Eleventh U.S. National Conference on Earthquake Engineering
Integrating Science, Engineering & Policy June 25-29, 2018 Los Angeles, California
EFFECT OF LATERAL LOADING PROTOCOLS ON SEISMIC PERFORMANCE OF RC COLUMNS A. Nojavan1, A.E. Schultz2, and S-H. Chao3 ABSTRACT Structural elements in buildings and bridges may experience varying levels of damage during seismic events. The extent of damage in RC columns during earthquakes is related to their material and cross sectional properties, as well as to the characteristics of the loading history. Unlike bridge piers, very few research studies have investigated the effect of loading histories on the behavior of RC building columns. Moreover, previous experiments lack sufficient information to understand the softening behavior of RC columns up to collapse level as they were terminated after the columns typically exhibited only a 20% reduction in their lateral load capacity. The effects of several monotonic and cyclic, lateral loading protocols on the behavior of RC columns were investigated during seven full-scale tests at the Multi-Axial Subassemblage Testing (MAST) Laboratory of the University of Minnesota. To study the post-peak behavior of RC columns, the loading protocols included large deformations, similar to those that columns may experience during extreme seismic events, and continued until the specimens lost approximately 80% of their lateral load capacity. The extent and evolution of damage in the column specimens is quantified by several cumulative and noncumulative damage indices. Quantified damage values are compared against visually observed damage in the column specimens to assess the accuracy of the indicators in tracking damage for the various loading protocols. The damage indicators are considered along with force-deformation cyclic envelopes to investigate the effect of the loading protocols on the RC column specimens. 1
Structural Engineer, Dominion Energy, Innsbrook Technical Center, Glen Allen, VA 23060 Formerly Ph.D. Candidate, Dept. of Civil, Environmental and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455 (email:
[email protected]) 2 Professor, Dept. of Civil, Environmental and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455 (email:
[email protected]) 3 Professor, Dept. of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019 Nojavan A, Schultz AE, Chao S-H. Effect of lateral loading protocols on seismic performance of RC columns. Proceedings of the 11th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Los Angeles, CA. 2018.
Eleventh U.S. National Conference on Earthquake Engineering
Integrating Science, Engineering & Policy June 25-29, 2018 Los Angeles, California
Effect of Lateral Loading Protocols on Seismic Performance of RC Columns A. Nojavan1, A.E. Schultz2, and S-H. Chao3
ABSTRACT Structural elements in buildings and bridges may experience varying levels of damage during seismic events. The extent of damage in RC columns during earthquakes is related to their material and cross sectional properties, as well as to the characteristics of the loading history. Unlike bridge piers, very few research studies have investigated the effect of loading histories on the behavior of RC building columns. Moreover, previous experiments lack sufficient information to understand the softening behavior of RC columns up to collapse level as they were terminated after the columns typically exhibited only a 20% reduction in their lateral load capacity. The effects of several monotonic and cyclic, lateral loading protocols on the behavior of RC columns were investigated during seven full-scale tests at the Multi-Axial Subassemblage Testing (MAST) Laboratory of the University of Minnesota. To study the post-peak behavior of RC columns, the loading protocols included large deformations, similar to those that columns may experience during extreme seismic events, and continued until the specimens lost approximately 80% of their lateral load capacity. The extent and evolution of damage in the column specimens is quantified by several cumulative and noncumulative damage indices. Quantified damage values are compared against visually observed damage in the column specimens to assess the accuracy of the indicators in tracking damage for the various loading protocols. The damage indicators are considered along with force-deformation cyclic envelopes to investigate the effect of the loading protocols on the RC column specimens.
Introduction Structural performance of building and bridge elements can deteriorate when they are subjected to seismic events. Large cyclic load reversals during an earthquake can result in a reduction of the load-carrying capacity and stiffness of structural elements and cause varying levels of 1
Structural Engineer, Dominion Energy, Innsbrook Technical Center, Glen Allen, VA 23060 Formerly Ph.D. Candidate, Dept. of Civil, Environmental and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455 (email:
[email protected]) 2 Professor, Dept. of Civil, Environmental and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455 (email:
[email protected]) 3 Professor, Dept. of Civil Engineering, University of Texas at Arlington, Arlington, TX 76019 Nojavan A, Schultz AE, Chao S-H. Effect of lateral loading protocols on seismic performance of RC columns. Proceedings of the 11th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Los Angeles, CA. 2018.
damage. In the case of an RC column, damage can be in the form of minor cracking, cover spalling, yielding of reinforcing bars or transverse hoops, bar buckling and fracturing, and cracking and disintegration of the core concrete. The extent of damage is related to structural properties and to the characteristics of the loading history during an earthquake. Unlike RC bridge columns, there are very limited experimental efforts that have focused primarily on the effects of applied loading protocols on RC building columns and during which identical columns were subjected to monotonic and cyclic loading protocols. Considering the uncertainty in the amplitude and number of cycles that RC columns in a building structure may sustain during an earthquake, their performance under distinct simulated loading protocols will be beneficial in the estimation of their force-deformation backbone capacity curves and characterization of damage during various stages of loading. Almost all of the previous RC column tests lack sufficient information to study their behavior in the post-peak region. This lack of knowledge in the softening regime of response for columns is mainly due to the fact that almost all of the previous tests were terminated once specimens typically lost no more than approximately 20% of their lateral load capacity. However, this arbitrarily defined structural failure point does not provide useful information regarding the behavior of RC columns near collapse, especially the influence of the P-Delta effect. Therefore, a series of tests is needed to enhance knowledge on the softening behavior of RC columns when they lose most of their lateral load capacity. Such an understanding is essential, especially for defining seismic collapse safety limit states of RC columns in performance-based design. The effect of distinct loading protocols on RC columns can be investigated by characterizing damage at various stages of loading. Damage characterization is also an essential part of the recent performance-oriented seismic design philosophy in which structural design objectives are defined based on accepted levels of damage (i.e. limit states) under distinct levels of earthquake loads that are expected during the lifetime of the structure. The state of damage in structures is often quantified by damage indices that are usually scaled to a value of zero in the case of an undamaged structure, and unity in the case of collapse. Several damage indices have been proposed to quantify the extent of physical deterioration in structures and their residual capacity. Most of the existing damage measures are described in terms of lateral deformation (i.e. displacement, rotation, or curvature), stiffness, hysteretic energy, fatigue behavior or a combination of these parameters. However, application of different measures often leads to differing results, for which recognition of the actual state of structural damage is challenging. In this paper, observations from a series of tests on full-scale RC column specimens that were recently conducted at the MAST Lab are employed to study the effect of distinct loading protocols on seismic performance of RC columns. During these tests, the column specimens were loaded beyond the common stopping point in previous tests until they lost most (nominally 80%) of their lateral load capacity and exhibited severe deterioration. The effect of several loading protocols, including monotonic, uniaxial and biaxial symmetric cyclic, and near collapse loading protocols, is investigated by calculating damage indices at various stages of loading.
Previously Proposed Damage Indices Several damage index models have been proposed to quantify the state of physical deterioration and strength loss in structures under various loading conditions. Element-level damage indices are usually described in terms of local member deformation (e.g., lateral displacement, rotation, or curvature), stiffness, hysteretic dissipated energy, fatigue behavior, or a combination of these parameters. Five of the most popular damage indices are considered here. A simple form for damage indices, the noncumulative damage index, depends only on the magnitude of the applied load and ignores the effect of cycling. Lybas and Sozen [1] proposed a damage index based on the ratio of the initial tangent stiffness (Ko) to the reduced (secant) stiffness at maximum displacement of the current cycle (Km):
DR
Ko Km
(1)
Roufaiel and Meyer [2] included the secant stiffness corresponding to failure (Kf) and proposed a modified flexural damage ratio for the positive loading direction as follows: FDR
K m K o K f K o
(2)
where “+” sign refers to the loading direction. A similar calculation is performed for the negative loading direction. Since the state of damage during loading depends on both the amplitude of the applied load and the number of cycles, cumulative damage indices have also been proposed that include the effect of both loading magnitude and cycling. Cumulative damage indices are typically expressed in terms of accumulation of plastic deformation or strain in a formulation based on low-cycle fatigue, reduction of stiffness, normalized dissipated energy, or a combination of these parameters. Stephens and Yao [3] proposed a damage index that accounts for the accumulation of plastic deformations due to cyclic loading on RC structural elements: n
D Di
(3)
i 1
where D is the damage due to n cycles and Di is estimated as follows: pi Di f
1br
(4)
where Di is the damage associated with the ith cycle, Δδpi+ is the incremental positive plastic deformation of the ith cycle, Δδf is the value of Δδpi+ in a single cycle test resulting in the
specimen failure, b is recommended as 0.77, and r is the ratio of the plastic deformation in the positive direction (Δδpi+) to that in the negative direction (Δδpi-) during the ith cycle. A more detailed damage index based on cumulative energy was developed by Kratzig and Meskouris [4]. In their proposed method, dissipated energy terms are calculated separately for each loading direction and are based on dissipated energy during the loading half-cycle with a displacement larger than that in the previous cycles (primary half-cycle) and the follower halfcycles. For the loading in the positive direction, the accumulated damage is defined as: D
E
pi
Ei
(5)
E f Ei
where E+pi, E+i, and E+f represent dissipated energy during the primary half-cycle, the follower half-cycle and a monotonic test to failure, respectively. The accumulated damage during loading in the negative direction is calculated in a similar approach and yields the overall damage as:
D D D D D
(6)
Another damage index, which has been used extensively, was developed by Park and Ang [5] assuming a linear combination of normalized displacement to characterize noncumulative effects and normalized dissipated energy to characterize cyclic loading effects:
D
m dE Fy u u
(7)
where Δm is the maximum displacement, Δu is the ultimate displacement capacity under monotonic loading, Fy is the yield strength, dE is the dissipated energy increment, and β is the strength deterioration factor due to cyclic loading. Experimental Program The damage indices above were evaluated using data from the series of seven full-scale tests of RC columns, representative of members located at the ground floor of a high-rise building. The MAST Lab column specimens were designed according to seismic provisions of ACI 318-11 [6] and featured either a rectangular cross section of 36×28 in. with 16 No. 9 longitudinal bars or a square cross section of 28×28 in. with 12 No. 8 longitudinal bars. Both section types featured No. 5 transverse hoops spaced at 5 in. (Fig. 1). Longitudinal bars and transverse hoops were made of ASTM A706 [7] and ASTM A615 [8] steel, respectively, with a nominal yield strength of 60 ksi. All of the column specimens were constructed using normal weight concrete with a nominal 28-day compressive strength of 5 ksi. Each test started with the application of an axial load. The magnitude of the applied axial loads was 756 and 1176 kips, equivalent to an axial load ratio (P/f′cAg) of 0.15 and 0.3, respectively, for the larger (i.e. 36×28 in.) and smaller (i.e. 28×28 in.) columns. While keeping
Loading Direction
(b) (a) Figure 1. Column specimen assembly and detailing: (a) 3D rendering of specimens (b) crosssectional detailing of rectangular and squared column sections ([9], [10]). the axial load constant and vertical throughout testing, the specimens were subjected to lateral loading protocols in the form of displacement excursions as shown in Fig. 2. Application of the lateral loading on the specimens continued until either the actuators reached their stroke capacity or the specimens lost approximately 80% of their peak lateral load capacity in either direction. The cross-sectional size of the specimens and the loading protocols are summarized in Table 1 along with calculated yield, maximum, and ultimate drift capacities and corresponding lateral loads. The first specimen (i.e. SP1) was subjected to a monotonic displacement until the stroke capacity of the actuators was exhausted at 15.61 in. of the crosshead displacement. The loading direction on SP1 was then reversed to estimate the reserve capacity of the specimen following the initial monotonic push (Fig. 2(a)). The loading protocol on specimens SP2 and SP5 included progressively increasing symmetric displacement excursions designed based on procedures in the ACI 374-05 [11]. The magnitudes of displacement cycles were gradually increased with an approximate growth of 25% to 50% in the drift ratio (Fig. 2(b)). The loading at each drift cycle included three main cycles followed by a small cycle at a magnitude equal to one-third of that in the preceding cycle group. The loading protocols on specimens SP3 and SP4 initially sustained the same displacement cycles as of those described for specimens SP2 and SP5. However, these cycles
were followed by a monotonic push in the positive and negative displacement directions after applications of 5.67% and 3.66% drift cycles for specimens SP3 and SP4, respectively (Figs. 2(c) and 2(d)). The final monotonic push was also applied to specimen SP6, but it was preceded by symmetric and asymmetric cycles (Figs. 2(e)). The loading protocol on SP6, the near-collapse loading protocol, was developed from time history analysis on low- and high-rise buildings subjected to far-field earthquake motions.
2
3
Cycle
15
30
30
45
60
12 8 4 0 -4 0 -8 -12
2
4
6
Cycle
Cycle
(d)
(e)
45
60
Cycle
(c)
8
6 4.5 3 1.5 0 -6 -4.5 -3 -1.5 -1.5 0 1.5 3 4.5 6 -3 -4.5 -6
DriftY' (%)
30
15
(b)
Drift (%)
Drift (%)
15
60
Cycle
(a) 12 8 4 0 -4 0 -8 -12
45
12 8 4 0 -4 0 -8 -12
Drift (%)
1
12 8 4 0 -4 0 -8 -12
Drift (%)
Drift (%)
12 8 4 0 -4 0 -8 -12
10
DriftX' (%)
(f)
Figure 2. Loading protocols for specimens: (a) SP1; (b) SP2, and SP5; (c) SP3; (d) SP4; (e) SP6; (f) SP7 [9]. Table 1.
Characteristics of specimen response to the applied loading protocols.
Sp.
Cross Sec. (in.xin.)
Load Protocol
SP1
36x28
Monotonic
SP2 SP3 SP4 SP5 SP6 SP7
36x28 36x28 36x28 28x28 36x28 28x28
Load Dir. Pos
δy (%)
δFmax (%)
δult (%)
Fy (kips)
Fmax (kips)
Fult (kips)
Fult / Fmax
0.80
3.10
12.09
238
290
212
0.73
-4.00
-11.43
-239
-172
0.72
0.65
1.07
6.91
258
314
58
0.19
Neg
Symmetric cyclic (ACI 374)
Pos Neg
-0.70
-1.09
-6.91
-235
-278
-53
0.19
Symmetric cyclic (ACI 374)+monotonic push
Pos
0.76
2.29
11.63
246
297
222
0.75
Neg
-0.74
-3.51
-10.84
-235
-278
-64
0.23
Symmetric cyclic (ACI 374)+monotonic push
Pos
0.75
4.74
11.63
257
310
61
0.20
Neg
-0.76
-1.51
-10.85
-241
-288
-21
0.07
Symmetric cyclic (ACI 374)
Pos
0.52
1.51
5.53
155
192
53
0.27
Near-collapse Biaxial
Neg
-0.60
-1.08
-5.53
-137
-168
1
-0.01
Pos
0.90
3.44
10.43
232
280
52
0.19
Neg
-0.71
-1.09
-11.62
-214
-257
-198
0.77
Pos
0.91
3.52
5.53
227
279
57
0.21
Neg
-0.98
-3.52
-5.53
-218
-268
-33
0.12
The biaxial loading protocol on specimen SP7 was designed based primarily on the same pattern used for SP2, but along both X and Y directions (Figs. 2(f)). The lateral loading on specimen SP7 started with application of a displacement along the positive Y direction similar to that initially applied to specimen SP2. The specimen was then subjected to the target displacement along the X direction while it was unloaded along the Y direction. The resulting displacements along the negative X and Y directions completed a full cycle at a desired drift level. This pattern was continued to create gradually increasing displacements along both directions. Damage Estimation and the Effect of Loading Protocols One of the primary goals of this study was to characterize the lateral loading protocols applied to the specimens in terms of severity of observed damage. The applied loading protocols, resulted in various degrees of damage to the specimens including concrete cracking (due to flexure, shear, and flexural expansion under axial compression), yielding of transverse ties, and buckling and fracture of longitudinal reinforcement. While all of the loading protocols applied to the specimens resulted in significant strength reduction and stiffness deterioration, the column specimens exhibited distinct behavior in terms of ultimate displacement ductility, rate of softening, energy dissipation and damage propagation. To investigate the effect of the loading protocols, the cyclic load-deformation envelope for each column specimen was defined by connecting the peak lateral displacements at the first cycle of each new drift level. The envelope for specimen SP2 is shown in Fig. 3(a). Comparison of the cyclic envelopes indicates that among all seven specimens, specimen SP5, which had a larger axial load ratio (P/f′cAg = 0.3), and specimen SP7, which was subjected to biaxial loading, exhibited the smallest drift capacities (Fig. 3(b)). Specimen SP2 also reached its ultimate strength at a drift level smaller than those for specimens SP3, SP4, and SP6 which lost most of their strength during the final monotonic push at the end of their loading protocols. The displacement during the monotonic push applied to these specimens resulted in rapid strength reduction and stiffness deterioration during the ultimate push cycle.
(a)
(b)
Figure 3. Force-deformation cyclic envelopes for: (a) specimen SP2 (b) all specimens.
The cumulative energy dissipation during loading of the specimens up to a 50% strength loss is shown in Fig. 4. Among all specimens, specimen SP7, which was subjected to biaxial loading, and specimen SP5, which incorporated smaller cross-sectional dimensions, exhibited the largest and the smallest dissipated energy. The calculated dissipated energy for specimens SP1 and SP6 were essentially quite similar, except that specimen SP6 sustained more cycles than specimen SP1, which dissipated energy over one cycle.
Figure 4. Calculated dissipated energy up to 50% strength loss. Damage values based on the models by Lybas and Sozen [1], Stephens and Yao [2], Roufaiel and Meyer [3], Kratzig and Meskouris [4] and Park and Ang [5] are estimated from Eqs. 1-7 and are shown in Fig. 5. The calculated damage values based on all models except Stephens and Yao indicate that applied monotonic displacement resulted in major, rapid strength loss in specimens SP1, SP3, SP4, and SP6 such that the calculated damage values for these specimens at 50% strength loss are generally larger than those for specimens SP2 and SP5 which were subjected to symmetric displacement cycles only (Figs. 5(a), 5(c)-5(e)). When compared to specimen SP2, all models except Park and Ang suggest a higher extent of damage in specimen SP5 that experienced similar displacement excursions as of those for specimen SP2, but under a larger axial load ratio (Figs. 5(a)-5(d)). Calculated damage values by the Stephens and Yao [2], Roufaiel and Meyer [3], and Kratzig and Meskouris [4] models do not capture the extent of damage in specimen SP7 under the biaxial loading protocol. However, the model by Park and Ang [5] can capture the effect of loading in two directions provided that the energy dissipation during loading in both directions is included in the calculation of the damage index (i.e. dE in Eq.7). The calculated damage indices obtained from the Park and Ang model exhibited better correlation with the observed damage trends during the seven test series compared to the other damage indicators. While all the damage models could track specific levels of damage that were observed during the tests, they had a major shortcoming in the estimation of the rates of damage accumulation in the specimens. In this regard, damage values by the Park and Ang model exhibited a wide spread over distinct observed damage and could better estimate the observed extreme damage to the specimens by the end of the tests than the other damage indicators.
(a)
(b)
(c)
(d)
(e) Figure 5. Calculated damage values based on models by (a) Lybas and Sozen (b) Stephens and Yao (c) Roufaiel and Meyer (d) Kratzig and Meskouris and (e) Park and Ang. Conclusions The study shows that column specimen SP5, which had a similar loading protocol as of that for SP2, but under a larger axial load ratio, sustained a more severe extent of damage. In addition, the ultimate monotonic push displacement that was applied following a number of cyclic
displacement reversals resulted in a rapid strength reduction in the specimens and a higher extent of damage as of that in the case of pure cyclic or monotonic displacements. Finally, the results of this study indicate that the column specimen subjected to biaxial loading (i.e. SP7) experienced more damage than specimen SP2 under gradually increasing cyclic displacements. The damage model by Park and Ang exhibited the best correlation with observed damage during each test and it was the only model that could indicate the larger extent of damage in specimen SP7 as it can directly include the effect of biaxial loading provided that the calculated energy dissipation includes both directions. References 1.
Lybas JM, Sozen MA. Effect of Beam Strength and Stiffness on Dynamic Behavior of R/C Coupled Walls. Dep Civ Eng Univ Ill. 1977.
2.
Roufaiel MS, Meyer C. Analytical modeling of hysteretic behavior of R/C frames. J Struct Eng. 1987;113(3):429–44.
3.
Stephens JE, Yao JT. Damage assessment using response measurements. J Struct Eng. 1987;113(4):787–801.
4.
Kratzig WB, Meskouris M. Nonlinear seismic analysis of reinforced concrete frames. Earthq Progn. 1987;453– 62.
5.
Park Y-J, Ang AH-S. Mechanistic seismic damage model for reinforced concrete. J Struct Eng. 1985;111(4):722–39.
6.
ACI Committee 318. Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary. Farmington Hills, MI: American Concrete Institute; 2011. 503 p.
7.
ASTM A706/A706M-03a. Standard Specification for Low-Alloy Steel Deformed and Plain Bars for Concrete Reinforcement. In ASTM International, West Conshohocken, PA; 2003.
8.
ASTM Standard A615/A615M-03a. Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement. In ASTM International, West Conshohocken, PA; 2003.
9.
Nojavan A, Schultz AE, Haselton C, Simathathien S, Liu X, Chao S-H. A New Data Set for Full-Scale Reinforced Concrete Columns under Collapse-Consistent Loading Protocols. Earthq Spectra. 2015;31(2):1211– 31.
10. Nojavan A, Schultz AE, Chao S-H, Haselton CB, Simasathien S, Palacios G, et al. Preliminary Results for NEESR Full-Scale RC Column Tests under Collapse-Consistent Loading Protocols. In Anchorage, AK; 2014. 11. ACI Committee 374. Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary (ACI 374.1–05). American Concrete Institute, Detroit, MI, USA; 2005.
