Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

SEISMIC DESIGN OF SLENDER CONCRETE WALLS

J.S. Pugh1, L.N. Lowes2, and D.E. Lehman3

ABSTRACT Slender concrete walls are used commonly as the lateral-load resisting system for mid- to high-rise buildings constructed in regions of high seismicity in the United States. The results of recent research suggest that current US design methods may result in slender walls that exhibit rapid strength loss under earthquake loading due to development of a compression-controlled flexural response mechanism or shear-controlled response mechanism. This paper presents an overview of research focused on advancing the seismic design of slender concrete walls to ensure that walls exhibit desirable and predictable performance under earthquake loading. A numerical model is presented that enables accurate simulation of the flexural response of slender walls, including accurate simulation of drift capacity. A series of idealized walled buildings were designed and this model was used to simulate the response of these buildings under earthquake loading. Analysis results were used to develop recommendations for i) sizing walls to ensure shear demand does not exceed shear capacity and ii) flexural design up the height of the wall to ensure that significant inelastic flexural response occurs only in expected locations.

1Structural Engineer, EDG, Inc. Houston, TX, josh.s.pugh@gmail.com 2Associate Professor, Dept. of Civil and Environmental Engineering, University of Washington, lowes@uw.edu 3Associate Dean for Infrastructure and Associate Professor of Civil and Environmental Engineering, College of Engineering, University of Washington, delehman@uw.edu. Pugh, J.S., Lowes, L.N., Lehman, D.E.. “Seismic Design of Slender Concrete Walls.” Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Seismic Design of Slender Concrete Walls

J.S. Pugh1, L.N. Lowes2, and D.E. Lehman3

ABSTRACT Slender concrete walls are used commonly as the lateral-load resisting system for mid- to high-rise

buildings constructed in regions of high seismicity in the United States. The results of recent research suggest that current US design methods may result in slender walls that exhibit rapid strength loss under earthquake loading due to development of a compression-controlled flexural response mechanism or shear-controlled response mechanism. This paper presents an overview of research focused on advancing the seismic design of slender concrete walls to ensure that walls exhibit desirable and predictable performance under earthquake loading. A numerical model is presented that enables accurate simulation of the flexural response of slender walls, including accurate simulation of drift capacity. A series of idealized walled buildings were designed and this model was used to simulate the response of these buildings under earthquake loading. Analysis results were used to develop recommendations for i) sizing walls to ensure shear demand does not exceed shear capacity and ii) flexural design up the height of the wall to ensure that significant inelastic flexural response occurs only in expected locations.

Introduction Slender walls are used commonly as the lateral-load resisting system for mid- to high-rise buildings; walls can easily be configured to meet architectural constraints, are relatively stiff and strong under service-level loading, and are commonly understood to provide a high level of ductility under earthquake loading. However, a review of laboratory testing of slender walls and post-earthquake reconnaissance reports shows that these walls may exhibit compression-controlled flexural response under earthquake loading [1]. In the laboratory, compression-controlled flexural response is associated with low drift capacity and typically accompanied by rapid strength loss [2,3]. This paper presents an overview of research to assess the earthquake performance of slender walls designed using current codes and standard practice and to advance the earthquake design of these walls to achieve desired collapse risk.

Simulation of the Earthquake Response of Flexure-Controlled Walls Numerical simulation was used to investigate earthquake design methods for slender concrete walls. Suites of idealized walled buildings were designed using standard practice, and nonlinear dynamic analysis was used to simulate the response of these buildings to suites of earthquake 1Structural Engineer, EDG, Inc. Houston, TX, josh.s.pugh@gmail.com 2Associate Professor, Dept. of Civil and Environmental Engineering, University of Washington, lowes@uw.edu 3Associate Dean for Infrastructure and Associate Professor of Civil and Environmental Engineering, College of Engineering, University of Washington, delehman@uw.edu. Pugh, J.S., Lowes, L.N., Lehman, D.E.. “Seismic Design of Slender Concrete Walls.” Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

ground motions scaled to multiple intensity levels. To accomplish this, a numerical model for slender concrete walls was required that provided i) accurate simulation of load-deformation response under cyclic loading, ii) computational efficiency and robustness, and iii) objective calibration such that model definition was based solely on wall geometry and material properties. Previous research provides models for concrete walls. These include multi-spring models, beam-column elements with lumped and distributed plasticity, and continuum models. To identify models meeting the above requirements, Pugh [4] reviewed previous research and compared simulated and observed response for three commonly employed models: the distributed-plasticity force- and displacement-based fiber-type beam-column elements in OpenSees (http://opensees.berkeley.edu) and the plane-stress RC continuum model in VecTor2 [5]. The results of the model evaluation show that for simulation of flexure-controlled walls i) fiber-type beam-column elements provide accurate simulation of stiffness to yield, strength, and cyclic response but inaccurate mesh-dependent simulation of deformation capacity, ii) displacement-based beam-column elements provide poor simulation of axial load at the section, and iii) VecTor2 continuum models provide accurate simulation of strength, over-predict stiffness to yield by approximately 10%, and provide inaccurate, mesh-dependent prediction of deformation capacity. Pugh concluded that i) no existing model meets the above requirements and ii) the distributed-plasticity force-based fiber-type beam-column element in OpenSees provides the greatest opportunity for development to meet the above requirements. To achieve accurate and mesh-objective simulation of response for flexural walls, Pugh [4] built on work by Coleman and Spacone [6] addressing simulation of RC components using distributed-plasticity fiber-type beam-column elements. Coleman and Spacone demonstrate that for flexural RC components that exhibit softening due to concrete crushing, simulated drift capacity exhibits mesh sensitivity due to localization of deformation at the controlling section, and they propose regularization of the concrete constitutive model to achieve mesh-objective results. Regularization entails defining a unique concrete stress-strain curve for each fiber section in the beam-column element, with the post-peak portion of the concrete stress-strain curve defined by the integration length associated with the section (LIP) and the concrete crushing energy ( ) (Figure 1a). Coleman and Spacone recommend values for the crushing energy of unconfined and confined concrete and demonstrate mesh-objective simulation of response for a reinforced column tested in the laboratory. Pugh [4] demonstrates that achieving accurate, mesh-objective simulation of drift capacity for a set of 11 flexural walls exhibiting softening requires regularization of concrete and steel material models; Chiaramonte [7] demonstrates similar results for simulation of concrete piles. Regularization of the stress-strain curve for reinforcing steel entails defining a unique steel stress-strain curve for each fiber section in the beam-column element, with the post-yield portion of the steel stress-strain curve in tension and compression defined by the integration length associated with the section (LIP) and the steel post-yield energy (Gfs). Figure 1b shows the definition of Gfs as a function of material test data and the gage length used in material testing (lgage); Figure 1c shows the regularized steel response model in which the post-yield stiffness and strain capacity are functions of Gfs and LIP. Using experimental data for 11 planar flexural wall test specimens that exhibited softening due concrete crushing and steel buckling under cyclic loading, Pugh [4] developed recommendations for defining the crushing energies of unconfined ( ) and confined concrete

( ) for use with the force-based beam-column element. Experimental data suggest that is a function of the volume and configuration of confining reinforcement; however, sufficient data were not available to enable development of a predictive model.

(a) Regularized concrete model (b) Measured steel response (c) Regularized steel model Figure 1. Stress-strain response histories employed in regularization of material response. The regularized wall model was validated through comparison of simulated and observed response for a series of planar wall tests [4]. Tests specimens were cantilever walls typically subjected to a shear load applied to the top of the specimen and were modeled using meshes comprising three force-based beam-column elements with three, five and seven integration points (i.e. fiber-type section models) along the length of the element. A one-dimensional fiber-type discretization of the wall section was employed with an approximately constant fiber thickness of 1/32 of the depth of the confined boundary element. Concrete stress-strain response was simulated using the OpenSees Concrete02 material model with post-peak concrete stress-strain response defined using regularized material response parameters (Figure 1a) and additional model parameters defined using measured quantities and standard models [4]. Steel material response was simulated using the OpenSees Steel02 model with post-yield tangent stiffness defined using regularized material response parameters (Figure 1c); additional model parameters were defined using measured material properties. The OpenSees MinMax material wrapper was used to simulate steel strength loss in tension at the regularized steel strain at ultimate strength (εu'' in Figure 1c), and in compression at the regularized confined concrete strain at 80% strength loss (ε20u in Figure 1a). Shear flexibility was included in the model, with elastic shear stiffness defined equal to 10% of the gross section stiffness per Lowes et al. [8].

A data set comprising 18 planar wall test specimens was used to validate the model. Wall test specimens exhibited flexural response with failure resulting from simultaneous concrete crushing and steel buckling (CB), steel fracture following buckling (BR), or steel fracture prior to buckling (R). Table 1 presents statistics for the ratio of simulated to observed stiffness, strength and drift capacity for specimens grouped according to failure mode and for entire data set. Note that yield stiffness was defined using the displacement at the strength corresponding to simulated first yield of longitudinal reinforcement and that drift capacity was defined as the drift at 20% strength loss. Figure 2 presents simulated and observed response histories for a typical specimen where response is simulated using the basic, unregularized model (Figure 2a) and the regularized model (Figure 2b). Results of the validation study show that using the regularized model i) accurate and precise simulation of yield stiffness, and strength is achieved for the data set, ii) some mesh dependency and inaccuracy in simulated drift capacity is observed; however, results are considered to be acceptably accurate (maximum error in predict response of 6%) and precise (maximum coefficient of variation of 19%) for use in the current study.

Table 1: Ratio of simulated to observed response quantity for regularized wall model. Failure Mode

No. of Tests

Yield Stiffness Ratio Strength Ratio Drift Capacity Ratio 3 IP 5 IP 7 IP 3 IP 5 IP 7 IP 3 IP 5 IP 7 IP

CB 11 Mean 1.01 1.02 1.02 0.95 0.94 0.94 0.96 0.97 1.02 COV 0.09 0.09 0.10 0.04 0.04 0.04 0.14 0.14 0.17

BR 5 Mean 1.01 1.01 1.01 0.96 0.95 0.95 1.06 1.08 1.11 COV 0.11 0.11 0.11 0.06 0.05 0.05 0.29 0.22 0.23

R 2 Mean 1.05 1.04 1.04 0.99 1.00 0.99 1.04 1.11 1.18

All 21 Mean 1.02 1.02 1.02 0.96 0.95 0.95 1.00 1.02 1.06 COV 0.09 0.09 0.09 0.05 0.04 0.04 0.19 0.17 0.19

(a) Standard, unregularized material models (b) Regularized material models

Figure 2. Simulated and measured normalized base shear versus drift response for planar wall RW1 tested by Thomsen and Wallace [9].

The Earthquake Performance of Modern US Walled Buildings

To improve understanding of the earthquake performance of modern concrete walls, a series of idealized buildings was designed using current US codes and standard practice and assessed using the regularized beam-column model presented above and the FEMA P695 assessment methodology [10]. Four core-wall buildings ranging in height from 16 to 20 stories were designed. Details of the design process included the following: i) 100 ft by 100 ft. building footprint with a core wall system comprising two c-shaped walls; response parallel to the web of the c-shaped walls was considered, ii) assumed seismic weight of 170 psf, gravity weight of 190 psi and wall axial load at the base of 0.1fcAg, iii) earthquake base shear demands determined per ASCE 7 [11] for seismic design category D with R = 6 and Cd = 5, iv) the equivalent lateral force (ELF) procedure was used to determine shear and moment demands over the height of the wall, v) walls were sized for shear per NIST GCR 11-917-11 [12], vi) wall longitudinal reinforcement layout was uniformly distributed over the cross section of the wall, designed to meet strength requirements at the base of the wall, and continued up the entire height of the wall, and vii) wall capacities and detailing were determined using the ACI Code [13]. OpenSees models of the idealized walled buildings were created that included i) regularized beam-column elements with elastic gross-section shear stiffness used to model the wall, ii) seismic mass uniformly distributed

to wall nodes, iii) gravity load uniformly distributed over the height of the building, with a portion of the load applied to wall nodes to generate the desired axial load at the base of the wall and the remaining load applied to a p-delta column that contributed no lateral stiffness to the model, and iv) 2% Rayleigh damping. Incremental time-history analyses (ITHAs) were performed for each of the ground motion records included in the P695 far-field ground motion set, with ground motions scaled on the basis of the spectra acceleration at the design period of the building (T1), which was the ASCE 7 upper period limit of CuTa. Figure 3 shows results of the evaluation study. Specifically, Figure 3 shows the ratio of the median shear demand predicted by the ITHA to the design shear demand (VITHA/Vu) versus ground motion intensity, defined as the ratio of the median spectral acceleration of the suite of ground motions at the design period of the building to the spectral acceleration of the maximum considered earthquake (MCE) at the design period of the building (ST1/SMT). Note that the ground motion intensity of the design-basis event (DBE) is 0.67 and that the average ratio of probable shear capacity to design demand is 1.6. The data in Figure 3 show that the ratio of predicted to design shear demand exceeds 1.0 for all ground motion intensity levels considered in the study, that ratio of probably shear capacity to design shear demand exceeds 1.0 for almost all ground motion intensity levels considered in the study and that the ratio of predicted to design shear demand exceeds 2.0 for the DBE. Thus, the data in Figure 3 suggest that mid- to high-rise walls designed using current US codes and standard practices could be expected to exhibit shear failure at earthquake demands levels substantially smaller than those associated with the DBE.

Figure 3. Median simulated shear demand versus ground motion intensity.

Recommendations for Seismic Design of Slender Walls: Capacity Design for Shear

To reduce the likelihood of shear failure in slender walls, a capacity-design approach for shear was developed. Previous research has addressed amplification of seismic shear demand in walls and calculation of design shear demand to account for this. Blakeley et al. [14] first identified flexural over-strength and dynamic amplification as the primary mechanisms by which shear demand is amplified when walls exhibit nonlinear response under earthquake loading; Blakeley as well as others developed capacity-design procedures for shear [15,16]. These procedures are the basis for capacity-design requirements included in various design codes and recommendations [17-19]. However, studies by others [20,21] show that these procedures can significantly under predict shear demand.

The results of nonlinear ITHA of idealized walled buildings were used to evaluate and advanced existing capacity-design procedures for shear. A series of 64 idealized builds ranging in height from 6 to 24 stories were designed using the design process outlined above, with the following exceptions: i) for buildings 12 stories or less, rectangular walls were employed, ii) for each building height, walls were sized to achieve fundamental periods ranging from 0.08N to 0.20N, where N is the number of building stories and the period range is approximately equal to the ASCE 7 empirical upper limit on the design period, CuTa, and iii) for each building height and period, strength reduction factors of 2, 3 and 4 were used to design longitudinal reinforcement; these strength reduction factors were applied directly to demands determined from modal response spectrum analysis (MRSA) and were not scaled to meet demands determined from the ELF procedure. Nonlinear ITHA were conducted for all of the walled building designs using a suite of seven synthetic ground motions. The synthetic motions were constructed to provide a best fit to the ASCE 7 design spectrum and employed to reduce variability in simulated response resulting from earthquake ground motion variability. Figure 4 shows the results of the study. Figure 4a shows the ratio of the maximum simulated to design shear demand. Figure 4b shows flexural over-strength, Ωo = Mpr/Mn, where Mpr is the flexural strength computed using probable material properties and Mu is design moment demand. Figure 4c shows the dynamic amplification factor for shear, ωv = VITHA/Vu /Ωo, where VITHA is the maximum shear demand computed for the ITHA of the walled building, Vu is the design shear demand and Ωo is the flexural over-strength. The data in these figures show that i) the ratio of the median shear demand from ITHA to design shear demand exceeds 2.0 and increases with increasing strength reduction factor, ii) flexural over-strength is relatively constant with building height and strength reduction factor and equal to 1.4 on average, and iii) dynamic amplification varies from 1.0 to 2.4 and is greatest for mid-rise buildings.

(a) Median simulated shear demand (b) Flexural over-strength (c) dynamic amplification Figure 4. Results of ITHA for 64 walled buildings ranging in height from 6 to 24 stories. The data in Figure 4c were used to evaluate previously proposed models for predicting dynamic amplification [15-19]. Figure 5a shows the ratio of the dynamic amplification factor proposed by Eibl [15], ωv, to that computed from ITHA, ωITHA. Evaluation of data such as that shown in Figure 5a [4] show that i) the Eibl method [15] most accurately predicts amplification for the entire suite of designs, ii) the simplified Priestely [16] method is similarly accurate for building heights less than 12 stories but becomes increasing conservative as building height increases, iii) the models included in the New Zealand [18] and Canadian [17] codes are unconservative for buildings designed using a force reduction factor greater than three.

Here the Eibl method was modified to provide improved prediction of shear demand for design. Using the Eibl method, shear demand is computed as the sum of the reduced first-mode shear and unreduced higher mode shear demands. This follows from the assumptions that i) first-mode response dominates system response, ii) inelastic action is limited to the first-mode with higher-modes responding essentially elastically, and, thus, iii) shear demand may be estimated as the sum of the reduced first-mode shear and the unreduced higher-mode contributions to base shear. However, evaluation of the ITHA data shows that as building height increases, higher mode contributions to base shear begin to dominate over first mode contributions. This results in inaccurate prediction of dynamic amplification for taller buildings (Figure 5a). Thus a modified MRSA method was developed in which the mode that contributes most to the base shear is identified (typically the first or second mode) and the design shear is defined equal to sum of the reduced shear forces associated with this mode and the unreduced forces associated with all other modes. Using this approach, dynamic amplification of shear can be computed accurately for the full range of building heights typically considered in design (Figure 5b). Evaluation of buildings designed using this approach suggests that median shear demand does not exceed factored design shear capacity for the DBE and does not exceed probably shear capacity for the MCE.

(a) Eibl method (b) Proposed modified MRSA method Figure 5. Evaluation of existing and proposed dynamic amplification factor. Recommendations for Seismic Design of Slender Walls: The Flexural Demand Envelope The next phase of the research effort focused on the flexural response of walls designed per US codes and standard practice. In the US, flexural demands are defined by ACSE 7 and computed using elastic analysis and either MRSA or the ELF procedure. For a building with uniform mass and stiffness, this results in a moment demand envelope in which demand is maximum at the base and decreases to zero at the top of the wall. Flexural capacity is determined per the ACI Code. Because significant inelastic flexural action is assumed to occur at the base of the wall, the ACI Code requires a large volume of closely spaced transverse reinforcement at the base of the wall to ensure that strength and integrity are maintained under multiple earthquake load cycles. To improve understanding of the earthquake performance of walls responding in flexure, a series of 12 walled buildings ranging in height from 6 to 20 stories were designed using the basic design process described previously, the shear capacity-design procedure developed as part of this study, and three different approaches for defining the shape of the moment demand envelope: i) directly from the MRSA analysis, ii) following the recommendations of Paulay and

Priestley [22] in which the moment demand at the base is assumed to extend up a height equal to the horizontal length of the wall and then diminish linearly to zero at the top of the wall, and iii) per the dual-hinge design method proposed by Panagiotou and Restrepo [23] with the cross-section at the base of the wall maintained over the entire height of the wall except for a region at mid-height where flexural strength is reduced. In all cases, the factored flexural strength of the walls exceeded the reduced flexural demands and the flexural demand envelope was determined from MRSA with a strength reduction factor of 3 applied directly to the MRSA demand. The earthquake performance of the idealized buildings was assessed on the basis of nonlinear dynamic analyses performed using the previously described numerical modeling approach and the suite of seven synthetic ground motion records scaled to the DBE and MCE. Figure 6 shows median curvature demand for the ground motion suite for the 12-story building, the three demand envelopes, and the MCE; curvature demand is defined as the maximum simulated curvature normalized by the yield curvature. These data show that when demands are determined i) directly from MRSA, inelastic flexural response occurs over the entire height of the walls with large ductility demands at the base of the wall, ii) using the Priestly and Paulay envelope, inelastic action is limited to the base of the wall, iii) using the Panagiotou and Restrepo dual hinge method inelastic action is limited to the base of the wall and the second-hinge location and ductility demands at the base of the wall are not significantly reduced. Similar results were observed for the 6- and 20-story buildings. Given that copious volumes of transverse reinforcement are required at locations of significant inelastic action, the results of this study suggest that the Priestley and Paulay envelope is the preferred approach for design.

Figure 6. Median curvature demand results for different flexural demand envelopes for 12-story

walled building subjected to suite of seven synthetic motions scaled to the MCE.

Conclusions A numerical modeling approach for flexure-controlled concrete walls that employs force-based fiber-type beam-column elements and regularized material models was developed and validated using a data from 18 laboratory wall tests. The results of nonlinear dynamic analyses using the validated model suggest that concrete walls in buildings ranging in height from 6 to 30 stories and designed using US codes and standard practice may exhibit shear failure at earthquake demand levels well below design demands. Nonlinear analysis results and previous research were used to develop a capacity-design procedure for shear that enables accurate prediction of shear demand for use in design and thereby significantly reduces the risk of shear failure under earthquake loading. The results of nonlinear analyses using the validated model show also that for walls in buildings ranging in height from 6 to 20 stories and designed using the proposed

capacity-design procedure for shear in combination with US codes and standard practice, flexural yielding is not limited to the base of the wall where transverse reinforcement is required to provide enhance ductility and that significant inelastic deformation may occur over the entire height of the wall. The results of nonlinear dynamic analyses are used to demonstrate that moment-demand envelopes proposed by others result in inelastic flexural deformation being limited to expected regions of the wall where transverse reinforcement may be provided to provide enhance performance under earthquake loading.

Acknowledgments The research presented here was funded by the National Science Foundation through the Network for Earthquake Engineering Simulation Research Program, Grants No. 0421577 and 0829978, Joy Pauschke, program manager.

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