1 Introduction
Damage level | Description of damage |
---|---|
I (slight) | Visible narrow cracks on concrete surfaces. Crack widths are less than 0.2 mm |
II (light) | Visible cracks on concrete surface. Crack widths in the range 0.2–1 mm |
III (moderate) | Localized crushing of concrete cover. Noticeable wide cracks. Crack widths in the range 1–2 mm |
IV (severe) | Crushing of concrete with exposed reinforcing bars. Spalling off of cover concrete. Crack widths are greater than 2 mm |
V (total damage or collapse) | Buckling of reinforcing bars. Cracks in core concrete. Visible vertical deformation in columns, walls, or both. Visible settlement, tilting of the building, or both |
2 Quantification of Seismic Damage to RC Column Members
2.1 Definition of Reduction Factors of Seismic Capacity
Damage level | RC column | RC wall | RC beam | ||||
---|---|---|---|---|---|---|---|
Shear | Flexural–shear | Flexure | Shear | Flexure | Shear | Flexure | |
I | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 |
II | 0.6 | 0.7 | 0.75 | 0.6 | 0.7 | 0.7 | 0.75 |
III | 0.3 | 0.4 | 0.5 | 0.3 | 0.4 | 0.4 | 0.5 |
IV | 0 | 0.1 | 0.2 | 0 | 0.1 | 0.1 | 0.2 |
V | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
2.2 Reduction Factors of Seismic Capacity of Damaged RC Columns
Damage level | Flexural member | Shear member | ||||
---|---|---|---|---|---|---|
\( \eta_{s} \)
|
\( \eta_{d} \)
|
\( \eta_{h} \)
|
\( \eta_{s} \)
|
\( \eta_{d} \)
|
\( \eta_{h} \)
| |
I | 1 | 1 | 0.95 | 1 | 1 | 0.9 |
II | 1 | 0.95 | 0.8 | 1 | 0.85 | 0.7 |
III | 1 | 0.85 | 0.75 | 1 | 0.75 | 0.6 |
IV | 0.6 | 0.75 | 0.7 | 0.4 | 0.7 | 0.5 |
V | 0 | 0 | 0 | 0 | 0 | 0 |
Damage level | Flexural failure | Flexural–shear failure | Shear failure |
---|---|---|---|
I | 0.9 | 0.9 | 0.9 |
II | 0.7 | 0.6 | 0.6 |
III | 0.5 | 0.3 | 0.3 |
IV | 0.1 | 0.1 | 0 |
V | 0 | 0 | 0 |
2.3 Relationship Between Residual Crack Width and Residual Deformation
3 Experimental Set-Up and Results
3.1 Experimental Set-Up
Specimen | Failure mode | L (mm) | Cross section (mm2) | Concrete cover (mm) | fc’ (MPa) | fy (MPa) | fyt (MPa) | S (mm) | ρsh (%) | Axial force |
---|---|---|---|---|---|---|---|---|---|---|
FF-15S | Flexural failure | 1800 | 400 × 400 | 40 | 21 (37.0a) | 420 | 280 | 150 | 0.61 | 0.1Agfc’ |
Flexural failure | 1800 | 400 × 400 | 40 | 21 (33.1a) | 420 | 280 | 150 | 0.61 | 0.2Agfc’ | |
FSF-15S | Flexural–shear failure | 1800 | 400 × 400 | 40 | 21 (34.6a) | 420 | 280 | 150 | 0.31 | 0.1Agfc’ |
Flexural–shear failure | 1800 | 400 × 400 | 40 | 21 (30.8a) | 420 | 280 | 150 | 0.31 | 0.2Agfc’ | |
SF-30S | Shear failure | 1800 | 400 × 400 | 40 | 21 (34.1a) | 420 | 280 | 300 | 0.15 | 0.1Agfc’ |
Shear failure | 1800 | 400 × 400 | 40 | 21 (33.2a) | 420 | 280 | 300 | 0.15 | 0.2Agfc’ |
3.2 Experimental Results
Specimen | Initial flexural crack | Initial shear crack | Initial yielding of main bars | Initial yielding of stirrup | maximum forward loading | maximum reverse loading | concrete spalls | Final step (strength < 60%) |
---|---|---|---|---|---|---|---|---|
FF-15S-0.1 | ± 0.25% (1st) | 1% (1st) | 1.5% (1st) | 4% (3rd) | 2% (1st) | − 3% (1st) | − 3% (1st) | 8% (1st) |
FF-15S-0.2 | ± 0.25% (1st) | − 1% (1st) | 1.5% (1st) | 3% (1st) | 2% (1st) | − 2% (1st) | 3% (1st) | 6% (2nd) |
FSF-15S-0.1 | ± 0.25% (1st) | 0.75% (1st) | 1.5% (1st) | 2% (3rd) | 3% (1st) | − 2% (1st) | − 2% (1st) | 6% (2nd) |
FSF-15S-0.2 | ± 0.25% (1st) | 0.75% (1st) | 1.5% (1st) | 2% (3rd) | − 2% (1st) | 3% (1st) | 3% (1st) | 4% (3rd) |
SF-30S-0.1 | ± 0.25% (1st) | 0.75% (1st) | 1.5% (1st) | ±2% (1st) | 2% (1st) | − 2% (1st) | 3% (1st) | − 4% (1st) |
SF-30S-0.2 | ± 0.25% (1st) | 0.75% (1st) | 1.5% (1st) | 1.5% (1st) | 2% (1st) | − 2% (1st) | 2% (1st) | 3% (1st) |
3.3 Relationship Between Crack Width and Deformation of an RC Column Member
Crack types | Suggested values | Reference (AIJ 2004) | ||
---|---|---|---|---|
Flexural crack |
n
f
|
n
f,max
|
n
fp
|
n
f
|
2 | 2 | 2.5 | 2 | |
Shear crack |
n
s
|
n
s,max
|
n
sp
|
n
s
|
2 | 1.5 | 2 | 3–4 |
4 Reduction Factors of Mechanical Properties of Seismic Capacity
4.1 Reduction Factor of Energy Dissipation Capacity
Failure mode | Specimen | Drift ratio (%) |
---|---|---|
Flexural failure | FF-15S-0.1 | 5.99 |
6.03 | ||
FF-15S-0.2 | 5.86 | |
6.00 | ||
Flexural–shear failure | FSF-15S-0.1 | 5.66 |
6.29 | ||
FSF-15S-0.2 | 3.93 | |
3.93 | ||
SF-30S-0.1 | 3.02 | |
2.94 | ||
Shear failure | SF-30S-0.2 | – |
Damage level | Suggested values | Reference (JBDPA 2015) | ||||
---|---|---|---|---|---|---|
Flexural failure | Flexural–shear failure | Shear failure | Flexural failure | Flexural–shear failure | Shear failure | |
I | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 | 0.95 |
II | 0.75 (0.85) | 0.7 (0.8) | 0.6 (0.85) | 0.75 | 0.7 | 0.6 |
III | 0.5 (0.7) | 0.4 (0.6) | 0.3 (0.5) | 0.5 | 0.4 | 0.3 |
IV | 0.1 | 0.1 | 0 | 0.2 | 0.1 | 0 |
V | 0 | 0 | 0 | 0 | 0 | 0 |
4.2 Reduction Factor of Strength
Damage level | Suggested values | Reference (Ito et al. 2015) | |||
---|---|---|---|---|---|
Flexural failure | Flexural–shear failure | Shear failure | Flexural failure | Shear failure | |
I | 1 | 1 | 1 | 1 | 1 |
II | 1 | 1 | 1 | 1 | 1 |
III | 1 | 1 | 1 | 1 | 1 |
IV | 0.6 | 0.6 (0.75) | 0 | 0.6 | 0.4 |
V | 0 | 0 | 0 | 0 | 0 |
4.3 Reduction Factor of Stiffness
Damage level | Suggested factors | ||
---|---|---|---|
Flexural failure | Flexural–shear failure | Shear failure | |
I | 1 | 1 | 1 |
II | 0.8 | 0.8 | 0.8 |
III | 0.7 | 0.7 | 0.7 |
IV | 0.5 | 0.5 | 0 |
V | 0 | 0 | 0 |
5 Seismic Performance Assessment Method for RC Buildings
5.1 Mechanical Behavior of RC Columns
5.1.1 Shear Drift Capacity
5.1.2 Axial Drift Capacity
5.1.3 Shear Strength
5.1.4 Shear Force Related to Flexural Strength
5.2 Assessment of Seismic Performance
5.3 Definition of Nonlinear Plastic Hinges for Damaged RC Column Members
5.4 Case Study
Mechanical properties | Before earthquake | After earthquake | Reduction ratio |
---|---|---|---|
Strength (kgf) | 343,851 | 302,061 | 87.9% |
Stiffness (kgf/cm) | 42,724 | 33,417 | 74.7% |
Performance-based ground acceleration (g), Ap | 0.199 | 0.145a | 72.7% |
Code-required ground acceleration (g) (MOI 2005), AT | 0.308 |
6 Conclusions
Damage level | Flexural failure | Flexural–shear failure | Shear failure | ||||||
---|---|---|---|---|---|---|---|---|---|
η
E
|
η
V
|
η
K
|
η
E
|
η
V
|
η
K
|
η
E
|
η
V
|
η
K
| |
I | 0.95 | 1 | 1 | 0.95 | 1 | 1 | 0.95 | 1 | 1 |
II | 0.75 | 1 | 0.8 | 0.7 | 1 | 0.8 | 0.6 | 1 | 0.8 |
III | 0.5 | 1 | 0.7 | 0.4 | 1 | 0.7 | 0.3 | 1 | 0.7 |
IV | 0.1 | 0.6 | 0.5 | 0.1 | 0.6 | 0.5 | 0 | 0 | 0 |
V | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |