Dynamic and Probabilistic Seismic Performance Assessment of Precast Prestressed Rcfs Incorporating Slab In uence Through Three- Dimensional Spatial Model

The dynamic and probabilistic seismic performances of precast prestressed RCFs are assessed in this paper, and the slab influence in the overall structural behavior is considered during the process. The threedimensional spatial model is established to provide the numerical basis, and the slab is modelled through L-/T-section beam-slab fiber-sections considering the effective width and centroid positions. The adopted model is verified with the experimental data, and the slab influence in hysteresis curves is investigated by parametric study. Then, two groups of precast prestressed RCFs are well designed to evaluate the slab influence in dynamic responses through seismic excitations, and the modal analysis, roof displacement analysis, maximum and residual drift ratio analysis are conducted for discussion. Moreover, the incremental dynamic analysis and fragility analysis are also conducted to investigate the probabilistic performance of precast prestressed RCFs with or without slabs. In general, different demand parameters may result in the variability of analyzing results, and ignoring the slab influence may underestimate the structural capacity under the frequent earthquakes (i.e., elastic stage) and overestimate the structural capacity under the rare earthquakes (i.e., plastic stage). In a sense, the research proves the significance of slabs in the seismic performance of dry-connected precast prestressed RCFs, and meanwhile provides the reference for the further explorations of slab factors in precast concrete structures.

most important part that affects the seismic performance of the whole structure significantly, thus the re-13 search focuses are mainly on it. At this stage, the beam-column connection of precast RCFs can be divided 14 into two types (e.g., wet-connection and dry-connection) according to whether there is cast-in-place con-15 crete in the core area of the beam-column connection [5,6]. In the early stage of precast technology, the 16 wet-connection is widely studied and broadly applied because of its excellent performance equivalent to 17 monolithic operation. 18 Im et al. [3] investigated the seismic performance of emulated precast wet-connection of beams to 19 columns. Six full-scale specimens were adopted with U-shaped beam shells, and the parameters of rein-20 forcement ratio as well as interface details were compared specifically. Besides, the headed reinforcing bars 21 were selected at the connections to prevent the energy dissipation and stiffness degradation, which proved  The test data demonstrated the satisfactory seismic performance compared with the monolithic connection, and reflect the shear-lag phenomenon of stress distributions from a micro perspective, which means an im-100 portant structural factor in performance assessment. Gao et al. [23] researched on the seismic performance 101 of precast steel reinforced concrete connection with or without slabs, and seven specimens were experimen-102 tally tested under cyclic loading to analyze the variation of structural capacities. The results signified better 103 performance for the specimen with slabs, and the peak strength was decreased under the influence of bolt-104 slip. Santarsiero and Masi [24] discussed the effects of slab action on the structural behavior of beam-column 105 connections, and the tension flange functions of slabs were evaluated specifically. The results showed the 106 significant influence of reinforcing ratio in slabs, and the suggestions about slab effective width were also 107 provided. Feng et al. [25] investigated the seismic performance of precast reinforced concrete beam-slab 108 assembly in light of layered shell models, and the results showed the significant influence of slab thickness 109 in the hysteretic behaviors. Besides, the slab width was found to have an obvious effect under a certain 110 limit, but the effect was decreased distinctly after the slab width exceeded the boundary. Wang et al. [26] 111 developed a prestressed beam-column connection with damage-free slabs, and experimental performance was 112 analyzed compared to conventional connection. The results indicated satisfactory self-centering and energy 113 dissipating capacities of the proposed joint, and the slab was damage-free even under large displacements.

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Moreover, the slab cracks were well reduced and the slab reinforcements were kept in elastic stage. Park  From the literature review above, we can find that although extensive researches on dry-connection have 121 been conducted, the existing approaches mainly focus on the experimental explorations of different config-122 urations on the joint-level. The theoretical analyses, dynamic evaluations or engineering applications on 123 the structural-level are not enough at present stage. Besides, although the significance of slabs on struc-124 tural behaviors has been valued, the existing researches mainly focus on the cast-in-place monolithic joints 125 or precast wet-joints. Due to the complicated mechanism and multiple forms of precast dry-connections, 126 the evaluations of slab effects on this joint type are necessary. Moreover, the existing researches of pre-127 cast beam-column-slab dry-connections mainly focus on the two-dimensional plane sub-assembly, while the 128 corresponding researches from the aspect of three-dimensional spatial system are still in great need.

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In this paper, the dynamic and probabilistic seismic performance assessments of precast prestressed of the element is strictly satisfied, thus the mechanical characteristics of the entire beam and column can be 150 described with fewer elements. The fiber sections are assigned to the nonlinear beam-column elements, and 151 the whole section is divided into the concrete fiber and steel fiber to reflect the uniaxial characteristics of the 152 materials. To be specific, the concrete fiber is defined by Concrete02 material and the steel fiber is defined by 153 Steel02 material. Worth mentioning is the confined effects of stirrups on the concrete compressive strength, 154 and an amplification factor of k can be introduced to enhance the corresponding stress-strain relationship 155 for the concrete fibers within the stirrup ranges, as expressed in Eq. 5. Scott et al. [32] conservatively took 156 the ultimate compressive strain of the concrete in the core area as the value when the first stirrup is broke.

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In calculation, the ultimate compressive strain of unconfined concrete cover is determined as 0.004, and the 158 ultimate compressive strain of the confined concrete core is calculated according to the Eq. 6.
where ⇢ s denotes the stirrup ratio in volume, f yh denotes the stirrups yielding strength, f 0 c denotes the 160 cylinder compressive strength, and " max denotes the ultimate compressive strain of confined concrete.

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To reflect the bending moment-rotation characteristics of beam-column joints, the zerolength elements 162 are adopted in the plane X-Y and plane Y-Z, respectively. The zerolength element defines two nodes at 163 the same coordinates with the unit length of one, and the mechanical properties in different directions 164 can be considered by assigning different constitutive materials. As the structure is excited with loads, the 165 zerolength elements deform with two nodes separating, thus the constitutive materials can be functioned.

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In this modelling, the hysteresis material is selected in the rotation direction of joints, which can reflect at the joint center, respectively.

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To reflect the slab effects on the structural performance, some researchers utilized the layered shell model 182 to prove the ideal results [35, 25], but also a few drawbacks were found such as the complicated modeling 183 process to couple the degrees-of-freedom between layered shell floor elements and beam-column elements.

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Moreover, the calculation is often prone to non-convergence in the middle or later stages, even for the two-

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(S rec + S sb ) · y tol = S rec · y rec + S sb · y sb where b T-section beam-slab Inverted L-section beam-slab To verify the effectiveness of the proposed numerical model, the static loading data of two precast   to 5(f) present the comparing results with the numerical data by layered shell models of specimen DP1.  indicates the effectiveness of the proposed model in a sense, which lays the foundation for the further dynamic 224 evaluation and probabilistic assessment of the precast prestressed system with slabs in the following sections.  1840 mm and 2040 mm are set as group 3. Fig. 6(a) to 6(c) present the hysteresis curves of the three groups,  (f) Skeleton curves with group 3  Although the structural stiffness and peak capacity increase slightly, the overall energy consumption mode, T 6 , especially for the torsional periods of T 3 and T 6 , which indicates that the models with slabs obviously 294 improve the integrated stiffness and reduce the spatial effects than the models without slabs.

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The spatial displacement patterns for the first three modes of 5F-slab and 10F-slab are displayed in Fig. 8.

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It can be seen that the main modes corresponding to the first and second periods are characterized with  (f) 10F-mode3 the same condition, as presented in Fig. 9(b). The target response spectrum, mean response spectrum and 314 individual response spectrum are depicted in red, blue and gray in Fig. 9, respectively. Worth mentioning 315 is that when selecting ground motions, the difference of spectral acceleration between the target and mean   generally present a smaller roof residual displacement, which can be observed from the gaps between the 346 final roof displacements of red and black lines in Fig. 10 and Fig. 11. In a sense, the results demonstrate the 347 importance to consider the slab influence in structural performance assessment, and indicate that ignoring 348 the slab effects may overestimate the maximum and residual vibration responses of the overall structure.  It can be observed from Fig. 12(a) and Fig. 12(c) that the individual MIDRs of both the 5F and 5F-slab 356 models are smaller than threshold, and the average values show the obvious redundancy, which indicates 357 the design rationality and structural safety of the precast prestressed frames under the FE condition. The 358 same conclusions can be drawn for the 10F and 10F-slab models in Fig. 12(b) and Fig. 12(d), but one 359 ground motion in 10F model shows the MIDR that exceeds the threshold. For the four models in Fig. 13 360 under the RE conditions, all the individual and average results are within the limitations of 1/50, which 361 demonstrates the satisfactory seismic performance of this structural form. However, the MIDRs of models 362 5F-slab 5F-without-slab

Frequent earthquake
Roof displacement/mm

Rare earthquake
Roof displacement/mm

Rare earthquake
Roof displacement/mm

Rare earthquake
Roof displacement/mm   RIDR value should be calculated by subtracting the initial drift ratio caused by gravity load and prestress 375 from the final drift ratio. It can be seen from Fig. 12(e) and Fig. 12(g) that the models with slabs commonly 376 reflect a smaller RIDR than the models without slabs, and two conclusions can be acquired correspondingly.

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First, the structural type is almost non-destructive under the FE condition, and the self-centering efficiency 378 of this structural type is well exerted. Second, the models with slabs commonly have larger structural 379 rigidity and better spatial integrity, thus the plastic development of the whole structure is not as fast as 380 the models without slabs. As a result, the self-centering and recovering capacities of the models with slabs 381 commonly present a better tendency. In addition, from Fig. 12(e) and Fig. 12(f), it can be observed that 382 the individual RIDR results for the models with slabs are obviously less discrete and have smaller deviation 383 than the models without slabs. Moreover, as for the average RIDR distributions under the RE condition in 384 Fig. 13(g) and Fig. 13(h), the maximum RIDRs appear at different weak storeys. To be specific, storey-two 385 is for 5F-slab model, storey-three is for 5F model, storey-one is for 10F-slab model, and storey-three is for 386 10F model, which denotes that the models with or without slabs may change the results of structural damage 387 assessments and self-centering assessments under the RE condition. The above discussions indicate that the 388 slab influence is important to consider in the simulation of precast prestressed frames and the accuracy of 389 this analyzing approach can be realized with more value for reference.  it is necessary to adopt the models with slabs for performance evaluation. to the results from the EDP of MIDR, the fractile curves of model 5F without slabs are almost above the 439 curves of model 5F with slabs during the whole IDA process (Fig. 15(c)). For the 50% fractile curve, the 440 development of RIDR accelerates sharply when the S a (T 1 ) is over 3.0g. Although the difference between 441 the 10F and 10F-slab is smaller in Fig. 15( with the IM can be expressed by the power exponential regression, as shown in Eq. 5: where x and y denote the regression factors acquired by the least squares approach in the logarithmic 464 scale. d|IM is the logarithmic standard deviation for demand and can also be acquired from the logarithmic 465 linear regression (Eq. 6). c is the logarithmic standard deviation for capacity, and the value can be used .
where D n denotes the nth MIDR or RIDR value for each intensity level, and m denotes the total number  For the EDP of MIDR (Fig. 17(a) and Fig. 17(b) and larger S a (T 1 ) under the same exceeding probability. In a sense, if the slab influence is neglected in the 483 analysis, the structural capacity and seismic performance may be underestimated.

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For the EDP of RIDR (Fig. 17(c) and Fig. 17(d)), the same curve tendency is observed from NO to CP 485 states, but the positions of fragility curves between the two models with and without slabs show difference.

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At the initial growing stage of S a (T 1 ), the exceeding probability of the models without slabs is slightly greater 487 than that of the models with slabs, especially for the NO

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In this paper, the dynamic and probabilistic seismic performance assessments of precast prestressed 505 RCFs are performed, and the slab influence in the overall structural behavior is considered through three-506 dimensional spatial model. The conclusions may be drawn as follows:

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(1) The three-dimensional numerical model incorporating the slab influence is established based on the 508 OpenSees software. To reflect the bending moment-rotation characteristics of beam-column joints, the 509 zerolength elements are adopted in the plane X-Y and plane Y-Z, respectively. To reflect the gap opening- and probabilistic assessment of the precast prestressed system with slabs.

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(2) Two groups of precast prestressed RCFs are designed to evaluate the slab influence in dynamic 518 responses through 7 seismic excitations. The modal analysis shows smaller vibration periods for models with 519 slabs, which is in agreement with the theoretical assumption that the structures with slabs shall have larger 520 stiffness than those without slabs. Beside, the roof displacement analysis reflects that the deformation of 521 models without slabs is greater than that of the models with slabs, although there exists reversal phenomenon storeys also change after incorporating the slab influence, especially under the RE condition.

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(3) The incremental dynamic analysis and fragility analysis are conducted to investigate the probabilistic 529 seismic performance of precast prestressed RCFs with or without slabs through 22 seismic excitations. Two 530 response indicators, three fractile curves and four limit states are incorporated, and the slab influence in the 531 exceeding probabilities as well as the engineering decision is well compared. As for the EDP of MIDR, the 532 models with slabs require larger S a (T 1 ) than the models without slabs, which means that the models with 533 slabs can undertake larger seismic intensity corresponding to the same MIDR thresholds and indicate better 534 seismic performance under the same intensity level. However, in the later stage after the CP limit state, 535 the curves of the two conditions intersect and the models without slabs show larger S a (T 1 ) comparatively.

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It reflects that the models with slabs degenerate more seriously and deteriorate more rapidly when entering 537 into the plastic stage. Besides, the fragility curves move towards right from the NO to CP states, and 538 the models with slabs are commonly on the right of the models without slabs under the same conditions,

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We declare that we have no financial and personal relationships with other people or organizations that 556 can inappropriately influence our work.