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(1)PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE ESCUELA DE INGENIERÍA. PERFORMANCE OF A RC WALL BUILDING SUBJECTED TO EARTHQUAKE AND TSUNAMI LOADS IN SEQUENCE. SANTIAGO JOSÉ TAGLE LIZANA. Thesis submitted to the Office of Research and Graduate Studies in partial fulfillment of the requirements for the degree of Master of Science in Engineering. Advisor: ROSITA JÜNEMANN. Santiago de Chile, March 2019 © MMXIX, SANTIAGO JOS É TAGLE LIZANA.

(2) PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE ESCUELA DE INGENIERÍA. PERFORMANCE OF A RC WALL BUILDING SUBJECTED TO EARTHQUAKE AND TSUNAMI LOADS IN SEQUENCE. SANTIAGO JOSÉ TAGLE LIZANA. Members of the Committee: ROSITA JÜNEMANN JUAN CARLOS DE LA LLERA TIZIANA ROSSETTO FRANCO PEDRESCHI Thesis submitted to the Office of Research and Graduate Studies in partial fulfillment of the requirements for the degree of Master of Science in Engineering. Santiago de Chile, March 2019 © MMXIX, SANTIAGO JOS É TAGLE LIZANA.

(3) Gratefully to my parents for their love and unconditional support. You made me into who I am.

(4) ACKNOWLEDGEMENTS. I would like to thank my advisor, Dr. Rosita Jünemann, for her guidance, support and motivation to develop this investigation. Her input and patience has been invaluable in helping me to learn how to do research. In addition, I must show my gratitude to Dr. Matı́as Chacón for his wise advices in moments of difficulty along this investigation. Special thanks to my girlfriend, Robin Kelly, for her support, encouragement and help in language editing of this thesis. I would also like to thank Dr. Tiziana Rossetto (thanks for let me work in your office) and Dr. Marco Baiguera for the guidance, feedback and suggestions during my internship at UCL. This research has been sponsored by the National Science and Technology Council of Chile, CONICYT, under grant Fondecyt 11170514, and by the National Research Center for Integrated Natural Disaster Management CONICYT/FONDAP/15110017.. iv.

(5) TABLE OF CONTENTS. ACKNOWLEDGEMENTS. iv. LIST OF FIGURES. vi. LIST OF TABLES. ix. ABSTRACT. x. RESUMEN. xi. 1.. INTRODUCTION. 1. 2.. Inelastic Finite element model of a RC wall. 5. 2.1.. Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 5. 2.2.. Model Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7. 3.. Simplified FEM for a reinforced concrete wall building. 13. 4.. Analysis results and model validation. 18. 5.. Earthquake Loading. 22. 6.. Tsunami Load. 24. 7.. Earthquake and Tsunami in Sequence. 28. 8.. Tsunami load comparison on 3D model. 38. 9.. Summary and Conclusions. 43. REFERENCES. 45. v.

(6) LIST OF FIGURES. 2.1. Schematic Menegotto-Pinto parameters. . . . . . . . . . . . . . . . . . . . . .. 2.2. a) WSH4 cross section; b) WSH4 element by Dazio et al (Dazio et al., 2009); c). 6. WHS4 FEM 6 elements mesh; d) WHS4 FEM 12 elements mesh; e) SW11 cross section; f) SW11 element by Lefas et al (Lefas et al., 1990); g) SW11 FEM 6 elements mesh; h) SW11 FEM 12 elements mesh. . . . . . . . . . . . . . . . . 2.3. 8. a) Analytical and experimental results comparison for specimen WSH4 tested by Dazio et al (Dazio et al., 2009); b) analytical and experimental results comparison for specimen SW11 tested by Lefas et al (Lefas et al., 1990); c) plastic strains at point A for specimen WSH4 with damaged areas after test; d) crack pattern at point B for specimen SW11 with cracks after test. . . . . . . . . . . . . . . . . 12. 3.1. a) Wall at axis Q damaged after earthquake Jünemann et al; b) section A-A of wall at axis Q (dimensions in m); c) structural specifications wall at axis Q (dimensions in m); d) section B-B of wall at axis Q (dimensions in m). . . . . . . . . . . . . 14. 3.2. Typical story floor plan (dimensions in meters). . . . . . . . . . . . . . . . . . . 15. 3.3. Simplified model and their variables. . . . . . . . . . . . . . . . . . . . . . . . 16. 4.1. Critical section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18. 4.2. (a-d) Results of parameter Sw ; (b-e) results of parameter Ws ; (c-f) results of parameter Fbw .. 4.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20. a) Plastic strains on BC model under load pattern R; b) load comparison for moment at critical section (CS) for BC; c) load comparison for ALR at critical section (CS) for BC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21. 5.1. a) Damage states simplified model; b) loading - unloading simplified model for different damage states. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 vi.

(7) 6.1. Interaction tsunami-structure: a) CHPO; b) VHPO. . . . . . . . . . . . . . . . . 24. 6.2. Location of tsunami load as nodal forces along the strong axis of the wall and location of base shear web. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26. 6.3. Shear web comparison for 3D model of the building and simplified model. . . . . 27. 7.1. Loading sequence on simplified model: a) loading seismic pushover; b) unloading seismic pushover; c) loading positive tsunami. . . . . . . . . . . . . . . . . . . 28. 7.2. Earthquake and tsunami in sequence on simplified model for Fr = 0.6 and Fr = 1.27: a) tsunami without previous earthquake; b) tsunami from DI ; c) tsunami from DII ; d) tsunami from DIII ; e) tsunami from DIV . . . . . . . . . . 31. 7.3. Tsunami pushovers with damage observed for Fr = 0.6 and Fr = 1.27: a) no previous earthquake; b) from damage state DI ; c) from damage state DII ; d) from damage state DIII ; e) from damage state DIV . . . . . . . . . . . . . . . . . . . 34. 7.4. Normal crack strains (Eknn) at maximum capacity for tsunami without previous earthquake with Fr = 0.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35. 7.5. Normal crack strains (Eknn): a) damage state DIII due to earthquake pushover; b) maximum capacity of the structure under a negative tsunami after an earthquake pushover with damage state DIII ; c) maximum capacity of the structure under a positive tsunami after an earthquake pushover with damage state DIII . . . . . . . 36. 7.6. Normal crack strains (Eknn): a) damage state DIV due to earthquake pushover; b) maximum capacity of the structure under a negative tsunami after an earthquake pushover with damage state DIV ; c) maximum capacity of the structure under a positive tsunami after an earthquake pushover with damage state DIV . . . . . . . 37. 8.1. Loads on 3D model of the building for the case of tributary area (TA). . . . . . . 38. 8.2. Loads on the 3D model of the building for the case of load on the corridor (LC). . 39 vii.

(8) 8.3. a) Tsunami pushover results without previous damage on 3D model of the building; b) damaged areas of first floor and basements of 3D model of the building at point A with TA approach; c) damaged areas of first floor and basements of 3D model of the building at point B with LC approach. . . . . . . . . . . . . . . . . . . . . . 40. 8.4. Pushover result until damage state DIV for 3D model of the building. . . . . . . 41. 8.5. a) Tsunami pushover results with previous damage on 3D model of the building; b) damaged areas of first floor and basements of 3D model of the building at point A with TA approach; c) damaged areas of first floor and basements of 3D model of the building at point B with LC approach. . . . . . . . . . . . . . . . . . . . . . 42. viii.

(9) LIST OF TABLES. 2.1. Properties for concrete. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2.2. Steel Properties for specimens WSH4 and SW11. . . . . . . . . . . . . . . . . . 10. 2.3. Concrete properties for specimens WSH4 and SW11. . . . . . . . . . . . . . . . 11. 3.1. Values of parameters (dimensions in m). . . . . . . . . . . . . . . . . . . . . . 16. 4.1. Percentage error at peak displacement for the different parameters and load. 8. patterns of the simplified model. . . . . . . . . . . . . . . . . . . . . . . . . . 20 7.1. Maximum tsunami height in meters for simplified model. . . . . . . . . . . . . . 30. 7.2. Maximum total base shear in kN for simplified model. . . . . . . . . . . . . . . 32. 7.3. Maximum top displacement in cm for simplified model. . . . . . . . . . . . . . 33. 8.1. Maximum tsunami heights (m) for 3D model. . . . . . . . . . . . . . . . . . . . 39. ix.

(10) ABSTRACT. The present study investigates the behavior of a typical RC wall Chilean building under the sequential action of earthquake and tsunami using a double pushover analysis. A real building damaged after the MW = 8.8 2010 Maule earthquake is considered as a case study building. A simplified model of the building is proposed and validated with a full 3D nonlinear model of the building. Results show that the simplified model successfully replicates the expected behavior for both earthquake and tsunami actions independently. The validated simplified model is subjected to earthquake and tsunami loading in cascade. Different tsunami load cases where applied to different earthquake damage states of the structure. The analysis of these tsunami load cases showed that the capacity and behavior of the structure is conditioned by the Froude number of the flow. Results show that the response of the building for tsunami loading is not strongly affected by previous earthquake, unless earthquake damaged is severe. In this latter case, the capacity of the building to the tsunami load is strongly reduced for action in the same direction of the earthquake.. Keywords: shear wall damage; earthquake and tsunami in sequence; inelastic finite element models; simplified model; reinforced concrete building x.

(11) RESUMEN. El presente estudio investiga el comportamiento de un edificio tı́pico chileno de hormigón armado, bajo la acción secuencial de un sismo y tsunami utilizando un doble análisis de pushover. Un edificio real dañado luego del terremoto del Maule en 2010 (MW = 8.8) es considerado como edificio de estudio. Un modelo simplificado del edificio es propuesto y validado con un modelo 3D no lineal del edificio. Los resultados muestran que el modelo simplificado replica satisfactoriamente el comportamiento para sismo y tsunami. El modelo validado es sujeto a una carga en cascada de sismo y tsunami. Diferentes casos de tsunami son aplicados a diferentes estados de daño en la estructura producto de un sismo. El análisis de la carga de tsunami mostró que la capacidad y comportamiento de la estructura depende del número de Froude en el flujo. Además, la respuesta del edificio ante un tsunami no se ve afectado por el sismo previo, excepto si el sismo es severo. En este último caso, la capacidad del edificio frente a un tsunami se reduce considerablemente si este actúa en la misma dirección del sismo.. Palabras Claves: daño en muro de corte, sismo y tsunami en serie, modelo inelastico de elementos finitos, modelo simplificado, edificio hormigón armado xi.

(12) 1. INTRODUCTION Strong ground motions along the Chilean basin of the Andes are usually followed by significant tsunamis (Palermo, Nistor, Saatcioglu, & Ghobarah, 2013). Notably, the 1960 MW = 9.5 Valdivia earthquake and the 2010 MW = 8.8 Maule earthquake were followed by several sea waves that killed hundreds of people along the coast (Palermo et al., 2013);(de la Llera et al., 2017). Moreover, inundation heights were run from a few to over 20 meters, causing damage to any infrastructure and objects along it way. The damage to objects range from the complete destruction of cars to small houses, lifting and displacement of big objects, boats and even buildings. Tsunamis have caused significant human and economic losses. Just as an example, the 2011 Great East Japan earthquake and tsunami caused 19,000 deaths and around US$ 211 billions in direct losses (Kajitani, Chang, & Tatano, 2013). Along its more than 4.200 km of coastline, the country has several large urban centers exposed to tsunami action. Modern RC shear wall buildings showed good behavior after the tsunami that followed the 2010 Maule earthquake, though some scouring of foundations was observed (EEFIT, 2010). After the 2015 Illapel earthquake, about ten RC buildings with more than 8 stories were inundated by the tsunami. In all cases, only non-structural damage was observed due to the hydrodynamic forces applied in the first story (Rivera et al., 2017). Tsunamis are massive waves triggered on a body of water by earthquakes, landslides or other disturbances. Once the wave or series of waves, reach the shore with high speed, light structures are dragged by the flow flow while other systems are impacted by the flow causing significant hydrodynamic forces. This forces may act on a structure that has already undergone structural damage due to seismic action. Therefore, the question that motivated this research is to understand if the tsunami loads may or may not take the damage structure into a more critical damage state, and under what conditions this might occur. Nowadays, Chilean seismic codes Nch433 (INN, 2012), Nch2369 (INN, 2017) and Nch2745 (INN, 2013) provide guidelines for seismic analysis and design, but not for consider tsunami actions. On the other hand, the Chilean code Nch3363 (INN, 2015), Japanese code MLIT 1.

(13) 2570 (MLIT/Ministry of Land, Infrastructure, Transportation and Tourism, 2011) and US code ASCE 7 (ASCE, 2016) provide minimum design requirements for structures located in zones exposed to tsunami flows. These codes consider that the main action of a tsunami on a structure can be replaced by the following equivalent loading cases: i) a hydrostatic force caused by a static fluid on a surface; ii) a buoyancy force represented by a vertical force experienced by the object submerged; iii) a hydrodynamic force caused by a fluid at a certain speed acting on a surface; iv) a debris force caused by the impact of objects transported by the tsunami, like vehicles, on a surface; and v) an uplift vertical pressure on a slab after a wave hits a wall. These codes consider the tsunami actions in different ways. For instance, lateral tsunami load in the Chilean code is defined as hydrostatic and hydrodynamic loads based on the expected inundation depth obtained from available inundation maps (INN, 2015). ASCE 7 considers the same loads (hydrostatic and hydrodynamic), but instead inundation depth and velocity are required (ASCE, 2016). Finally, the Japanese code considers the lateral tsunami load only as a hydrostatic load, where the inundation depth is taken also from a tsunami inundation map. This hydrostatic load is amplified by a factor depending on the distance from the shore and the presence of structures that dissipate the energy of the flow (MLIT/Ministry of Land, Infrastructure, Transportation and Tourism, 2011). Most research on the earthquake and tsunami behavior and performance of structures has been focused on either action separately, but limited literature is found on the sequential actions of earthquake and tsunami. De la Barra (de la Barra, 2017) studied the behavior of a RC building subjected to seismic action followed by tsunami using pushover analysis. In this study, a shear wall building constructed in 1979 and designed with an old Chilean code was considered as a case study, and a resisting plane of the building was modeled using fiber elements in OpenSees. This research concluded that, independently of the previous damage caused by the earthquake, the system can sustain a tsunami net force greater than the earthquake and does not present a considerable reduction in the tsunami capacity. This is because the earthquake behavior is controlled by flexure and in the case of tsunami it is controlled by 2.

(14) shear. A study developed by Rossetto et al (Rossetto et al., 2018) studied different approaches to analyse a structure subjected to seismic action followed by tsunami. For this, a Japanise tsunami evacuation building is considered and was subjected to different analysis approach on each phase. For the earthquake phase, non-linear response history analysis (DY) and nonlinear pushover (PO) were considered. For the tsunami phase, non-linear response history analysis (TDY), constant height pushover (CHPO) and variable height pushover (VHPO) were considered. This study concluded that the tsunami strength after an earthquake is little affected, except if the earthquake damage is significant. The double pushover approach PO-CHPO is the faster to run but with a poor accuracy. For the PO-VHPO approach, compared to DY-TDY approach, presented a worse estimation of the global displacements but a reasonable estimation of shear internal forces. Also, Latcharote (Latcharote, 2015) studied a RC building under the sequential action of earthquake and tsunami. A wall-frame model of a 7 story wall-frame building was developed and subjected to earthquake ground motion, followed by static pushover analysis with a uniform pressure to represent the tsunami load. The conclusion of this investigation is that more damage is observed after tsunami load, specially at first floor. Additionally, structural properties of the building can be changed and because of that is necessary to consider the sequential action of these loads. The objective of this research is to study the behavior of a typical Chilean RC shear wall building, subjected to the sequential action of earthquake and tsunami through double pushover analysis. The structure is first analyzed for a seismic pushover until a certain damage state is reached, and then tsunami loads are applied up to reaching the capacity of the building. The building is a medium rise RC wall building constructed in 2005 in Santiago, which was damaged during the Maule earthquake. The seismic performance of this building has been previously studied in detail (Jünemann, de la Llera, Hube, Vásquez, & Chacón, 2016);(Vásquez, Jünemann, de la Llera, & Hube, 2018). Two dimensional simplified models of isolated walls have shown that conventional 2D pushover analyses are not able to reproduce the expected seismic behavior due to 3D coupling effects neglected by the model. On the other hand, 3D inelastic models of the entire building have shown good results in reproducing the expected behavior, but are expensive in computational time and interpretation (Vásquez 3.

(15) et al., 2018). Thus, a new simplified model is proposed in this research, capable of capturing the 3D interaction between the wall and the rest of the building, and simple enough to significantly reduce computational time. The simplified model consists of an inelastic finite element model (FEM) of a fictitious slice of the building, which is first validated with the complete 3D model of the building. A sensitivity analysis of the simplified model was done considering different geometric variables: wall separation, slab width and flange width at the basement. The nonlinear FEM are developed using the software DIANA (DIANA FEA, 2017) and the formulation is first validated with two RC walls tested experimentally and considering both shear and flexure behavior. The simplified model proposed in this research is subjected to the seismic action using inelastic pushover analysis. Four different seismic damage states are evaluated, and tsunami loading is applied for each case. Tsunami action is considered through a variable height pushover (VHPO) (Petrone, Rossetto, & Goda, 2017) formulation, which is based on Qi’s previous work defining the tsunami hydrodynamic force acting on an obstacle (Qi, Eames, & Johnson, 2014). Additional effects such as flooding at the back of the building, buoyancy, uplift and debris impact were neglected. A set of tsunami load cases are investigated by applying different loading directions and Froude numbers, while considering different damage states caused by the preceding earthquake. Based on these results, the impact of the previous earthquake damage relative to the tsunami capacity of the building is discussed. Finally, two different tsunami load patterns are applied on the detailed 3D model of the building, considering the existence or not of previous earthquake damage. Based on these results, final observations of building performance and recommendations are obtained for applying tsunami loads on this kind of buildings.. 4.

(16) 2. INELASTIC FINITE ELEMENT MODEL OF A RC WALL This section describes the inelastic finite element formulation that is considered throughout this research, which is validated with experimental results.. 2.1. Model Description Nonlinear finite element models of RC walls are developed in the software DIANA 10.2 (DIANA FEA, 2017) since it has shown good results in previous research regarding RC wall behavior (Jünemann et al., 2016);(Vásquez et al., 2018);(Dashti, Dhakal, & Pampanin, 2017). The total strain rotating crack approach was used to model concrete behavior, in which the principal stress tensor is evaluated in the principal strain directions (DIANA FEA, 2017). The parabolic model was considered to model compressive concrete behavior, while the Hordijk model (Hordijk, 1991) was considered for tensile behavior; both models are based on fracture energy. The compressive fracture energy for the parabolic model (Gc ) was obtained from recommendations given by Pugh et al (Pugh, Lowes, & Lehman, 2015), given by Equation 2.1, 0. where fc is the concrete compressive strength.. 0. Gc = 2fc N/mm. (2.1). For tensile behavior, the tensile fracture energy was obtained according to the CEB-FIP code recommendations (Comité Euro-International du Béton, 1990), given by Equation 2.2, where Gf o is the fracture energy according to a maximum aggregate size and fco = 10 M P a. Additionally, the tensile strength is evaluated according to ACI 318-14 recommendations 0. (ACI Committee 318, 2014), given by Equation 2.3 where λ = 1 and fc is the compressive concrete strength in MPa.. 5.

(17) 0. fc 0 fco. Gf = Gf o ·. !0.7 (2.2). p fr = 0.62λ fc0. (2.3). To model the steel behavior, the Menegotto-Pinto model (Menegotto & Pinto, 1973), schematically presented in Figure 2.1, was used. In this model, the parameter b is related to the initial hardening branch and R0 conditions the initial curvature for the hardening branch. The values of the parameters are assumed according to recommendations from the literature (Papadrakakis, Charmpis, Tsompanakis, & Lagaros, 2008); (Deaton, 2013), and the model does not include bar buckling and fracture. b·E. σy. 0. Stress. R. E. Strain. Figure 2.1. Schematic Menegotto-Pinto parameters. The type of element used to model concrete elements in the analysis is the Q20SH DIANA (DIANA FEA, 2017). This is a curved shell quadrilateral element with four nodes and four Gauss quadrature points (DIANA FEA, 2012). It was selected because it has shown good results in reproducing the expected behavior of RC walls (Dashti et al., 2017) and is able to capture the out of plane buckling of the wall. The element used to model the reinforced steel is the ”bar” element, which is an embedded element that assumes perfect bonding (DIANA FEA, 2017).. 6.

(18) 2.2. Model Validation In this section, the inelastic finite element model (FEM) formulation is validated with experimental results of two RC specimens: (i) results obtained by Dazio et al (Dazio et al., 2009) for specimen WSH4 is considered to validate flexural behavior; and (ii) results by Lefas et al (Lefas et al., 1990) for specimen SW11 is used to validate shear behavior. Figures 2.2a and 2.2b show the cross section and geometry of WSH4 specimen tested by Dazio et al (Dazio et al., 2009), respectively. This corresponds to a slender unconfined shear wall, similar to the typical walls that were damaged after the 2010 Maule earthquake. The aspect ratio of the wall is 2.01 and it was subjected to an axial load ratio (ALR) of 5.7%. During the test, a displacement cyclic load was applied. The experimental results, obteined by Dazio et al (Dazio et al., 2009) showed that the failure mode was crushing in the compresion zone. Figures 2.2e and 2.2f show the cross section and geometry of SW11 specimen, respectively. This corresponds to a squat RC wall tested by Lefas et al (Lefas et al., 1990), with an aspect ratio of 1 and a very low confinement ratio. No vertical load was applied in this case and an incremental horizontal load at a rate of 0.04 kN/sec was applied at the top until 8.6 mm top displacement was reached. After the test, shear failure was observed in the specimen. The FEM is developed for each specimen in DIANA (DIANA FEA, 2017) considering material parameters in Tables 2.3 and 2.2 for concrete and steel, respectively. For concrete (Table 2.3), compressive strength is obtained from material test results of each experimental campaign. Young’s modulus for WSH4 is obtained from experimental campaign and for SW11 is estimated from ACI-318 recommendations (ACI Committee 318, 2014). Compressive fracture energy, tensile fracture energy and tensile strength are estimated from the equations presented in Section 2.1. Cracked concrete is assumed, and because of that, Poisson’s ratio is zero, which is based on Eurocode 2 guidelines (EN 1992-1-1 Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, 2004). For steel properties (Table 2.2) the values of Young’s modulus and yield stress are obtained from material test 7.

(19) Section AA’. CL. ∅6@15. 22 ∅8. 6 ∅12. 15. 6 ∅12. 3 10 10 12.5 12.5 12.5 12.5 12.5 14.5. a). 200. 14.5. 12.5 12.5. 12.5 12.5 12.5 10. 10 3. 92. 40. 555 403. 15. 200. A. 60. A’. b). d). c). 70. 280. Section BB’ 14 ∅ 8. 6 ∅8. 23.5. 14. 7. CL. 115. 6.2 mm @8. 15. e). 4 mm @ 8. 20. B 75. 7. 75. B’. 30. 75. f). 115. 20. h). g). Figure 2.2. a) WSH4 cross section; b) WSH4 element by Dazio et al (Dazio et al., 2009); c) WHS4 FEM 6 elements mesh; d) WHS4 FEM 12 elements mesh; e) SW11 cross section; f) SW11 element by Lefas et al (Lefas et al., 1990); g) SW11 FEM 6 elements mesh; h) SW11 FEM 12 elements mesh. results of each experimental campaign. In the case of the specimen SW11 a typical Young’s modulus for steel is considered. A Poisson ratio of 0.3 is used in all cases and the hardening modulus is estimated from the expected ultimate strain for each rebar. 8.

(20) Table 2.1. Properties for concrete. Parameter. WSH4. SW11. Young's modulus (MPa). 38500† 30459. Poisson's ratio. 0. 0. Compressive fracture energy (Pa-mm) 81.8. 84. Compressive strength (MPa). 40.9†. 42†. Tensile fracture energy (MPa-mm). 0.155. 0.158. Tensile strength (MPa). 3.96. 0.4. † Property from test results. Different mesh sizes were considered to analyze mesh dependence of the response. For that, 6 and 12 elements were used along the width of the specimens, as shown in Figures 2.2c and 2.2d for specimen WSH4, and Figures 2.2g and 2.2h for specimen SW11. For each model, displacements are restrained at the base nodes and lateral displacements are applied at the same position as the one used on the test. For the specimen WSH4, the vertical load is distributed along the top nodes. A displacement loading control was used with a secant iterative method with a maximum of 1000 iterations. The tolerance used was 10−3 for force and 10−4 for energy.. 9.

(21) Table 2.2. Steel Properties for specimens WSH4 and SW11. WSH4. SW11. Parameter. 12 mm. 8 mm. 6 mm. 8 mm. 6.25 mm. 4 mm. Young’s modulus (E), GPa. 210.3†. 219.5†. 210.3†. 200. 200. 200. Poisson’s ratio. 0.3. 0.3. 0.3. 0.3. 0.3. 0.3.  Yield stress σy , MPa. 576†. 583.7†. 518.9†. 470†. 520†. 420†. Hardening modulus (b). 0.00745. 0.0089. 0.0043. 0.0044. 0.0052. 0.0021. Additionally, the following parameters for the Menegotto-Pinto model are used: Initial curvature R0 = 22, A1 = 18.5, A2 = 0.15, A3 = 0.01 and A4 = 0 (Papadrakakis et al., 2008); (Deaton, 2013). † Property from test results. For the specimen tested by Dazio et al (Dazio et al., 2009), Figure 2.3a shows experimental and analytical results for the two models: (i) discretization with 6 elements along the width of the wall; and (ii) discretization with 12 elements along the width of the wall. In the first case (blue), the peaks of the analytical model are the same as the test in the first 3 cycles and a strength reduction is observed in the fourth peak. Post peak softening is observed at the end of the test and a drop in strength is observed in the analytical model around the same top displacement as in the experimental results. Additionally, the stiffness in the analytical model is in good agreement with the experimental results. For the second case (red), the same trends as in the first case are observed. However, a strength reduction is observed in this case when smaller elements are used. The error with the experimental second peak strength is 1% in the first case and 3.5% in the second case. Figure 2.3c shows plastic strains according to point A in Figure 2.3a, and the experimental results at the end of the test are also shown. The failure mode (concrete crushing) and failure area are well predicted by the analytical model.. 10.

(22) Table 2.3. Concrete properties for specimens WSH4 and SW11. Parameter. WSH4. Young's modulus (MPa). 38500† 30459. Poisson's ratio. SW11. 0. 0. Compressive fracture energy (Pa-mm). 81.8. 84. Compressive strength (MPa). 40.9†. 42†. Tensile fracture energy (MPa-mm). 0.155. 0.158. Tensile strength (MPa). 3.96. 0.4. † Property from test results. For the specimen tested by Lefas et al (Lefas et al., 1990), Figure 2.3b shows experimental and analytical results for the two models: (i) discretization with 6 elements along the width of the wall, and (ii) discretization with 12 elements along the width of the wall. For both cases, analytical results are in good agreement with the experimental results, where the curves are almost exactly the same until the first 2 mm of top displacement. After 2 mm of top displacement, a small difference is observed in the lateral stiffness, but it is still a good approximation in both cases. Finally, at the end of the test, both models predict a capacity similar to that of the experiment. Peak strength error is 0.77% for the first case and 3.79% for the second case. According to Lefas et al (Lefas et al., 1990), the predominant failure observed in the specimen SW11 was shear with presence of cracks in the zone subjected to tensile behavior. As shown in Figure 2.3d, the cracked area at point B in Figure 2.3b is the same as the one observed in the experimental results and the failure mode is well captured by the analytical model. Based on the analysis of these two specimens, the developed inelastic models are in good agreement with the experimental results for both shear and flexure dominated RC walls. Additionally, the effect of the mesh size is minimized through regularization of the constitutive models.. 11.

(23) B A. b). a). c). d). Figure 2.3. a) Analytical and experimental results comparison for specimen WSH4 tested by Dazio et al (Dazio et al., 2009); b) analytical and experimental results comparison for specimen SW11 tested by Lefas et al (Lefas et al., 1990); c) plastic strains at point A for specimen WSH4 with damaged areas after test; d) crack pattern at point B for specimen SW11 with cracks after test.. 12.

(24) 3. SIMPLIFIED FEM FOR A REINFORCED CONCRETE WALL BUILDING A real RC wall building representing the typical Chilean residential building was selected as a case-study. The typical residential building has a floor plan configuration known as ''fishbone'', where a central corridor with large walls and shorter transverse walls produces a high wall density in both directions that provides high rigidity to the building, as presented by Riddell et al (Riddell, Wood, & de la Llera, 1987). This type of RC wall buildings showed a good behavior during the 2010 Maule earthquake, but around 2% of the buildings taller than 9 stories suffered substantial damage (Wallace et al., 2012). The damaged area was typically located in the first stories of the buildings, where in some cases, the walls presented a flag shape configuration (Jünemann, de la Llera, Hube, Cifuentes, & Kausel, 2015). The building under study has 18 floors and 2 basements, with a typical story floor plan schematically shown in Figure 3.2. Thickness of all the walls and slabs is 20 cm and 15 cm, respectively. This building suffered brittle failures in some RC walls after the Maule 2010 earthquake, particularly walls at axis U, Q and N, as shown in Figure 3.1a for wall Q. The damaged walls present an irregularity in height with a flag-shape configuration, as shown in Figure 3.1c. The damage was typically concentrated at the basements in the wall irregularity. The crack was propagated horizontally where concrete crushing and buckling of rebars was observed (Jünemann et al., 2016). This building was selected because it represents the typical Chilean RC wall building located in different cities throughout the country. Around 78% of the RC buildings in Chile are RC shear wall buildings (Gómez, 2001). It is estimated that around 258 construction permits were given in coastal cities and 682 in the capital city of Santiago to buildings with more than 13 floors between 2010 and 2017 (INE, 2018). This means that a 37.8% of these construction permits were given to buildings that could be exposed to a tsunami. A 3D inelastic finite element model of the building was developed in previous research by Vásquez et al (Vásquez et al., 2018). This model considered inelastic behavior concentrated in the first story and basements, and was subjected to a real ground motion recorded near the building. The model was able to replicate the brittle wall failure observed after the earthquake. 13.

(25) Section A-A 5.75. 5.6. 1.2. Cover=2 cm. DMV ∅8 @17 DMH ∅ 8 @ 17. Section B-B 2 ∅22 DMV ∅8 @ 20 DMH ∅ 8@ 20 Cover=2 cm 6.95 5.35. 2.96. 0.9. 2.22. 2.5 3.3. MHA e=20 DMV ∅8@ 17 DMH ∅ 8 @ 17. 0.2. 1 4 ∅22. 0.2. 4 ∅22 A. 0.54 0.2. 3.2 1.2. 0.2. B MHA e=20 DMV ∅ 8 @ 20 DMH ∅ 8 @20. A. 4 ∅25 0.2. 0.2 0.5 0.7. 2.5. B. c). Continuous. b). a). 2 ∅25. 5.55. d) 0.2. 8 ∅22 2 ∅22. Figure 3.1. a) Wall at axis Q damaged after earthquake Jünemann et al; b) section A-A of wall at axis Q (dimensions in m); c) structural specifications wall at axis Q (dimensions in m); d) section B-B of wall at axis Q (dimensions in m). for low drift ratios and high axial loads in the walls. This model showed very good results, but was complex and associated to a high computational cost. Additionally, it has been shown in previous research (Jünemann et al., 2016) that a conventional 2D cantilever wall model is not able to represent the expected behavior since it neglects the interaction between the wall and the rest of the building and does not predict the expected increase in the axial load due to the seismic action. Thus, a simplified model of the building is proposed in this section, with the aim of reproducing the response of the fully 3D model and capture the increase in axial load at a lower computational cost. The wall at axis Q (shown in red in Figure 3.2) is selected as a case study to be modeled. This wall has a flag-shaped configuration, as shown in Figure 3.1c. Additionally, this wall has a different cross section in the basements and from first story and up (Figures 3.1b and 3.1d). In the basements, the flange goes along all the building width. However, from the first floor and up the length of the flange is reduced to 2.96 m, as shown in Figures 3.1b and 3.1d.. 14.

(26) Y. N X. U. 8. Q. 8.4 3.1. 0.9. 11.3. V. 4.5. T. O. 5.5. 2.15. 0.9 2.96. 1.6 Z. 7.6. 3. R. 5.8. 15. X 5.7. P. 10.4. N. Figure 3.2. Typical story floor plan (dimensions in meters). In order to capture the 3D interaction between the wall and the rest of the building, it is necessary to include a complementary portion of the building. Since the building is not exactly symmetrical and a real ”slice” of the building is complex (Figure 3.2), the selected wall is replicated as in a mirror, as shown in Figure 3.3. 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 Figure 3.3. A case base (CB) was considered, based on the geometry of the original project. The wall separation Ws was taken as 1.6 m, which corresponds to the aisle width in the original project (Figure 3.2). The slab width Ws is taken equal to 3.8, which corresponds to the wall flange width on a typical story plus half of the door width (0.45 m) at each side (Figure 3.2). Finally, the wall flange at the basement Fbw was taken as 8 m, which coresponds to half the distance of each wall located next to wall Q at the basement level. Six models are considered in the sensitivity analysis and are shown in Table 3.1. First, cases Swi (i = 1...3) vary the wall separation considering values of 1.2, 1.4 and 1.8 m, while other variables are kept as in the BC. Second, cases Wsi (i = 1, 2) vary the slab width while other variables are kept as in the BC. The values considered for the slab width are based on the wall 15.

(27) Center of gravity. Identical replicated wall. .... ws Original wall. Sw. Z Y. Sww. Fbw. X. Figure 3.3. Simplified model and their variables. flange width on a typical story Ws1 = 2.9 m, and half the distance of each wall located next to the Q axis in the basement, Ws2 = 8 m. 1 Finally, case Fbw vary the flange width at the basement while other variables are kept constant 1 and equal to the base case. Fbw is considered equal to the flange width in the typical story, i.e.. 2.9 m. Table 3.1. Values of parameters (dimensions in m). Case Sw. Ws. Fbw. BC. 1.6. 3.9. 8. Sw1. 1.2. 3.9. 8. Sw2. 1.4. 3.9. 8. Sw3. 1.8. 3.9. 8. Ws1. 1.6. 2.9. 8. Ws2. 1.6. 8. 8. 1 Fbw. 1.6. 3.9. 2.96. 16.

(28) Material properties specified in the project are used. A yield stress of 420 MPa is considered 0. for steel, and concrete compressive strength of fc = 25 M P a is used. Only unconfined concrete is 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 (DIANA FEA, 2017) and described in Section 2. For boundary reinforcing steel bars, the bar element is used considering 22 mm and 25 mm. To model the distributed steel bars, a grid element was used, in which the horizontal and vertical steel ratios are specified. The translation in X,Y and Z directions are restricted at the base nodes of both walls. Additionally, the translation in the X direction is restricted at the free borders of the slab. No rigid diaphragm is considered.. 17.

(29) 4. ANALYSIS RESULTS AND MODEL VALIDATION First, the vertical loads are applied to the wall in the simplified model. These loads are obtained from a 3D elastic building developed in the software ETABS (CSI, 2016). The resulting loads, according to the combination of dead (D) and 0.25 live load (L), were divided in the number of nodes of the wall at each story and applied as nodal forces. Second, an earthquake pushover analysis is developed considering lateral forces according to the first mode of the wall in the Y direction, this load is called F1. The lateral forces are obtained from M φy1 (Chopra & Goel, 2004), where M is the mass matrix of concentrated masses at each story of the wall and φy1 corresponds to the first mode shape of the wall in the Y direction. These parameters are obtained from an elastic FEM of the building developed in ETABS (CSI, 2016). The load is applied to the simplified model at the center of gravity of each story, as schematically shown in Figure 3.3 for a typical story. The 7 cases of the simplified model described in Table 3 are subjected to pushover analysis with load pattern F1. Results of simplified models are compared to the results obtained in the 3D inelastic FEM of the building previously described, subjected to a modal force pushover analysis in the Y direction. Results are presented in terms of axial load ratio and bending moment at the critical section shown in Figure 4.1.. ion l Sect. a Critic. (CS). Figure 4.1. Critical section.. 18.

(30) Figure 4.2 shows results for the critical section moment and the critical section axial load 0. ratio (ALR = Axial Load/Ag fc ) for the different variables analyzed. Additionally, Table 4.1 shows the errors at peak with respect to the results of the 3D building model. It is important to mention that the initial moment and ALR at the critical section in the simplified model are different from the ones in the building. This occurs because the building has initial displacements due to self weight which are not predicted by the simplified model because of its symmetry. First, Figures 4.2a and 4.2d show the critical section moment and ALR for the cases when the wall separation Sw is varied. In all cases, results of the simplified models are in good agreement with the building results. Furthermore, Table 4.1 shows that maximum peak errors are 6.1% for critical section moment and 10.2% for ALR. Second, Figures 4.2b and 4.2e show the critical section moment and ALR for the cases when the slab width Ws is varied. Again results of the simplified models are in good agreement with the building, with maximum peak errors of 6.1% and 8.5% for bending moment and ALR, respectively (Table 4.1). Third, Figures 4.2c and 4.2f show the same results for the cases when the wall flange width in the basements Fbw is varied. Larger maximum peak errors are found in this case (Table 4.1), when 1 a reduced equivalent flange width is considered in the basements (Fbw ). When a larger flange. width is considered in the basements (BC), the model gets stiffer and results are closer to the building, since this case takes into account a more realistic geometry. Based on these results, the base case is selected for the simplified model of the building, since it is based on realistic geometry parameters and produce accurate results. Finally, a sensitivity analysis of the loading pattern is developed in order to check if the model can predict the failure observed in the building after the earthquake (Figure 4a). 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 additional loading patterns are considered for the earthquake pushover analysis and described below. i) Case M1: displacement associated to the first mode shape φy1 , applied at the center of gravity of each story, as shown in Figure 6. ii) Case CF: lateral displacement. 19.

(31) x10. 3. x10. 3. x10. a). b) d). c)f ). d). e). f). 3. Figure 4.2. (a-d) Results of parameter Sw ; (b-e) results of parameter Ws ; (c-f) results of parameter Fbw . applied at the center of gravity of the lateral force distribution F1. iii) Case R: lateral displacement at roof level applied to all the nodes of the roof. iv) Case FM1: in a first phase, lateral forces (F1) are applied until maximum load is reached, and then, the analysis is continued with displacement associated to mode 1 (M1). Table 4.1. Percentage error at peak displacement for the different parameters and load patterns of the simplified model. Case BC Sw1 Sw2 Sw3 Moment (%) 6.1 4.2 3.1 3.8 ALR (%). 8.1 4.7 6. Displacement load 1 Ws1 Ws2 Fbw. M1 CF R. FM1. 3.8. 4.9. 14.8 1.4 7.2 2.6 5.5. 10.2 8.5. 7.2. 13.2 9.6 9. 7.8 7.7. Figures 4.3b and 4.3c show the results for the different loading patterns in terms of critical section moment and ALR, respectively. A check mark indicates that the failure occurred at the critical section (Figure 4.3a), consistent with the observed damage after the earthquake (Figure 3.1a). In contrast, a cross mark indicates that the failure occurred in a different location of the wall. 20.

(32) According to the results presented in Figures 4.3b and 4.3c, the moment and ALR at the critical section obtained for the different load patterns are consistent with the results of the building. According to Table 4.1, the maximum peak error for moment and ALR at the critical section is lower than 10% in all cases. Results for all load patterns are in good agreement with the building results. However, only the load patterns R and M1 are able to represent the failure mode observed in situ, as shown in Figure 4.3a. Since the high axial load played a key role in the failure mode of this building, the load pattern R was selected due to the lower ALR peak error (Table 4.1). Failure area. EpZZ 6.09e-03 -1.77e-03 -9.64e-03 -1.75e-02 -2.54e-02 -3.32e-02 -4.11e-02 -4.90e-02 -5.68e-02. Z. x10. 3. a). Y. b) c). b) a). Figure 4.3. a) Plastic strains on BC model under load pattern R; b) load comparison for moment at critical section (CS) for BC; c) load comparison for ALR at critical section (CS) for BC.. 21.

(33) 5. EARTHQUAKE LOADING An earthquake pushover analysis is developed on the simplified base case model with load pattern R for different damage states. Damage state I (DI ) corresponds to the first crack in concrete, which occurs at 2.7 cm roof displacement. Damage state II (DII ) corresponds to boundary steel yielding in compression at 10.3 cm roof displacement. Damage state III (DIII ) corresponds to the peak strength of the structure at 13.9 cm. Finally, Damage state IV (DIV ) corresponds to the final state after a brittle failure occurred due to concrete crushing in the critical section. The different damage states are shown in Figure 5.1a. The model is loaded up to a specific damage level, and then is unloaded until zero base shear condition, which corresponds to the final state after earthquake loading and the initial state for tsunami loading. Figure 5.1b shows the loading and and unloading process of the earthquake pushover for the different damage states in terms of the total base shear, i.e., considering both walls. Figure 5.1b shows that for damage states DI , DII and DIII the behavior of the structure is essentially elastic. For damage state DI , the loading-unloading occurs trough the same curve and there are no residual deformations. For damage states DII and DIII , the unloading occurs through almost the same loading curve and the residual deformations are very small (0.1 cm and 0.15 cm for DII and DIII , respectively). In contrast, for damage state DIV , significant inelastic excursions occur and residual deformations of 4.7 cm are observed.. 22.

(34) 3. x 10. a). b). Figure 5.1. a) Damage states simplified model; b) loading - unloading simplified model for different damage states.. 23.

(35) 6. TSUNAMI LOAD In order to adequately represent the effect of the tsunami on the structure for assessment purposes, this research focuses on the hydrodynamic loading approach proposed by Petrone et al (Petrone et al., 2017). This study presents two different nonlinear static analysis approaches to model the hydrodynamic action of a tsunami on a structure: constant height pushover (CHPO) and variable height pushover (VHPO). On the one hand, the CHPO is based on a constant height inundation (h) while the flow velocity is increased. This is represented by an increase in the base pressure Pd , as shown in Figure 6.1a. On the other hand, VHPO applies the tsunami forces assuming a linear height increase and a constant Froude number. This is represented by a simultaneous increase in height (h) and base pressure (Pd ), as schematically shown in Figure 6.1b. Petrone et al (Petrone et al., 2017) have shown that the CHPO approach results in a worse prediction of the structure response than the VHPO, when compared to time-history analyses. Because of that, in this study only VHPO is used. a). b). h. F. h. F. Pd. Pd. Figure 6.1. Interaction tsunami-structure: a) CHPO; b) VHPO. The tsunami net force (F), experimentally obtained by Qi et al (Qi et al., 2014), is presented in equation 6.1, where Cd is the drag coefficient; u is the flow velocity; g is the acceleration of gravity; ρ is the density of the fluid; h the height of the wave; λ is a leading coefficient; b the √ tributary width where the tsunami is applied; Fr = u/ g · h is the Froude number and Frc is the Froude number threshold (Qi et al., 2014).. 24.

(36)   0.5Cd ρu2 h. F = sign(u)  b . λρg. 1/3 4/3 4/3. u. h. if Fr < Frc. (6.1). if Fr ≥ Frc. In the VHPO approach, the Froude number (Fr ) is kept constant and the wave height (h) is varied. For each wave height, the flow velocity is calculated according to equation 6.2. Then, the net force F is calculated from equation 6.1. Finally, a triangular pressure distribution is considered with a pressure Pd in the base, which is calculated from equation 6.3. The variables F, h and Pd are schematically shown in Figure 6.1b.. u = Fr. Pd =. p g·h. (6.2). 2·F h. (6.3). According to experimental tests developed by Qi et al (Qi et al., 2014), which assumes an impermeable building and a steady state flow, the variables Cd , λ and Frc depend on the blocking ratio b/w, which is defined as the ratio between building width b and flume width w. In this study a blocking ratio b/w = 0.6 is assumed, which represents a dense area of buildings (Petrone et al., 2017). With this assumption, values of Cd = 4.7, λ = 2 and Frc = 0.32 are assumed, based on Petrone et al (Petrone et al., 2017). The density of the fluid (ρ) is 1200 kg/m3 (INN, 2015). Additional effects as flooding at the back of the building, buoyancy, uplift and debris impact are neglected. The Froude number is a parameter depending on the height and speed wave, thus each tsunami event can be characterized by a specific Froude number. However, there is no recorded information on wave speed in past tsunami events in Chile. Nevertheless, investigations are being developed to estimate speed wave for Chilean coastline based on the nonlinear shallow water equation model (Berger, George, LeVeque, & Mandli, 2011), that has been used for tsunami hazard assessment (Leveque, George, & Berger, 2011). These investigations are not conclusive yet, so for the moment, there is no available information on Froude numbers in Chile. Thus, Froude numbers estimated by T. Asai et al (Asai et 25.

(37) al.,2012) in different locations after 2011 Great East Japan earthquake, will be used to perform a sensitivity analysis of this parameter. The values considered for the Froude number in the present investigation are 0.6 and 1.27, that may represent low and high Froude number limits for areas prone to tsunami inundation (Asai et al., 2012). With the aim to validate the behavior of the simplified model under tsunami action, a tsunami pushover analysis is developed in the simplified model and in the 3D inelastic FEM of the entire building. For all the analysis in this section Fr = 0.6 will be considered. In the case of the 3D model, the tsunami direction goes from north to south (Figure 3.2). Since the structure is considered impermeable, only the elements on the border of the north side are loaded with the VHPO. The tributary width (b) considered for each structural element is the sum of half the distance between the elements on the sides. For example, for wall Q, Figure 3.2 shows the distances of the structural elements next to this wall, as 3.1 m and 2.15 m, which traduced in a tributary width (b) equal to 2.625 m when half of the distances mentioned before are summed.. Z Y Base shear web. X. Figure 6.2. Location of tsunami load as nodal forces along the strong axis of the wall and location of base shear web. Since the real building has two basements, the hydrodynamic tsunami loading is applied above ground level, i.e, from first story and up. Due to the complexity of the building-soil interaction, the tsunami loading in the basement is not considered in this preliminary study. For the simplified model, the same tributary width as in the 3D model is considered for the VHPO, 26.

(38) and the load is located on one side of the structure above ground level, as schematically shown in Figure 6.2. Figure 6.3 shows the base shear web for both simplified and 3D models. The base shear is obtained in the web of the wall where the tsunami load is applied, as shown in Figure 6.2. Please notice that a tsunami from north to south induce a negative top displacement when the axis directions presented in Figure 3.2 are considered. As illustrated in Figure 6.3, the simplified model is able to predict the maximum shear force at the web with a 16% of error, which is acceptable considering the simplifications of the model. The top displacement at the peak force is -0.41 cm in the 3D model and -1.36 cm in the simplified model. However, due to the geometry of the real building, the 3D model has an initial top displacement of 0.48 cm. Thus, when the results of the simplified model are corrected considering this effect, the top displacement at the peak in the simplified model is reduced to -0.9 cm.. Figure 6.3. Shear web comparison for 3D model of the building and simplified model. The maximum tsunami heights obtained with the simplified model and with the 3D model are 13.5 m and 14.1 m, respectively. A relative error of 4.5% is obtained for the maximum tsunami height, which is very low. Therefore, the simplified model will be used to represent the expected tsunami behavior of the building.. 27.

(39) 7. EARTHQUAKE AND TSUNAMI IN SEQUENCE A double pushover analysis of earthquake and tsunami in sequence is applied in this section to the simplified model. The schematic loading sequence is described in Figure 7.1. First, the loading of the seismic pushover is developed, by applying lateral displacement ∆u to all nodes on the roof level until a specific damage state is reached (Figure 7.1a). Second, the seismic pushover is unloaded by applying lateral displacement to all nodes on the roof level, but in the opposite direction until zero total base shear is obtained (Figure 7.1b). Finally, tsunami pushover is applied from ground level following the VHPO approach (Figure 7.1c). A positive tsunami pushover means that the direction is the same as the seismic pushover and a negative tsunami pushover means that this load is applied in the opposite direction of the seismic pushover. Du. Du. VHPO. Roof displacement. Base shear. a). Base shear. Base shear. Damage state. b) Roof displacement. c). Roof displacement. Figure 7.1. Loading sequence on simplified model: a) loading seismic pushover; b) unloading seismic pushover; c) loading positive tsunami. As was mentioned before, two values of Froude number are considered: Fr = 0.6 and Fr = 1.27. Additionally, two different directions of the tsunami action are evaluated: positive and negative. Finally, the four different damage states DI , DII , DIII and DIV are considered, 28.

(40) as well as the case with no previous earthquake (D0 ). This produces a total of 18 double pushover sequential analyses, since in the case without previous earthquake damage (D0 ), the direction of the tsunami has no effect due to the symmetry of the simplified model. Results for each analysis are presented in terms of base shear versus top displacement in Figure 7.2. Results for Fr = 0.6 are shown in blue, while results for Fr = 1.27 are shown in red. Seismic pushover is shown in black. Figure 7.3 shows results for each analysis but in terms of tsunami height versus top displacement. The latter figure also includes the damage observed due to the tsunami pushover for each analysis. Tables 7.2, 7.3 and 7.1 show the maximum total base shear, maximum top displacement and maximum tsunami height for each analysis, respectively. Figure 7.2a shows tsunami pushover (positive or negative) without previous earthquake damage (D0 ) for Froude numbers Fr = 0.6 (blue) and Fr = 1.27 (red). The total base shear is shown with a continuous line, while the base shear of walls 1 and 2 is shown with dotted and dashed lines, respectively. The results show that the behavior in terms of the pushover curve shape is similar for both Froude numbers, but the peak values are different. For Fr = 1.27 higher total shear force is obtained compared to Fr = 0.6 (Table 7.2), while higher top displacement is observed for Fr = 0.6 (Table 7.3). The results also show that for both Froude numbers, most of the shear force is carried out by the wall with higher axial load (wall 2). Figure 7.3a shows a significant influence of the Froude number in the tsunami height. For Fr = 1.27 the maximum tsunami height is 8.7 m, while for Fr = 0.6 is 13.4 m (Table 7.1). Concrete cracking and compression steel yielding are reached at considerably lower heights for Fr = 1.27.. 29.

(41) Table 7.1. Maximum tsunami height in meters for simplified model. Fr = 0.6 Earthquake. Fr = 1.27. Positive. Negative. Positive. Negative. 0. 13.4. -. 8.7. -. I. 13.6. 13.5. 8.7. 8.6. II. 13.5. 13.5. 8.6. 8.6. III. 13.4. 13.5. 8.8. 8.7. IV. 12.6. 13.2. 8.0. 8.5. damage. Figure 7.2b shows the double pushover analysis considering earthquake damage state DI for positive (right) and negative (left) tsunami directions. The earthquake loading-unloading is shown with a black continuous line. Results show that previous damage state DI has no significant influence in this case, since the peak base shear (Table 7.2), peak top displacement (Table 7.3) and curves in Figure 7.2b for each wall are very similar to the case without a previous earthquake (Figure 7.2a). Most of the load is carried out by the wall with higher axial load (wall 2) and the tsunami direction has no influence on the results. The maximum tsunami height at peak is also very similar to the case without previous earthquake damage (D0 ), which is also shown in Table 7.1 and Figure 7.3b. From Figure 7.3b, concrete cracking and compression steel yielding is observed at the same tsunami height as the case without a previous earthquake (Figure 7.3a). This is valid for both Froude numbers and both tsunami directions. The different behavior for each Froude number is also observed in this case.. 30.

(42) 3. x10. Wall numeration Earthquake direction 1. 2. Positive tsunami Negative tsunami. a) 3. x10. Negative tsunami. b). Positive tsunami. 3. x10. Negative tsunami. Positive tsunami. c) 3. x10. Negative tsunami. Positive tsunami. d) 3. x10. Negative tsunami. Positive tsunami. e). Figure 7.2. Earthquake and tsunami in sequence on simplified model for Fr = 0.6 and Fr = 1.27: a) tsunami without previous earthquake; b) tsunami from DI ; c) tsunami from DII ; d) tsunami from DIII ; e) tsunami from DIV . 31.

(43) Table 7.2. Maximum total base shear in kN for simplified model. Fr = 0.6 Earthquake. Fr = 1.27. Positive. Negative. Positive. Negative. 0. 5.8 · 103. -. 6.5 · 103. -. I. 5.7 · 103. 5.7 · 103. 6.5 · 103. 6.5 · 103. II. 5.8 · 103. 5.7 · 103. 6.4 · 103. 6.6 · 103. III. 5.7 · 103. 5.8 · 103. 6.5 · 103. 6.5 · 103. IV. 4.9 · 103. 5.5 · 103. 5.5 · 103. 6.2 · 103. damage. In the same way, Figure 7.2c shows the double pushover analysis for the earthquake at damage state DII for both tsunami directions. In this case, the earthquake pushover reaches a higher base shear and higher top displacement than in the case of damage state DI . The curve shape, peak base shear and top displacement are again very similar to the cases without previous earthquake damage (D0 ) and case DI . This is also observed from results in Tables 7.2 and 7.3 for peak base shear and peak top displacement, respectively. Maximum tsunami height is also similar to the previous cases, as shown in Table 7.1. Figure 7.3c shows that concrete cracking and compression steel yielding occur at the same tsunami height as in cases D0 and DI . The same observations can be derived from Figures 7.2d and 7.3d, regarding damage state DIII , i.e., the influence of the Froude number is significant in terms of the expected behavior and peak values, but the previous earthquake damage has almost no influence in the response. Finally, Figure 7.2e shows the results for the earthquake with damage state DIV . In this case, the earthquake unloading produces a condition of significant residual displacement where the tsunami loading starts. As a consequence, the maximum tsunami height and base shear are smaller in this case than in previous ones for both Froude numbers (Tables 7.1 and 7.2). Additionally, the positive tsunami loading is the worst case scenario where lower tsunami height is reached for both Froude numbers (Table 7.1). Figure 7.3e shows that the structure 32.

(44) presents compression steel yielding when the tsunami load begins. Additionally, higher top displacement is observed in the positive tsunami respect to the other damage states (Figure 7.3e). This is explained fundamentally by the significant initial displacement and the reduction in stiffness due to the failure located at the critical section after the earthquake for damage state DIV . Based on these results, it is possible to conclude that the effect of previous earthquake damage in the tsunami capacity of the building is negligible for damage states DI , DII and DIII for both tsunami directions. These results are consistent with the ones obtained by De la Barra (de la Barra, 2017). However, the effect of previous earthquake is considerable for damage state DIV followed by a positive tsunami, where the tsunami height difference with respect to the case without previous damage is 0.8 m and 0.7 m for Fr = 0.6 and Fr = 1.27, respectively. This is much higher compared to damage states DI , DII and DIII where no significant difference is observed in terms of maximum tsunami height (Table 7.1) with the case without previous earthquake (D0 ). Additionally, for damage state DIV , a reduction in the maximum total base shear (Table 7.2) and an increase of maximum top displacement (Table 7.3) respect to other damage states are observed, this is due to the significant residual displacement of the earthquake pushover. Table 7.3. Maximum top displacement in cm for simplified model. Fr = 0.6 Earthquake. Fr = 1.27. Positive. Negative. Positive. Negative. 0. 5.4. -. 4.9. -. I. 5.3. -5.5. 5.0. -5.1. II. 5.4. -5.6. 4.9. -5.1. III. 5.9. -5.4. 5.4. -5.0. IV. 16.6. -2.8. 13.6. -1.6. damage. 33.

(45) a). Negative tsunami. Positive tsunami. Negative tsunami. Positive tsunami. Negative tsunami. Positive tsunami. Negative tsunami. Positive tsunami. b). c). d). e). Figure 7.3. Tsunami pushovers with damage observed for Fr = 0.6 and Fr = 1.27: a) no previous earthquake; b) from damage state DI ; c) from damage state DII ; d) from damage state DIII ; e) from damage state DIV . 34.

(46) Figure 7.4 shows the crack pattern at the maximum capacity of the structure under a tsunami pushover for the case with no previous earthquake (D0 ). Most of the cracks are located in the basements of wall 1. There are normal crack strains with a 45◦ angle is observed. Tsunami. First floor. Wall numeration First basement. Eknn. 1. 2. 2.21e-03 1.80e-03 1.40e-03 1.00e-03. Second basement. 6.02e-04 2.01e-04 0. Figure 7.4. Normal crack strains (Eknn) at maximum capacity for tsunami without previous earthquake with Fr = 0.6. Figure 7.5 shows the crack pattern for earthquake damage state DIII (Figure 7.5a), the peak of negative tsunami after the earthquake pushover with damage state DIII (Figure 7.5b), and peak of positive tsunami after earthquake pushover with damage state DIII (Figure 7.5c). For damage state DIII (Figure 7.5a), maximum normal crack strains (Eknn) are observed in wall 1 at the first floor and also wall 1 presents more cracks than wall 2. In the case of a negative tsunami after an earthquake with damage state DIII (Figure 7.5b), higher cracks are located in the first basement of wall 1, in an area where little damage is observed from the earthquake (Figure 7.5a) and most of the cracks are located in wall 2, in zones not previously cracked by the earthquake (Figure 7.5a). In the case of a positive tsunami after an earthquake with damage state DIII (Figure 7.5c), crack strains presented on the first floor of wall 1 are reduced compared to the cracks strains presented in Figure 7.5a. Additionally, higher crack strains are now located in the first basement of wall 2. Thus, the areas with higher damage due to the tsunami (positive or negative) are different than the areas damaged by the earthquake for damage state DIII . Additionally, the magnitude and location of cracks caused by a negative or positive tsunami starting from damage state DIII (Figures 7.5b and 7.5c) are very similar to the ones obtained in the case without previous earthquake D0 , as shown in Figure 7.4. This supports the preceding conclusion that the previous earthquake damage has no significant influence on tsunami behavior for damage states DI , DII and DIII . 35.

(47) Earthquake. First floor. Wall numeration Earthquake direction 1. First basement. 2. Eknn. 2.20e-03 1.80e-03 1.40e-03. Second basement. Positive tsunami Negative tsunami. 9.99e-04 6.00e-04. a). 2.00e-04 0. Positive tsunami. Negative tsunami. Eknn. 2.28e-03. Eknn. 1.86e-03 1.45e-03 1.03e-03 6.21e-04. b). c). 2.07e-04 0. 2.27e-03 1.86e-03 1.44e-03 1.03e-03 6.19e-04 2.06e-04 0. Figure 7.5. Normal crack strains (Eknn): a) damage state DIII due to earthquake pushover; b) maximum capacity of the structure under a negative tsunami after an earthquake pushover with damage state DIII ; c) maximum capacity of the structure under a positive tsunami after an earthquake pushover with damage state DIII . Analogously to Figure 7.5, Figure 7.6 shows the crack pattern for the earthquake damage state DIV (Figure 7.6a), the peak of negative tsunami (Figure 7.6b), and peak of positive tsunami (Figure 7.6c). Maximum crack strains at damage state DIV (Figure 7.6a) are nearly 3.8 times the maximum crack strains observed in the earthquake at damage state DIII (Figure 7.5a). In the case of positive tsunami, crack strains are increased in the critical section of wall 2 (Figure 7.6c), respect to damage state DIV (Figure 7.6a). This behavior is different from the crack strains shown in Figure 7.5c for a positive tsunami, where no cracks are observed in the critical section of wall 2. Thus, the structure with damage state DIV followed by a positive tsunami will present a concentration of cracks located in the same area previously damaged by the earthquake. This is the reason why a positive tsunami loading from damage state DIV is the worst case scenario (for both Froude numbers) when maximum tsunami height is compared (Table 7.1).. 36.

(48) In the case of a negative tsunami starting from damage state DIV (Figure 7.6b), crack strains located in the zone damaged by the earthquake (critical section of wall 2) reduce their magnitude, because of the direction of the tsunami loading. The new cracks with higher magnitude are located at the bottom of wall 2, in a zone that was not previously damaged by the earthquake. This situation traduces in larger tsunami height for the tsunami in the negative direction from damage state DIV , compared to the positive tsunami from damage state DIV (Table 7.1). Based on this, the tsunami loading direction presents a different behavior only for an earthquake with damage state DIV . Earthquake. First floor. Wall numeration Earthquake direction. First basement. 1. Eknn. 2. 8.43e-03 6.90e-03 5.36e-03. Positive tsunami Negative tsunami. 3.83e-03. Second basement. 2.30e-03. a). 7.66e-04 0. Negative tsunami. Positive tsunami. Eknn. 8.14e-03. Eknn. 6.66e-03 5.18e-03 3.70e-03. b). 2.22e-03. c). 7.40e-04 0. Figure 7.6. Normal crack strains (Eknn): a) damage state DIV due to earthquake pushover; b) maximum capacity of the structure under a negative tsunami after an earthquake pushover with damage state DIV ; c) maximum capacity of the structure under a positive tsunami after an earthquake pushover with damage state DIV .. 37. 1.61e-02 1.32e-02 1.03e-02 7.34e-03 4.40e-03 1.47e-03 0.

(49) 8. TSUNAMI LOAD COMPARISON ON 3D MODEL Different ways to apply the tsunami loading on a RC wall building are exposed in this section. This is done because no guidelines are found in design codes or in the literature that discuss how to apply tsunami loading in buildings with high wall density like the fish-bone type building typically found in Chile. Two different loading patterns for the VHPO approach are evaluated in this section for the 3D building model considering Froude number Fr = 0.6. The loading patterns considered in this case are: i) tributary area (TA); and ii) load on the corridor (LC). In the first case, the tsunami load is applied on each structural element present in the north side of the building, as shown in Figure 8.1. On each of this elements a VHPO is applied, considering a tributary width (b) equal to the sum of half the distance between adjacent elements, as shown as an example in Figure 8.1. With this approach the exterior of the building is considered impermeable. In the second case, i.e. load on the corridor, the tsunami load is applied along the walls that are part of the central corridor, as shown in Figure 8.2. Is important to mention that in presence of an opening in a wall of the corridor, the load over that section is distributed to the adjacent walls. This is because the structure is considered impermeable in the interior. N b. Figure 8.1. Loads on 3D model of the building for the case of tributary area (TA).. 38.

(50) N. Figure 8.2. Loads on the 3D model of the building for the case of load on the corridor (LC). Figure 8.3a shows the tsunami pushover results for both loading patterns. Please notice that a tsunami from north to south induce a negative top displacement when the axis directions presented in Figure 3.2 are considered. It is observed that global results are very similar in both cases, with a significant top displacements. The maximum tsunami height reached by TA and LC approaches are 14.1 m and 13.8 m, respectively (Table 8.1). However, when analyzing local results, significant damage is observed in the columns located near axis U, as shown in Figure 8.3b for the TA approach. Table 8.1. Maximum tsunami heights (m) for 3D model. Without previous With previous earthquake. earthquake. TA. 14.1. 13.9. LC. 13.8. 13.8. This is not observed in the LC approach as shown in Figure 8.3c. This occurs because a large tributary width is considered for those elements in the TA approach when the structure is assumed impermeable. Nevertheless, in a real tsunami probably the windows glasses and non-structural elements in this area would break and let the water flow pass, which would reduce the load over this columns and could produce a scenario like the LC approach. Despite that, the rest of the damaged areas presented in Figures 8.3b and 8.3c are very similar with 39.

(51) both load patterns. From these results it can be concluded that global behavior is similar for both approaches, but some differences are observed at local level. 4. 10. A B. a) U. N. U. Q. Q. N. N. V. V. Damaged area P. P. b). c). Figure 8.3. a) Tsunami pushover results without previous damage on 3D model of the building; b) damaged areas of first floor and basements of 3D model of the building at point A with TA approach; c) damaged areas of first floor and basements of 3D model of the building at point B with LC approach. An additional analysis is done to see if this trend is also observed when previous earthquake damage exist. Seismic pushover with roof displacement is applied on the 3D model of the building from south to north until damage state DIV is reached. Figure 8.4 shows the results for the earthquake pushover. First the structure starts from point A with gravitational loads. Then, roof displacement is applied until maximum capacity is reached (point B). Next, a brittle failure occurs in walls located at axis Q and N, and the base shear drops to point C. Then, the earthquake is unloaded by applying roof displacement in the opposite direction until zero base shear is obtained (point D). 40.

(52) 3. 10. B C. A. D. Figure 8.4. Pushover result until damage state DIV for 3D model of the building. Starting from this damaged configuration due to earthquake (point D in Figure 8.4), a tsunami load is applied to the structure with each of the two approaches considered in this section: TA and LC. Figure 8.5a shows the results of the tsunami pushover after the seismic pushover previously described. It is important to mention that a negative tsunami is considered in this case because the geometry on the north side of the building is more simple, and the objective of this section is to analyze the loading approaches and not other variables. The behavior observed in Figure 8.5a is very similar to the one observed in Figure 8.3a for the case without previous earthquake damage. The maximum tsunami height for the tributary and corridor approaches in this case are 13.9 m and 13.8 m, respectively (Table 8.1). Thus, no significant difference is observed when these loading approaches are used after an earthquake in terms of maximum tsunami height (Table 8.1). Figures 8.5b and 8.5c present the damaged areas at maximum tsunami height with previous earthquake until damage state DIV , where only walls and columns of first floor and basements are showed. The trend observed in the local results in this case (Figures 8.5b and 8.5c) is very similar to the case without previous earthquake (Figures 8.3b and 8.3c ). In the TA approach, columns near axis U show damage, while this is no observed in the LC approach. Results show that the damaged areas are almost the same for each of the tsunami approaches, independent of the presence of a previous earthquake damage.. 41.

(53) 4. 10. BA. a) U. U. N. Q. Q N. N. V. V. Damaged area P. P. b). c). Figure 8.5. a) Tsunami pushover results with previous damage on 3D model of the building; b) damaged areas of first floor and basements of 3D model of the building at point A with TA approach; c) damaged areas of first floor and basements of 3D model of the building at point B with LC approach. Based on the previous results it is possible to conclude that both tsunami approaches, TA and LC, show the same global behavior. Still, for local behavior the TA approach produces damage in some walls where high tsunami loads are applied, while the LC approach avoids strain concentration in those walls.. 42.

Figure

Figure 2.1. Schematic Menegotto-Pinto parameters.
Figure 2.2. a) WSH4 cross section; b) WSH4 element by Dazio et al (Dazio et al., 2009); c) WHS4 FEM 6 elements mesh; d) WHS4 FEM 12 elements mesh;
Table 2.1. Properties for concrete.
Table 2.2. Steel Properties for specimens WSH4 and SW11.
+7

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