10NCEE

Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska

DUCTILE DESIGN OF SLENDER REINFORCED CONCRETE STRUCTURAL WALLS Sriram Aaleti1, Hongbo Dai2 and Sri Sritharan3 ABSTRACT Slender reinforced concrete structural walls are commonly used in mid- to high-rise buildings as a main lateral load resisting element in earthquake regions. Past research has shown these walls to be efficient and effective in limiting the building lateral drifts due to their large in-plane stiffness. However, the damage sustained by concrete walls in recent earthquakes have demonstrated that current design requirements of these walls may need modifications, which is further supported by a NEES experimental study completed on slender concrete walls. To further understand the behavior of concrete walls and address the shortcomings of the current design requirements, an analytical study was conducted on slender rectangular concrete walls designed according to ACI 318-11. First, a simplified computational method to estimate force-displacement response of a structural wall, utilizing the moment-curvature relationship, was developed and validated using experimental data. Next, the influence of the following six design parameters on the structural behavior of slender rectangular walls was investigated: aspect ratio; longitudinal reinforcement ratio; volume ratio of spiral reinforcement in wall boundary elements; length of confined wall boundary elements; axial loading ratio; and distribution of longitudinal reinforcement. The results of the analytical study found that the current code requirements for boundary element length and amount of the transverse reinforcement are not sufficient and need to be increased for improved performance. More details of the analysis and design recommendations to improve the performance of concrete walls are presented in this paper.

1

Assistant Professor, Dept. of Civil, Construction & Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487; Email: [email protected] 2 Graduate Student Researcher, Dept. of Civil Engineering, University of Delaware 3 Professor, Dept. of Civil, Construction & Environmental Engineering, Iowa State University, Ames, IA, 50011 Aaleti. S, Dai. H., and Sritharan, S. Ductile Design Of Slender Reinforced Concrete Structural Walls. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

DOI: 10.4231/D3B853J5Q

DUCTILE DESIGN OF SLENDER REINFORCED CONCRETE STRUCTURAL WALLS Sriram Aaleti1 , Hongbo Dai2 and Sri Sritharan3

ABSTRACT Slender reinforced concrete structural walls are commonly used in mid- to high-rise buildings as a main lateral load resisting element in earthquake regions. Past research has shown these walls to be efficient and effective in limiting the building lateral drifts due to their large in-plane stiffness. However, the damage sustained by concrete walls in recent earthquakes have demonstrated that current design requirements of these walls may need modifications, which is further supported by a NEES experimental study completed on slender concrete walls. To further understand the behavior of concrete walls and address the shortcomings of the current design requirements, an analytical study was conducted on slender rectangular concrete walls designed according to ACI 318-11. First, a simplified computational method to estimate force-displacement response of a structural wall, utilizing the moment-curvature relationship, was developed and validated using experimental data. Next, the influence of the following six design parameters on the structural behavior of slender rectangular walls was investigated: aspect ratio; longitudinal reinforcement ratio; volume ratio of spiral reinforcement in wall boundary elements; length of confined wall boundary elements; axial loading ratio; and distribution of longitudinal reinforcement. The results of the analytical study found that the current code requirements for boundary element length and amount of the transverse reinforcement are not sufficient and need to be increased for improved performance. More details of the analysis and design recommendations to improve the performance of concrete walls are presented in this paper..

Introduction Reinforced concrete structural walls are one of the most commonly employed lateral-load resisting system for mid- and high-rise buildings. They have relatively high in-plane stiffness, which helps in limiting inter-story drifts leading to reduced structural damage under lateral loads. Additionally, the concrete walls can be easily incorporated into architectural layout of buildings with minimal impact to the functional space. The relatively superior performance of the buildings consisted of structural walls as the primary lateral loading system in previous earthquakes is well documented in the literature [1]. However, the recent 2010 Chilean and the 2011 Christchurch earthquake resulted in severe damage to concrete walls in numerous buildings leading to partial or complete collapse of buildings [2, 3]. This has led to necessity for 1

Assistant Professor, Dept. of Civil, Construction & Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487; Email: [email protected] 2 Graduate Student Researcher, Dept. of Civil Engineering, University of Delaware 3 Professor, Dept. of Civil, Construction & Environmental Engineering, Iowa State University, Ames, IA, 50011 Aaleti. S, Dai. H., and Sritharan, S. Ductile Design Of Slender Reinforced Concrete Structural Walls. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

examination of the expected performance of the concrete walls in the United States designed in compliance with current ACI 318 code. Also, in recent experimental study done by Aaleti et al. [4] and Brueggen [5] on rectangular and T-shaped reinforced concrete walls designed accordance with the ACI 318-08 [6], has exposed some unexpected observations such as fracture of confinement reinforcement and sliding along shear cracks. Similar failure modes were observed in the field in during Christchurch and Chilean earthquakes. In modern seismic design, concrete structures are designed to provide sufficient strength and adequate flexural ductility without experiencing any brittle failures due to insufficient shear capacity or inadequate reinforcement anchorage length, and sliding shear capacity at the wall-tofoundation interface. The structural system ductility under lateral loading is considered as a measure of the structural performance and plays a significant role in the current day design codes. Therefore, to ensure adequate ductility, modern design codes adopt the capacity design philosophy [7] for design and detailing of reinforced concrete structural walls. The specially designed walls undergo inelastic deformations and dissipate seismic energy through flexural yielding of the reinforcement, along with the prevention of aforementioned undesirable failure mechanisms. As per this philosophy, the locations of plastic hinges (i.e., critical regions) in the walls are preselected and detailed carefully by providing adequate transverse confining reinforcement to accommodate significant inelastic deformations and providing the necessary ductility without compromising the structural integrity. Large inelastic deformations in the plastic hinge regions dissipate significant amounts of energy and thus provide a significantly effective damping mechanism for the structural system to reduce the structural force demands. The current ACI 318-11 [8] code, implicitly implements the capacity design philosophy to achieve the ductile performance of concrete walls by requiring a stringent detailing requirements for the special structural walls in Chapter 21. The design and detailing requirements in the current ACI 318-11 also implicitly considers the displacement-based design [9], relating the system level ductility to the local damage (section level response) in the critical regions. Therefore, the expected performance of the structural walls designed and detailed according to the current ACI 318 is dependent on the accuracy of estimating the global force vs. Displacement response using the sectional level response. In keeping with the observed performance and failures of code compliance structural walls in the recent earthquakes and experimental studies, this paper suggests modifications to design requirements based on simplified analytical models developed using moment-curvature analysis for global response prediction and validated using experimental studies. The modifications provide a consistent improved performance of structural walls. Concrete Wall Behavior and Design Requirements Reinforced concrete walls are designed to carry flexural, shear and axial loads under earthquake loads. These design force demands influences the geometry of the wall along with layout of longitudinal reinforcing steel, horizontal reinforcing steel, and confinement steel placed in the boundary regions of the wall. The force-displacement behavior of a structural wall depends on the ratio of wall height to wall length, which defines the wall aspect ratio (AR). When the AR is greater than 2.0, the walls are classified as “slender walls” and the flexural deformation is considered to be the prominent contributor to their lateral displacements. However, it is important to realize that, slender structural walls undergo several other deformation modes when subjected to lateral loads, including shear deformation mode, and deformation due to strain

penetration in the form of rotation at the wall base. The slender structural walls designed in compliance with design code requirements will experience flexural yielding of longitudinal reinforcement with development of horizontal flexural cracks in the boundary regions of the wall and diagonal shear cracks within the web of the wall. These walls typically fail due to fracture of longitudinal steel or due to compressive failure of a boundary region (crushing of core concrete or buckling of longitudinal steel). Force-Displacement Response The force-displacement behavior of slender reinforced concrete structural walls can be accurately predicted by accounting the individual contributions of different deformation modes. Several analytical models using 3D solid (brick) elements [10], 2D shell elements [11, 12], macro model elements [13] and fiber based beam-column elements [14] were used to predict the observed lateral load behavior of concrete walls. All these models captured the overall behavior of the walls with reasonable accuracy as long as shear and strain penetration deformations were taken into consideration. However, the above analytical models require significant computational time and can’t be easily used for design purposes. A simplified analytical method based on the plastic hinge length and moment-curvature analysis is proposed to estimate the lateral-load response of concrete walls. The curvature distribution along the height of the wall can be idealized as shown in Fig.1. The flexural deformation at the top of the cantilever wall can be estimated by double integrating the curvature along the height of the wall. The plastic component of the flexural deformation is calculated by multiplying the height of the wall with the plastic rotation at the base of the wall. The large inelastic strains in the longitudinal steel at the wall-tofoundation interface caused an additional flexibility, which can be included along with the flexural deformation as shown in Eqn. 1.

Figure 1. Curvature distribution along the wall height

1 2 (1)  f   sp  e hw2  e Lsp hw   p Lp hw 3 3 Where Lp = plastic hinge length; Lsp  0.15 f y dbl ; dbl  diameter of longitudinal bar ; e =elastic

curvature; p = plastic curvature The shear deformation in slender concrete walls is estimated using the empirical equation developed by Beyer et al. [15] as shown in Eqn.2. This empirical equation was developed based on a series of experimental and analytical studies of slender reinforced concrete walls under seismic loading,  m  1  s  1.5 f  (2)    tan   hw Where, f = total flexural deformation; s = shear deformation; m = axial strain at the center of wall section, = curvature of the wall,  = crack angle. The crack angle value is estimated using Eqn.3,   jd   A f  (3)   tan 1     fl bw  sw yw    90o s   V  Where, jd = lever arm between the compression and tensile resultant; V = the shear force; fl = the tensile strength orthogonal to the crack; bw = the wall thickness; Asw = the area of shear reinforcement; s = spacing of shear reinforcement; and fyw = the yield strength of shear reinforcement. The total deformation at the top of the cantilever wall can be estimated using Eqn.4,  m  1  2 1  u   f   sp   sh   e hw2  e Lsp hw   p Lp hw  1  1.5  (4)   3 3    tan   hw  The empirical equations available in literature to estimate the plastic hinge length in rectangular walls based on experimental results are shown in Table 1. As presented in the previous section, for a given rectangular concrete wall, the plastic hinge length calculations significantly influence the estimation of the force-displacement response of that wall in the inelastic region. In order to obtain an accurate force-displacement relationship from moment-curvature response of a wall section, a realistic value or empirical equation to compute the plastic hinge length is required. Table 1 Empirical equations for the plastic hinge length for rectangular walls Proposer name Plastic hinge length (Lp) 1. Paulay & Priestley, 1992 [7] 0.2 lw + 0.044 hw 2. Priestley et al., 1996 [16] 0.08 hw + 0.15 fy dbl 3. Panagiotakos & Fardis, 2001 [17] 0.12 hw +0.014 fy dbl 4. Kowalski, 2001 [18] 0.5 lw 5. Wallace, 2004 [9] 0.33 lw 6. Bohl & Adebar, 2011 [19] (0.2lw + 0.05hw)(1 – 1.5P/ Ag) < 0.8Lw lw= length of wall; hw = height of wall; fy = yield strength of longitudinal steel; P = axial load; fc’ = concrete strength; Ag= wall cross-section area

The accuracy of the above plastic hinge length equations in predicting the force-displacement behavior of reinforced concrete walls using the Eqn.4, is evaluated using the using the experimental results from RWN [4] and RW1 [20]. The cross-section details of RWN and RW1 are shown in Fig. 2. The moment-curvature responses for the walls were estimated using a zero length fiber-based beam-column element in OpenSEES [21]. The stress-strain behavior of confined concrete in the boundary elements and the longitudinal reinforcement was modeled using Concrete 07 and Steel 02 material models respectively. The equivalent bilinear momentcurvature curve is determined as described by Priestley et al. (2007) [22].

Figure 2. Cross-section details for RW1 [9] and RWN [4] Table 2. Comparison of experimental and estimated displacements for RWN and RW1 at firstyield and ultimate displacements Plastic hinge equation

Experimental 1. Paulay & Priestley, 1992 2. Priestley et al., 1996 3. Panagiotakos & Fardis, 2001 4. Kowalski, 2001 5. Wallace et al., 2004 6. Bohl & Adebar, 2011

RW1

RWN y (in.) (% u (in.) (% error) error) 1.109 6.08

y (in.) (% error) 0.486

0.852 (16.4%)

6.275 (3.2%)

0.49 (7.3%)

u (in.) (% error) 2.57 3.755 (46.1%)

0.872 (14.4%)

6.458 (6.2%)

0.509 (10.7%)

3.997 (55.5%)

0.806 (20.9%)

6.719 (10.55)

0.47(3.3%)

4.291 (67%)

0.801 (21.4%)

9.135 (50.2%)

0.468 (2.9%)

5.622 (118.8%)

0.801 (21.4%)

6.443 (6%)

0.468 (2.9%)

3.922(52.6%)

0.801 (21.4%)

6.619 (8.9%)

0.468 (2.9%)

4.122 (60.4%)

The comparison of estimated displacements with the experimental values at yield and failure of the specimens using the different plastic hinge lengths are presented in Table 2. The ultimate displacement of RW1 was significantly overestimated (46% to 119%), when compared to RWN (3.2% to 10.5%) using the empirical equations for the plastic hinge lengths. The discrepancy can be due to not accounting the influence of axial load on the plastic hinge length. To address this issue, the experimental test results from six rectangular walls found in the literature including RWN by Aaleti etal. [4], RW1 and RW2 by Wallace et al. [20], and WSH3, WSH5 and WSH6 by Dazio et al. (2009) [23], were considered. The longitudinal steel ratio (l) and axial load ratio (P/Agfc) are varied among these specimens from 0.4% to 2.22% and 0 to 12.5% respectively.

Comparing the experimental displacement capacity for these walls with the predicted displacements at the ultimate condition, the plastic hinge length was estimated. The plastic hinge length can be represented using Equation 5. 0.6   P    l (5) Lp  0.07hw 1  10e   0.15 f y dbl  0.01hw  0.15 f y dbl  A f '     g c   Where l = longitudinal steel ratio (in %). The force-displacement responses for the aforementioned six walls were estimated from the moment-curvature of the critical section using Eq.4. The comparison of predicted responses with experimental responses is shown in Fig 3. The simplified method using Eq.4, with the plastic hinge length given by Eq.5, captured the force-displacement response accurately. The estimated ultimate displacement capacities for the walls were with in the 5% of the measured values.

Figure 3 Comparison of predicted and experiemental force-dispalcement of reinfroced concrete walls Current ACI 318-11 Requirement and Parametric Study Chapter 21 in the ACI 318-11 [8] provides the minimum requirements for special reinforced concrete walls in seismic regions. The majority of longitudinal reinforcement is typically located in boundary elements at the wall ends with a minimum reinforcement distributed along the wall between the boundaries. The benefit of this arrangement is that it increases the moment resistance of the walls for a given reinforcement area. The ACI 318 requires that volumetric ratio of distributed horizontal, and longitudinal steel in the web, must be at least 0.0025 with spacing not exceeding 18 inches (21.9.2.1, 21.9.2.2) and must be provided in at least two layers. Also, special boundary elements must be provided if the neutral axis depth, c, is equal to or exceeds lw , where lw is length of the wall, hw is the height of the wall and u is the design  600 u hw  displacement of the wall. The in-plane length of special boundary elements must extend at least

c-0.1lw and c/2 for the load conditions associated with the calculation of c. Also, the boundary elements are provided with confinement steel to allow the concrete in those regions to sustain large compressive strains at higher displacements without losing the load carrying capacity. ACI318 requires the cross-sectional area of rectangular hoop reinforcement, Ash must be at least 0.09sbc f c'' f yt . In recent experimental investigations on reinforced concrete walls designed in compliance with current design codes, hoop failures and significant degradation of wall region between the boundaries, leading to unsatisfactory performance at higher ductility were observed [4, 24]. In light of those observations, an analytical study was done to examine the adequacy of the current code requirements using a series of prototype walls designed in compliance with current codes. Several design parameters such longitudinal steel ratio (l), boundary element length (lbe), transverse steel ratio in boundary elements (transverse), distribution of longitudinal steel, axial load were considered. The details of the prototype walls are presented in Table 3. The prototype walls were 15ft long, 12 in. thick and 37.5 ft. tall and designed for 1.5% lateral drift. All the walls were designed with 4 ksi concrete and grade60 steel. Set1 to Set3 walls were designed with different longitudinal reinforcement ratios (from 1% to 2.2%) meeting all the requirements of ACI 318-11. Each set consisted of 4 walls with varied axial load ratios (from 0 to 0.15). Set1D to Set3D walls were designed by uniformly distributing the longitudinal reinforcement from corresponding walls in Set1 to Set3. More details and design calculations for prototype walls are presented in Dai (2012) [25]. The force-displacement response for the walls was estimated using the simplified method described in previous section. The moment-curvature response for all the sections was estimated using a zero-length beam column element in the OpenSEES software [21]. The confined concrete behavior in the boundary elements was modeled using Mander’s model [26] represented by Concrete07 material model available in the OpenSEES [21]. The failure of the section was dictated by either fracture of reinforcement or the crushing of concrete. The failure strains of 0.06 in/in. and crushing strain by Mander’s model was used as the limiting strains for reinforcement and concrete respectively. The predicted ultimate displacement and the concrete strains at the inside edge of the boundary elements are listed in the Table 3. The concrete strains at the inside edge of the boundary element are found to be in the order of 0.004 in./in. to 0.009 in./in., which is close to crushing strain of unconfined concrete (concrete in the web region), indicating possible failure at the section adjacent to the boundary element. Similar damage was observed in recent tests on rectangular walls [4, 24], where significant distress in the web region concrete adjacent to boundary elements was observed. The observed damage in the experimental wall tests is shown in Fig.4. Also, with walls with higher axial stress ratio and distributed steel, the ultimate condition was dictated by the crushing of concrete, indicating insufficient confinement steel ratio. These observations indicate that the boundary element length and confinement steel ratio should be increased compared to code required value to mitigate such failures. Based on the analysis results from the Set-1 to Set-3 walls, the confined boundary element length (lbe) was increased horizontally, until the strain in at the inside edge of boundary element is equal to 0.0015 in./in. This value for the concrete strain was chosen to account for cyclic loading and shear cracking in the web regions. A new set of walls (Set1R to Set 3R) were designed with increased boundary element length and their behavior was predicted using the simplified method. The overall performance of these walls in terms of over strength, ductility

was stable and consistent compared to Set1-Set3 walls. Set1DRR-Set3DRR walls included the increased boundary element length along with increased confinement steel area. Increasing the confinement by 30% prevented crushing of concrete in the boundary elements, especially walls with distributed reinforcement. However, it should be noted that the increase in the confinement was only necessary for wall with axial stress ratios less than 10%. Table 3 Summary of prototype walls details and analytical results $

Axial load l (%) ratios

transverse

SET1

2.21 0,0.5,1,015

ACI minimum

SET2

1.62 0,0.5,1,015

ACI minimum

SET3

1.02 0,0.5,1,015

ACI minimum

SET1D

2.21 0,0.5,1,015

ACI minimum

SET2D

1.62 0,0.5,1,015

ACI minimum

SET3D

1.02 0,0.5,1,015

ACI minimum

SET1R

2.21 0,0.5,1,015

ACI minimum

SET2R

1.62 0,0.5,1,015

ACI minimum

SET3R

1.02 0,0.5,1,015

ACI minimum

lbe

##

12.3 in.– 29.6 in. (ACI 318) 10.1 in. – 26.5 in. (ACI 318) 10 in. – 28.5 in. (ACI 318) 24.9 in. – 44.5 in. (ACI 318) 17.8 in. – 40.4 in. (ACI 318) 13.3 in. – 35 in. (ACI 318) 18.8 in.– 40.5 in. (> ACI 318) 13.5 in. – 44.2 in. (> ACI 318)

8.4 in.– 11.2 in. 6.8 in.– 10.3 in. 4.6 in.– 8.95 in.

Predicted conc At B.E inside edge 0.0040.006 0.00280.009 0.0020.0085

NA

0.008

NA

0.01

NA

0.01

Pattern of ult (in.)# Rebar Concentrated in B.E Concentrated in B.E Concentrated in B.E Uniformly distributed Uniformly distributed Uniformly distributed Concentrated in B.E Concentrated in B.E

9.3 in.– < 0.0012 11.1 in. 7.63 in.– < 0.0014 10.27 in.

13.4 in. – 43.2 in. Concentrated 5.0 in.– ( > ACI 318) in B.E 8.95 in.

< 0.0015

10%, 20%, 30% 39.4 in. – 58 in. Uniformly more than ACI NA < 0.0015 ( > ACI 318) distributed minimum 10%, 20%, 30% 39.1 in. – 60.5 in. Uniformly SET2DRR 1.62 0,0.5,1,015 more than ACI NA < 0.0015 ( >ACI 318) distributed minimum 10%, 20%, 30% 22.6 in. – 58.3 in. Uniformly SET3DRR 1.02 0,0.5,1,015 more than ACI NA < 0.0015 ( >ACI 318) distributed minimum # ult is the displacement corresponding to fracture of reinforcement (strain = 0.06) [22] or crushing of concrete in the boundary element. Crushing strain estimated using Mander’s model [26] * transverse = ACI minimum = minimum reinforcement required by ACI 318-11 (eqn 21-5) ## Boundary element length (lbe) = ACI 318 = required length eqn 21.9.6.4 (a) section $ Strain in concrete at the inside edge of the boundary element SET1DRR

2.21 0,0.5,1,015

Figure 4 Damage in RWN and TUB walls outside the boundary element region

Conclusions A simplified computational method to estimate the force-displacement response of reinforced concrete walls from the moment-curvature was proposed and validated using experimental wall tests. The proposed method was able to estimate the ultimate displacement capacity of walls within 5% accuracy. The adequacy of the current ACI 318 requirements for special structural walls was evaluated using the lateral load performance of 48 walls designed in compliance with current code requirements. Based on the analytical study following conclusions are derived. 





The boundary element length required by ACI 318-11 is not adequate for the slender concrete walls, especially for walls with high axial stress ratio. The boundary element length around 0.18 lw was found to provide better performance for most of the walls analyzed in this paper The amount of confinement required by ACI 318-11was found to be insufficient for walls with distributed reinforcement and high axial stress ratio. Based on the analysis, it is suggested to increase the required confinement steel area by 20% to 30% from the current requirements. Distribution of the longitudinal steel along the length of the wall didn’t cause significant drop in capacity. The change was found to be less than 10%. However, based on the experimental test results from the literature cited in this paper, the distribution of steel improved overall performance of slender walls.

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