Earthquake damage assessment of reinforced …Earthquake damage assessment of reinforced concrete...

Earthquake damage assessment of reinforced concrete wall buildings using inelastic models

Jorge A. Vásquez1,2, Rosita Jünemann1,2, Juan Carlos de la Llera1,2, Matías Hube1,2, Santiago Tagle1 1Department of Structural and Geotechnical Engineering, Pontificia Universidad Católica de Chile

2 National Research Center for Integrated Natural Disaster Management (CIGIDEN), CONICYT/FONDAP/15110017, Vicuña Mackenna 4860, Santiago, Chile

Abstract

Reinforced concrete (RC) shear walls are commonly used in seismic environments for lateral building resistance. This type of buildings has shown an adequate performance in past seismic events in general terms. However, a localized damage pattern was observed in recent earthquakes in some shear walls usually located in lower stories of these buildings, characterized by concrete crushing over a short height of the wall and spread almost over its entire wall length. These walls generally had vertical irregularity and lack of transverse reinforcement. This research investigates analytically this damage pattern observed during the 2010 Chile earthquake, and compares different modeling assumptions and the associated uncertainties in these models. A 20-story RC wall building was selected as a case study, and the following building models are presented and discussed: i) two-dimensional models of isolated walls; ii) three-dimensional simplified models of a representative building slice; and iii) three-dimensional models representing the entire building. Different loading patterns and model formulations are presented and discussed, ranging from inelastic finite element models to fiber element models using different software. It was found that high axial stresses played a major role in reproducing the observed damage, and failure was characterized by a sudden loss in strength and stiffness. This failure mechanism was not captured by some of the models, and the key modeling assumptions, such as the effect of induced vertical deformations on the walls, are presented and discussed.

Keywords: Reinforced concrete, nonlinear model, shear wall, damage, failure, axial load

XII Chilean Conference on Seismology and Earthquake Engineering ACHISINA2019 Valdivia, April 3 to, 5, 2019

1 Introduction

Reinforced concrete (RC) wall buildings are widely used in seismic regions to withstand both lateral and vertical actions. Countries such as Canada, Colombia, New Zealand and Chile [1],[2],[3],[4], among others, use this building typology. In Chile, approximately 78% of the RC building stock are shear wall buildings [5],[6],[7] typically intended for residential use and with a “fish-bone” type floor plan configuration; this is a typical plan with a central longitudinal corridor with shear walls and transverse walls that runs from the corridor towards the building exterior and separate building apartments and interior rooms [8].

Although a large majority of medium to tall RC buildings performed well during the 2010 Maule Earthquake, extensive localized brittle damage occurred in some of these structures. Observed damage was typically concentrated in first story and basements, characterized by concrete crushing over a short eight of the wall but in most cases almost over its entire length. Reinforcement buckling and fracture was observed, and global wall buckling was also found in some cases [9],[10],[11],[12],[13]. Damaged buildings were in large majority modern buildings constructed after year 2000, with slender walls with high axial load ratios and low confinement [8].

Significant experimental and analytical research has been conducted in order to analyze and explain the observed behavior. Regarding experimental research on RC walls, the focus has been placed on studying isolated RC walls and few experimental programs have focused on the effect of high axial loads in slender walls. It has been demonstrated that for high axial load ratios, the wall failure is brittle, with low drift capacity [14][15][16]. Additionally, experimental tests have shown that providing confinement might not be enough to achieve an acceptable ductility for thin elements since the effective confinement zone cannot be developed [17][18]. Regarding analytical research on RC walls and RC wall buildings, different analytical tools have been used in the past. A broad initiative developed by NHERP [19] discusses approaches for analytical modeling of RC wall buildings and presents a series of studies using these models to capture behaviors observed in experimental tests and buildings damaged in the 2010 Maule earthquake. Additionally, different authors have studied the collapse of Alto Rio building using different software and types of analysis [20],[21],[22],[23]. Research conducted so far has mainly focused in the only total collapse, and results show that there are several differences in the estimated softening behavior, peak strength, and displacement demands.

This research investigates analytically the damage pattern observed in RC wall fish-bone type buildings during the 2010 Chile earthquake using different models. To do this, a case-study building that suffered significant damage in RC walls at the basements is studied. The different models are: i) two-dimensional models of isolated walls; ii) three-dimensional simplified models of a representative building slice; and iii) two different three-dimensional models representing the entire building. Different modeling assumptions and loading patterns are evaluated and analyzed in order to find the ability of these models for capturing the essential behavior of this particular type of buildings.

2 Case Study Building

Around 40 RC wall buildings located in Santiago, Viña del Mar and Concepción experienced significant damage during the 2010, Chile earthquake [10],[11],[12],[13]. One of these buildings located in Santiago was selected as a case study building to try to reproduce the observed damage pattern. The building has 18 stories and 2 basements and a typical “fish-bone” like configuration with central longitudinal walls running in the East-West direction, and transverse walls in the North-South


direction. Fig. 1a and 1b show the floor plan of the first basement and first story, respectively. Walls in the building are typically 20 cm thick, and floor slabs 15 cm thick. The average total wall density is 6.5%, defined as the total area of walls in both directions divided by the tower plan area, and computed at the first level above grade. The building was designed with concrete characteristic strength fc’ = 25MPa and steel A630-420H with fy = 420 MPa. The basements are used for car parking and present an enlarged floor plan area with RC columns and perimeter RC walls along the perimeter of the basement. Foundation soil corresponds to Soil C following the NEHRP soil classification [24].

An evaluation conducted after the earthquake showed that severe damage was localized in the transverse RC walls at the north side of the building and at the first basement level, as shown in Fig. 1a, where critically damaged walls are encircled.

Fig. 1 – (a) First basement floor plan with most damaged walls encircled; and (b) first story floor plan.

The observed damage in walls U, Q, and NN is shown in Fig. 2a, b, and c, respectively and is characterized by concrete crushing and reinforcement buckling. This damage affected almost the entire length of the walls, compromising their vertical stability and transferring vertical load to other elements. Additionally, other elements at the basement suffered moderate damage, but no significant damage was observed in RC slabs, which implies that the slab could have fully transferred forces between walls, columns, and beams.

Fig. 2 – Observed damage in the first basement of the studied building: (a) wall U; (b) wall Q; (c) wall NN.

Walls U, Q and NN are the most seriously damaged, and they have a similar flag-shape configuration in height, with a reduction in the cross-section area in the transition from the first story to the basement, were damage was concentrated. The focus of this article will be placed in wall Q, which


from first story and up has the cross section shown in Fig. 3a and at the basements has the cross section shown in Fig. 3b.

Fig. 3 – (a) Cross section of wall Q from first story and up; (b) cross section of wall Q at basements; (c) scheme of finite element model of wall Q.

3 Two dimensional models of isolated wall

An inelastic finite element model of resisting plane Q was developed in DIANA [25], aimed to replicate the damage pattern observed in Fig. 2b by means of an inelastic pushover analysis. The total strain rotating crack model is considered to model concrete behavior. The Parabolic and Hordijk models are used in compression and in tension respectively. These constitutive models were considered among other alternatives evaluated [26] since the stress-strain relationship is regularized according to the mesh size [25]. Concrete is modeled using the Q8MEM element, which is a four-node quadrilateral iso-parametric plane stress element. Reinforcement is modeled using the BAR element, which is an embedded element and follows the assumption of perfect bonding [25]. Reinforcing steel is modeled using exponential hardening. It is important to notice that this stress-strain constitutive model is equal in tension and compression, and the model does not include the effect of bar buckling or fracture.

The nominal properties specified in the project were used (fc'=25 MPa, fy=420 MPa), and following the CEB-FIP recommendations [27] the tensile fracture energy used in the model is Gf=0.111 MPa-mm. For the compressive fracture energy, recommendations by Nakamura and Higai [28] were used which results in Gc=44 MPa-mm.

Fig. 3c shcematically shows the model developed of the isolated wall Q. The web of the wall is modeled using 0.2 m thick elements, while the wall flange is modeled using 2.9 m thick elements in all the height of the wall. The orthogonal wall flanges in the first story (Fig. 3a) are modeled with 70 cm thick elements. Because the model is planar, the implicit assumption is that the behavior of these orthogonal flanges is equivalent to that of elements symmetrically placed relative to the central plane of the wall. Both, horizontal and vertical displacements, are fixed at the base of the wall, and


gravitational loads are applied to the nodes at each floor level. These loads were obtained from a 3D linear finite-element model of the building developed in ETABS [29] using dead load plus 25% of live load (D+0.25L). The axial load ratio (ALR) due to these gravitational loads is 19% at the first basement. The ALR is calculated as N/Agfc’, where N is the axial load in the wall, Ag the gross section of the wall and fc’ the concrete copressive strength.

To determine the strength and failure mechanisms of wall Q, a pushover analysis with controlled displacements was performed considering four different displacement load cases, which are schematically shown in Fig. 4: (i) case R, which consists in a constant lateral displacement at all roof nodes of the wall (Fig. 4a); (ii) case T, which consists in floor lateral nodal displacements that increase in height according to an inverted triangular pattern (Fig. 4b); (iii) case M1, which consists in floor lateral nodal displacements that result from the predominant elastic mode shape in the direction of the wall (Fig. 4c); and (iv) case MV1, which consists in floor lateral and vertical nodal displacements that result from the predominant elastic mode shape (Fig. 4d). By including vertical displacements, the 2D model tries to represent the interaction between the wall and the rest of the structure around.

Fig. 4– (a) Load case R; (b) load case T; (c) load case M1; (d) load case MV1; (e) critical section ALR versus roof displacement.

Fig. 4e summarizes the results from the inelastic pushover analysis of the four loading cases in terms of ALR in the critical section versus the lateral roof displacement. The concrete plastic deformations of the bottom portion of the wall are also identified in the figure for the final step in each case. In general, Fig. 4e shows huge differences in axial load ratios. Since the lateral displacement pattern does not impose vertical loads in load cases R, T and M1, the ALR remains constant. This effect translates into poor outcomes of the three loading cases when trying to represent the damage pattern observed in the wall. None of the damage patterns observed, resemble the observed damage pattern. On the contrary, in the load case MV1 an evident increase in ALR is observed reaching a peak around the failure point of the wall. In this case, the damage pattern predicted by the analytical model resembles the observations after the earthquake in terms of damage concentration and propagation. Additionally, a maximum ALR of 50% is obtained for case MV1, which is more consistent with results of more complex models that will be discussed in the following sections.


Results show then, that modeling a cantilever isolated wall and using traditional loading patterns is not a good alternative to reproduce the observed damage since these models are not able to capture the interaction between the wall and the rest of the structure. However, an alternative to represent this effect is including vertical displacements associated to the first mode.

4 Three-dimensional simplified models of a representative building slice

In order to improve the analytical model and be able to capture the 3D interaction between the wall and the rest of the building, a representative building “slice” is considered in this section. Since the building is not exactly symmetrical and a real “slice” of the building is complex (Fig. 1c and e), the selected wall is replicated as in a mirror, as shown in Fig. 5a and b. As the simplified model is composed by a fictitious slice of the building, three variables are selected for sensitivity analysis in order to find which of them has a more significant influence on the behavior: (i) the wall separation Sw; (ii) the slab width Ws; and (iii) the flange width at the basements Fbw. These variables are schematically shown in Fig. 5a and b.

Fig. 5– (a) First floor plan with the representative fictitious slice to be modeled; (b) finite element

model of the building slice.

Nine models are considered in the sensitivity analysis, which are shown in Table 1. First, cases Siw vary the wall separation between 1.2 m and 1.8 m, including the value of 1.6 m, which corresponds to the wall separation in the original project (Fig. 1a). The slab width (Ws) is kept constant and equal to 3.8 m, which corresponds to the wall flange width on a typical story plus half of the door width (0.45 m) at each side. Finally, the wall flange width at the basement (Fbw) is also kept constant and equal to 8 m, which corresponds to half the distance of each wall located next to wall Q on the basement level. Second, cases Wis vary the slab width while other variables are kept constant. The original wall separation of the project (Sw = 1.6 m) and a flange width at the basement (Fbw) of 8 meters are used. The values considered for the slab width (Ws) are based on the wall flange width on a typical story, Ws = 2.9m; half the distance of each wall located next to the Q axis in the basement, Ws = 8 m and wall flange width at the typical story plus half of the door width at each side of the Q axis, Ws = 3.9 m. Finally, cases Fibw vary the flange width in the basement while other variables are kept constant. A wall separation Sw = 1.6 m and a slab width Ws = 3.9 m are considered. The wall flange width in the


basement is considered equal to the flange width on a typical story, Fbw = 2.96 m; or equal to half the distance of each wall located next to the Q axis in the basement, Fbw = 8 m.

Table 1: Values of parameters for sensitivity analysis (dimensions in m).

Case Sw1 Sw

2 Sw3 Sw

4 Ws1 Ws

2 Ws3 Fbw

1 Fbw2

Sw 1.2 1.4 1.6 1.8 1.6 1.6 1.6 1.6 1.6

Ws 3.9 3.9 3.9 3.9 2.9 8 3.9 3.9 3.9

Fbw 8 8 8 8 8 8 8 2.96 8

The same material parameters and modeling assumptions than in section 3 are considered. For computational economy, nonlinear concrete and reinforcing steel rebars are considered only until the 5th floor and from 6th floor and up, only linear concrete is considered. The element used to model concrete elements is the Q20SH, as defined by the software DIANA [25] which is a curved quadrilateral shell element. Additionally, the translation in the longitudinal direction of the building is restricted at the free borders of the slab. No rigid diaphragm is considered.

An inelastic pushover analysis is developed considering lateral forces according to the first building mode applied in the center of gravity of each story. Fig. 6 shows results in terms of critical section axial load ratio (CS ARL) versus top displacement for each analysis case described in Table 1.

Fig. 6– (a) Results for models varying wall separation Siw; (b) results for models varying slab width Wis;

(c) results varying wall flange width at the basements Fibw; and (d) results varying loading pattern.

First, Fig. 6a shows results when the wall separation Sw is varied. It is observed that the wall separation does not produce significant changes in response, thus a value of Sw = 1.6 m will be considered for the final model, since this is the aisle width in the real building. Second, Fig. 6b shows the ALR for the cases when the slab width Ws is varied. Again, results of the simplified models are in good agreement between them. A slab width of Ws = 3.8m will be considered because it is more realistic according to the typical floor plan. Finally, Fig. 6c shows the same results for the cases when the wall flange width in the basements Fbw is varied. Further analyses showed than when the flange is reduced in length, the damage pattern was not properly reproduced, thus a flange width in the basement of Fbw = 8 m is considered.

As the force pushover analysis is not able to capture the post-peak behavior of the wall, a sensitivity analysis of the loading pattern is developed to check if the model can predict the failure observed in the building after the earthquake. The sensitivity analysis of the loading pattern is developed for the selected model with: Sw = 1.6 m, Ws = 3.8 m and Fbw = 8 m.

Four loading patterns are considered : i) case M1, which corresponds to horizontal displacements of the first building mode; (ii) case CF, which corresponds to a lateral displacement applied at the center of gravity of the lateral force distribution; (iii) case R, which corresponds to roof displacements; and (iv) case FM1, which corresponds to lateral forces at a first stage and then lateral displacements


associated to mode 1. Fig. 5e shows the results for the different loading patterns in terms of critical section ALR. A check mark indicates that the failure occurred at the critical section consistent with the observed damage after the earthquake, while a cross mark indicates that the failure occurred in a different location of the wall. The load patterns R and M1 are able to represent the failure mode observed in situ.

5 Three-dimensional models representing the entire building

Finally, two different 3D inelastic models of the entire building are developed in this section: (i) a finite element model in the software DIANA (FE-NL); and (ii) a model in MATLAB (Fiber-NL) based on force-based fiber elements (FEE) developed previously by Vásquez et al. for RC wall elements [30]. In both models the elements with nonlinear behavior are concentrated in the first three stories of the building i.e. two underground levels and first story. All structural elements from second story and above were assumed linear-elastic. Slabs were assumed elastic at all levels. These assumptions are justified since most of the wall damage was localized in the first basement and no damage was observed in the slabs.

On the one hand, the 3D finite element model in DIANA follows the same assumptions that the models described in sections 3 and 4 and is schematically shown in Fig. 7.

Fig. 7– Finite element model in DIANA: (a) 3D view of the building; and (b) inelastic elements at first three levels.

On the other hand, the fiber model combines an elastic finite element model extracted from SAP2000, with inelastic force based fiber elements (FFE) for walls in the first three levels. Fig. 8a shows a wall of shell elements connected to the FFE. The fiber element maintains the cross section given by the shell elements but incorporates several nonlinear behaviors for each type of fiber. The stress-strain relationship of concrete in compression is based on Kent and Park Error! Reference source not found., while tensile strength is neglected, as shown in Fig. 8e. For the steel stress-strain relation, the monotonic curve is used as an upper bound of the cyclic behavior including the Bauschinger effect. Additionally, bar buckling is represented with a softening region in the compression zone with a reduced stiffness when reloading from this zone, as shown in Fig. 7d. For the sake of simplicity, shear was modeled linearly elastic. Additionally, no strain penetration effects were modeled, and perfect bonding was assumed between steel and concrete.

a) b)


Fig. 8– Modeling walls using fiber elements: a) connection between shell and fiber elements; b) restrained fiber element for flexibility based analysis; c) cross section of the fiber element and d)

schematic constitutive models for steel and concrete.

Time history analysis are developed in this case for different seismic records. Fig. 9 shows results for critical wall Q for the PuenteAlto record which was registered during the 2010 Chile earthquake close to the building and with similar soil conditions (NEHRP site class C). Fig. 9a shows results for the NS component of the seismic record applied in the same direction of the building; Fig. 9b shows results for both horizontal components of the seismic record; and Fig. 9c shows results for the three seismic record components. Results are presented in terms of critical section ALR versus roof displacement for both inelastic models, and also for a linear elastic model in SAP2000 [29]. Three distinctive phases are identified in the wall behavior as shown in Fig. 8a: i) an essentially linear-elastic zone with some inelasticity in the tension side due to concrete cracking; ii) a brittle failure characterized by large axial stresses (ALR larger than 50%); and iii) residual cycles. The same trend is observed when two or three seismic record components are included (Fig. 9b and c).

Fig. 9– Results for wall Q: (a) Y component; (b) XY components; and (c) XYZ components.

Results show that both models predict a brittle failure in critical wall Q for similar ALRs and roof displacements.

6 Summary and Conclusions

This article presents different inelastic modelling alternatives to assess damage in a RC wall that suffered significant damage during 2010 Chile earthquake. A real building was selected as a case-study building, and one of the damaged walls was analyzed in detail.

First, an inelastic finite element model of the isolated cantilever wall was developed. Results showed that this model was not able to reproduce the expected behavior in the wall when conventional pushover analysis are developed. However, results from inelastic pushover analysis showed good agreement with the damage observed after the earthquake when a load pattern that includes lateral


and vertical displacements associated with the first mode of the building was considered (MV1). The model reproduced the wall failure that localizes just below the vertical irregularity and spreads toward the interior of the wall. The displacement pattern proposed is capable of accounting for the large axial load ratios in the wall, which were also validated by more sophisticated models, and become a key factor in reproducing the wall strength and damage pattern.

Second, an inelastic finite element model of a fictitious building slice was developed. Results in this case are in good agreement with the expected seismic behavior. A sensitivity analysis was developed in terms of geometric variables of the simplified model, and results showed that an important variable to reproduce the expected behavior is the wall flange at the basements, probably because the wall flange significantly increases at the basements where the failure occurred. Results for inelastic pushover analysis were sensitive to the load pattern in terms of reproducing the expected damage pattern, however the peak ALR and roof displacement were much less sensitive to the loading pattern than in the isolated cantilever wall model. This is because whatever the lateral load pattern, opposite walls are always coupled through the slab, producing a significant change in axial loads.

Finally, two different 3D inelastic models of the entire building were developed using different approaches: (i) finite element model in DIANA; and (ii) a fiber model in MATLAB. Nonlinear response history analyses were carried out using a real seismic record registered during 2010 earthquake and measured in the same city and in a site with similar soil conditions than the studied building. Although with very different formulations, both models predict that the failure of walls was brittle, with a sudden loss of load carrying capacity after reaching ALR larger than 50% and associated to roof drift ratios around 0.3% approximately. The cyclic response of the walls shows that they behaved essentially elastic in compression until they reached a peak ALR. The main source of inelasticity before failure was due to concrete cracking in tension, without significant steel yielding.

It is remarkable that the two inelastic models, with completely different formulations predict a comparable brittle behavior, with similar forces and displacements. Additionally, a simplified model of a fictitious building slice also provides reasonable results, consistent with the 3D building model responses. However, considering an isolated wall without including the coupling effects is not a good alternative for damage assessment of this type of RC walls.

7 Acknowledgments

This research has been sponsored by the National Science and Technology Council of Chile, CONICYT, under grant Fondecyt 1170836 and grant Fondecyt 11170514, and by the National Research Center for Integrated Natural Disaster Management CONICYT/FONDAP/15110017. The authors are grateful for this support and would like to thank also the company Spoerer Ingenieros Asociados SpA for providing all the building information.

8 References

[1] Pao J., Brzev S. Concrete shear wall highrise buildings. World Housing Encyclopedia, Report 79.

[2] Mejia L.G., Ortiz J.C., Osorio L.I. RC Structural Wall Buildings. World Housing Encyclopedia, Report 109.

[3] Moroni O., and Gomez C. Concrete shear wall buildings. World Housing Encyclopedia, Report 4.


[4] Kam W.Y., Pampanin S., Elwood K. Seismic Performance of Reinforced Concrete Buildings in the 22 February Christchurch (Lyttelton) Earthquake. Bulletin of the New Zealand Society for Earthquake Engineering 2011; 44(4), 239-278.

[5] Guzmán MA. Structural Characteristics used in Design of High Buildings in Chile. Civil Engineering Thesis 1998. University of Chile. (In Spanish).

[6] Gómez CE. Structural System Characteristics used in RC and Reinforced Masonry Building Construction in Chile. Civil Engineering Thesis 2001. University of Chile, 215 pp. (In Spanish).

[7] Calderón JA. Update on structural system characteristics used in RC building construction in Chile. Civil Engineering Thesis 2007. University of Chile. p. 76 [in Spanish].

[8] Jünemann, R., de la Llera, J. C., Hube, M. a., Cifuentes, L. a., & Kausel, E. A statistical analysis of reinforced concrete wall buildings damaged during the 2010, Chile earthquake. Engineering Structures 2015; 82, 168–185.

[9] Rojas, F., Naeim, F., Lew, M., Carpenter, L. D., Youssef, N. F., Saragoni, G. R., & Adaros, M. S. Performance of tall buildings in Concepción during the 27 February 2010 moment magnitude 8.8 offshore Maule, Chile earthquake. The Structural Design of Tall and Special Buildings 2011; 20(1), 37–64.

[10] Carpenter, L. D., Naeim, F., Lew, M., Youssef, N. F., Rojas, F., Saragoni, R. G., & Adarosr, M. S. Performance of tall buildings in Viña del Mar in the 27 February 2010 offshore Maule, Chile earthquake. The Structural Design of Tall and Special Buildings 2011, 20, 17–36.

[11] Westenenk, B., De La Llera, J. C., Besa, J. J., Jünemann, R., Moehle, J., Lüders, C., Hwang, S. J. Response of reinforced concrete buildings in Concepción during the Maule earthquake. Earthquake Spectra 2012; 28(SUPPL.1), 257–280.

[12] Westenenk, B., de la Llera, J. C., Jünemann, R., Hube, M. A., Besa, J. J., Lüders, C., Jordán, R. Analysis and interpretation of the seismic response of RC buildings in Concepción during the February 27, 2010, Chile earthquake. Bulletin of Earthquake Engineering 2013, 11(1), 69–91.

[13] Wallace, J. W., Massone, L. M., Bonelli, P., Dragovich, J., Lagos, R., Lüders, C., & Moehle, J. Damage and implications for seismic design of RC structural wall buildings. Earthquake Spectra 2012; 28(SUPPL.1), 281–299.

[14] Alarcon, C., Hube, M. A., & de la Llera, J. C. Effect of axial loads in the seismic behavior of reinforced concrete walls with unconfined wall boundaries. Engineering Structures 2014; 73, 13–23.

[15] Su, R., & Wong, S. Seismic behaviour of slender reinforced concrete shear walls under high axial load ratio. Engineering Structures 2007; 29(8), 1957–1965.

[16] Zhang, Y., & Wang, Z. Seismic behavior of reinforced concrete shear walls subjected to high axial loading. ACI Structural Journal 2000; (97), 739–750.

[17] Arteta, C. A., To, D. V, & Moehle, J. P. Experimental response of boundary elements of code-compliant reinforced concrete shear walls. Tenth U.S. National Conference on Earthquake Engineering 2014; Anchorage, Alaska.

[18] Massone, L. M., Polanco, P., & Herrera, P. Experimental and analytical response of RC wall boundary elements. Tenth U.S. National Conference on Earthquake Engineering 2014; Anchorage, Alaska.


[19] NERHP (2014). “Recommendations for seismic design of reinforced concrete wall buildings based on studies of the 2010, Maule, Chile Earthquake.” NIST GCR 14-917-25. US Departemt of Commerce.

[20] Deger, Z. T., & Wallace, J. W. Collapse Assessment of the Alto Rio Building in the 2010 Chile Earthquake. Earthquake Spectra 2015, 31(3), 1397–1425.

[21] Maffei, J., Bonelli, P., Kelly, D., Lehman, D. E., Lowes, L., Moehle, J., Telleen, K., Wallace, J., and Willford, M., 2014. Recommendations for Seismic Design of Reinforced Concrete Wall Buildings Based on Studies of the 2010 Maule, Chile Earthquake. Tech. rep.

[22] Restrepo, J., Conte, J., Dunham, R., Parker, D., Wiesner, J., and PAC, D., 2017. Detailed Nonlinear FE Pushover Analysis of Alto Rio Building. In 16th World Conference on Earthquake Engineering, Santiago, Chile.

[23] Zhang, P., Restrepo, J. I., Conte, J. P., and Ou, J., 2017. Nonlinear finite element modeling and response analysis of the collapsed Alto Rio building in the 2010 Chile Maule earthquake. The Structural Design of Tall and Special Buildings 26.

[24] Building Seismic Safety Council, 2003. The 2003 NEHRP recommended provisions for new buildings and other structures, Part 1: Provisions (FEMA 450).

[25] Diana, T., 2011. Finite element analysis user’s manual-release 9.4. 4. TNO DIANA .

[26] Jünemann, R., Llera, J. C., Hube, M. A., Vásquez, J. A., and Chacón, M. F., 2016. Study of the damage of reinforced concrete shear walls during the 2010 Chile earthquake. Earthquake Engineering & Structural Dynamics 45, 1621–1641.

[27] Comité Euro-International du Béton. (1990). CEB-FIP model code 1990, Thomas Telford, London.

[28] Nakamura, H., & Higai, T. (2001). “Compressive fracture energy and fracture zone length of concrete.” Modeling of Inelastic Behavior of RC Structures under Seismic Loads, ¬¬p471-487.

[29] Computers and Structures, Inc. (2010). CSI Analysis Reference Manual for SAP2000,ETABS, SAFE and CSIBridge. Berkeley, California.

[30] Vásquez, J. A., de la Llera, J. C., and Hube, M. A., 2016. A regularized fiber element model for reinforced concrete shear walls. Earthquake Engineering & Structural Dynamics 45, 2063–2083.

[31] Scott, B., Park, R., and Priestley, M., 1982. Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. In Journal Proceedings, vol. 79, pp. 13–27.

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