Seismic Performance Assessment of High Asphalt Concrete Core Rockll Dam Considering Shorter Duration and Longer Duration

12 Current research trends in seismic frequent regions aim at developing the appropriate 13 performance – based design approach for high asphalt concrete core rockfill dams (ACCRDs). Under 14 intense ground motions (GMs), the seismic performance of dams depends on seismological 15 characteristics mainly containing the frequency, amplitude, and duration. Recently, the characteristic 16 of frequency and amplitude of GMs which can trigger severe damages to the dams has been accepted 17 and incorporated into the seismic design codes in most countries. As one of the key characteristics of 18 earthquakes, the duration of strong GMs also should be fully understood in order to carry out more reasonable performance – based design approach of dams. This paper explores the effect of the 20 duration of strong GMs, investing the seismic performance of high ACCRDs by employing integrated 21 duration concept, which can reflect the duration of all components of GMs. The high ACCRD was 22 built in the commercial software ABAQUS considering the dam-reservoir-foundation interaction 23 systems. Additionally, the coupling multiple stripe analysis and maximum likelihood estimate method 24 are used to generate seismic fragility curves for the dam according to two damage indicators. Findings 25 from this study revealed that the longer duration GMs can give rise to higher probability of exceedance 26 (POE) of the dam than shorter duration. It is recommended that in the work of the current seismic 27 design and seismic performance evaluate, the effects of GM duration in addition to frequency and 28 amplitude should be considered. 29


Introduction 32
High dams are regarded as critical components of a nation's lifeline engineering, which can 33 effectively alleviate the contradiction between water supply and demand. Over the past few decades, 34 the rapidly development of water resource has witnessed a boom and a larger number of embankment 35 dams has been constructed all over the word because of their low cost, rapid, and adaptability. Recently,36 owing to the optimization and improvement of downstream water resources, the development and of GMs are propagation path of seismic waves, spatial site conditions, source mechanism, ground 51 motion duration (GMD), frequency and amplitude, each of which may plays a critical part in the 52 seismic performance assessment. Generally, the characteristic of amplitude, which is one of effective 53 engineering parameters on seismic performance assessment of structures, is illustrated by the peak 54 ground displacement (PGD), the peak ground velocity (PGV) and the peak ground acceleration (PGA). 55 Moreover, the Fourier spectrum of the GM is usually employed to reveal the frequency content. 56 Conversely, present seismic design code and analysis methodology do not directly or indirectly 57 consider the impact of GMD on the seismic performance of high ACCRDs. Besides, the length of the 58 spatial distribution of GMDs is influenced by defining methods, site conditions, basin effects and 59 rupture directivity (see Fig. 1

67
The effect of strong GMD on structural performance remains a rising controversial topic. It is 68 well-known that GMD have a significant impact on some types of earthquake damage, such as 69 containing high dams (Zhang et al., 2013), bridges (Ou et al., 2014), and liquefaction (Green and Terri,70 7 to the total energy content (Trifunac and Brady, 1975

126
It can be seen from Fig. 2 and Eq. (2) that the SD can only properly express the duration of GM 127 in single direction (horizontal or vertical component). On the contrary, the ID regards the Arias 128 intensity in multi-directions as the weighting function, which is applied to weighted average the 129 corresponding single direction duration to overcome the above shortcomings. Based on the work of 130

139
To reveal the seismic performance of ACCRDs considering the shorter duration and longer 140 duration effect, Forty -six bidirectional GMs are originated from the Pacific Earthquake Engineering 141 Research center (PEER) strong database. For each of these short -duration bidirectional GMs, a 142 corresponding long -duration bidirectional GMs with duration threshold longer than 25s (Barbosa et 143 al., 2017), and having original spectral acceleration and matching spectral acceleration is determined. 144 The detailed earthquake information is present in Table 1 and Table 2. On the other hand, it is crucial 145 to avoid the impact of frequency, amplitude and other characteristics of GMs on the seismic 146 performance assessment. All original GMs obtained PEER database are matched the target design 147 spectrum by using time domain wavelet correction method to adjust the amplitude and shape of 148 spectrum through the software of SeismoMatch. By doing so, the spectral acceleration of each 149 bidirectional earthquake records is adjusted and scaled to have a good compatible with the target 150 spectrum, reflecting that the influence of amplitude and shape of acceleration response spectrum can 151 be minimized, as shown in Fig. 5. Figure. 6 illustrates the distribution of GMDs of matched GMs. 152 Table 1 153 List of short -duration database with two directions (matched records

Fragility function 167
The development of fragility curves of ACCRDs under short -and long -duration GMs are 168 significant steps for seismic performance assessment according to the performance-based earthquake 169 engineering (PBEE) framework. For the purpose of assessing the seismic performance of high dams, 170 there have been several in-depth approaches to collecting the results for generating fragility curves, 171 such as incremental dynamic analysis (IDA) (Vamvatsikos and Cornell, 2004), multiple stripe analysis 172 (MSA) (Baker, 2015), and cloud analysis (Celik and Ellingwood, 2010). IDA is an efficient 173 performance evaluation methodology, which linearly scaled from a low seismic intensity level to an 174 extremely high seismic intensity level for each selected GMs. MSA is conducted at a specified set of 175 seismic intensity level, each of which has engineering demand parameters (EDP). As the type of results 176 collected in these two methods differs, the effectively approach for estimating fragility curves from 177 the results also differs. It is worth noting that the efficient fragility estimates of IDA may be lower than 178 MSA for a given number of high performance structures. In this study, the fragility curves for the 179 ACCRD are investigated employing the MSA approach. Besides, the PGA of GMs is acknowledged 180 as the variable on behalf of the intensity measure (IM) of short -and long -duration GMs, and is 181 scaled from 0.1g to 0.7g in gaps of 0.1g. 182 As a critical and integrated component of a PBEE framework (Fajfar, 2000), the mainly purpose 183 of FR is to quantify the probability of exceedance (POE) relationships between structural damage state 184 with the various IM level. The fragility curves of an ACCRD can be conducted by a lognormal 185 cumulative distribution function (Baker, 2015): 186 where i p is the probability of collapse of the structure under short -and long -duration GMs with Following the MLE approach, the way to identify the fragility function for i p is to select the 205 function that gives us the highest probability of observing the collapse data that was originated from 206 nonlinear dynamic analysis. Subsequently, the product of binominal probabilities according to Eq. (5) 207 at each IM levels, is employed to get the likelihood in the entire database. 208 collapses in short and long ground motions 1 where m is the number of short -and long -duration GMs at each IM levels;  represent a 211 product over all dates. 212 To conduct this maximize the likelihood function, i p is replaced by the Eq. (4), and estimation 213 of the key parameters  and  (logarithmic mean and standard deviation) are then obtained by this 214 likelihood function. It is worth noting that the estimation of parameters by maximizing the logarithm 215 of the likelihood, which is equivalent and numerically more efficient and easier than the maximizing 216 the likelihood function itself, so that the fragility function can be explicit as follows: 217 Standard commercial software packages such as Matlab, R, python, or Microsoft Excel can be 219 utilized to calculate the Eq. (7), and detailed code can be found in the work of Baker (Baker, 2015). 220

Definitions of seismic performance indicators 221
After the earthquake disaster, the potential failure mode (PFM) of high dams is generally depicted 222 as a function of concrete stiffness degradation, concrete strength degradation, dam crest settlement, 223 landslide, cracks and liquidation among others. Due to the complex combination of these PFMs, the 224 unsatisfactory performance and uncontrolled failure mode of high dams can be regarded as a chain of 225 events. In addition, high ACCRDs are the complex system mainly composed of rockfill, transition and 226 asphalt concrete core, as shown in Fig. 6. Therefore, from the perspective of safe operation of complex 227 hydraulic engineering, the employ of a single damage index to evaluate performance level of high 228 ACCRDs may not be accurate enough and overestimate its ability to resist earthquakes. In this study, 229 two damage indicators from different aspects have been applied to evaluated seismic performance of 230 high ACCRDs under shorter duration and longer duration GMs.

245
The seismic performance of the asphalt concrete core, employed as an indispensable component 246 of the impervious system, is one of major concerns in high ACCRD design. To account for the impacts 247 of cyclic earthquake loading, a qualitative methodology assessed the seismic performance of concrete 248 materials structure is firstly proposed by Ghanaat (2004). Subsequently, the performance index is 249 widely employed to forecast the seismic performance of concrete gravity dams ,  The CID refers to the total duration of cyclic stress above a certain stress strength, which is related 268 to different DCR levels. As shown in Fig. 8(a) for all DCR's, and 286 overstressed regions are less than 15% of the asphalt concrete core, it is considered that the asphalt 287 concrete core is acceptable with no possibility of failure, as shown in Fig. 9  288 3. Severe Damage. The damage state of the asphalt concrete core is regarded as severe when 2 DCR  , 289 or 3.5 CID  for all DCR's given in Fig. 9.

Finite element model considering the damwaterfoundation interaction system 313
The FE model is developed utilizing in the commercial software ABAQUS. The FE model of 314 dam -reservoir -foundation (DRF) interaction system is discretized into an assemblage of solid 315 element, as decipted in Fig. 11. In these models, rockfill zone, transition zone, asphalt concrete core, 316 concrete cushion, foundation rock and reservoir water have 41742, 4032, 1344, 108, 132840 and 51318 317 finite elements, respectively. Moreover, 672 interface elements were defined in asphalt concrete core 318 -transition zone interface. The total numbers of integration points of the Dashimen dam body, 319 foundation rock and reservoir water are 57232, 157990 and 61138, respectively. To more precisely 320 simulate the seismic behaviour of the asphalt concrete core, four layers of spatial 8-node isoparametric 321 elements is employed to model the core thickness. 322 Before the time-history dynamic analyses, the initial stress condition for Dashimen dam needs to 323 be determined by static analysis. As shown in Fig. 11, the Dashimen dam reproducing a staged 324 construction and staged water impounding are step -by -step and are modelled with 11 steps and 12 325 steps, respectively. To reflect the extremely unfavorable water table of Dashimen dam, the presence of 326 water in the reservoir is assumed the case of full reservoir, which is impounded from dam base to dam 327 crest after dam construction was completed. Moreover, the water pressure is applied on the upstream 328 face of asphalt concrete core and concrete cushion by means of a triangular hydrostatic profile. The  Table 3.   The cycle earthquake load will induce the high ACCRDs to generate irrevocably permanent  Table 5. 371  For the concrete cushion, the mechanical responses and dynamic cracking mechanism is 373 specifically described by the concrete damage plastic (CDP) model in the ABAQUS material library. 374 The CDP model is firstly proposed by Lubliner et al. (1989) and improved by Lee and Fenves (1998).  Table 6 present the detailed material parameters of foundation rock and concrete cushion. 379 Generally, to obtain more accurate numerical results, the contact element should be defined to 381 reflecting the interface behavior between two materials with significantly different mechanical 382 property. In this paper, the Goodman zero-thickness contact element is used to simulate the transition 383 -concrete interface. Moreover, the thin-layer contact element ( 5 cm ) is applied between transition and 384 asphalt concrete to revel the contact behavior. Although many models have been proposed to reflect 385  Tables 7 and 8. 390 Table 7 Parameters for static contact element (Ji, 2006)  For embankment dams, hydrodynamic pressure generally has no significantly effect on the dam 393 crest accelerations (Pelecanos et al., 2016). However, the stress and strain of the upstream dam body 394 may be sensitive to hydrodynamic pressure (Pelecanos et al., 2020). To simulate the DRF dynamic 395 interaction system, fluid elements, which represent a linearly elastic inviscid, irrotational, and 396 compressible medium, are used to model the reservoir. In addition, the coupled Lagrangiann 397 formulation of FE method is directly conduct for seismic dynamic analysis of interacting DRF systems. 398 As illustrated in Fig. 11(a), the upstream face of the reservoir is set as non-reflecting boundary 399 condition to enable energy dissipation during the dynamic analysis process. The direction normal 400 displacement is assumed to simulate the interface between the reservoir and the dam following the 401 recommendations of Wang et al. (2018). At the dam -foundation interface, the reservoir is tied with 402 the foundation of the dam. The material mechanical properties of the fluid element can be found in our 403 previous work of . The typical damping ratio for DRF dynamic interaction system 404 is assumed as 5% in time -history dynamic analyses. Rayleigh damping, calculated by two parameters 405 obtained from modal damping ratios of the DRF dynamic interaction system, is considered in time-406 history dynamic analyses. 407

Seismic wave input mechanism 408
An effective and reasonable GM input mechanism is required to ensure the stability and accuracy

439
The seismic fragility curves for the minor, moderate and severe performance levels obtained from 440 Eq. (7) are given in Fig. 14. For simplicity of illustration, this figure provides presents the comparison 441 of seismic fragility curves of short -and long -duration GMs for different performance levels. For the 442 same performance levels, the seismic fragility curve for the short -duration is uniformly situated to 443 the right of the seismic fragility curve of long -duration, meaning the increasing POE when the high 444 ACCRD is excited by long -duration GMs. Currently, the seismic design of high dams generally 445 consider two seismic levels to assure structural safety, containing the operating basis earthquake (OBE) 446 and the maximum credible earthquake (MCE). For this high ACCRD, the OBE and MCE stipulated in 447 the actual engineering project situation is defined as 0.4g PGA and 0.54g PGA, respectively. Figure  448 15 further list the POE of RSR in different performance level. The highest POE is given by long -

The stress demand-capacity ratios and cumulative inelastic duration index 462
The seismic performance evaluation based on the DCR-CID is utilized to assess the performance 463 levels of the ACCRD subjected to short -and long -duration GMs. Figures 16(a) presents the 464 maximum principle tensile stress time histories for short -and long -duration GMs with a PGA level 465 of 0.5g. The corresponding performance evaluation curves are illustrated in Fig. 16(b). It is clear from 466 Fig. 16(a) that the long -duration records make the number of cycles that excess of the tensile strength 467 of the asphalt concrete greater than the short -duration. Results in Fig, 16(b) display that the stress 468 DCR exceed 1 or 2 and the CID under long -duration GMs are significantly greater than the short -469 duration. In addition, the DCR-CID under short -duration GMs with a PGA level of 0.5g are in the 470 range of low to moderate damage. The DCR-CID seismic fragility curves obtained at each damage 471 levels for the asphalt concrete core is shown in Fig. 17. It is evident from this figure that the effect of 472 GMD on the seismic fragility curve of the high ACCRD is maximal for the two damage levels, while 473 a significantly difference value of POE can be found. Overall, the probability of exceeding the each 474 performance levels under long -duration is greater that the POE under short -duration. Furthermore, 475 the probability of exceeding the severe performance level under strong GMs is below the 50%, which 476 means the asphalt concrete core can perform its engineering function under extremely earthquake 477 excitation. For simplicity of illustrate the difference characteristic of short -duration and long -478 duration, Fig. 18

Summary and conclusions 495
This study entirely studied the impact of short -and long -integrated duration (ID) on the seismic 496 fragility analysis (FR) of a high asphalt concrete core rockfill dam (ACCRD) considering dam -497 reservoir -foundation (DRF) dynamic interaction system. A series of seismic dynamic analysis of 498 finite element model were conducted to generate 322 numerical results to determine the seismic 499 fragility curves of a high ACCRD via coupling multiple stripe analysis and maximum likelihood 500

estimate. 501
In this particular study, the developed multiple stripe data showed that the relative settlement ratio 502 (RSR) of a high ACCRD is more vulnerable to moderate damage or severe damage when subjected to 503 longer duration. Furthermore, the results of the system fragility curves indicate that for damage states 504 for which the high ACCRD behaves under strong GMs, there is significantly effect due to the different 505 ID on the fragility curves and risk. The damage state of a high ACCRD under shorter duration exhibit 506 smaller seismic fragilities. Such phenomenon is explained by the fact that for the the operating basis 507 earthquake (OBE) or the maximum credible earthquake (MCE), the longer duration may trigger severe 508 damage of a high ACCRD. 509 The impact of ID on the stress DCR and CID demonstrates that the stress DCR exhibits sensitivity 510 to the longer duration, while the CID also shows relatively strong sensitivity to the longer duration. It 511 is reasonable that the longer duration, the greater DCR-CID, since the performance index is related to 512 the duration of cycles exceeding the tensile strength of the asphalt concrete core. Similarly, the 513 developed seismic fragility curves for the asphalt concrete core under longer duration exhibited 514 significantly higher POE than shorter duration. In addition, the difference value of POE between short 515 -duration and long -duration is increase along with the increase seismic intensity. The study provides 516 important insight into the seismic behavior of the high ACCRD and highlights the need for further 517 development of seismic design codes in consideration of the impact of ground motion duration, 518 frequency, amplitude. 519 Finally, several restrictions of the present study should be paid more attention. Among the effect 520 of real environment, the dam-reservoir-foundation dynamic interaction system is more complex, so 521 only the effect of hydrodynamic pressure is considered. Further, the tensile strength of asphalt concrete 522 is approximately determined according the work of Ghanaat (2004). Further research should consider 523 the shaking model test and numerical analysis with more than two performance indictors or with 524 different elastic-plastic analysis combinations of the multi-field coupling approach. 525 Figure 1 Spatial distribution of signi cant duration recorded from Wenchuan earthquake (Mw7.9, 2008). (a) 0-90% signi cant duration; (b) 5-75% signi cant duration. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its