# Seismic Performance Assessment of Reinforced Concrete Frame-Shear Wall Structures in Hydropower Plants Based on Material Damage

Authors: Changzheng Shi; Lei Hu; He-Gao Wu; Qi-Ling Zhang; Kai Su
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

For the reinforced concrete frame-shear wall (RCF-SW) structures in hydropower plants (HPs), the tensile cracking and compressive crushing of the reinforced concrete (RC) members are considered as the main potential damage. This paper presents a methodology to assess the seismic performance of RCF-SW structures. In this methodology, a concrete damage plasticity model is employed to simulate the reinforced concrete, and the structural seismic responses are investigated through nonlinear incremental dynamic analysis (IDA). Several engineering demand parameters (EDPs) based on the material damage are proposed to identify the structural engineering limit states and damage states at the member level. The case of x HP is provided as an example to illustrate the methodology and discuss the probable nonlinear response and structural damage state. The concrete damage evolution, reinforcement stresses, and drift ratios of the RCF-SW structure are presented, and the engineering limit states and structural damage states are identified. In comparison with the drift ratio index, the EDPs based on material damage are more suitable for identifying the damage state of the RCF-SW structure, whose damage is controlled by the damage of the RC members.


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## Body

## 1. Introduction

In recent years, performance-based seismic design (PBSD) has emerged as one of the most important advances in seismic engineering [1–3]. In this methodology, the structural criteria are expressed in terms of achieving a performance objective, which is the coupling of an expected structural damage level and an expected earthquake severity level. The performance levels describe the structural damage states and consequential losses which may be incurred in terms of casualties, property, and operational capacity [4–6].In the design of hydraulic structures, the traditional seismic design focuses on protecting human life by preventing local or global collapse at a specific earthquake level. In recent years, engineering communities have been aware of the importance of property and other economic losses caused by more frequent earthquakes. Thus, PBSD has become useful for the seismic evaluation of hydraulic structures, such as dams and water intake towers. The seismic performance assessment methods and nonlinear dynamic analysis methods of dams are well established [7–13]. However, few experimental and analytical studies have investigated the seismic performance of hydropower plants (HPs). In fact, the investigation of damage incurred by hydropower stations during the Wenchuan earthquake indicates that HPs are damaged more heavily than dams [14].Generally, an HP can be divided into three parts: the main powerhouse, erection bay, and auxiliary powerhouse. The main powerhouse and auxiliary powerhouse house the turbine generator units and auxiliary electrical and mechanical equipment (see Figure1). The safety of HPs ensures the power generation and staff safety. Thus, the seismic performance of HPs should be taken seriously. Typically, HPs are divided into substructures and superstructures according to their distinctive structural features (see Figure 1). The substructures are mass concrete structures, wherein turbine generator units are set, while the superstructures are composed of reinforced concrete (RC) frames and shear walls. A bridge crane travels along the tracks supported by the RC frame in the main powerhouse and erection bay. The crane is used for the installation or maintenance of the generator units and other types of equipment. Because of the sharp distinctions in mass and stiffness between the substructure and the superstructure, the superstructures are vulnerable during earthquakes [15, 16]. For example, the superstructure of the CaoPo HP was severely damaged during the Wenchuan earthquake. As shown in Figure 2, several cracks appeared, and the joints between the endwalls and the sidewalls opened. Though the HP did not collapse in the earthquake, the repair of structures and equipment was time-consuming and expensive. Moreover, a long-lasting outage led to a great financial loss. Therefore, the need to shift the focus of HP seismic design from strength to performance has been highlighted.Figure 1
Basic components of an HP: (a) typical layout and (b) typical profile of the main powerhouse.
(a)(b)Figure 2
Damage caused by Wenchuan earthquake in CaoPo HP.In the PBSD process, the identification and assessment of the structural performance are critical tasks. The PBSD implementation requires the prediction of structural demands and capacities and the identification and quantification of the damage state associated with different performance levels. In traditional design, the seismic performance of HPs is assessed on the basis of simple stress or section-force checks, which are obtained by linear earthquake analysis [17, 18]. However, it is difficult to use linear analysis to identify the structural performance levels when the structural responses change from the elastic state to a failure limit state. Incremental dynamic analysis (IDA) is a well-known method of quantitatively estimating the structural limit states. In IDA, the intensity of the ground motion applied to the structure is increased incrementally until the limit states are reached [19]. This method has been widely applied to assess the collapse capacity of buildings and bridges [20–22].In an IDA study, the results are presented in terms of earthquake intensity-damage measure curves. The earthquake intensity is defined by the intensity measure (IM). The damage is defined as the degradation of structural bearing capacity and durability. The PGA and spectral accelerations are often used as the IM. Generally, to evaluate the damage in a structure, the damage measures (DMs) or engineering demand parameters (EDPs) are used. Commonly used DMs or EDPs include stress, strain, deformation, reactions, crack length and stiffness, and energy dissipations [4, 8, 23–27]. Previous experimental studies indicate that none of these DMs consistently predict observed damage limit state [28–30]. Thus, the quantitative relationships between the EDPs and the performance levels and a clear definition of limit states are still under investigation. For RC frame structures, global responses of the structure are evaluated in terms of peak roof drift ratios, peak interstory drift ratios, interstory drift ratios envelopes, normalized roof displacements relative to the motion of the center of gravity of the roof, and dissipated energy. Local responses assessed include moment-curvature or moment-rotation response in beams and columns as well as the hysteretic energy dissipated at selected sections of the structure [31]. In the structural damage assessment of RC frame structures, the story drift ratio is well known and frequently utilized. FEMA-273 [4], FEMA-356 [5], GB 50011-2010 [32], Smith [33], and Xin et al. [34] provide various deformation limits or drift limits for RC frames and shear walls to define the structural performance levels. However, Ghobarah et al. [35] and Hancock et al. [36] showed that story drift ratio did not account for the influence of cumulative damage due to repeated inelastic deformation and was properly considered for the damage caused by extreme displacement. Belejo et al. [31] and Chandramohan et al. [37] concluded that the drift ratio index had a lack of capability to capture the effect of degrading energy capacity and in-cycle strength degradation. Moreover, although the story drift is suitable for interpreting the overall structural damage state, it cannot predict the progressive damage incurred by the RC members. However, the damage incurred by an RC structure is generally related to the failure of component members. Particularly, in the HP, the RC columns and beams are much stronger than those of ordinary buildings. Thus, the prediction of damage at element level is more important.Generally, the failure of RC members is mainly caused by the crushing of concrete, which begins with the spalling of the concrete cover and ends with the crushing of the concrete core. Because finite element analysis (FEA) tools and computer technology have been rapidly evolving in recent years, given the advances in computational methods for nonlinear structural analysis, it has become feasible and more convenient to use damage constitutive models to track the process of damage occurrence in RC structures [38–40]. The mechanical properties of concrete are controlled by the generation and growth of microcracks. The microcracks in concrete will expand, grow, and converge under various loads, and then the macrocracks form, leading to strength degradation or even material failure. In the damage constitutive model, damage variables are introduced to characterize the effect of microcracks on macromechanical properties of concrete. The damage variables of concrete are usually defined as the degradation of elastic modulus. According to tensile and compression tests of concrete, semiempirical relationships between damage variables and macromechanical parameters, such as strain, can be obtained. The applications of the damage constitutive model exhibit computational efficiency and suitability to the simulation of the initiation and propagation of concrete material deterioration against strong earthquakes, and the calculated tensile and compressive damage variables reveal the essential reasons for the occurrence of structural damage at the material level. Therefore, in recent years, various EDPs and DMs based on the material damage have been proposed [41–43]. Most of these DMs consider the damage of the most critical fibers of concrete and reinforcement as representative damage for each section, and the structural damage indices are typically defined as the function of the maximum material damage values of concrete and reinforcement. However, the maximum material damage cannot demonstrate the structural damage extent and progress at all times. For example, the large tensile damage and the large damage in the local area cannot predict the failure of an RC member. Therefore, the structural damage indices based on material damage require further investigation.In this study, to assess the damage incurred by RC frame-shear wall (RCF-SW) structures in HPs, an IDA investigation was conducted. The plastic-damage model for concrete proposed by Lee and Fenves [44] was used to carry out nonlinear analysis and determine the material damage propagation in RCF-SW structures. Several EDPs based on material damage have been proposed to predict the structural damage states of the RCF-SW at the member level. These EDPs are linked to engineering limit states such as the cracking, spalling, and crushing of concrete, and the relationships between the engineering limit state and the structural damage state have been established. Finally, the structural damage states have been assessed by the EDPs.


## 2. Nonlinear FEA

Using the commercial FEA software ABAQUS [44], nonlinear time-history analyses were performed to predict the performance of the HPs. The main issues that significantly influence the seismic responses of HPs are the constitutive behavior relationships employed for concrete and steel.


### 2.1. Plastic-Damage Model of Concrete

The plastic-damage model of concrete proposed by Lee and Fenves [45] was employed to simulate the nonlinear constitutive behavior of concrete, and this model is available in ABAQUS. The basic notion of the plastic-damage model is the coupling of isotropic damaged elasticity with isotropic tensile and compressive plasticity to describe the irreversible damage incurred during the loading process. In this model, the stress-strain relationship of concrete is expressed as follows:(1)σ=1−dD0el:ε−εpl=Del:ε−εpl,where ε is the total strain; εpl is plastic strain; D0el is the initial elastic stiffness of the undamaged concrete; Del equaling 1−dD0el is the elastic stiffness of the damaged concrete; d is the damage variable reflecting the degradation of stiffness. With the accumulation of concrete damage, the value of d varies from 0 (no damage) to 1 (fully damaged).The definition of the scalar degradation variabled must be consistent with the uniaxial monotonic responses (uniaxial damage variable in compression dc and uniaxial damage variable in tension dt) and should also capture the complexity associated with the degradation mechanisms under cyclic loading. With regard to the general multiaxial stress conditions, the model makes the following assumption:(2)1−d=1−stdc1−scdt,0≤st,sc≤1,st=1−wtrσ¯^,0≤wt≤1,sc=1−wc1−rσ¯^,0≤wc≤1,where variables st and sc represent the stiffness recovery effect as a function of stress state rσ. rσ is a stress weight factor equal to one if all principal stresses are positive or equal to zero if all principal stresses are negative. The parameters wt and wc control the recovery degree of the tensile stiffness and compressive stiffness. In most quasibrittle materials, including concrete, it has been observed experimentally that the compressive stiffness is recovered upon crack closure as the load shifts from tension to compression. However, once crushing microcracks have developed, the tensile stiffness is not recovered as the load shifts from compression to tension. This behavior is used by default in ABAQUS, as shown in Figure 3.Figure 3
Uniaxial load cycle assuming default values for the stiffness recovery factors (wt=0 and wc=1) [44].


### 2.2. Model of Reinforcing Bars

The bilinear kinematic hardening constitutive model (see Figure4(a)) was recommended for the reinforcing bars [46]. The hardening modulus was determined according to the stress-strain relationship of the steel material shown in Figure 4(b). By drawing a straight line between the yield strength point (fy; εy) and the ultimate strength point (k4fy; k2εy), it can be seen that the slope of the straight line is the equivalent hardening modulus of the steel material.Figure 4
Constitutive model of steel bar. (a) Bilinear kinematic hardening constitutive model. (b) Response of bars under uniaxial tensile load [45].
(a)(b)


### 2.3. Comparison to Test Data

To validate the nonlinear FE model, predictions using the model are compared to cyclic quasistatic test on reinforced concrete columns conducted by Du [43]. The predictions of the tested column specimen are shown in Figure 5. It can be seen that the overall behavior is well predicted as evidenced by the loading and unloading branches. The largest tensile damage concentration predicted was located in the plastic hinge region at the column base. As can be seen from the figure, the predicted damage in tension and compression is in a good agreement with the concrete cracks and spalling shown in the test. The excellent prediction reflects that the model does a good job of taking into account the concrete crack closure mechanism, and the local behavior of the reinforced concrete element, such as cracking of concrete, progressive spalling of the concrete cover, and yielding of the reinforcement, can be well predicted.Figure 5
Prediction of the behavior of column tested by Du [43]. (a) Column specimen. (b) Force-displacement response. (c) Damage in tension prediction. (d) Damage in plastic hinge zone at the end of the test. (e) Damage in compression prediction.
(a)(b)(c)(d)(e)


## 2.1. Plastic-Damage Model of Concrete

The plastic-damage model of concrete proposed by Lee and Fenves [45] was employed to simulate the nonlinear constitutive behavior of concrete, and this model is available in ABAQUS. The basic notion of the plastic-damage model is the coupling of isotropic damaged elasticity with isotropic tensile and compressive plasticity to describe the irreversible damage incurred during the loading process. In this model, the stress-strain relationship of concrete is expressed as follows:(1)σ=1−dD0el:ε−εpl=Del:ε−εpl,where ε is the total strain; εpl is plastic strain; D0el is the initial elastic stiffness of the undamaged concrete; Del equaling 1−dD0el is the elastic stiffness of the damaged concrete; d is the damage variable reflecting the degradation of stiffness. With the accumulation of concrete damage, the value of d varies from 0 (no damage) to 1 (fully damaged).The definition of the scalar degradation variabled must be consistent with the uniaxial monotonic responses (uniaxial damage variable in compression dc and uniaxial damage variable in tension dt) and should also capture the complexity associated with the degradation mechanisms under cyclic loading. With regard to the general multiaxial stress conditions, the model makes the following assumption:(2)1−d=1−stdc1−scdt,0≤st,sc≤1,st=1−wtrσ¯^,0≤wt≤1,sc=1−wc1−rσ¯^,0≤wc≤1,where variables st and sc represent the stiffness recovery effect as a function of stress state rσ. rσ is a stress weight factor equal to one if all principal stresses are positive or equal to zero if all principal stresses are negative. The parameters wt and wc control the recovery degree of the tensile stiffness and compressive stiffness. In most quasibrittle materials, including concrete, it has been observed experimentally that the compressive stiffness is recovered upon crack closure as the load shifts from tension to compression. However, once crushing microcracks have developed, the tensile stiffness is not recovered as the load shifts from compression to tension. This behavior is used by default in ABAQUS, as shown in Figure 3.Figure 3
Uniaxial load cycle assuming default values for the stiffness recovery factors (wt=0 and wc=1) [44].


## 2.2. Model of Reinforcing Bars

The bilinear kinematic hardening constitutive model (see Figure4(a)) was recommended for the reinforcing bars [46]. The hardening modulus was determined according to the stress-strain relationship of the steel material shown in Figure 4(b). By drawing a straight line between the yield strength point (fy; εy) and the ultimate strength point (k4fy; k2εy), it can be seen that the slope of the straight line is the equivalent hardening modulus of the steel material.Figure 4
Constitutive model of steel bar. (a) Bilinear kinematic hardening constitutive model. (b) Response of bars under uniaxial tensile load [45].
(a)(b)


## 2.3. Comparison to Test Data

To validate the nonlinear FE model, predictions using the model are compared to cyclic quasistatic test on reinforced concrete columns conducted by Du [43]. The predictions of the tested column specimen are shown in Figure 5. It can be seen that the overall behavior is well predicted as evidenced by the loading and unloading branches. The largest tensile damage concentration predicted was located in the plastic hinge region at the column base. As can be seen from the figure, the predicted damage in tension and compression is in a good agreement with the concrete cracks and spalling shown in the test. The excellent prediction reflects that the model does a good job of taking into account the concrete crack closure mechanism, and the local behavior of the reinforced concrete element, such as cracking of concrete, progressive spalling of the concrete cover, and yielding of the reinforcement, can be well predicted.Figure 5
Prediction of the behavior of column tested by Du [43]. (a) Column specimen. (b) Force-displacement response. (c) Damage in tension prediction. (d) Damage in plastic hinge zone at the end of the test. (e) Damage in compression prediction.
(a)(b)(c)(d)(e)


## 3. IDA

### 3.1. Earthquake Ground Motions and IM

In an IDA study, a series of earthquake ground motions is applied to the structure. By increasing the shaking intensity, the structural initial elastic state shifts to an inelastic state and finally to a collapsed state. Thus, the seismic performance and progressive limit states of the structure can be identified up to its collapse. The most frequently selected IMs are the PGA, PGV, and 5%-damped spectral acceleration at the fundamental period of the structureSaT1,5%. Alembagheri and Ghaemian [9] reported that using SaT1,5% can obtain less scattered results. Thus, in this study, SaT1,5% was selected as the IM.


### 3.2. EDPs

Considering the huge loads and importance of HPs, the size of the RC members and the quantity of reinforcement are frequently large. Thus, the collapse of the entire HPs hardly ever occurs during earthquakes. Related studies [15, 16] have shown that the cracking and crushing of the RC columns and walls, which is induced by cyclic shaking and flexural loads, is the main damage mode of HPs.Kunnath et al. [28] conducted a comprehensive experimental study to investigate cumulative damage in RC columns under cyclic loads and typical earthquakes. Du [43] conducted pseudostatic tests on RC columns, and the structural damage process and the failure modes were presented in detail. A set of 21 RC column specimens test at the University of Sherbrooke under cyclic flexure represented the structural damage evolution of RC columns [47]. These experimental studies correlated visually observed damage during testing with damage limit states. The correlations of damage limit states with visual observations are summarized in Table 1. As is shown in the table, the critical task of the damage state identification is tracking the cracking and spalling process of concrete and the buckling process of bars.Table 1
Correlation of damage limit states with visual observation [28, 43, 47].
Damage stateDescriptionVisual observationNoneNo visible damage, either cosmetic or structuralNo visible cracksInsignificantDamage requires no more than cosmetic repair. No structural repairs are necessaryHairline cracksMinor spallingModerateRepairable structural damage has occurred. The existing element can be repaired essentially in place, without substantial demolition or replacement of elementsExcessive spallingExposed reinforcementNo buckling of barsHeavyDamage is so extensive that repair of elements either is not feasible or requires major demolition or replacementBuckling/fracture of barsBased on the test results, the material damage zone distribution diagram of RC columns can be simplified to the shadows shown in Figure6. Usually, the tensile and compressive damage originate at the column base and develop along the section height and column height directions. Under earthquake excitation, tensile damage may originate at one side of the column, and d is defined as the tensile damage evolution depth at the column base. However, tensile damage develops quickly, occurs at the other side of the column, and extends over the entire column base. The tensile damage reduces slowly above the column base over the height of the column. Additionally, the cracks cutting through the sections appear in sequence over the height of the column. Then, a plastic hinge zone starts to form near the column base [43, 47]. Once the reinforcement yields and the plastic hinge zone forms, the displacement of the column increases more rapidly as the loads increase. Therefore, the formation of the plastic hinge is a limit state for the RC columns.Figure 6
Material damage distribution in column under flexural loads [43].Generally, the tensile damage incurred by the RC columns under flexural loads will be more severe than the compressive damage. However, the collapse of the RC columns is related to the severe crushing rather than cracking. As shown in Figure6, the compressive damage decreases rapidly from the concrete cover to the concrete core owing to the reinforcement. The spalling of the concrete cover occurs first, and then the concrete core begins to crush as the compressive damage evolves [43, 47]. The extent of spalling and crushing of the concrete reveals the damage state incurred by the RC frame. The damage distribution of the wall in the thickness direction is similar to that of the column. For the walls, h represents the wall thickness.Cardona et al. [48] conducted a series of experimental tests and numerical calculations with RC columns and reported the relationship between the concrete material damage and engineering limit state, such as cracking, spalling, and crushing. Based on related investigation on the damage incurred by RC columns, in this study, several EDPs are proposed based on material damage to evaluate the damage state of the RC members. These EDPs include the following:(i)
d/h, the ration of tensile damage (≥ 0.7) evolution depth d at the column base section to section height h.(ii)
Dc−cover, the average compressive damage of concrete cover at the column base section.(iii)
Dc−core, the average compressive damage of concrete core at the column base section.(iv)
σs, the maximum value of reinforcement stress.For normal strength concrete, macroscopic cracks appear when the tensile damage value reaches approximately 0.6-0.7. Therefore, the tensile damage evolution indexd/h is obtained according to the profile of tensile damage values larger than 0.7 to describe the crack propagation lengthening at the column base. When d/h=1, the crack cutting through the column base appears, and the plastic hinge initiates. The spalling of the concrete cover begins at Dc−cover=0.1, and the crushing of the concrete core begins at Dc−core=0.1. When Dc−cover is equal to 0.5, obvious spalling of concrete cover occurs. When Dc−cover is equal to 0.8, the concrete cover spalling becomes severe. Moreover, the crushing of the concrete core becomes severe when Dc−core is equal to 0.5 [48].


### 3.3. Damage States

This current study linked EDPs based on the material damage to the engineering limit states such as concrete cracking, concrete cover spalling, and concrete core crushing (Table2). Then, in accordance with the engineering limit states, this current study divided the damage states into four levels: negligible, light, moderate, and severe.Table 2
Relationship between damage states, engineering limit states, and material damage.
Damage stateEngineering limit stated/hDc−coverDc−coreσsNegligibleConcrete cover cracking onset0.1≈0≈0LightConcrete cover spalling onset0.1Plastic hinge initiating1ModerateConcrete cover important spalling0.5Concrete core crushing onset0.1Reinforcement yieldingσySevereConcrete cover severe spalling0.8Concrete core important crushing0.5Note.σy is the yield strength of reinforcement.At the first damage level, most of the concrete is still in the elastic stage. Because the tensile strength is far less than the compressive strength, cracks may appear at the local zones, such as the ends or surface of the RC members. However, these small cracks do not exert significant influence on the bearing behavior of the members. Therefore, at this stage, the damage of the entire structure is negligible.At the second damage level, the stiffness of the structure is reduced owing to the rapid evolution of concrete tensile damage. The cracks at the column base penetrate the entire section, and new cracks appear continuously along the height of the members. Concurrently, the reinforcement stresses increase rapidly. At this stage, the plastic hinge begins to form at the column base. While the concrete compressive damage in the RC member is still at a low level, only the spalling of the concrete cover initiates at local zones. At this stage, the structure incurs only light damage.At the third damage level, the stiffness of the structure is reduced owing to the evolution of concrete compressive damage. The compressive damage in concrete cover has gone through a rapid development stage and enters into a smooth development stage. The spalling of concrete cover becomes important because serious spalling of concrete cover leads to the exposure of reinforcement. With the increase of the compressive damage zones and extent of compressive damage, the spalling of the concrete cover and crushing of the concrete core become obvious, and the reinforcement yields concurrently. The degeneration of compressive capacity exerts a significant influence on the structural bearing capacity. Thus, at this stage, the damage incurred by the structure is regarded as moderate.At the last damage level, the concrete compressive damage accumulates, and the spalling of the concrete cover and the crushing of the concrete core become severe. The plastic hinge enters into the failure stage, and the stiffness of the structure becomes low and results in a significant decrease of the structural bearing capacity. At this damage state, the structure tends to collapse.


## 3.1. Earthquake Ground Motions and IM

In an IDA study, a series of earthquake ground motions is applied to the structure. By increasing the shaking intensity, the structural initial elastic state shifts to an inelastic state and finally to a collapsed state. Thus, the seismic performance and progressive limit states of the structure can be identified up to its collapse. The most frequently selected IMs are the PGA, PGV, and 5%-damped spectral acceleration at the fundamental period of the structureSaT1,5%. Alembagheri and Ghaemian [9] reported that using SaT1,5% can obtain less scattered results. Thus, in this study, SaT1,5% was selected as the IM.


## 3.2. EDPs

Considering the huge loads and importance of HPs, the size of the RC members and the quantity of reinforcement are frequently large. Thus, the collapse of the entire HPs hardly ever occurs during earthquakes. Related studies [15, 16] have shown that the cracking and crushing of the RC columns and walls, which is induced by cyclic shaking and flexural loads, is the main damage mode of HPs.Kunnath et al. [28] conducted a comprehensive experimental study to investigate cumulative damage in RC columns under cyclic loads and typical earthquakes. Du [43] conducted pseudostatic tests on RC columns, and the structural damage process and the failure modes were presented in detail. A set of 21 RC column specimens test at the University of Sherbrooke under cyclic flexure represented the structural damage evolution of RC columns [47]. These experimental studies correlated visually observed damage during testing with damage limit states. The correlations of damage limit states with visual observations are summarized in Table 1. As is shown in the table, the critical task of the damage state identification is tracking the cracking and spalling process of concrete and the buckling process of bars.Table 1
Correlation of damage limit states with visual observation [28, 43, 47].
Damage stateDescriptionVisual observationNoneNo visible damage, either cosmetic or structuralNo visible cracksInsignificantDamage requires no more than cosmetic repair. No structural repairs are necessaryHairline cracksMinor spallingModerateRepairable structural damage has occurred. The existing element can be repaired essentially in place, without substantial demolition or replacement of elementsExcessive spallingExposed reinforcementNo buckling of barsHeavyDamage is so extensive that repair of elements either is not feasible or requires major demolition or replacementBuckling/fracture of barsBased on the test results, the material damage zone distribution diagram of RC columns can be simplified to the shadows shown in Figure6. Usually, the tensile and compressive damage originate at the column base and develop along the section height and column height directions. Under earthquake excitation, tensile damage may originate at one side of the column, and d is defined as the tensile damage evolution depth at the column base. However, tensile damage develops quickly, occurs at the other side of the column, and extends over the entire column base. The tensile damage reduces slowly above the column base over the height of the column. Additionally, the cracks cutting through the sections appear in sequence over the height of the column. Then, a plastic hinge zone starts to form near the column base [43, 47]. Once the reinforcement yields and the plastic hinge zone forms, the displacement of the column increases more rapidly as the loads increase. Therefore, the formation of the plastic hinge is a limit state for the RC columns.Figure 6
Material damage distribution in column under flexural loads [43].Generally, the tensile damage incurred by the RC columns under flexural loads will be more severe than the compressive damage. However, the collapse of the RC columns is related to the severe crushing rather than cracking. As shown in Figure6, the compressive damage decreases rapidly from the concrete cover to the concrete core owing to the reinforcement. The spalling of the concrete cover occurs first, and then the concrete core begins to crush as the compressive damage evolves [43, 47]. The extent of spalling and crushing of the concrete reveals the damage state incurred by the RC frame. The damage distribution of the wall in the thickness direction is similar to that of the column. For the walls, h represents the wall thickness.Cardona et al. [48] conducted a series of experimental tests and numerical calculations with RC columns and reported the relationship between the concrete material damage and engineering limit state, such as cracking, spalling, and crushing. Based on related investigation on the damage incurred by RC columns, in this study, several EDPs are proposed based on material damage to evaluate the damage state of the RC members. These EDPs include the following:(i)
d/h, the ration of tensile damage (≥ 0.7) evolution depth d at the column base section to section height h.(ii)
Dc−cover, the average compressive damage of concrete cover at the column base section.(iii)
Dc−core, the average compressive damage of concrete core at the column base section.(iv)
σs, the maximum value of reinforcement stress.For normal strength concrete, macroscopic cracks appear when the tensile damage value reaches approximately 0.6-0.7. Therefore, the tensile damage evolution indexd/h is obtained according to the profile of tensile damage values larger than 0.7 to describe the crack propagation lengthening at the column base. When d/h=1, the crack cutting through the column base appears, and the plastic hinge initiates. The spalling of the concrete cover begins at Dc−cover=0.1, and the crushing of the concrete core begins at Dc−core=0.1. When Dc−cover is equal to 0.5, obvious spalling of concrete cover occurs. When Dc−cover is equal to 0.8, the concrete cover spalling becomes severe. Moreover, the crushing of the concrete core becomes severe when Dc−core is equal to 0.5 [48].


## 3.3. Damage States

This current study linked EDPs based on the material damage to the engineering limit states such as concrete cracking, concrete cover spalling, and concrete core crushing (Table2). Then, in accordance with the engineering limit states, this current study divided the damage states into four levels: negligible, light, moderate, and severe.Table 2
Relationship between damage states, engineering limit states, and material damage.
Damage stateEngineering limit stated/hDc−coverDc−coreσsNegligibleConcrete cover cracking onset0.1≈0≈0LightConcrete cover spalling onset0.1Plastic hinge initiating1ModerateConcrete cover important spalling0.5Concrete core crushing onset0.1Reinforcement yieldingσySevereConcrete cover severe spalling0.8Concrete core important crushing0.5Note.σy is the yield strength of reinforcement.At the first damage level, most of the concrete is still in the elastic stage. Because the tensile strength is far less than the compressive strength, cracks may appear at the local zones, such as the ends or surface of the RC members. However, these small cracks do not exert significant influence on the bearing behavior of the members. Therefore, at this stage, the damage of the entire structure is negligible.At the second damage level, the stiffness of the structure is reduced owing to the rapid evolution of concrete tensile damage. The cracks at the column base penetrate the entire section, and new cracks appear continuously along the height of the members. Concurrently, the reinforcement stresses increase rapidly. At this stage, the plastic hinge begins to form at the column base. While the concrete compressive damage in the RC member is still at a low level, only the spalling of the concrete cover initiates at local zones. At this stage, the structure incurs only light damage.At the third damage level, the stiffness of the structure is reduced owing to the evolution of concrete compressive damage. The compressive damage in concrete cover has gone through a rapid development stage and enters into a smooth development stage. The spalling of concrete cover becomes important because serious spalling of concrete cover leads to the exposure of reinforcement. With the increase of the compressive damage zones and extent of compressive damage, the spalling of the concrete cover and crushing of the concrete core become obvious, and the reinforcement yields concurrently. The degeneration of compressive capacity exerts a significant influence on the structural bearing capacity. Thus, at this stage, the damage incurred by the structure is regarded as moderate.At the last damage level, the concrete compressive damage accumulates, and the spalling of the concrete cover and the crushing of the concrete core become severe. The plastic hinge enters into the failure stage, and the stiffness of the structure becomes low and results in a significant decrease of the structural bearing capacity. At this damage state, the structure tends to collapse.


## 4. FEA of Jx HP

The Jx hydropower station is still in the design process. The installed generation capacity of the plant is 560 MW and is provided by four water-turbine generator sets. The HP is located at the toe of the concrete gravity dam. The site of the hydropower station is in a seismically active region. The PGA with a probability of exceedance 2% per 50 years is 0.331 g, and that with a probability of exceedance of 1% per 100 years is 0.498 g.A finite element (FE) model was developed as shown in Figure7. The model consists of the HP and foundation. The ABAQUS software was used to conduct the analysis. The concrete structure and foundation were meshed using C3D8 solid elements, the steel structure was meshed using S4 shell elements, and the roof grid was meshed using T3D2 truss elements. A viscous-spring artificial boundary was used to simulate the effect of radiation damping, and the spring-dashpot system was modeled using spring elements and dashpot elements. Considering the material nonlinearity of the RC structure, the steel bars were also simulated. In this study, an embedded discrete reinforcement model was employed and a 2-node truss element was used. The reinforcement elements were assumed to be fully embedded in the solid concrete element without sliding. The FE model contains 329,667 elements and 347,956 nodes.Figure 7
Geometry and FE mesh of Jx HP. (a) Global model. (b) Details of the powerhouse. (c) Substructure. (d) RCF-SW. (e) Reinforcement grids.
(a)(b)(c)(d)(e)The seismic analysis focuses on the superstructure of the powerhouse; therefore, only the steel bars in the walls, columns, and floors above the generator floor were included in the model. The mass concrete structure under the generator floor has a good seismic performance, and cracks are typically induced by internal water pressure. However, the local cracks in the mass concrete cannot significantly influence the seismic performance of the superstructure. Thus, the reinforcement in the concrete mass under the generator floor was not simulated, and the material nonlinearity of the mass concrete was ignored. A previous study [49] has reported that this assumption has little effect on the dynamic characteristics of the superstructure and can reduce the required computational cost.The plastic-damage model was used to describe the damage caused by the yielding of the concrete, and the Mazars damage model was used to calculate the tensile and compressive damage values according to the stress and strain states of the concrete. A bilinear kinematic hardening model was employed for steel. A linear elastic constitutive model was used for the foundation rock to reduce the computational cost. The material properties used in the simulation are listed in Table3. The uniaxial stress-strain and damage-strain curves in tension and compression of concrete are shown in Figure 8. According to GB 50010-2010 [46], the ultimate strain of the bars is taken as 0.05, so the yield strain εy = 0.002 and k2=25.Table 3
Mechanical properties of materials.
MaterialYoung’s modulus (MPa)Poisson’s ratioUnit weight (kN/m3)Axial tensile strength (MPa)Axial compressive strength (MPa)Ultimate tensile strength (MPa)Concrete28,0000.167241.7816.7Steel bar200,0000.378.5400400540Rock80000.2526Figure 8
Uniaxial stress-strain and damage-strain curves of concrete. (a) Compression and (b) tension.
(a)(b)In this study, the ten earthquake ground motions listed in Table4 were selected for IDA investigation. These records are downloaded from Pacific Earthquake Engineering Research Center (PEER) Ground Motion Database (https://peer.berkeley.edu/peer-strong-ground-motion-databases). The 5%-damped acceleration response spectrum curves of all earthquake records are shown in Figure 9. The spectral accelerations at the fundamental period of the structure 0.62 s (denoted as Sa) are also listed in Table 4. In the IDA, for each record, the IM SaT1,5% was set to increase from 0.05 g to 1.0 g with an interval of 0.05 g or 1.0 g, and for each earthquake intensity, a nonlinear analysis was done. If the original record is denoted as at, the amplitude modulation record used in the analysis aλt=λat. Here, the amplitude modulation factor λ is equal to SaT1,5%/Sa, and it is a positive value which can be greater than 1 or less than 1.Table 4
Earthquake ground motions used in the IDA.
Number (g)EarthquakeYearStationMagnitudeRjb (km)Rrup (km)PGA (g)Sa (5%) atT1 = 0.620 s1Kobe (Japan)1995Kakogawa (CUE90)6.922.522.50.34470.4312Chi-Chi (Taiwan)1999TCU0457.6226260.3610.4043Friuli (Italy)1976Tolmezzo (000)6.514.9715.820.3600.3354Imperial Valley (USA)1979El Centro Array #26.5317.3218.810.31520.6165Imperial Valley (USA)1979El Centro Array #96.530.560.560.2120.5116Loma Prieta (USA)1989Emeryville6.9376.8776.970.24980.59787Loma Prieta (USA)1989Gilroy Array #36.9312.2312.820.36740.4258Trinidad (USA)1983Rio Dell Overpass_ E5.768.0268.580.19360.12539Northridge (USA)1994Castaic-Old Ridge Route6.6920.1120.720.56830.793910Koyna (India)1967IIKD0066.30.4640.372Figure 9
Acceleration response spectrum curves of all earthquake records used in the IDA.For each seismic analysis, two steps were set. The first step is a static load step, during which the gravity, hydrostatic loads, and live loads on each floor under normal operation condition were added to obtain the initial displacement and stress states for the dynamic step. The second step is a dynamic load step, wherein the earthquake wave is input, and time-history analysis is carried out. Because, under earthquake conditions, the RCF-SW of HP is more vulnerable in the stream direction, in this study, the earthquake waves were only input in the stream direction. Structural damping was incorporated using Rayleigh-type damping and a 5% damping ratio was assumed.


## 5. Results and Discussion

### 5.1. Damage Evolution

The ultimate damage state of the superstructure depends on the structural features and the input earthquake waves. However, all of the results under each record reveal a similar damage propagation process. In this section, we present the damage of the RCF-SW structure under the Koyna record.During an earthquake, the RCF-SW structures are shaken cyclically, and the RC members will have flexure and shear behavior. When the intensity of the earthquake is large enough, the RC members will incur damage. Figure10 shows the tensile and compressive damage profiles of the RCF-SWs under the Koyna record scaled to various intensity levels. As can be seen in Figure 10, the damage to the columns at the downstream side was more severe than that of the columns at the upstream side. The reason for this is that the auxiliary powerhouse was on the downstream side; thus, it provided support to the downstream wall, such that the stiffness changed more abruptly at the downstream column bases. Figure 11 shows the tensile and compressive damage profiles of column B (see Figure 7(d)) at the downstream side. The simplified damage distribution diagrams shown in Figure 6 are in good agreement with the damage distribution profiles of column B.Figure 10
Ultimate damage profiles of RCF-SW structure under Koyna record.Figure 11
Ultimate damage profiles of column B under Koyna record.The tensile damage shown in Figure11 is larger than 0.7; therefore, the damage profiles show the possible cracking zones. Because the section size changes sharply at the column base, the cracking initiates at the column base when SaT1,5% is equal to 0.05 g. The cracks develop rapidly as SaT1,5% increases. When SaT1,5% is greater than 0.5 g, the concrete in approximately half the height of the column cracks and new cracks appear at the connection areas of the walls and floors. When SaT1,5% reaches 1.0 g, the RCF-SWs become severely damaged. The columns are completely damaged and a crack penetrates the bottom of the upstream wall.Additionally, the compressive damage initiates at the column base atSaT1,5%=0.2g and reduces from the column surface to the core. Moreover, there is no complete compressive damage, even at SaT1,5%=1.0g. The maximum compressive damage of the concrete cover does not exceed 0.6, and the maximum damage of the concrete core does not exceed 0.1 at SaT1,5%=1.0g. Increasing the shaking intensity may result in concrete crushing; however, the vastness and diffusion of the tensile damage are so significant that an accurate interpretation of the results is not possible.As can be seen, the main damage modes of the HP are the cracking, spalling, and crushing of the columns and walls. Owing to the plastic-damage model of concrete, we can obtain the detailed damage states of the RC members and predict the engineering limit states conveniently.


### 5.2. IDA Results for All Records

In this section, the IDA results of the RCF-SW structure under all records are present. Figure12 shows the IDA curves for the EDPs of individual records and their mean, median, and 16%, and 84% fractiles. Ideally, an IDA illustrates the responses of the structure by each ground motion record scaled to multiple intensities. Thus, it is possible to define the capacity and limit states of the structure, including the failure modes. However, for RC structures, the material damage induces nonconvergence problems when the intensity of the record is increased to a certain value. Nevertheless, this numerical instability indicates the dynamic instability from one aspect. In this study, when SaT1,5% exceeded 1.0 g, the tensile damage was so severe that convergence and accuracy could not be ensured simultaneously. Thus, all of the IDA curves were plotted until SaT1,5%=1.0g. At the point of SaT1,5%=1.0g, the PGA of the record varied from 0.7 g to 1.6 g. Moreover, the intensities of all records were sufficiently large, considering that the PGA at the station site with an exceedance probability of 1% per 100 years is 0.498 g.Figure 12
IDA curves of EDPs. (a)d/h. (b)Dc−cover of column B. (c) Dc−core of column B. (d) Reinforcement stress.
(a)(b)(c)(d)As can be seen, the curves under different records exhibited a similar trend. However, large variation existed between the different records, particularly at high-intensity levels. When the crack penetrated the column base and the reinforcement yielded, the variations of thed/h ratio and the reinforcement stress curves became small. The mean and median curves are in better agreement at low-intensity levels, which means that the response values are distributed more evenly at low intensity. At high-intensity levels, the results were scattered by the different damage processes under various earthquake conditions.Figure13 shows the mean IDA curves of the EDPs based on the material damage. As shown in Figure 13, cracking initiated at the column base even at very low-intensity levels. After SaT1,5%=0.1g, the crack extended rapidly. Up to SaT1,5%=0.3g, the crack penetrated the column base under all records. The plastic hinge formed and developed from SaT1,5%=0.3g onwards. When SaT1,5%≤0.05g, there was no compressive damage for most records. The average compressive damage of the column cover Dc−cover ranged from 0 to 0.55. The spalling of the concrete cover started at approximately SaT1,5%=0.3g on average and reached up to SaT1,5%=1.0g; severe spalling appeared only under three records. The compressive damage of the concrete core was slighter than that of the concrete cover. The average compressive damage of the column core Dc−core ranged from 0 to 0.3. The crushing of the concrete core started at approximately SaT1,5%=0.55g, on average, and reached up to SaT1,5%=1.0g; none of the results indicates severe crushing.Figure 13
Mean IDA curves of EDPs. (a)d/h. (b) Dc−cover of column B. (c) Dc−core of column B. (d) Reinforcement stress.
(a)(b)(c)(d)The reinforcement stresses were mainly affected by the tensile damage. FromSaT1,5%=0.05g onwards, the reinforcement stresses began to increase rapidly. After SaT1,5%=0.3g, the stress values of various records became obviously scattered. At this point, the concrete damage entered the quick developing stage, and the variation between the different records became larger. The yielding of the reinforcement began at SaT1,5%=0.7g, on average. After SaT1,5%=0.9g, the reinforcement yielded under all earthquake records.


### 5.3. Damage State Prediction Based on Material Damage

According to the list of EDP limitations in Table2, we can distinguish the engineering limit states and predict the damage states of the RC members. Table 5 lists the engineering limit states, damage states, and corresponding SaT1,5%. By using different EDPs, the damage state division points vary. For example, Dc−core predicts the moderate damage state at SaT1,5%=0.59g and the reinforcement stress at SaT1,5%=0.65g. However, the two division points are close to each other. By considering all of the engineering limit states, we can summarize this as follows: SaT1,5%=0.1g is considered as a negligible damage state; SaT1,5%=0.35g is considered as a light damage state; SaT1,5%=0.6g is considered as a moderate damage state.Table 5
Engineering limit state and damage state prediction.
SaT1,5% (g)EDPEngineering limit stateDamage state0.08d/h=0.1Concrete cover cracking onsetNegligible0.10Dc−cover≈0; Dc−core≈0No or slight compressive damageNegligible0.32Dc−cover=0.1Concrete cover spalling onsetLight0.36d/h=1Plastic hinge initiatingLight0.59Dc−core=0.1Concrete core crushing onsetModerate0.65σs=σySteel bar yieldingModerateThe results revealed that the RCF-SW structure of the HP had good aseismic capacity. Severe spalling, critical crushing, and collapse were not observed, even after scalingSaT1,5% up to 1.0 g. This means that the RC frame and shear wall incurred only moderate damage, even under rare earthquakes. The damage state prediction is in agreement with the design principle of hydraulic structures. The seismic-resistant objectives for hydraulic structures should be higher than those of ordinary buildings, considering the importance of hydraulic structures. In practice, hydraulic structures are designed to ensure that damage does not occur under minor earthquakes, repairable damage occurs under moderate earthquakes, and collapse does not occur under strong earthquakes.


### 5.4. Comparison of Damage State Prediction Based on Drift Ratio and Material Damage

Drift ratio is widely used in the seismic performance assessment of RC columns and walls. The drift ratio limitations that have been commonly used in related studies [4, 31–33] for each damage state are listed in Table 6. Employing the drift ratio as an EDP, the damage states are assessed, as shown in Figures 14 and 15.Table 6
Drift ratio limitations for column and wall at different damage states.
ElementDamage stateNegligibleLightModerateSevereColumn1/5501/2751/1401/50Wall1/10001/5001/2501/120Figure 14
IDA curves of drift ratio. (a) Column A and (b) wall.
(a)(b)Figure 15
Mean IDA curves of drift ratio. (a) Column A and (b) wall.
(a)(b)Even though the concrete damage appeared at a very low-intensity level, the drift curves exhibited linear behavior approximately up toSaT1,5%=0.6g. When SaT1,5%<0.6g, the tensile damage was severe, but the compressive damage was still at the early developing stage. This means that the tensile damage does not significantly influence the deformation of the RC frame, although the compressive damage does. Despite the severe damage at SaT1,5%=1.0g, the maximum drift ratios of the columns and walls during the earthquake did not exceed 0.8%. The damage limit states revealed by the column drift ratios are approximately the same as those revealed by the drift ratio of the shear wall. Using the drift ratio index, SaT1,5%=0.3g can be regarded as a negligible damage state, SaT1,5%=0.6g can be regarded as a light damage state, and SaT1,5%=0.9g can be regarded as a moderate damage state. These results are quite different from those obtained by the material damage EDPs.WhenSaT1,5% reached 0.3 g, the structural damage was regarded as negligible by using the limitation of the 1/550 elastic drift ratio. However, at this point, the column base had already been penetrated by the cracks, and the concrete was almost completely damaged from the column base to the half-height of the column. Additionally, the concrete cover at the column base became spalled. From the viewpoint of material damage and RC members, this damage cannot be ignored. When SaT1,5% reached 0.6 g, the crushing of the concrete cover and the yielding of the reinforcement were observed. This indicates that the cohesiveness between the concrete and the reinforcement was damaged and that a plastic region formed at the column base. The deformation of the structure increased faster when the earthquake intensity was increased further. Therefore, the columns should be rehabilitated before use. The damage at SaT1,5%=0.6g was regarded as moderate by using the material damage EDPs. However, a light damage state was recognized by the drift ratio index.Generally, the drift ratio represents the damage states of regular buildings at a global level, and the determination of the elastic and plastic drift ratio limitations is based on the investigation of ordinary RC members and frames. Additionally, the story displacement differential causing the structural damage is the story displacement differential in the direction parallel to the floors. However, the drift ratios are approximated using the horizontal displacement of the vertical members, but this calculation method introduces error. Particularly, for HPs, because of the huge sectional sizes, large reinforcement ratio, support of auxiliary powerhouse at the downstream side, and link provided by the roof grids, the drift ratios of the RC columns and shear walls are not large. Even atSaT1,5%=1.0g, the maximum drift ratio did not exceed 1%. Therefore, the material damage states of the RC members in the HP are not always consistent with the damage states identified by the drift ratio. For a structure whose damage is controlled by the members, the drift ratio is not always suitable.


## 5.1. Damage Evolution

The ultimate damage state of the superstructure depends on the structural features and the input earthquake waves. However, all of the results under each record reveal a similar damage propagation process. In this section, we present the damage of the RCF-SW structure under the Koyna record.During an earthquake, the RCF-SW structures are shaken cyclically, and the RC members will have flexure and shear behavior. When the intensity of the earthquake is large enough, the RC members will incur damage. Figure10 shows the tensile and compressive damage profiles of the RCF-SWs under the Koyna record scaled to various intensity levels. As can be seen in Figure 10, the damage to the columns at the downstream side was more severe than that of the columns at the upstream side. The reason for this is that the auxiliary powerhouse was on the downstream side; thus, it provided support to the downstream wall, such that the stiffness changed more abruptly at the downstream column bases. Figure 11 shows the tensile and compressive damage profiles of column B (see Figure 7(d)) at the downstream side. The simplified damage distribution diagrams shown in Figure 6 are in good agreement with the damage distribution profiles of column B.Figure 10
Ultimate damage profiles of RCF-SW structure under Koyna record.Figure 11
Ultimate damage profiles of column B under Koyna record.The tensile damage shown in Figure11 is larger than 0.7; therefore, the damage profiles show the possible cracking zones. Because the section size changes sharply at the column base, the cracking initiates at the column base when SaT1,5% is equal to 0.05 g. The cracks develop rapidly as SaT1,5% increases. When SaT1,5% is greater than 0.5 g, the concrete in approximately half the height of the column cracks and new cracks appear at the connection areas of the walls and floors. When SaT1,5% reaches 1.0 g, the RCF-SWs become severely damaged. The columns are completely damaged and a crack penetrates the bottom of the upstream wall.Additionally, the compressive damage initiates at the column base atSaT1,5%=0.2g and reduces from the column surface to the core. Moreover, there is no complete compressive damage, even at SaT1,5%=1.0g. The maximum compressive damage of the concrete cover does not exceed 0.6, and the maximum damage of the concrete core does not exceed 0.1 at SaT1,5%=1.0g. Increasing the shaking intensity may result in concrete crushing; however, the vastness and diffusion of the tensile damage are so significant that an accurate interpretation of the results is not possible.As can be seen, the main damage modes of the HP are the cracking, spalling, and crushing of the columns and walls. Owing to the plastic-damage model of concrete, we can obtain the detailed damage states of the RC members and predict the engineering limit states conveniently.


## 5.2. IDA Results for All Records

In this section, the IDA results of the RCF-SW structure under all records are present. Figure12 shows the IDA curves for the EDPs of individual records and their mean, median, and 16%, and 84% fractiles. Ideally, an IDA illustrates the responses of the structure by each ground motion record scaled to multiple intensities. Thus, it is possible to define the capacity and limit states of the structure, including the failure modes. However, for RC structures, the material damage induces nonconvergence problems when the intensity of the record is increased to a certain value. Nevertheless, this numerical instability indicates the dynamic instability from one aspect. In this study, when SaT1,5% exceeded 1.0 g, the tensile damage was so severe that convergence and accuracy could not be ensured simultaneously. Thus, all of the IDA curves were plotted until SaT1,5%=1.0g. At the point of SaT1,5%=1.0g, the PGA of the record varied from 0.7 g to 1.6 g. Moreover, the intensities of all records were sufficiently large, considering that the PGA at the station site with an exceedance probability of 1% per 100 years is 0.498 g.Figure 12
IDA curves of EDPs. (a)d/h. (b)Dc−cover of column B. (c) Dc−core of column B. (d) Reinforcement stress.
(a)(b)(c)(d)As can be seen, the curves under different records exhibited a similar trend. However, large variation existed between the different records, particularly at high-intensity levels. When the crack penetrated the column base and the reinforcement yielded, the variations of thed/h ratio and the reinforcement stress curves became small. The mean and median curves are in better agreement at low-intensity levels, which means that the response values are distributed more evenly at low intensity. At high-intensity levels, the results were scattered by the different damage processes under various earthquake conditions.Figure13 shows the mean IDA curves of the EDPs based on the material damage. As shown in Figure 13, cracking initiated at the column base even at very low-intensity levels. After SaT1,5%=0.1g, the crack extended rapidly. Up to SaT1,5%=0.3g, the crack penetrated the column base under all records. The plastic hinge formed and developed from SaT1,5%=0.3g onwards. When SaT1,5%≤0.05g, there was no compressive damage for most records. The average compressive damage of the column cover Dc−cover ranged from 0 to 0.55. The spalling of the concrete cover started at approximately SaT1,5%=0.3g on average and reached up to SaT1,5%=1.0g; severe spalling appeared only under three records. The compressive damage of the concrete core was slighter than that of the concrete cover. The average compressive damage of the column core Dc−core ranged from 0 to 0.3. The crushing of the concrete core started at approximately SaT1,5%=0.55g, on average, and reached up to SaT1,5%=1.0g; none of the results indicates severe crushing.Figure 13
Mean IDA curves of EDPs. (a)d/h. (b) Dc−cover of column B. (c) Dc−core of column B. (d) Reinforcement stress.
(a)(b)(c)(d)The reinforcement stresses were mainly affected by the tensile damage. FromSaT1,5%=0.05g onwards, the reinforcement stresses began to increase rapidly. After SaT1,5%=0.3g, the stress values of various records became obviously scattered. At this point, the concrete damage entered the quick developing stage, and the variation between the different records became larger. The yielding of the reinforcement began at SaT1,5%=0.7g, on average. After SaT1,5%=0.9g, the reinforcement yielded under all earthquake records.


## 5.3. Damage State Prediction Based on Material Damage

According to the list of EDP limitations in Table2, we can distinguish the engineering limit states and predict the damage states of the RC members. Table 5 lists the engineering limit states, damage states, and corresponding SaT1,5%. By using different EDPs, the damage state division points vary. For example, Dc−core predicts the moderate damage state at SaT1,5%=0.59g and the reinforcement stress at SaT1,5%=0.65g. However, the two division points are close to each other. By considering all of the engineering limit states, we can summarize this as follows: SaT1,5%=0.1g is considered as a negligible damage state; SaT1,5%=0.35g is considered as a light damage state; SaT1,5%=0.6g is considered as a moderate damage state.Table 5
Engineering limit state and damage state prediction.
SaT1,5% (g)EDPEngineering limit stateDamage state0.08d/h=0.1Concrete cover cracking onsetNegligible0.10Dc−cover≈0; Dc−core≈0No or slight compressive damageNegligible0.32Dc−cover=0.1Concrete cover spalling onsetLight0.36d/h=1Plastic hinge initiatingLight0.59Dc−core=0.1Concrete core crushing onsetModerate0.65σs=σySteel bar yieldingModerateThe results revealed that the RCF-SW structure of the HP had good aseismic capacity. Severe spalling, critical crushing, and collapse were not observed, even after scalingSaT1,5% up to 1.0 g. This means that the RC frame and shear wall incurred only moderate damage, even under rare earthquakes. The damage state prediction is in agreement with the design principle of hydraulic structures. The seismic-resistant objectives for hydraulic structures should be higher than those of ordinary buildings, considering the importance of hydraulic structures. In practice, hydraulic structures are designed to ensure that damage does not occur under minor earthquakes, repairable damage occurs under moderate earthquakes, and collapse does not occur under strong earthquakes.


## 5.4. Comparison of Damage State Prediction Based on Drift Ratio and Material Damage

Drift ratio is widely used in the seismic performance assessment of RC columns and walls. The drift ratio limitations that have been commonly used in related studies [4, 31–33] for each damage state are listed in Table 6. Employing the drift ratio as an EDP, the damage states are assessed, as shown in Figures 14 and 15.Table 6
Drift ratio limitations for column and wall at different damage states.
ElementDamage stateNegligibleLightModerateSevereColumn1/5501/2751/1401/50Wall1/10001/5001/2501/120Figure 14
IDA curves of drift ratio. (a) Column A and (b) wall.
(a)(b)Figure 15
Mean IDA curves of drift ratio. (a) Column A and (b) wall.
(a)(b)Even though the concrete damage appeared at a very low-intensity level, the drift curves exhibited linear behavior approximately up toSaT1,5%=0.6g. When SaT1,5%<0.6g, the tensile damage was severe, but the compressive damage was still at the early developing stage. This means that the tensile damage does not significantly influence the deformation of the RC frame, although the compressive damage does. Despite the severe damage at SaT1,5%=1.0g, the maximum drift ratios of the columns and walls during the earthquake did not exceed 0.8%. The damage limit states revealed by the column drift ratios are approximately the same as those revealed by the drift ratio of the shear wall. Using the drift ratio index, SaT1,5%=0.3g can be regarded as a negligible damage state, SaT1,5%=0.6g can be regarded as a light damage state, and SaT1,5%=0.9g can be regarded as a moderate damage state. These results are quite different from those obtained by the material damage EDPs.WhenSaT1,5% reached 0.3 g, the structural damage was regarded as negligible by using the limitation of the 1/550 elastic drift ratio. However, at this point, the column base had already been penetrated by the cracks, and the concrete was almost completely damaged from the column base to the half-height of the column. Additionally, the concrete cover at the column base became spalled. From the viewpoint of material damage and RC members, this damage cannot be ignored. When SaT1,5% reached 0.6 g, the crushing of the concrete cover and the yielding of the reinforcement were observed. This indicates that the cohesiveness between the concrete and the reinforcement was damaged and that a plastic region formed at the column base. The deformation of the structure increased faster when the earthquake intensity was increased further. Therefore, the columns should be rehabilitated before use. The damage at SaT1,5%=0.6g was regarded as moderate by using the material damage EDPs. However, a light damage state was recognized by the drift ratio index.Generally, the drift ratio represents the damage states of regular buildings at a global level, and the determination of the elastic and plastic drift ratio limitations is based on the investigation of ordinary RC members and frames. Additionally, the story displacement differential causing the structural damage is the story displacement differential in the direction parallel to the floors. However, the drift ratios are approximated using the horizontal displacement of the vertical members, but this calculation method introduces error. Particularly, for HPs, because of the huge sectional sizes, large reinforcement ratio, support of auxiliary powerhouse at the downstream side, and link provided by the roof grids, the drift ratios of the RC columns and shear walls are not large. Even atSaT1,5%=1.0g, the maximum drift ratio did not exceed 1%. Therefore, the material damage states of the RC members in the HP are not always consistent with the damage states identified by the drift ratio. For a structure whose damage is controlled by the members, the drift ratio is not always suitable.


## 6. Conclusions

In this study, the seismic performance of an RCF-SW structure in an HP was investigated by IDA employing a plastic-damage concrete model. Several EDPs based on material damage are proposed to track the damage extent to the structure. These EDPs associated with the mean IDA curves are suggested to identify the engineering limit states and damage levels of RCF-SW structures at the member level. By considering an HP in China as a case study, a large-scale FE model was developed, and IDAs were performed on ten records. Thus, the following conclusions were drawn.The main damage mode of the RCF-SW structure in the HP was the damage of the RC members. Generally, the RCF-SW structure incurred the cracking of the columns and walls and the crushing of the columns. The EDPs based on material damage revealed the material damage evolution of the RC members and easily distinguished the engineering limit states, such as cracking, crushing, reinforcement yielding, and plastic hinge forming. These engineering limit states were used to identify the damage state of the RC members. Therefore, a relationship between the EDPs and damage states was established. IDA and concrete damage mechanism were powerful tools to predict the damage states of RCF-SW structures in HPs. The EDPs based on material damage could be used to evaluate the seismic performance of RCR-SW structures as other indices, such as the peak drift ratios residual drift ratio, stiffness degradation, and dissipated energy.The mean IDA curves of the drift ratio exhibited a linear trend that ended at the beginning point of the crushing of the concrete core and the yielding of reinforcement. The damage states identified by the drift ratio were lighter than those identified by the EDPs based on material damage. For an RCF-SW structure whose damage was controlled by the members, it is more suitable to use the EDPs based on material damage to identify the damage states, instead of using the drift ratio. Additionally, the EDPs based on material damage were linked to engineering limit states; thus, this may provide useful information for the aseismic measure determination and postquake rehabilitation of RC members.



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*Source: 6198594-2020-09-10.xml*