CAMUS II Nice0.51g test

-25 -20 -15 -10 -5 0 5 10 15 20 25

-200

-150

-100

-50

0

50

100

150

200 Moment (kN.m)

Curvature (mrad/m)

Fig 10-Moment-curvature relationship for CAMUS II Nice 0.51g test

-30 -20 -10 0 10 20 30 -600

-400

-200

0

200

400

600 Bending Moment (kN.m)

Relative Displacement (mm)

5th

Storey – Melendy Ranch 1,35 g

Fig 11- Bending moment versus displacement at 5th storey for CAMUS III Melendy Ranch 1.35g test


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-10,0 -8,0 -6,0 -4,0 -2,0 0,0 2,0 4,0 -600

-400

-200

0

200

400

600

Base of the specimen–Melendy Ranch 1,35 g

Bending Moment (kN.m)

Rotation (mrad)

Fig 12- Bending moment versus rotation at the base for CAMUS III (Melendy Ranch 1.35g)

3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4-600

-400

-200

0

200

400

600M (kN.m) ou N (kN)

Time (s)

Bending Moment (M) Axial Force (N)

Test « MR r2 » - 1,35 g

Fig 13- Interaction between the evolution of bending moment and the variation of axial forces for CAMUS III (Melendy Ranch 1.35g)

4.3. Local behaviour

Damage pattern

During the first tests on CAMUS I, cracking occurred mainly at the construction joints. But large cracks appeared during the last test at the interruption of the steel bars of the second storey and developed in a diagonal direction (Fig 14). Visual inspection showed the steel bars were broken at this storey after the last test.

For CAMUS II, cracking remained concentrated at the construction joint, mainly at the base of the 2 first storeys (Fig 15). Wide crack opening were observed during the test.

For CAMUS III, cracking concentrated mainly at the construction joints at the base of the 1st storey (Fig 16). Residual crack opening could be observed after the Melendy Ranch 1.35g test. Failure occured during the Nice 1.0g test characterized by large crack opening, steel bar failure (both tension failure and buclking) and concrete crushing at the wall extremities (Fig 17 to 21).


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Fig 14- Cracking at the end of CAMUS I tests

Fig 15- Cracking at the end of CAMUS II tests


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Fig 16- Damage at the end of CAMUS III tests

Fig 17- Cracking and crushing of concrete in the right wall at the end of CAMUS III tests


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Fig 18- Details of the damages in the right wall at the end of CAMUS III tests

Fig 19- Damages in the left wall at the end of CAMUS III tests (south extremity)


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Fig 20- Damages in the left wall at the end of CAMUS III tests (north extremity)

Strain and cracks openings

The strain gages gave high values of strain at the level of the construction joints (more than 2%). For CAMUS I, the maximal strain values were measured at the 3rd and 4th floors and not at the 1st floor (Table 3). This is due to the design used for this specimen which allows yielding at several floors and does not concentrate the damage at the lower storeys at the opposite of Eurocode 8.

For CAMUS II, large crack opening was observed at the 1st and 2nd storeys. In order to compare the values given by the strain gages and the transducers, the crack openings have been converted to equivalent strain by dividing the values given by the transducers by their lengths (250mm). For CAMUS I, the values given by the strain gages are higher than those deduced from the transducers: the steel bars yielded on a concentrated area. The transducers gives a mean value of vertical strain on their length. At the opposite, for CAMUS II, the values given by the strain gages are lower than the strain deduced from the crack opening (Table 3). Furthermore, except for one gage, the strain values remained lower than the yielding strain. This may be explained by the degradation of the bond interface between steel and concrete. For the second specimen, the diameter of the steel reinforcement bars does not exceed 5mm and for such diameter, adherence between steel and concrete was provided only by diameter variation.

For CAMUS III, the strain gages gave few reliable results after Melendy 1.35g test due to important damage at the base of the specimen. Tables 3-c and 3-d show that cracking is concentrated at the base of the walls (250 mm long DZ1G and 900 mm long DZ2G transducers). The transducers DZ1G and DZ2G give coherent results : the DZ2G* elongation is always higher than the DZ1G* one. Important cracking (>10 mm for the transducers DZ2G*) and yielding of the steel bars were measured for the 3 tests Melendy Ranch 1.35g, Nice 0.64g and Nice 1.00 g. Comparisons between average strains deduced from the crack opening and the values directly measured by the strain gages are given on Fig 23 and 24. For the high level tests (Melendy Ranch 1.35g and Nice 0.64g and 1.0g), measured strains reach yielding value at the second construction joint.


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3 4 5 6 7

0,0

5,0

10,0

15,0

20,0

25,0 Crack opening DZ1G1/250 mm Crack opening DZ2G1/900 mm Strain gage

Strain (md)

Time (s)

3 4 5 6 7

0

5

10

15

20

25

30

35

40

Time (s)

Crack opening DZ1G2/250 mm Crack opening DZ2G2/900 mm Strain gage

Strain (md)

Fig 23- Comparison of strain measured by the strain gages on the steel bars and the values deduced from crack openings for CAMUS III Melendy Ranch 1.35g test

2,5 5,0 7,5 10,0 12,5 15,0

0

10

20

30

40

50

2,5 5,0 7,5 10,0 12,5 15,0

0

20

40

60

80

Crack opening DZ1G1/250 mm Crack opening DZ2G1/900 mm

Strain (md)

Time (s)

Crack opening DZ1G2/250 mm Crack opening DZ2G2/900 mm

Time (s)

Strain (md)

Fig 24- Comparison of strain measured by the strain gages on the steel bars and the values deduced from crack openings for CAMUS III Nice 1.0g test


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Moment-curvature relationship

The moment-curvature relationships give information on the behaviour of the R/C section useful for the validation of the numerical models. The curvature is deduced from the steel strains or the crack openings. The moment-curvature relationships present a much more pinched aspect which increased for the lightly reinforced section (Fig 10 and 12). For lightly reinforced bearing walls, the static axial force can not be neglected to estimate the bending strength. Although the moment-curvature relationships do not exhibit large dissipative plastic cycles, it seems such a behaviour can provide good seismic performance without having large bending strength.


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Table 2 – Maximum values of top displacement, bending moment, shear and axial forces at the 1st storey (for one wall)

a/ Camus I tests

Nice 0.24g SF 1.11g Nice 0.24g Nice 0.40g Nice 0.71g

Top displacement 7.0mm 13.2mm 6.3mm 13.4mm 43.3mm

Bending moment 211kN.m 280kN.m 164kN.m 279kN.m 345kN.m

Shear force 65.9kN 106kN 52.2kN 86.6kN 111kN

Axial force* – Traction

Axial force *– Compression

44.3kN

-36.5kN

102kN

-105kN

24.4kN

-30.4kN

50.0kN

-51.9kN

137kN

-146kN

b/ Camus II tests

Nice 0.10g Nice 0.23g Nice 0.52g Nice 0.51g

Top displacement 4.4mm 12.8mm 34.9mm 42.7mm

Bending moment 110kN.m 149kN.m 178kN.m 186kN.m

Shear force 34.1kN 51.9kN 73.8kN 70.7kN



16.3kN

-16.9kN

30.3kN

-43.3kN

86.4kN

-104kN

100kN

-125kN

c/ Camus III tests

Nice 0.42g Nice 0.22g Melendy 1.35g

Nice 0.64g Nice 1.0g

Top displacement 34.9 mm 58.8 mm

Displ. at 5th storey 7.0 mm 4.34 mm 29.2 mm 27.5 mm 47.1 mm

Bending moment 263 kN.m 147 kN.m 510 kN.m 401 kN.m 410 kN.m

Shear force 79.6 kN 48.2 kN 151 kN 124 kN 140 kN



41.4 kN(1)

56.6 kN(2)

-39.5 kN(1)

-59.3 kN(2)

17.8 kN(1)

23.6 kN(2)

-16.4 kN(1)

-24.9 kN(2)

194 kN(1)

276 kN(2)

-212 kN(1)

-304 kN(2)

124 kN(1)

193 kN(2)

-137 kN(1)

-180 kN(2)

134 kN(1)

184 kN(2)

-170 kN(1)

-260 kN(2)

*The values of axial force must be added or substracted to the static vertical load (166kN) (1)The first value of axial force is computed considering only the accelerometers on the left wall (2)The second value of axial force is computed considering the accelerometers on the left wall and the 2 accelerometers on the right wall


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Table 3: Maximal values of strain and crack opening during the high level tests a/ Camus I for Nice 0.71g

Storey Left transducer (average strain)

Left strain gage Right strain gage Right transducer (average strain)

4th floor 2.6mm 10.4/1000

1.43mm 5.71/1000

3rd floor 5.1mm 20.2/1000

25.3/1000* 25.3/1000* 1.83mm 7.34/1000

2nd floor 0.59mm 2.38/1000

2.64/1000 2.58/1000 0.42mm

1.69/1000

1st floor 0.29mm

1.16/1000 2.85/1000 2.66/1000 0.38mm

1.52/1000 b/ Camus II for Nice 0.51g

Storey Left transducer (average strain)

Left strain gage Right strain gage

Right transducer (average strain)

4th floor 0.61mm 2.46/1000

0.34mm 1.35/1000

3rd floor 1.8mm 7.26/1000

1.85/1000 2.85/1000 Out of service

2nd floor 6.5mm 26.1/1000

4.42/1000 Out of service 9.8mm 39.2/1000

1st floor 9.11mm 36.2/1000

2.15/1000 0.67/1000 4.1mm 16.6/1000

c/ Camus III for Melendy Ranch 1.35g Storey Left transducer

(average strain) Left strain gage Right strain gage Right transducer

(average strain)

3rd floor 2.75/1000 3.84/1000

2nd floor 900mm long transducers

3.13 mm 3.5/1000

3.41/1000 3.60/1000 3.26 mm 3.62/1000

1st floor 900mm long transducers

250mm long transducers

4.70 mm 5.22/1000 1.84 mm 7.4/1000

>25/1000 >25/1000 11.6 mm 12.9/1000 8.94 mm 35.8/1000

d/ Camus III for Nice 1.0g Storey Left transducer

(average strain) Left strain gage Right strain gage Right transducer

(average strain)

3rd floor 2.51/1000 1.81/1000

2nd floor 900mm long transducers

2.91 mm 3.23/1000

2.96/1000

1.23/1000

0.97 mm 1.1/1000


23

1st floor 900mm long transducers

250mm long transducers

14.7 mm 16.3/1000 8.61 mm* 34.4/1000*

OoO OoO 21.9 mm 24.3/1000 20.5 mm 82/1000

* Saturation of the strain gage or few reliable results OoO : Strain gage or transducer Out of Order


24

References about the CAMUS experiments

A. Aouamer, J.F. Semblat, F.J. Ulm, Analyse dynamique non linéaire de la réponse sismique d’un bâtiment (projet Camus), 5th French Earthquake Engineering Conference, Cachan, France, 1999.

A. Aouamer, J.F. Semblat, F.J. Ulm, Non linear seismic response of RC building mock-up: Numerical modelling by multilayered shell elements, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

P. Bisch and A. Coin. The CAMUS Research, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

C. Cremer, Modélisation du comportement non linéaire des foundations superficielles sous séisme. Macro element d’interaction sol-structure, ENS Cachan PhD, 24th January 2001

M. Fischinger, T. Isakovic, Benchmark analysis of a structural wall, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

N. Ile. J.M. Reynouard and O. Merabet. Seismic behaviour of sligthly reinforced shear walls structures, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

N. Ile,. J.M. Reynouard and O. Merabet. Dynamic non-linear 2-D and 3-D analyses of RC shear wall under seismic loading, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

N. Ile, JM Reynouard, Analyse non linéaire 2D du comportement sur table sismique de la première maquette du projet Camus, 5th French Earthquake Engineering Conference, Cachan, France, 1999.

N. Ile , JM Reynouard, Seismic behaviour of RC shear wall structures designed according to the French PS92 and EC8 codes. A comparison between shaking table response data and 2D modelling, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

N. Ile, Contribution à la comprehension du fonctionnement des voiles en béton armé sous sollicitation sismique: apport de l’expérimentation et de la modélisation à la conception , INSA Lyon PhD Thesi, 18th December 2000.

P. Kotronis: Cisaillement dynamique des murs en béton armé. Modèles simplifies 2D et 3D, ENS Cachan PhD, 12th December 2000.

G. Li Destri, D. Combescure, I. Politopoulos, P. Sollogoub, Etudes numériques sur la structure Camus 4 avec soulèvement partiel à la base, 5th French Earthquake Engineering Conference, Cachan, France, 1999.

G. Li Destri, Numerical and experimental studies of the Camus structural wall structure resting on sand soil, Tesi di Laurea of Catania University, October 1999.

J. Mazars. French advanced research on structural walls - An overview on recent seismic programs, Opening conference, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

J. Mazars, C. Cremer, P. Kotronis, Analyse du comportement sismique des voiles porteurs avec différents pourcentages de ferraillage et conditions aux limites, 5th French Earthquake Engineering Conference, Cachan, France, 1999.


25

J. Mazars, P. Kotronis, C. Cremer, Analyses of seismic behaviour of structural walls with various reinforcements and boundary conditions, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

J.C. Queval, D.Combescure, P.Sollogoub, A. Coin and J.Mazars. CAMUS experimental program. In-plane seismic test on 1/3rd scaled R/C bearing walls, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

J.C. Queval, D. Combescure, T. Chaudat, P. Sollogoub, Comportement des structures à murs porteurs sous chargement sismique, 5th French Earthquake Engineering Conference, Cachan, France, 1999.

F. Ragueneau, J.Mazars. Damping and boundary conditions, two points for the description of the seismic behaviour of R/C structures. Paper N°473. T2 Session 6, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

J. Rashid, R. Dameron, R. Dowell, Recent advances on concrete material modelling and application to the seismic evaluation and retrofit of California bridges, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

P. Sollogoub, D.Combescure, J.C. Queval, D.Bonnici and P.Labbé. Effect of near-field earthquake on a R/C bearing wall structures. Experimental and numerical studies, 11th European Conference on Earthquake Engineering, Paris, France, 1998.

P. Sollogoub, D. Combescure, JC Queval, Th. Chaudat, In plane behaviour of several 1/3rd scaled RC bearing walls. Testing and interpretation using non linear modelling, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.


26

Synthesis of the participant reports


27

The synthesis of the participant reports is organized in the following steps ;

1- Results from the Push-Over analysis

2- Synthetic tables showing the main assumptions of the participants models (type of modelling and constitutive laws, damping, natural frequency of the model…)

3- Synthetic table of the dynamic analysis for the high level tests (Melendy Ranch 1.35g, Nice 0.64g and Nice 1.00g). These tables contains the extreme values of displacement, internal forces and strains for each particpant

4- The report and the results of each team are resumed on 6 pages containing :

n A table resumes the specificities of the modelling considered for the static and/or the dynamic analysis (constitutive law, damping, assumption made, etc ...) and the main results provided

n Some figures extracted from each report illustrate the previous description. When possible, the drawings giving the predicted damage state are given.

n A series of curves relative to the global results corresponding to 2 high level seismic tests (displacement, axial and shear forces, bending moment) for both computation and experiment (Melendy Ranch 1.35g and Nice 1.00g)

n A series of curves relative to the local results: the computed strains in the extreme steel bars are compared directly to the values given by the strain gages or to a strain deduced from the crack opening at the base of the first storey.

DX5

DX6

Storey 1

Storey 2

Storey 3

Storey 4

Storey 5

Level 5

Level 2

Level 1

Level 3

Level 4

Level 6

Nz1

My1 Tx1

Position of the strain gages and the 250mm and 900mm long transducers

Figure - Positions where are given the values of internal forces, crack opening and equivalent strain


28

List of the participants to the CAMUS III Benchmark

Participant 1 : M.Fischinger, P. Fajfar, T.Isakovic, S.Krizaj, Y.Vidic

University of Ljubljana,Faculty of Civil and Geodetic Engineering

Institute of Structural Engineering, Earthquake and Construction IT

Jamova 2, P.O. Box 3422

1001 Ljubjana, Slovenia

Fax : 386 61 1250693

Mail :[email protected]_lj.si

Web : http ://www.ikpir.fgg.uni_lj.si/

Participant 2 : K.Maekawa, N.Fukuura, X. Briquet

University of Tokyo, Department of Civil Engineering

Hongo 7-3-1, Bunkyo-Ku

Tokyo 113, Japan

Fax : 81 3 5802 2904

Mail : [email protected]

: [email protected]

Participant 3 : R Faria, N.Vila Pouca , R.Delgado,

Faculdade de Engenharia da Universidade do Porto

R Dos Bragas

4099 Porto Codex

Fax : 351 2 200 36 40

Mail :[email protected], [email protected], [email protected]

Participant 4 : Tong-Seok Han

Graduate Research Assistant

639 Rhodes Hall

Cornell University Ithaca, NY 14853

Ph: (607) 254-8840

Mail: [email protected]


29

Participant 5 : Prof. Dr Ing. Y.LL. Mo

Departement of Civil Engineering

National Cheng Kung University

Taiwan 701, Taiwan

Tel: (06) 275 75 75

Fax: (06) 235 8542


Participant 6 : A. Ito, P. Kongkeo, T. Tanabe

Department of Civil Engineering

Nagoya University

Concrete Structure Laboratory

Furou-cho, Chikusa-ku

Nagoya-shi

Aichi 464-8603, Japan

Tel : 81 52 789 4484

Fax : 81 52 789 3738


Participant 7 : Dr. Eng. Nobuaki Shirai, K. Watanabe, T. Fujita

Structural Mechanics Laboratory

1-8, Kanda, Surugadai, Chiyoda-Ku

Tokyo 101-8308, Japan

Tel: +81 (3) 3259 0708

Fax: +81 (3) 3293 82**


Participant 8: Prof. Vladimir Sigmund, I. Guljas, Dj. Matosevic

University 77 Strossmayer

Faculty of Civil Enginering

Dranska 16A

31000 Osijek, Croatia

Tel/Fax: +385 31 274 444



30

Participant 9: Luca Martinelli, Alberto Gentina, Gianluca Pittelli

Politecnico di Milano

Dept. Structural Engineering

P. Leonardo da Vinci,32

20133 Milano, Italie

Fax : 39- 02 2399 4220


Participant 10: I.Olariu, L. Kovacs, V.Stoain, M. Mosoarca

Technical University of Cluj-Napoca

Str. Daucoviciu, 15

3400 Cluj-Napoca, Romania

Politehnica University of Timisoara

Fax : 40 64 194967


Participant 11 : Dr. Joe Rashid, R.S.Dunham, Y.S.Rashid, A.L. Gilbert

Anatech

5435 Oberlin Drive

San Diego, CA 92121, USA

Fax : 619 455 1094



31

Overview of the finite elements and constitutive laws used by the participants

R I R II R III R IV R V R VI R VII R VIII R IX R X R XI

Global or semi-global models

Bilinear or trilinear global laws

Multilayer or fibre type model

Non linear law possible for shear

/

X

X

/

/

/

/

/

/

/

/

/

X

X

/

/

/

/

/

/

/

X

/

X

/

X

/

X (Dyn)

/

/

/

/

/

Type of beam element

Number of elemnts/wall

Number of nodes/element

Number of Gauss point/element

28

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

7

/

90

5

3

5

/

/

/

/

/

/

Local 2D FEM Model (plane stress)

Number of nodes/element

Number of Gauss point/element

/

/

/

X

8

2x2

X

8

/

X

8

3x3

/

/

/

X

/

/

X

4

2x2

/

/

/

/

/

/

X (Stat)

3

/

/

/

/

Local 3D FEM Model

/ / / / / / / / / / X

Local 2D/3D Constitutive law

Fixed crack model

Rotating crack model

Damage law

Plasticity model for compression

/

/

/

/

X

/

/

/

/

/

X

/

/

X

/

/

/

/

/

/

/

/

/

/

X

/

/

X

/

/

/

/

/

/

/

/

X

/

/

X

/

X

/

X


32

Lattice model / / / / / X / / / / /


33

Push-Over analysis – Loading and main results


Loading

Uniform acceleration

Inverted triangular acceleration

Concentrated load at top

Concentrated load at 2/3 of the height

Cyclic loading

X

X

/

/

/

/

X

X

/

X

/

/

/

X

/

/

/

X

/

/

/

/

/

/

/

/

/

X

/

/

X

/

/

/

/

X

/

/

/

/

/

/

/

/

/

/

X

/

/

/

/

/

/

X

/

Main results

Base shear force versus top displacement

Bending moment versus top displacement

Hor. Acceleration versus top displacement

Cracking pattern

Failure mechanism

Compressive stresses

Strain in the steel bars or vertical strain

Displacement corresponding to failure

X

/

/

/

X

/

/

/

X

/

X

X

X

/

/

/

/

X

/

X

X

X

X

/

X

/

/

/

/

/

/

1% drift

/

/

/

/

/

/

/

/

X

/

/

/

/

/

/

/

X

/

/

/

/

/

/

/

X

X

/

/

/

/

/

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/

/

/

/

/

/

/

X

/

/

X

/

/

/

/

X

/

/

X

X

/

X

2.5cm at 2/3


34

Dynamic analysis – Natural frequencies and tuning

Exp. R I R II R III R IV R V R VI R VII R VIII R IX R X R XI

Natural frequency

1st mode : - Initial

(bending) - Modified

2st mode : - Initial

(vertical) - Modified

6.88 Hz

9.29 Hz

44 Hz

/

/

9.4 Hz

6.91 Hz

45.0 Hz

19.0 Hz

9.60 Hz

6.81 Hz

45.9 Hz

24.2 Hz

/

/

8.40 Hz

42.6 Hz

10.4 Hz

6.77 Hz

20 Hz

19 Hz

8.82 Hz

(6.63 Hz)

/

8.51 Hz

33.1 Hz

/

/

8.66 Hz

Frequency Tuning Method

Modelling of the shaking table

Modification of the table flexibility

Modelling of the footing

Modelling of the anchorages to the table

Modification of the footing modulus

Or the anchorages to the table

/

/

X

/

/

X

X

X

/

/

X

/

X

X

/

X

/

X

X

X

/

/

/

/

/

/

/

X

/

/

X

/

X

/

X

X

/

X

/

/

X

/

X

/

/

/

/

/

/

/

X

/

X

/

/

Value of concrete modulus - Initial

(MPa) - Modified

31140 / 31000

24000

31000

21700

/ / 31100 31139 / / 31100


35

Dynamic analysis – Damping and Failure Criteria


Type of damping

Rayleigh damping

Proportionnal to stiffness matrix

Modification of damping in non linear range

Numerical damping (high frequency)

No damping (included in constitutive laws)

/

/

/

/

/

/

/

/

/

X

/

X

X

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X

/

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X

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X

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X

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/

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/

/

/

X

/

/

/

/

Values of damping

1st mode

2nd mode

2%

/

0%

/

1.9%§

/

2%

5%

/

/

1.94%

/

2%

5%

2%

/

1.94%

/

/

0.6% at 6Hz

Failure Criteria

Strain in the steel bars (tension)

Principal tensile strain or damage index

Total or Plastic Rotation

Total displacement

X

/

/

X

/

X

/

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/

X

/

/

X

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X

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X

/

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X

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X

/

/

/


36

Main results of the dynamic computation for CAMUS III-Melendy Ranch 1.35 g

Test R I R II R III R IV R V R VI R VII R VIII R IX R X R XI

DXR6

(=DX6 - DX1)

/ mm mm mm mm mm mm mm mm mm mm 42 mm

DXR5

(=DX5 - DX1)

29.2 mm mm mm mm mm mm mm mm mm mm mm mm

MY1 510 kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m

TX1 151 kN kN kN kN kN kN kN kN kN kN kN kN

NZ1

(Dynamic)

+194 kN(1)

+276 kN(1)

-212 kN(2)

-304 kN(2)

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

Strain

900 mm transd.

250 mm transd

Strain gages.

12.9/1000

(11.6 mm)

35.8/1000

(8.94 mm)

>25/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000


37

Table: Maximum values of displacement, bending moment, axial (compression only) and shear forces (Level 1) and strain in the steel bars


38

Main results of the dynamic computation for CAMUSIII –Nice 1.00 g

Test R I R II R III R IV R V R VI R VII R VIII R IX R X R XI

DXR6

(=DX6 - DX1)

58.8 mm mm mm mm mm mm mm mm mm mm mm 42 mm

DXR5

(=DX5 - DX1)

47.1 mm mm mm mm mm mm mm mm mm mm mm mm

MY1 410 kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m kN.m

TX1 140 kN kN kN kN kN kN kN kN kN.m kN kN kN

NZ1

(Dynamic)

+134 kN(1)

+193 kN(2)

-170 kN(1)

-180 kN(2)

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

+kN

-kN

Strain

900 mm transd.

250 mm transd

Strain gages.

24.3/1000

(21.9 mm)

82/1000

(20.5 mm)

OoO

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000

/1000


39

Table: Maximum values of displacement, bending moment, axial (compression only) and shear forces (Level 1) and strain in the steel bars


40

Participant n°1

IDENTIFICATION

Organisation, Company, University

University of Ljubljana, Slovenia

Authors Matej Fischinger, Tatjana Isakovic, Peter Kante

Computer Software Drain 2D with a specific multiple-vertical-line element (MVLE)

MODELLING

Geometrical Model Description

Mesh Elements

MVLE (Fig I.1)– 6 vertical springs for each MVLE, modelled as RC truss elements (to represent axial and flexural behaviour). Rigid beams at the top and bottom level connect them. Horizontal springs model the shear behaviour. Elastic shear behaviour is assumed.

Meshing 28 MVL elements in one wall. Wall modelled as simple beam-column cantilever (Fig I.2).

Masses Translational and rotational (Fig I.3).

Boundary Conditions Fixed support at upper level of shaking table (base of model)

Behaviour Description

Constitutive Laws Elastic behaviour of springs. The behaviour of concrete in compression followed the vertical spring hysteretic rule (Fig I.4). Tensile strength neglected in basic analysis.

Damping 2 %, defined for first natural node and used for all analyses.

CALCULATIONS – RESULTS

Calculations Description - Results

Static Loading Pushover with inverse triangular loading and uniform static loading

Static Analysis - Results Base shear vs. top displacement graphs for uniform load and inverse triangular load, for the model footing.

Dynamic Loading Nice 0.22g, Melendy Ranch 1.35g, Nice 0.64g, Nice 1.00g, all in same sequence.

Dynamic Analysis - Results First natural frequency was higher than test frequency. Time history graphs to show horizontal and horizontal top displacements, base shear vs time, base bending moment vs time, axial force vs time, vertical strain, top displacement vs base shear, vertical hysteresis.

Estimation of Collapse EC8 capacity design prevented yielding in upper stories of wall and shear failure. Non- parametric multidimensional regression method (neural network) predicted seismic capacity of wall using a database of laboratory studies – predicted shear capacity of 400 kN and top displacement of 6-10 cm. Numerical model could not confirm prediction. Failure criteria not specified.

OBSERVATIONS


41

Separate studies show that damage from previous tests, had considerable influence on response during subsequent tests, particularly the Nice 0.64g test after considerable damage from Melendy Ranch.

Modal and response spectrum analyses performed to check the design, for dynamic studies. The wall was modelled as a simple beam-cantilever.

Due to unstable response of the chosen model, particularly for short time lapses, the hardening ratio of the vertical springs (6 %) was higher than usual, to stabilise the response.

BIBLIOGRAPHY

Fischinger, M., Vidic, T., Fajfar, P., Non-linear seismic analysis of structural walls using the multiple-vertical-line-element model. Paper presented at the workshop “Non-linear Seismic Analysis and Design of Reinforced Concrete Buildings”, Bled, Slovenia. Proceedings (edited by Peter Fajfar and Helmut Krawinkler), pp.191-202, 1992.

Fischinger, M., Isakoviæ, T., Benchmark analysis of structural wall. Paper presented at the 12th World conference on earthquake engineering, Auckland, New Zealand, 2000.

Peruš, I., Fajfar, P., Grabec, I., Prediction of the seismic capacity of RC structural walls by non-parametric multidimensional regression, Earthquake Engineering and structural dynamics, Vol. 23, pp. 1139-1155, 1994.


42

Figure I.1 : MVLE Model

499.

5

90

499.

5

409.

5

319.

5

LEV

.3

EL

EM

EN

T P

RO

PE

RT

IES

EL

EM

EN

T N

UM

BE

RS

NO

DE

NU

MB

ER

S

LEV

.1F

OO

T.2

LEV

.2

229.

5

139.

5

50

89.5

50

90

LEV

.4

90

90

Figure I.2 : Wall Model Figure I.3 : Mass repartition

γ (umax - uy)

α Fy

Fy

uy

k''

β Fy

k'

umax

k'' = k' (uy / umax)δ

Fy

uy

Figure I.4: Axial and shear spring behaviour


43


44


45


46

Participant n°2

IDENTIFICATION


University of Tokyo, Japan

Authors K. Maekawa, N. Fukuura, X. Briquet

Computer Software WCOMD-SJ version 7.2

MODELLING


Mesh Elements 2D finite element mesh using 8 node isoparametric quadric elements (Fig II.1) Mesh discretization conducted in accordance with the steel arrangement and the location of floors

Masses Mass of steel_concrete blocks & floors as beeing uniformly distributed over the mass block finite elements (considered perfectly elastic) and are connected to the wall along a solid line at each floor location

Boundary Conditions For the push over analysis, the wall is considered fixed on the base For the dynamic analysis, the shaking table is modelled according to instruction given by Benchmark organizers (Fig II.1)


Constitutive Laws Concrete : Elasto-plastic and continuum damage model (Maekawa et al., 1991) The concrete element model account for 4 direction fixed smeared cracking process For cyclic properties unloading stiffness is related to plastic evolution Tension stiffness and softening are dependent on the reinforcement ratio and size/shape of the elements Figure II.1 sumarized the main features of the concrete model For complete information see Okamura & Maekawa "Nonlinear Analysis and Constitutive models of reinforced concrete"

Steel reinforcement : Kato’s model (CEB 1967) & Multi-yield plane model for reinforcement by Maekawa et al. (2000) Localization of yield in steel bars close to cracking is implictly taken into account

Damping No viscous damping. Hysteretic damping through contitutive laws of materials

Specificities Scale effect is accounted through zoning process and shear transfert

CALCULATIONS - RESULTS


Static Loading Horizontal static force is specified proportionnal to the attached mass of each floor and applied to the wall through the attached floors (Fig II.2). Newton method is applied.

Static Analysis - Results Under push over loading a failure at the base of the wall is observed (Fig II.3)

A cyclic response of the structure is also analysed

Dynamic Loading Time history analysis with Newmark β-method (β=0.36 and� γ=0.7)�

Dynamic Analysis - Results Calculation chained with the following signals Nice 0.22g, Melendy Ranch 1.35g, Nice 0.64g and Nice 1.0 g.

Estimation of Collapse Not really predicted, however implicitly given in push-over analysis and time history analysis

OBSERVATIONS


47

Static loading : analysis is performed for only one wall and without modelling of the shaking table, normal and reduced strength in tension is considered (ft & 0.8ft). For dynamic analysis : the entire mock-up and the shaking table (mass and stiffness) are considered, full tensile strength is used and no account of joints is tried.

BIBLIOGRAPHY

Okamura, H. and Maekawa, K., Nonlinear analysis and constitutive models of reinforced concrete, Giho-do Press, Tokyo, 1991

Maekawa, K., An, X., Shear failure and ductility of RC columns after yielding of main reinforcement, Engineering Fracture Mechanics 65 (335-368), 2000

Maekawa, K., Irawan, P. and Okamura, H., Three-dimensionnal path-dependent constitutive laws for reinforced concrete, Int. J., Structural Engineering and Mechanics, November, 1997

Fukuura, N. and Maekawa, K., Muti-directional crack model for in-plane reinforced concrete under reversed cyclic action, Proc. of EURO-C Paris 1998.

8-nodes isoparametric element

Mixed element C=C m h e

Element

=

σ

RC C RC =0.4

PL C=C pl

σ

ε

A PL × (l e -h e ) A m i x × l e

Plain concrete zone

RC zone

σ

ε

A RC × h e l e

ε

Tension stiffening Tension softening

ε

RC and plain concrete zoning

Tension stiffening model for mixed element

Mass Blocks

Footing

Wall

Vertical rods

Shaking table

( rigid body)

170

47 353 353 47

800

90

90

90

90

80

60

10

( unit:

100

no transferred bending actionno transferred bendingaction

Mass block is connected to

the wall on this line

510

Figure II.1 : Particularities of the constitutive model used and finite element modeling of

entire specimen


48

-1.5

-1

-0.5

0

0.5

1

1.5

-5 -4 -3 -2 -1 0 1 2 3 4 5

Horizontal Disp. δ (cm)

Horizontal acceleration (statically applied) n*G

Tension Reduced tensile strength case

n *G

δ

Figure II.2 : Static force versus displacement relations of shear wall – cyclic response

Input Wave: Melendy Ranch 1.35g

Crack pattern (last step)

Strain ranges % (lower limit)

0.080 0.035 0.020 0.010

Maximal Principal strain ( at max. displ.)

Figure II.3 : Dynamic analysis –Melendy Ranch 1.35g- Crack pattern and maximal principal strain


49

Input Wave: Nice 1.0g

Crack pattern (final step) Maximum principal strain (at max. displ.)

Crack Strain % (lower limit)

0.080.030.020.01

Figure II.4 : Dynamic analysis – Nice 1.0g - Crack pattern and maximal principal strain


50


51


52

Participant n°3

IDENTIFICATION


Faculdade de Engenharia, Universidade do Porto

Authors N. Vila Pouca, R. Delgado

Computer Software Not precised

MODELLING


Mesh Elements 2D 8 node plane stress elements and 2 noded truss elements

Meshing Wall (2D plane stress 8 node elements) + reinforcements bars (2 noded trus elements) + footing (2D plane stress 8 node elements) + vertical anchorage bars (2 node beams) + shaking table (7 finite elements with strong stiffness) + 3 elastic rods (see Fig III.1)

Masses Distributed

Boundary Conditions Shaking table + anchorage bars + table supports


Constitutive Laws (see fig 3.2) For concrete: Continuum damage 2D model taking into account the confinement effect

For steel: Giuffré et Pinto model (including cyclic loops effects but no buckling)

No bond slip

Damping Rayleigh-type matrix considered (C=aK0) calibrated with 1,94% of damping on the 1st mode and a decrease is considered when local damage occurs.


Calculations Description - Résults

Static Analysis Loading applied under a displacement control at 2/3 of the height of the specimen

Static Analysis - Results Large tensile damage and large plastic deformation observed at the base of the wall (Fig III.3)

Dynamic Loading Modal analysis is performed with rigidly fixed base & considering shaking table. The 4 signals Nice 0.22g, Melendy Ranch 1.35 g, Nice 0.64g, Nice 1.0g are applied successively once the vertical static loading imposed.

Dynamic Analysis - Results Hilbert-Hugues-Taylor α-method, with a time step = 0.01 sec. Time histories for :

Top horizontal displacement, Axial, shear forces and bending moment at the base of the wall

Bending moment at the base versus displacement at the top. Stress-strain diagram in the steel bars at the base level. Cracking pattern (concrete tensile damage) and compressive stresses with the direction of the principale stresses

Estimation of Collapse

OBSERVATIONS

The natural frequencies computed with 2 different boundary conditions (with and without the shacking table) and Young’s modulus for concrete (31 & 24 Gpa)

BIBLIOGRAPHY


53

Faria, R. and Oliver, J. ,A rate dependent Plastic-Damage constitutive model for large scale computations in concrete structures, CIMNE Monograph n° 17, Barcelona, Spain, 1993.

Faria, R., Oliver, J., Cervera, M., A strain-based Plastic Viscous-Damage model for massive concrete structures, Int. J. Structures, Vol. 35, n° 14, pp. 1533-1558, 1998.

ε

Confined

Unconfined

σ

εcoεcm

fco

fcm

εts

fo+ = fto

Figure III.1 : Materials modelling :

1D behaviour for confined and unconfined concrete (left). Steel cyclic model (right).

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

4.5E+05

5.0E+05

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Top displacement (m)

Moment MY1 (N.m)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

0.00 0.01 0.02 0.03 0.04 0.05

εεmáx

Z (m)

φ 8 bar

Figure III.2 : Push over analysis – distribution of :


54

Tensile damage (left); Plastic deformation on left φ φ 8 bar (center); Compressive stresses (right)

Figure III.3 : Dynamic analysis (Nice 1.0g) Tensile damage (left); Compressive stresses (right).

-4.E+05

-3.E+05

-2.E+05

-1.E+05

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

-0.010 -0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008 0.010


Ben

ding

mom

ent (

N.m

)

signal V2S6

-6.E+05

-5.E+05

-4.E+05

-3.E+05

-2.E+05

-1.E+05

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

-0.050 -0.040 -0.030 -0.020 -0.010 0.000 0.010 0.020 0.030 0.040 0.050


Ben

ding

mom

ent (

N.m

)

s i gna l V3S2

a/ Nice 0.22g b/ Melendy Ranch 1.35g

-6.E+05

-5.E+05

-4.E+05

-3.E+05

-2.E+05

-1.E+05

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

-0.050 -0.040 -0.030 -0.020 -0.010 0.000 0.010 0.020 0.030 0.040 0.050


Ben

ding

mom

ent (

N.m

)

signal V2S8

-6.E+05

-5.E+05

-4.E+05

-3.E+05

-2.E+05

-1.E+05

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

-0.060 -0.050 -0.040 -0.030 -0.020 -0.010 0.000 0.010 0.020 0.030 0.040 0.050 0.060


Be

nd

ing

mo

me

nt (

N.m

)

signal V2S10

c/ Nice 0.64g d/ Nice 1.0 g

Figure III.4 : Bending moment at the base (MX1) of the wall versus top displacement (DX6)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0

t ime (s)

Da

ma

ge

in

de

x D

+

s ignal V2S6 signal V3S2 signal V2S8 signal V2S10


55

Figure III.5 : Evolution of a tensile damage index D+ for all sequence of the analysis.


56


57


58


59

Participant n°4

IDENTIFICATION


Cornell University

Authors Tong-Seok Han, Sarah L. Billington, Anthony R. Ingraffrea

Computer Software Finite Element Code DIANA

MODELLING


Mesh Elements

Concrete : eight-noded plane stress elements – 3x3 Gauss points

Shaking table : three-noded rigid beam (Fig IV.1)

Shaking table supports : one-noded spring element (Fig IV.1)s

Meshing 1 shear wall represented (Fig IV.1)

Masses Translational at mass elements instead of distributed masses. Rotational effects of point masses neglected. Point masses located at the bolted connections.

Boundary Conditions Equivalent boundary model – interface of shear wall and shaking table modelled using elastic beam elements connecting 4 nodes at base of structure to 2 nodes in the table. Table modelled as rigid bar with finite stiffness springs for supports (Fig IV.1).


Constitutive Laws Material properties based on tests from CAMUS (1999), except tensile and compressive fracture energy. Concrete:

Two sets of concrete material properties used – one representing hidden columns at the ends of the wall and the other for the rest of the wall (unconfined concrete). For unconfined concrete: elasticity-based total strain rotating crack model. Tensile strength assumed to be 1/10 the compressive strength. The tensile fracture energy calculated by multiplying tensile strength of the concrete by the steel yield strain divided by two. Linear softening is used for the post -peak tensile behaviour of concrete.

For confined concrete: Fracture-energy based parabolic, total strain model. The concrete peak stress and the failure strains are increased. The concrete compressive strength increased by 20% for the 1st storey hidden columns and by 10% for the 2nd storey. The longitudinal strength reduction due to cracking is considered.

Steel bars : Von Mises criterion used for the non-linear material model. Young’s modulus of 190 Gpa for the steel found from experiments. Only isotropic hardening. No Bauschinger effect.

Damping Rayleigh damping for mass and stiffness damping : 2 % for 1st eigenmode, 5 % for 2nd.


Calculations Description – Results

Static Loading Pushover, to provide overall non-linear static behaviour of the calibrated model and estimate failure load and displacement for the wall. A horizontal point force at the top of the wall.

Static Analysis - Results Base shear vs displacement at the loading point. Incremental displacement plot – each small peak is identified as substantial crack propagation.

Dynamic Loading 4 earthquakes in a continuous sequence to provide a benchmark simulation, then separated as individual load cases to determine the relationship between maximum drift and PGA.


60

Dynamic Analysis - Results Reduction of the displacement response frequency in the shear wall due to consecutive seismic loading is large than the reduction due to individual loadings. Time-histories of displacement, strain, axial force, shear force, bending moment (all for consecutive loading) and a graph of moment vs curvature for consecutive and individual loading cases.

Estimation of Collapse Definition : using maximum roof drift related to PGA, defined from Pushover. Maximum roof drift estimated at 0.05 m or 1.0 %. For the Nice earthquakes, the maximum roof drift vs PGA is obtained from non-linear transient analysis. The shear wall is predicted to fail during Nice 1.0g and Melendy Ranch 1.7g. The PGAs of Nice and Melendy Ranch earthquakes which cause failure are predicted.

OBSERVATIONS

Parametric Studies Eigenvalue analyses on three different models of shear wall and boundary conditions to obtain the natural frequencies and eigenmodes. Fixed boundary model : the natural frequencies and eigenmodes of the fixed boundary model without the shaking table are obtained. Detailed boundary model : shaking table included in the FE model.

Frequency Tuning Method Model calibrated to reproduce the first natural frequency from experiments. Energy norm of 1.0% used for convergence criterion of incremental-iterative non-linear analysis. Spring stiffness recommended by CAMUS (1999) is used for shaking table supports.

Comparison of near/far field earthquakes

Near-field quakes’ peaks and frequency contents (i.e. Melendy Ranch) similar to the natural frequency, leading to large permanent displacement. Far-field (i.e. Nice) – smaller peak but fails due to longer duration.

BIBLIOGRAPHY

Kwan, WP, and Billington, SL, Cyclic FE Analyses of Structural Concrete, ASCE Journal of Structural Engineering, under review, 1999.

Mander, JB, Priestley, JN, and Park, R , Theoretical Stress-Strain Model for Confined Concrete, Journal of Structural Engineering, Vol 114, N° 8, PP 1804-0826, August 1998.

Vecchio, FJ, and Collins, MP, Compression Response of Cracked Reinforced Concrete, Journal of Structural Engineering, Vol 119, N° 12, PP 3590-3610, December 1993.

Figure IV.1 Finite Element Mesh (Detailed Boundary Model)


61

Spring stiffness of rods b- Initial stiffness of concrete

(E/E0 = 1.0) (k/k0=1.0) Figure IV-2 : Sensitivity of Natural Frequency (k0 : Gross spring stiffness, EI0 : Gross

concrete stiffness)

Figure IV-3: Point Load Location of Pushover Simulation

Figure IV-4 : Load versus Roof Displacement (Pushover Simulation)


62


63


64


65

Participant n° 5

IDENTIFICATION


University of Houston, USA and National Cheng Kung University, Taiwan

Authors Y.L. Mo & C.T. Hsu

Computer Software ETABS version 5.30 for modal analysis, self-developed program for push over analysis and nonlinear dynamic analysis.

MODELLING


Mesh Elements 3D finite elements for modal analysis, 1D elements for push over analysis and nonlinear dynamic analysis.

Masses Lumped mass at each floor for modal analysis, lumped mass at the centroid of the structure for nonlinear dynamic analysis.

Boundary Conditions Fixed end at the bottom for modal analysis and push over analysis. The signals given by Benchmark organizers were used for nonlinear dynamic analysis.


Constitutive Laws For concrete: Unconfined Kent & Park model. For steel: Bilinear stress-strain curve. For Hysterisis loops model : Mo’s model.

Damping Obtained from the test report.



Static Analysis Push over analysis

Dynamic Loading Modal analysis, time-history analysis with Wilson-θ method.

Dynamic Analysis - Results Mode 6 governs in the direction of the shear wall plane (Period: 0.046 sec) Response to Nice0.42g, Nice 0.22g, Melendy Ranch 1.35g, Nice 0.64g, and Nice 1.0g.

Estimation of Collapse Failure at the bottom of the first floor. The failure mode is flexural at the bottom of the first floor.

OBSERVATIONS

More pertinent results were obtained in the second stage of the work, the experimental results giving the opportunity to have a better calibration of the modelling. However for this participant, as well as for the others, appear in this synthesis only the “blind” calculations.

BIBLIOGRAPHY

MO, Y.L., Dynamic behavior of concrete structures, Elsevier science B.V., Amsterdam, 1994.


66


67


68


69

Participant n°6

IDENTIFICATION


Nagoya University, Japan

Authors Atsushi Ito, P. Kongkeo, Tada-aki Tanabe

Computer Software Not specified

MODELLING


Mesh Elements Lattice equivalent continuum model: net of inclined members (Fig VI.1)

Meshing Two orthogonal struts and one element for the reinforced laid = the main lattice. One other set which considers the shear transfer between the main lattice.

Masses Not specified

Boundary Conditions Fixed at base. Shaking table and spring not considered. Rotation of shaking table and springs not considered.


Constitutive Laws Material model for main lattice:

Concrete model for tension (Fig VI.2a): fracture energy is assumed to be 0.1N/mm.

Tension stiffening model (Fig VI.2b): strain of crack assumed to be 0.0001. Stress strain behavior due to bond effect.

Concrete model for compression (Fig VI.2c)

Steel reinforcement (Fig VI.2d): bilinear model with a tangential stiffness after yielding assumed to be 1/1000 of initial stiffness.

Material model for shear lattice (Fig VI.3)

Cyclic behavior of main lattice (Fig VI.4)

Damping 1.94 %, using numerical algorithms (Newmark scheme integration with β=0.25 γ=0.5



Static Loading Concentrated load applied at the top of the wall. Boundary and loading conditions given in Fig VI.2.

Static Analysis - Results Load-top displacement curve

Dynamic Loading 4 seismic excitations introduced directly to the numerical model.

Dynamic Analysis – Results Time histories of wave acceleration, top-displacement responses, top acceleration responses, and maximum deformation for each earthquake (individual loading cases).

Estimation of Collapse None

OBSERVATIONS

Modal analysis performed to determine the initial natural frequencies and eigenmodes.


70

BIBLIOGRAPHY

Tanabe Tada-aki, Ishtiag Ahamed Syed, Dvelopment of Lattice Equivalent Continuum Model for Analysis of Cyclic Behaviour of Reinforced Concrete, Seminar on Post -Peak Behaviour of RC Structures to Seismic Loads, Volume 2, pp. 105-123, 1999

Belarbi A., Hsu T.T.C., Constitutive Laws of Concrete in Tension and Reinforcing Bars Stiffened by Concrete, ACI Structural Journal, pp. 465-474, 1994.

Reinforcing in RC element

Cracked concrete

Reinforcement lattice modeling

X

Y

Concrete lattice modelingX

Y

1α1α 1α

2α2α

w

Smeared

Local coordinate

1ξ2ξ3ξ

4ξ

Reinforcement lattice components

X

Y

Concrete main lattice components

X

Y αξ

αη

2α1α

βξβη

Reinforcing in RC elementReinforcing in RC element

Cracked concreteCracked concrete


X

Y


X

Y


Y

1α1α 1α

2α2α


Y

1α1α 1α

2α2α

w

SmearedSmeared

Local coordinate

1ξ2ξ3ξ

4ξ

Local coordinate

Local coordinate

1ξ2ξ3ξ

4ξ


X

Y


X

Y

X

Y


X

Y αξ

αη

2α1α

βξβη


X

Y αξ

αη

2α1α

βξβη

X

Y αξ

αη

2α1α

βξβη

Figure VI.1: Lattice equivalent continuum model – Uniform Strain Field

Figure VI.2 : Material Model


71

Figure VI.3 : Main Lattice Figure VI.4 : Shear Lattice


72


73


74


75

Participant n°7

IDENTIFICATION

Organisation, Company, University Institute of technology, Tokyu Construction Co., Ltd., Japan

Authors Ken WATANABE, Takashi FUJITA, Nobuaki SHIRAI

Computer software 2D- non linear DIANA version 7

MODELLING

Geometrical model Description

Mesh elements Figure 1 Concrete and shaking table: 4 nodes iso-parametric elements 1st storey vertical reinforcing steel: truss elements 2nd to 5 th storey vertical reinforcing steel: smeared embedded elements horizontal reinforcing steel and hoops: smeared embedded elements interface elements between the footing and the wall bottom

Masses The self weight and additional weights are taken into account by the mass density of each elements

Boundary conditions The footing is rigidly connected to the shaking table

Interface elements between the footing and the wall bottom


Constitutive laws Concrete in the footing: elastic law Concrete in the wall: non linear law (Von Mises criterion in compression and cut off in tension) Reinforcing bars: non linear law

Damping Rayleigh damping: h1=2% and h2=5%


Calculation Description - Results

Static Loading Uniform distribution of lateral force

Static Analysis Base shear versus lateral top displacement curves (Fig.VII. 6)

Dynamic loading Nice 0.22g, Melendy 1.35g, Nice 0.64g, Nice 1.00g have been successively applied. The base shear was obtained by multiplying the response acceleration of each floor by the corresponding concentrated masses at each floor.

Dynamic Analysis Base shear, axial force, lateral top displacements, moment at the wall base time histories, moment-curvature and lateral top displacements versus lateral top displ. curves

Estimation of Collapse ----

OBSERVATIONS

Parametric studies : In addition to the base shear obtained with the original response accelerations as described above, the base shear was evaluated by a filtered response acceleration eliminating the higher mode exceeding 45 Hz and also by assuming that the shear stresses in the elements of the wall specimen at the bottom along the footing were the output. The base shear was obtained by summing up the internal shear forces in each element calculated by multiplying the shear stresses by the corresponding cross sectional area of wall element.

Frequency Tuning method : The calculated natural frequency (10.4 Hz) differs from the experimental one (6.88 Hz). Three orthogonal elastic springs are introduced into the interface between the footing and the shaking table top. The natural frequency obtained is closer to the experimental one (6.77 Hz).


76

BIBLIOGRAPHY

Watanabe, K., Shirai, N. Oh-Oka and Moriizumi, K., “Compression Softening Behaviour of Various Type of Concrete”, Proc. of JCI, vol. 22, No.1, (in Japanese), 2000.


77

Fixed Supports for Static Push-Over Analysis

Lateral Load for Static Push-Over Analysis

Input Acceleration for Dynamic Analysis

Vertical Spring

K r =400MN/m

at the end supports

2K r =800MN/m

at the middle support

Figure VII.1: Finite Element Model and Boundary Conditions

f c

1/3 f c

0 ε 1/3

Compressive Stress ( MPa )

Compressive Strain ε (µ)

f c

0 d 1 β d 1

G Fc = 0.5(1+ αβ) f c d 1

Compressive Stress σ c ( MPa )

Plastic Deformation δ c (mm)

G Fc : Compressive Fracture Energy α : Coefficient Representing Stress at Bifurcation d 1 : Plastic Deformation at Bifuration

β : Coefficient Representing Limit Plastic Deformation

G Fc E c

σ c

ε c

ε c = 14.6 f c +1515

α f c

Figure VII.2: Ascending Branch of Figure VII.3: Compressive Softening Model

Stress Strain Curve under Compression


78

f t

0 W 1 W cr

G F = (0.23 f c +136)/1000

Tensile Stress σ t ( MPa )

Crack Opening Displacement W (mm)

G F :Tensile Fracture Energy

α : Coefficient Representing Stress at First Bifurcation W 1 : Crack Opening Displacement at First Bifuration

β : Coefficient Representing Stress at Second Bifurcation W 2 : Crack Opening Displacement at Second Bifuration W cr : Limit Crack Opening Displacement

G F

W 2

α f t β f t

Figure VII.4: Tension Softening Model

(a) Specified Values

Young’s Modulus

Ec (Gpa)

Compressive Strength

fc (MPa)

Poisson’s Ratio

νν

31.1 39.6 0.187

(b) Model Parameters for Compression

Coefficients

Strain at 1/3 of Compressive Strength

εε 1 / 31 / 3 ( µ )( µ )

Strain at Compressive Strength

ε ( µ )ε ( µ )

Compressive Fracture Energy

Gfc(N/mm) d1(mm) αα ββ

424 2093 25.55 0.848 0.218 2.393

(c) Model Parameters for Tension

Coefficients Tensile strength

(MPa)

Fracture Energy

Gf (N/mm) W1(mm) W2(mm) Wcr(mm) αα ββ

3.01 0.145 0.029 0.106 0.279 0.4 0.1

Table VII.1: Material Properties for Concrete

Analysis Natural Frequencies (HZ)1st Mode 2nd M ode 3rd Mode 4th Mode 5th Mode

Case-1 10.39 13.73 20.04 52.25 56.21Case-2 6.77 13.64 19.14 34.15 42.91


79

Table VII.2: Calculated Natural Frequencies for First Five Modes


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82


83

Participant n° 8

IDENTIFICATION

Organisation, Company, University University of J.J. Strossmayer, Faculty of civil engineering, Drinska 16a, Croatia

Authors Vladimir Sigmund, Ivica Guljas, Djurdjica Matosevic

Computer software 2D non-linear numerical model with a structure defined in terms of its geometry and moment-curvature relationship for its individual

elements (Lopez, 1988)

MODELLING

Geometrical model Description

Mesh elements Macro wall element model

Meshing 7 macro elements divided in sub-elements

Masses Mass of the structure is assumed to be lumped at each story level

Boundary conditions The wall is assumed fixed at the base Anchorage to the shaking table is simulated by increase of reinforcement in lower segment (6 and 7)


Constitutive laws Concrete: parabola combined with a straight line (Hognestad) Steel: piece wise linear stress strain relationship Moment-curvature: derived from the section geometry, axial force is assumed to remain constant during excitation and , for each wall, shear deformation is taken into account by separate hysteresis rule for shear.

Damping 2% of viscous damping


Calculation Description - Results

Static Loading Inverted triangular and uniform distribution of horizontal storey forces along the wall were considered.

Static Analysis Base shear, top displacement, base moment and rotation curves (Fig VIII.4)

Dynamic loading Registered accelerations at the table top are used as earthquake loading. Nice 0.22g, Melendy 1.35g, Nice 0.64g, Nice 1.00g have been applied one after another.

Dynamic Analysis Acceleration and displacement response spectra. Good match for far field earthquakes (Nice) but they failed to represent near field earthquake

Estimation of Collapse Ultimate failure depends mainly on the ductility of hinge on element 5 node 6

OBSERVATIONS

Parametric studies : Inverted triangular and uniform distribution of horizontal storey forces along the wall were considered.

Frequency Tuning method : By including the table interaction with the one of a model using 50% of the wall section, the natural frequency of the model is very close to the experimental one (6.63 Hz to 6.88 Hz).

BIBLIOGRAPHY


84

Sigmund, V, Bosnjak-Klecina M., Herman K., Methods of Evaluation of Seismic Drift in R/C Frames, 11th European Conference on Earthquake Engineering, Paris, France, 1998.


85

Figure VIII.1: Wall Elements, Nodes and Places of Calculated Response

Flexural Io N Mc My Mu ϕy ϕuSegment (cm4) (kN) (kNcm) (kNcm) (kNcm) (1/cm) (1/cm)

1 2.46E+06 3.15E+01 7259 13008 14627 1.18E-05 3.15E-052 2.46E+06 6.50E+01 8207 23169 23253 1.98E-05 5.27E-053 2.46E+06 9.84E+01 9155 25877 25886 2.48E-05 6.62E-054 2.46E+06 1.32E+02 10103 33164 33178 3.51E-05 9.37E-055 2.46E+06 1.65E+02 11050 35761 35787 4.39E-05 1.17E-046 5.72E+06 1.68E+02 18561 37887 37958 3.70E-05 9.87E-057 7.72E+06 1.79E+02 22056 86744 86920 4.72E-05 1.26E-04

Shear As N Vc Vy Vu dy du(cm2) (kN) (kN) (kN) (kN) (cm) (cm)

1 1020 3.15E+01 100.7 160.2 161.8 0.434 0.8692 1020 6.50E+01 100.7 160.2 161.8 0.356 0.7123 1020 9.84E+01 100.7 160.2 161.8 0.278 0.5564 1020 1.32E+02 100.7 173.9 175.7 0.200 0.3995 1020 1.65E+02 100.7 173.9 175.7 0.121 0.2436 1900 1.68E+02 187.5 324.0 327.2 0.052 0.1047 2100 1.79E+02 207.2 358.1 361.6 0.043 0.087

Table VIII.1: Initial Moment-Curvature and Force-Displacement Relationship of the Element


86


87


88


89

Participant n° 9

IDENTIFICATION

Organisation, Company, University Politecnico di Milano, Italy

Authors Luca Martinelli, Alberto Gentina, Gianluca Pittelli

Computer Software NONDA

MODELLING


Mesh Elements Timoshenko beam elements with 3 nodes (Fig IX.2). Order 3 shape function for transverse displacements Order 2 shape function for rotations Constant shear and linear curvature (central node not completely free) Numerical integration with 5 Gauss-Lobatto points

Mesh 1 non linear element by storey (Fig IX.1)

Masses Lumped masses at each floor


Constitutive Laws

Steel Uniaxial law with buckling (Monti & Nuti, 1992)

Concrete : Modified Mander, Priestley, Park model for compression Modified Yankelevsky, Reihards model for tension Aggregate Interlock described with an interface behaviour (Contact Density Model) Stevens, Uzumeri, Collins model for non linear shear

Damping Modified viscous damping matrix. 1.94 % on the first mode



Time integration schemes Hilbert, Hughes and Taylor α_method for dynamic integration Modified Newton Raphton iterative cheme for equilibrium

Dyanmic Analysis Modal analysis Time history analysis of 4 seismic tests

Dynamic Analysis - Results Mode 1 to 6 are provided : 1st natural frequency : 8.51 Hz (bending mode)

2nd natural frequency : 33.1 Hz (Vertical mode) Displacements at 6th and 5th storey, bending moment, shear and axial forces have been provided.

Estimation of Collapse Local steel strain remains lower than 2.5% (lower than the collapse strain).

OBSERVATIONS

Bending moment and axial force increase with the shaking table acceleration The model takes into account the interaction between axial force and bending moment The non linear beam element is described in [Martinelli, 2000 and 1998]

BIBLIOGRAPHY

Martinelli L., The Behaviour of Reinforced Concrete Piers undr Strong Seismic Actions, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000. Martinelli L., Modellazione di pile di ponti in C.A. a travata soggetti ad eccitazione sismica, PhD Thesi of Milano University, 1998. Monti G., Nuti C., Nonlinear Cyclic Behaviour of Reinforcing Bars including Buckling, ASCE Journal of Structural Engineering, 118, 12, 1992.


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Linear element corresponding to base of the frame model

Elem. 2

Elem. 1

Elem. 4

Elem. 3

Elem. 5

node 13

node 14

node 15

node 16

node 17

node 18

node 19

node 20

node 21

node 22

node 23

node 24

Figure IX.1: Beam finite element model of the wall

Figure IX.2: 3 nodes Timoshenko Beam finite element


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Participant n° 10

IDENTIFICATION

Organisation, Company, University INCERC, Technical University of Cluj-Napoca, Romania

Technical University of Timisoara, Romania

Authors Ioan Olariu -- Levente Kovacs (Cluj-Napoca Univ. for dynamic analysis)) Valeriu Stoian Marius Mosoarca (Timisoara Univ. for static analysis))

Computer Software Biograf 03 (nonlinear static) and Anelise 03 (nonlinear dynamic)

MODELLING


Mesh Elements Triangular finite elements in plane stress state for static study. Beam elements for dynamic study.

Meshing (fig IX .2) Meshing of one single wall without the table for static study.

Masses Constant gravity loadings are uniformly distributed at each level for static study.


Constitutive Laws

Concrete (static): Definition of a limit loading surface (behaviour under biaxial stresses) - use of a Cervenka type criteria which combines a Navier criteria for tension-tension or tension-compression behaviour with a Von Mises criteria for compression-compression behaviour (Fig X.3). ft=1.0 MPa , fc=39.6 MPa and E=31139 MPa

Steel reinforcement (static): Stress-strain bilinear diagram (Fig X.3). fy=486 MPa

Global law (dynamic): Bilinear M-θ law with hardening lumped at the extremities of beam elements.

Damping Rayleigh viscous damping



Static Loading Horizontal forces applied at each level with a triangular distribution on the vertical direction for static study (Fig X.1)

Static Analysis - Results Nodal forces, horizontal resultant forces,maximum horizontal displacement at each load step Stresses in concrete and reinforcement Strains and physical state of the EF Crack distribution (Fig X.2)

Dynamic Analysis - Results Horizontal acceleration and displacement at each floor for Melendy Ranch 1.35g, Nice 0.22g, 0.64g and 1.0g. M-θ relationships at the base of each level

Estimation of Collapse For the static analysis, the collapse is produced by a pastic hinge which developpes ont he 3 first levels. The tension vertical steel reinforcement yields at step 32 and the concrete crushing occurs at the wall base at the step 100 (top displacement about 18 mm)

OBSERVATIONS

Avram B., Bob C.,, Friedrich R., Stoain V., Numerical Analysis of Reinforced Concrete Structures, Elsevier, Amsterdam, 1993.

Negoita A., Pop I., Olariu I., Computer Program for the Nonlinear Seismic Response of Structures, The First National Symposium on Computer Programs for Constructions, Proceeding, Vol. I, Sibiu, p.180-185, 1979.


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Figure X.1 : Mesh and loading used Figure X.2 : Cracking pattern for a 1.8 mm

for the static analysis top displacement

Figure X.3 : Constitutive laws used for steel and concrete


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Participant n° 11

IDENTIFICATION

Organisation, Company, University Anatech, USA

Authors R.S. Dunham, Y.R. Rashid, A.L. Gilbert

Computer Software Abaqus + Anacap-U

MODELLING


Mesh Elements 3D model with 8 node solid brick elements of one wall (1/2 of the structure) see Fig XI.1. Diagonal steel beams were provided to stabilize the structure in the out of plane direction

Masses Masse of the table is accounted

Boundary Conditions Shaking table is represented by rigid elements Springs between the table and the floor were provided according to benchmark organizers Symetry conditions to account for the second wall


Constitutive laws Concrete :

Fully cyclic model accounting for cracking in tension and strain softening in compression with shear shedding (reduced transmission of shear stress through open crack). Fc=39.6 MPa and E=31100 MPa.

Steel reinforcement : Embedded steel is modelled by adjusting concrete element stiffness Stress-strain curve is adjusted to follow measured response on steel coupons provided by benchmark organizers.

Damping Rayleigh viscous damping with 0.6% on the first mode

Specificities Cracking is directed with reducing the tensile strenght to zero at construction joint location


Calculations Description – Résults

Static Loading Horizontal force applied at 2/3 of the height of the model (displacement control)

Static Analysis - Results Damage is concentrated at the base of the first storey (Fig. XI.2). Failure mechanism is due to excessive strain in longitudinal bars Monotonic displacement-force curve is provided (Fig XI.3)

Dynamic Loading Modal analysis Time history analysis : implicit time integration with time step = 0.02 s

Dynamic Analysis - Results Mode 1 to 5 are provided Response to the 4 specified earthquakes (imposed successively) are provided

Estimation of Collapse Flexural failure mode with shear cracking Possible failure for Melendy Ranch 1.35g after 4.0 s (top displ : 4.2cm and 2% strain in the steel bars). Residual compressive strain in the steel bars for the 3 last signals (0.5, 1% and 4% respectively forMelendy Ranch 1.35g, Nice 0.61g and Nice 1.0g). Failure criteria : Steel strain (see Table XI.1)

OBSERVATIONS

The autors finds the ductility capacity of small diameter bars steel bars are very low. The variations of axial force can be very important : 500 kN in compression for Melendy Ranch 1.35g (value for one wall) No Tuning for the initial Frequency : Use of the stiffness and the model given by benchmarck organizers

BIBLIOGRAPHY


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Dowell R.K., Zhang L., Reinforced Concrete Building Prediction Analysis, ASCE Structures Congess, New Orleans, 1999.

Rashid J., Dameron R., Dowell R., Recent advances on concrete material modelling and application to the seismic evaluation and retrofit of California bridges, 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000.

Figure XI.1: First eigenmode of the 3D model Figure XI.2 : Failure pattern

(for the push over analysis)

Figure XI.3 : Force-displacement curve given by the push over analysis


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Table XI.1 : Characteristics considered for the steel rebars


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camus iii international benchmark

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