Experimental study on seismic performance of precast concrete frame with viscous damper

Abstract

Viscous dampers are widely used in reinforced concrete (RC) structures due to their effective energy dissipation under seismic loading. This study investigates the seismic performance of three single-story, single-bay RC frames: a precast concrete (PC) frame with a viscous damper, a cast-in-place (CIP) frame with a viscous damper, and a PC frame without a damper. A sinusoidal steady-state excitation test was conducted to evaluate structural behavior under varying frequencies. The experimental analysis covered failure modes, hysteresis response, displacement ductility, stiffness degradation, energy dissipation capacity, and equivalent viscous damping. The results show that adding a viscous damper significantly improved lateral resistance, initial stiffness, and energy dissipation capacity, while slightly reducing displacement ductility. The PC frame with a damper showed seismic behavior similar to the CIP frame, indicating that dampers can effectively compensate for construction-related discontinuities in precast systems. The calculated-to-experimental strength ratio ranged from 0.57 to 0.62, highlighting the conservative nature of code-based predictions. These findings support the application of viscous dampers in PC frames and provide valuable experimental data for enhancing seismic resilience in building design.

Graphical abstract

Keywords

precast concrete frame / viscous damper / seismic behavior / energy dissipation / failure mode

1 Introduction

Strong earthquakes result in numerous casualties globally annually. Traditional seismic designs have historically emphasized optimizing the structural members, often resulting in increased building strength and stiffness, consequently leading to higher material consumption [1]. Moreover, the increased stiffness results in greater seismic forces, rendering these designs less cost-effective. Consequently, many researchers have sought new alternatives. Energy dissipation devices, such as active and passive controllers, are deemed effective supplementary tools for enhancing the seismic performance of structures [2]. The energy dissipative device is a distinct structural element designed to absorb or dissipate a fraction of the incoming energy when integrated into a structure. This process helps reduce the energy dissipation requirements of the primary structural components, thereby mitigating the risk of potential damage to the overall structure [3]. Currently, structural vibration control methods that incorporate energy dissipation devices are typically divided into four categories: passive [4,5], active [6,7], semi-active [8,9], and hybrid control strategies [10,11]. Compared to active, semi-active, and hybrid control strategies, passive structural control offers a reliable method to protect structures under extreme loading conditions [12,13]. Passive devices are characterized by their simplicity, low cost, and ease of installation, making them the most widely accepted approach for mitigating seismic loads [14,15].

Viscous dampers are passive energy dissipation devices that are velocity-dependent, exerting damping force solely based on velocity. This characteristic facilitates the generation of responses inherently out of phase with structural deformations, consequently reducing stresses and deformations within structures. Furthermore, the viscous damper does not alter the stiffness characteristics of the primary structure, thereby maintaining the natural vibration frequency and the integrity of the original design [16,17]. As a result, the application of viscous dampers has garnered considerable attention and increasingly been implemented across various architectural contexts [18]. Reinhorn et al. [19] performed a series of shaking table experiments on a 1:3 scale model of a reinforced concrete (RC) frame, demonstrating that the incorporation of dampers effectively mitigates the need for excessive inelastic deformation and damage. Lu et al. [20] tested a three-story cast-in-place (CIP) frame structure with viscous wall dampers, demonstrating an increase of over 20% in structural damping ratio and a decrease in displacement response of 30% to 60%. Hwang et al. [21] investigated the seismic behavior of frames incorporating “non-structural” lightweight CIP exterior/interior walls and upper diagonal braces with viscous dampers, finding that viscous dampers are effective even when relative velocity and displacement are restricted by non-structural walls. Several studies on viscous dampers also investigate their role in controlling impact vibrations [22], limit states, and failure mechanisms [23], as well as the development of novel dampers [24] and associated design methodologies [25–29]. The aforementioned studies have collectively demonstrated the beneficial impact of installing viscous dampers on seismic behavior of buildings.

Currently, the construction industry is encountering significant challenges related to labor shortages and resource inefficiency. These issues are particularly prevalent in projects utilizing the CIP concrete framework construction method, which is increasingly strained by aging populations and the finite availability of natural resources [30]. Utilizing precast concrete (PC) framework structures in certain areas of construction serves as a viable solution [31]. Components of PC framework structures are prefabricated in factories, ensuring higher precision and better quality control. After transportation to the construction site, they are assembled into a complete structure through reliable connections. This method requires less labor and proceeds rapidly, thus ensuring timely completion of the construction plan [32]. Furthermore, this method contributes to reducing environmental effects, including dust and noise pollution [33]. Consequently, PC framework structures have been adopted in countries like China, Europe, the United States, and Japan. However, research on the seismic behavior of PC frameworks equipped with viscous dampers remains limited [34]. In contrast to previous studies, which primarily focus on either CIP frames or numerical simulations, this research provides a comprehensive experimental investigation comparing the seismic performance of precast and CIP concrete frames with and without viscous dampers under controlled sinusoidal steady-state excitation. Unlike traditional pseudo-static tests, this loading protocol enables the evaluation of damping effectiveness across varying frequencies, offering deeper insight into the dynamic response characteristics of damper-equipped frames. Moreover, the study evaluates whether viscous dampers can enhance seismic performance without altering the failure modes of PC systems. This dual focus, on experimental frequency-based behavior and structural failure patterns, addresses a significant gap in current literature and contributes new data and design implications for the implementation of viscous damping in precast construction.

To further investigate the seismic behavior of viscous dampers in PC frames, this study examines the seismic behavior of PC frames equipped with viscous dampers. Furthermore, a comparison is made between the seismic performance of PC frames without viscous dampers and those with viscous dampers, as well as CIP frames equipped with viscous dampers. Experimental tests were conducted to thoroughly examine the hysteresis behavior and failure characteristics of the specimens. In-depth analysis was performed on key seismic performance indicators, including ductility, stiffness degradation, energy dissipation, equivalent viscous damping, and deformation patterns. The results from this study offer valuable insights and can be used as a reference for implementing viscous dampers in PC frames.

2 Experimental program

2.1 Specimens design and material properties

To study the seismic performance of PC frame with viscous damper (PCFV), three single-story, single-bay RC frames were built in this study. As depicted in Fig.1, the specimens were divided into two distinct categories based on their composition: with and without viscous damper (with and without “V” in the specimen label). The specimens can be classified into two distinct groups based on their composition: PC frame and CIP frame (“PC” and “RC” in the specimen label). The specimens were designed in compliance with the relevant Chinese standards, such as GB 50010-2010 [35], GB 50011-2010 [36], and JGJ 1-2014 [37].

All the specimens had the same external dimensions and reinforcement. The test specimens feature a story height of 2100 mm and a span of 3900 mm. The concrete beams have a cross-section of 200 mm × 350 mm, while the columns are designed with a cross-section of 350 mm × 350 mm. To ensure stability, the foundation beam was securely anchored, providing a fixed base. The specific dimensions and reinforcements of the PCFV are illustrated in Fig.2. To enhance the structural integrity of PCFV and PC frame without viscous damper (PCF) specimens, composite beams with a topping of 100 mm were selected. The upper surfaces of the PC beams were roughened using a stiff wire brush, achieving an average roughness amplitude of 6 mm. Additionally, mechanical shear keys were positioned at the ends of both the beams and columns. To effectively connect the columns and the foundation beam, grouted sleeve connections were adopted. The sleeves being used are 410 mm long and have an outer diameter of 54 mm. For attachment to the foundation beam, all the vertical reinforcement in the columns were grouted into sleeve for 200 mm. A 20 mm thick grouted joint was provided at this interface. Moreover, the longitudinal reinforcement in the beams and columns were all anchored by anchor plates. To prevent the core region of each connection from flexure failure in oblique sections, the U-bars were adopted at the corner. The three specimens were identical except that the vertical bars in RC frame with viscous damper (RCFV) specimen were continuous into the foundation beam. Consequently, the specimens were designed to align with the seismic design principles of strong column-weak beam, strong connection-weak member, and strong shear-weak bending.

All specimens were fabricated using concrete of grade C40 (compressive cube strength of 40 MPa). In accordance with GB/T 50081-2002 [38], three standard concrete cubes, each with dimensions of 150 mm × 150 mm × 150 mm, were used to conduct compressive strength tests. The mechanical properties of the concrete are presented in Tab.1. And all the specimens were reinforced with HRB400E steel bar. Direct tensile tests were conducted on three bars for each diameter, following the guidelines specified in the Chinese standard GB/T 228.1-2010 [39]. The mechanical properties of steel bars are shown in Tab.2. According to Chinese standard JG/T 408-2019 [40], the flexural strength and fluidity of the grout were determined and are shown in Tab.3. Tab.4 presents the specific parameters for the nonlinear viscous dampers used in both “PCFV” and “RCFV” systems. The viscous dampers employed in specimens PCFV and RCFV were nonlinear fluid viscous dampers, characterized by a damping coefficient C=100\mathrm{k}\mathrm{N}/{(\mathrm{m}/\mathrm{s})}^{\alpha } and an exponent \alpha =0.2. Each damper was designed with a maximum force capacity of 100 kN, a velocity limit of 60 mm/s, and a displacement capacity of ±100 mm. These devices were placed horizontally between the beam ends and foundation, using rigid steel connections to ensure force transmission. The dampers used in this experiment were commercially available and selected to simulate practical implementation in mid-rise frame buildings. Additionally, the ultimate lateral resistances reported in Tab.5 were calculated using the formulation specified in GB 50010-2010 [35]. These values were derived using the characteristic strength values of concrete and reinforcement, without the application of partial safety factors. As such, the results reflect the nominal structural capacity intended for comparison with experimental measurements.

2.2 Test setup and instrumentations

Fig.3 illustrates the schematic of the complete experimental setup. During the experimentation, a series of sinusoidal excitations, varying in amplitude and frequency, were applied to the specimens. The foundation beam is anchored to the laboratory floor with eight steel bolts. On both sides of each specimen, two steel transfer beams were positioned and interconnected by four rods, each with a diameter of 42 mm. Subsequently, the left-side transfer beam was secured to the MTS hydraulic actuator using bolts. The horizontal cyclic forces generated by the actuators were transmitted to the test specimen via steel plate transfer beams. To prevent out-of-plane deformation, four lateral supports, composed of rollers, were positioned on either side of the specimen using a triangular reaction frame. Additionally, the horizontal cyclic load applied to the specimens was regulated by a single MTS hydraulic actuator, which was fixed to the reaction wall.

2.3 Testing procedures

The procedure outlined in the Chinese standard JGJ/T 101-2015 was proposed as the recommended protocol [41]. Considering that the experiment mainly studies the performance of specimens under the action of seismic force, and the gravity load has a small effect on the lateral displacement, so there’s no vertical load applied to the specimens in the test [42].

A 1000 kN MTS hydraulic actuator was used to apply horizontal loading. The experiment was loaded by sinusoidal steady-state excitation and controlled by the displacement amplitude and frequency. That is, a sine wave displacement is applied in the horizontal direction. The load function is defined as x = Asin2πft, where the excitation period T ranged from 1 to 10 s and the amplitude value of displacement A ranged from 1 to 90 mm. The lists of the loading cases are listed in Tab.6. The loading is carried out in the order of the displacement amplitude from small to large and frequency from low to high, and each loading stage consisted of three cycles. Under a certain displacement amplitude condition, the protocol of the loading procedure is shown in Fig.4. The peak displacement and peak acceleration of the test are 90 mm and 250 mm/s², respectively. The test was halted during the loading procedure if any of the following conditions were met: 1) the specimen experienced sudden failure and was no longer able to support the applied load, or 2) the specimen’s bearing capacity peaked and the load subsequently dropped below 85% of the maximum load (ultimate P_max).

2.4 Measurements

Fig.5 illustrates the arrangement of measurement points for recording specimen displacement and strain. For the instrumentation of specimen PCF, two linear variable differential transducers (LVDTs), designated as D1 and D2, were employed to monitor the in-plane lateral displacements at both the beam and the foundation beam. The relative slips at the interface of beam ends were measured by D3a, D3b, D4a, and D4b. The relative slips at the interface of column bottoms were measured by D5a, D5b, D6a, and D6b. Shear deformation in the specimens was quantified using two sets of cross LVDTs (D7a, D7b, and D8a, D8b), which were positioned at the joint areas. In the instrumentation of specimens RCFV and PCFV, the placement of the LVDTs was identical to that in specimen PCF, as previously described. However, an additional LVDT (denoted as D9) was incorporated in these two specimens to measure the relative displacement of the damper, as illustrated in Fig.5(a).

Strain gauges were employed to measure the strains in the longitudinal reinforcement and stirrups of beams and columns. Additionally, the strains in the stirrups and U-bars within the joint regions were also monitored using strain gauges. The arrangements of stain gauges in specimen PCFV are shown in Fig.5(b). The arrangements of strain gauges used in three specimens were identical except that CL5a–CL8a and CL5a–CL8a were only been used in PCFV and PCF specimens, BL14a–BL15a and BL14b–BL15b were only been used in PCFV and RCFV specimens.

3 Experimental results

3.1 Global response and failure behaviors of different specimens

3.1.1 Precast concrete frame without viscous damper

The load and displacement values of the specimens are considered positive when the actuator applies force in the pushing direction, while they are negative when the force is applied in the pulling direction. Additionally, the drift ratio (DR) is calculated as the ratio of the lateral displacement at the loading point to the story height. Fig.6–Fig.8 illustrate the damage features observed at the failure load for the beam ends, column bottoms, and joint regions, respectively.

Initially, under lateral loading, the PCF specimen remained in the elastic phase, and no cracks were observed. At the displacement (Δ) of 1 mm (DR = 0.05%) and applied lateral load (P) of 33.7 kN, a minor horizontal crack was observed in the grout layer at the base of the left column. As the load continued to increase, horizontal cracks appeared at the top of the left column, while vertical cracks were observed along the beam ends for Δ = 4 mm (DR = 0.19%) and P = 94.3 kN. For Δ = 6 mm (DR = 0.29%) and P = 124.7 kN, a small number of diagonal cracks were detected in the left joint area. With increase of displacement up to Δ = 18 mm (DR = 0.86%) and applied lateral load (P) of 237.5 kN, the longitudinal rebar at the left beam end began to yield. For Δ = 22 mm (DR = 1.05%) and P = 269.4 kN, the longitudinal rebar at left column bottom began to yield. By increasing the displacement (Δ) to 48.2 mm (DR = 2.27%), The specimen attained its peak lateral resistance, measuring P = 336.9 kN. In this cycle, grout layer in the extent of 10 mm on the both sides of column bottoms were crushed, many diagonal cracks pointing to the column bottoms occurred. Crushing of the concrete was observed at the beam corner ends, accompanied by cross-diagonal cracking at the joint areas. Additionally, noticeable slip was detected between the columns and the foundation beam. At the displacement (Δ) of 81.1 mm (DR = 3.85%), the lateral resistance of the specimen decreased to 85% of its peak value. At this point, grout layer in the extent of 100 mm on the both sides of column bottoms were crushed and the damage region was concentrated in a small vertical extent of column bottoms (Fig.7(a)). Moreover, the concrete in the horizontal of 150 mm at beam ends were crushed, the longitudinal reinforcement bars at the top of the beam ends experienced fracture, and the cracks at the joint regions were propagated but with small width.

3.1.2 Precast concrete frame with viscous damper

In comparison with specimen PCF, the nonlinear viscous damper was added in specimen PCFV. Initially, under lateral loading, the specimen remained within the elastic phase, with no visible cracks forming. At the displacement (Δ) of 2 mm (DR = 0.09%) and applied lateral load (P) of 61.5 kN, a minor horizontal crack was observed at the grout layer located at the base of the right column. As the load increased further, horizontal cracks appeared at the top of the right column, while vertical cracks were noted at the left beam end, corresponding to a displacement of Δ = 6 mm (DR = 0.29%) and a load of P = 159.4 kN. For Δ = 14 mm (DR = 0.67%) and P = 244.9 kN, few diagonal cracks were observed at both joint regions. With increase of displacement up to Δ = 18 mm (DR = 0.86%) and applied lateral load (P) of 281.6 kN, the longitudinal rebar at the left beam end began to yield. For Δ = 22 mm (DR = 1.05%) and P = 307.2 kN, the longitudinal rebar at right column bottom began to yield. By increasing the displacement (Δ) to 46 mm (DR = 2.19%), the specimen attained its peak lateral resistance, measured at P = 388.7 kN. During this cycle, the grout layer, extending 10 mm on both sides of the column bases, was fractured. Numerous diagonal cracks radiated from the column bottoms, while the concrete at the beam end corners also experienced crushing. Additionally, cross-diagonal cracks were observed at the joint regions. Moreover, the slip between the columns and the foundation beam were observed. At the displacement (Δ) of 73.2 mm (DR = 3.49%), the specimen’s lateral resistance decreased to 85% of its peak value. At this point, the grout layer in the extent of 125 mm on the both sides of column bottoms were crushed and the damage region was concentrated in a small vertical extent of column bottoms (Fig.7(b)).

3.1.3 Reinforced concrete frame with viscous damper

Initially, when lateral loading was applied, the RCFV specimen remained in the elastic phase, with no cracks developing. At the displacement (Δ) of 4 mm (DR = 0.19%) and applied lateral load (P) of 110.9 kN, horizontal cracks were observed at the lower part of the right column. Moreover, at the displacement (Δ) of 10 mm (DR = 0.48%) and applied lateral load (P) of 212.5 kN, vertical cracks occurred at the left beam end. As the load continued to increase, horizontal cracking was noted at the top of the left column, while diagonal cracking appeared in the right joint region, particularly at a displacement of Δ = 14 mm (DR = 0.67%) and an applied lateral load of P = 266.6 kN. With increase of displacement up to Δ = 22 mm (DR = 1.05%) and applied lateral load (P) of 321 kN, the longitudinal rebar at left beam end began to yield. For Δ = 26 mm (DR = 1.24%) and P = 359.3 kN, the longitudinal rebar at right column bottom began to yield. By increasing the displacement (Δ) to 51.2 mm (DR = 2.44%), the specimen achieved its peak lateral resistance at a force of 416.6 kN and the stirrups at the column bottoms began to yield. Throughout this cycle, numerous diagonal cracks developed in the columns. Additionally, the concrete at the lower corners of the columns and at the ends of the beams exhibited signs of crushing. Cross-diagonal cracks were also observed in the joint regions. At the displacement (Δ) of 74.4 mm (DR = 3.54%), the specimen’s lateral resistance decreased to 85% of its maximum value. At this point, concrete at the corner of the column bottoms were crushed, the damage region was in the vertical extent of 300 mm at column bottoms and there was a large shear deformation observed (Fig.7(c)). Moreover, the concrete in the horizontal extent of 150 mm at beam ends were crushed and peeled off and the cracks at the joint regions were propagated.

3.1.4 Comparison of failure modes

Fig.9 illustrates the ultimate crack patterns for each specimen. A comparison between the failure modes of specimens PCF and PCFV reveals significant similarities in their behavior. The beams are typically flexural failure at beam ends. Upon failure, the concrete at the beam corners was crushed, and the longitudinal reinforcement experienced yielding. No slippage was observed at the ends of the beams. The columns are also subjected to flexural failure. When the failure occurred, the longitudinal bars at column bottoms were yielded, and the grout layers at the bottom of the columns were crushed. Additionally, the primary failure occurred within the grout layers at the base of the columns. The plastic hinge zones were relatively small, and significant slippage was observed at the column bottoms.

By comparing the failure modes of specimen PCFV and RCFV, it is evident that the failure modes of the PCFV and RCFV specimens differ significantly. The beams of the two specimens are both subjected to flexural failure at the beam ends. Upon failure, the concrete at the beam corners was crushed, while the longitudinal reinforcement bars experienced yielding. The columns of the PCFV specimen experienced flexural failure. Upon failure, the grout layers at the base of the columns were crushed, and the longitudinal reinforcement bars at the bottom yielded. Moreover, the failure was concentrated in a small extent of grout layer and the plastic hinges were in a small region. The columns of specimen RCFV are subjected to flexural-shear failure. During the failure, the concrete at column bottoms were crushed, the longitudinal bars in the extent of 400 mm at column bottoms were yielded, and the plastic hinges were in a large region. At the same time, a large shear deformation at column bottoms were observed, and the stirrups at column bottoms were slipped.

Fig.10 illustrates the strain distribution of the longitudinal rebars and stirrups at the right beam ends, as well as at the bottoms of the right columns, along with the stirrups and U-bars in the right joint regions. The detailed analysis revealed that the stirrups and U-bars within the joint areas did not exceed their yield strain limits, aligning with the specimen’s observed failure mode. Furthermore, all specimens successfully satisfied the design principle of a strong connection-weak member. In Fig.10(b) and Fig.10(d), only the stirrups at the column bottoms in specimen RCFV were yielded and they were yielded later than the longitudinal rebars at the same position, which indicates that all specimens satisfied the design criteria of exhibiting strong shear-weak bending behavior. In Fig.10(a) and Fig.10(c), all the longitudinal rebars reached their yield strain value. Moreover, for all specimens, the initial formation of plastic hinges occurred at positions ① and ② in Fig.11, followed by their development at positions ③ and ④. This progression indicated that the specimen exhibited the typical behavior of a strong column and weak beam.

3.2 Hysteresis curves

Hysteresis curves illustrate the correlation between lateral load and displacement at the top of the specimens. The hysteresis behavior is a critical parameter for evaluating the seismic performance of structures. The hysteresis curves of each specimen under loading frequency f = 0.1, 0.2, 0.3, and 0.5 Hz are depicted in Fig.12–Fig.14.

All specimens exhibited symmetric and stable hysteresis responses. Initially, the curves were narrow and nearly linear, indicating elastic behavior. As displacement increased, plastic deformation developed, resulting in broader curves with significant area, representing energy dissipation. For specimen PCF (Fig.12), the hysteresis loops gradually expanded with increasing drift, but were relatively pinched and showed limited energy dissipation due to the absence of a damper. In contrast, specimens PCFV (Fig.13) and RCFV (Fig.14) displayed notably plumper hysteresis curves with larger enclosed areas at the same DRs. This behavior is attributed to the contribution of the nonlinear viscous dampers, which provide velocity-dependent resistance and thus enhance energy dissipation, especially under higher frequency excitations. The difference in loop shape becomes more apparent at higher loading frequencies (e.g., f = 0.5 Hz). In both PCFV and RCFV, the loops remained stable and full, indicating effective damping behavior. Moreover, the increase in frequency led to visibly larger loop areas, confirming that the damper’s force output grew with velocity, consistent with the theoretical model. This highlights the frequency-sensitive behavior of the dampers. Among the three specimens, RCFV demonstrated the fullest hysteresis loops, slightly exceeding PCFV in both area and peak load, reflecting better monolithic integrity and marginally higher stiffness. The loops for PCFV were slightly more symmetric and regular than RCFV, possibly due to the uniform boundary conditions achieved by precast assembly and damper configuration.

In summary, the hysteresis curve analysis confirms that: The use of viscous dampers significantly improves energy dissipation. Higher frequencies lead to greater damping force and hysteresis area. PCFV achieve hysteretic performance comparable to RCFV, validating their use in seismic applications.

3.3 Skeleton curves

A skeleton curve represents the peak load points of each cycle and typically reflects the underlying force mechanism or the physical characteristics of the specimen. Fig.15 illustrates the skeleton curves for each specimen subjected to a loading frequency of 0.1 Hz, with the corresponding characteristic values presented in Tab.7. The crack state refers to the condition when cracks first emerge in the load-bearing components of the specimens. In this investigation, the yield state was determined using the equivalent elastoplastic energy-absorption method [43], as depicted in Fig.16. The ultimate state was defined as the point at which the lateral resistance reduces to 85% of its peak value [41]. Overall, the skeleton curves of all specimens exhibited similar trends, with the inclusion of a damper resulting in enhanced initial stiffness and greater load resistance. These curves can be characterized by four key stages: cracking points, yield points, peak points, and ultimate points.

Prior to reaching the failure point, the skeleton curve exhibited near-linear behavior. The DR of the crack state of all specimens were almost the same. Moreover, the cracking loads of specimens PCFV and RCFV were almost the same but significantly greater than that of specimen PCF, which indicate that the damper started to work at a small lateral displacement. Between the cracking and yield points, the slope of the skeleton curves exhibited a noticeable reduction. The average value of positive and negative yielding load of specimen RCFV was slightly greater than that of PCFV. The main reason is that the CIP specimen is with a better integrity. Furthermore, the average positive and negative yielding loads of specimen PCFV are considerably greater than those of PCF. This suggests that the presence of the damper has a substantial effect on the specimen’s behavior under loading. Between the yielding and peak points, the slope of the skeleton curves exhibited a notable reduction. At the peak state, the maximum lateral resistance of specimen PCFV surpassed that of the PCF, though it was still lower than that of the specimen RCFV. The main reason is that the damper plays an important role while loading and the CIP specimen showed a better integrity. Ultimately, the slope of the skeleton curves for all specimens turned negative between the peak and ultimate points. Additionally, the specimens experienced a gradual reduction in strength after reaching the peak points, primarily due to concrete spalling and rebar yielding. In conclusion, the lateral resistance of the specimens PCFV and RCFV decreased significantly once they reached their peak resistance, in contrast to the specimen PCF, which exhibited a slower decline.

The ultimate load was estimated based on the peak load measurement. For specimen PCF, the average ultimate loads in both the positive and negative directions were found to be 286.3 kN, which corresponds to 86.7% of the ultimate load observed in specimen PCFV. This highlights the substantial contribution of the damper during loading conditions. Additionally, the average positive and negative ultimate loads of specimen PCFV were 348.2 kN, accounting for 93.3% of specimen RCFV, suggesting superior integrity in the CIP specimen.

4 Discussions

4.1 Displacement ductility and deformation ability

The failure modes of the specimens were closely linked to their displacement ductility. Displacement ductility µ is defined as the ratio of the displacement at the ultimate state to the displacement at the yield state [43], as illustrated in Eq. (1).

(1)\mu ={\mathrm{\Delta }}_{\mathrm{u}}{/\mathrm{\Delta }}_{\mathrm{y}}.

Tab.7 provides a summary of the displacement ductility values for all specimens. The results show that the ductility factor of the specimen PCFV was 3.20, which was about 1.3% and 11.3% lower than that of the specimen RCFV and the specimen PCF, respectively. The maximum displacement of the PCFV specimen was 73.2 mm, which represented a reduction of approximately 9.7% compared to the PCF specimen, and 1.6% less than the RCFV specimen. In terms of displacement ductility, the precast specimen equipped with a damper exhibited a similar performance to its corresponding CIP counterpart. However, it was found to have lower ductility than the corresponding precast specimen without the viscous damper. The main reason is that the stiffness of specimen PCF declined slowly in comparison with specimen PCFV and RCFV, so that the specimen PCF has a larger ultimate displacement and larger ductility coefficient.

4.2 Stiffness degradation

Typically, the stiffness of the specimens diminished as the number of displacement cycles increased. To examine the progression of stiffness degradation, a plot of secant stiffness versus displacement is presented in Fig.17. The secant stiffness of each cycle is calculated as follows:

(2){\mathit{K}}_{\mathit{i}}={\mathit{P}}_{\mathit{i}}{/\mathrm{\Delta }}_{\mathit{i}},

where P_i and Δ_i are the peak lateral resistance and corresponding displacement, respectively, of ith cycle. Fig.17 illustrates that the initial stiffness of the specimen PCFV exceeded that of the specimen RCFV by approximately 4.0%, and was 9.2% greater than the stiffness of the specimen PCF. Furthermore, as displacement increased, the stiffness of the specimen PCFV decreased much slower in comparison with the corresponding specimen PCF, but deceased slightly faster than that of the corresponding specimen RCFV in the positive direction.

4.3 Energy dissipation and equivalent viscous damping

Energy dissipation capacity plays a crucial role in evaluating the seismic performance of materials. To quantify this capacity, the energy dissipation for each specimen was determined by calculating the areas enclosed within each cycle of the corresponding load–displacement hysteresis curve. Fig.18 illustrates the correlation between the displacement and the single-cycle energy dissipation of each specimen. Additionally, it shows the relationship between the energy dissipation ratio of the damper (Φ) to the total energy dissipated and the displacement (Δ) across various frequencies. At frequencies of 0.1, 0.2, 0.3, and 0.5 Hz, the energy dissipation capacity of the PCFV specimen was comparable to that of the RCFV specimen, while being significantly greater than that of the PCF specimen. Moreover, the value of Φ of specimen RCFV was slightly higher than that of specimen PCFV, which indicates that the specimen RCFV was damaged slightly lighter than specimen PCFV and the reason is that the specimen RCFV was with better integrity. With the loading frequency increased, the energy dissipation capacity and the values of Φ of specimens PCFV and RCFV was improved. This trend aligns with the velocity-dependent behavior of the nonlinear viscous damper, in which a higher velocity at increased frequency produces a larger damping force. However, due to the relatively small damping exponent (α = 0.2), the growth in damping force was moderate. In comparison with existing literature, the energy dissipation performance observed in this study is consistent with values reported for similar damper-enhanced RC structures. For instance, previous studies reported that equivalent damping ratios ranging from 0.15 to 0.25 are typical for RC frames equipped with fluid viscous dampers [18,23]. In this study, the equivalent viscous damping ratio reached values of up to 0.22 for PCFV and 0.25 for RCFV, which fall within this range. Therefore, the effectiveness of the dampers observed here is not only significant but also aligns well with international experimental benchmarks. As the displacement increased, the energy dissipation capacity of all specimens improved due to further progression into the inelastic range. Meanwhile, the values of Φ for PCFV and RCFV decreased with increasing displacement, indicating that more energy was being absorbed by structural components rather than dampers at larger deformation levels.

This study calculates the equivalent viscous damping using the following approach:

(3){\xi }_{\mathrm{e}\mathrm{p}}=\frac{E_{\mathrm{s}\mathrm{i}}}{2\pi k_{\mathrm{s}\mathrm{i}}{\delta }_{max,i}}.

In the ith cycle, the energy dissipation of the specimen is denoted by E_{\mathrm{s}\mathrm{i}}, while k_{\mathrm{s}\mathrm{i}} represents the stiffness during the same cycle.

Fig.19 illustrates the correlation between the equivalent viscous damping ratio (ξ_eq) of each specimen and its displacement. At frequencies of 0.1, 0.2, 0.3, and 0.5 Hz, the equivalent viscous damping ratio (ξ_eq) of specimen PCFV was observed to be greater than that of specimen RCFV. This suggests that the RCFV specimen exhibited less damage compared to the PCFV specimen, maintaining better structural integrity. Moreover, the equivalent viscous damping ratio ξ_eq of specimens PCFV and RCFV was obviously higher than specimen PCF which indicates that the dampers dissipated lots of energy under loading. With the loading frequency increased, the equivalent viscous damping ratio ξ_eq of all specimens were increased. That shows that with increase in the frequency, the frame came into inelastic phase further for all specimens and the damping force increased for specimens PCFV and PCFV. As the displacement increased, the equivalent viscous damping ratio (ξ_eq) of all specimens initially decreased, but after reaching a certain point, it began to rise progressively with further displacement. That shows that with increase in the displacement, the frame came into inelastic phase further for all specimens and the damping force increased for specimens PCFV and PCFV.

4.4 Analysis of the lateral resistance

The comparison of calculated values and experimental values of lateral resistance are depicted in Tab.8, in which the calculated values of frames were calculated according to Chinese code GB 50010-2010 [35]. These design values were computed based on the characteristic strengths of materials (concrete and reinforcement), without the inclusion of partial safety factors. As such, they represent nominal capacity estimates meant for direct comparison with experimental measurements. The lateral resistance of the frame portion of the specimen PCFV was 338 kN, which was about 0.3% higher than that of the specimen PCF, and 7.7% lower than that of the specimen RCFV. Although the addition of the viscous damper in PCFV improved the overall seismic performance (e.g., energy dissipation and stiffness), its lateral resistance remained close to or slightly lower than that of PCF. This may seem counterintuitive, but can be explained by two key factors. First, the damper redistributes energy by providing external damping rather than contributing directly to the structural lateral strength. As a result, while it enhances the system’s capacity to absorb seismic energy, it does not substantially increase the peak load-bearing capacity of the structural frame itself. Second, the PCF specimen experienced a slower stiffness degradation, as discussed earlier, and due to the absence of a damper, more lateral load was resisted directly by the frame elements. This may have slightly elevated its measured peak lateral resistance. Regarding the CIP specimen RCFV, its lateral resistance was the highest among the three. This can be attributed to its superior integrity and monolithic construction, which enables more efficient stress transfer and reduced slip or joint deformation. The ratio of the calculated lateral resistance (based on design code) to the experimental values was 0.62 for PCF and PCFV, and 0.57 for RCFV. These ratios demonstrate that the code predictions are conservative. The conservative nature of GB 50010-2010 stems from its reliance on simplified assumptions and safety factors to account for material variability and construction uncertainties. Moreover, the code does not explicitly consider the effect of energy dissipation devices like viscous dampers, which can contribute significantly to real-world performance but are not reflected in strength-based calculations.

4.5 Theoretical interpretation of viscous damping mechanism

To further interpret the experimental findings, a theoretical analysis was conducted based on the working mechanism of nonlinear viscous dampers. The damping force generated by the damper can be expressed as Eq. (4).

(4)F_{\mathrm{d}}=C\cdot v^{\alpha },

where F_{\mathrm{d}} is the damping force, C is the damping coefficient, v is the relative velocity across the damper, and \alpha is the velocity exponent. In this study, the dampers used had parameters C=100\mathrm{k}\mathrm{N}/{(\mathrm{m}/\mathrm{s})}^{\alpha } and \alpha =0.2.

A simplified single-degree-of-freedom model was employed to analyze the influence of loading frequency on structural response. Under harmonic excitation x\left(t\right)=A\mathrm{s}\mathrm{i}\mathrm{n}\left(2\pi ft\right), the damper velocity v\left(t\right)=\dot{x}\left(t\right)=2\pi fA\mathrm{c}\mathrm{o}\mathrm{s}\left(2\pi ft\right). Thus, the instantaneous damping force is frequency-dependent, as shown in Eq. (5).

(5)F_{\mathrm{d}}\left(t\right)=C\cdot (2\pi fA\mathrm{c}\mathrm{o}\mathrm{s}(2\pi ft){)}^{\alpha }.

The equivalent energy dissipated per cycle is proportional to the integral of F_{\mathrm{d}}\cdot v over time. Since , the damping force increases with frequency, but at a sublinear rate. This explains why higher excitation frequencies led to greater energy dissipation and fuller hysteresis curves, as observed experimentally. The theoretical model aligns with the experimental observation that the contribution of the damper becomes more pronounced at higher frequencies, despite the nonlinear characteristic of the damper limiting the rate of increase.

4.6 Collapse mechanisms and the role of dampers

The failure modes of the specimens reveal key differences in structural behavior, particularly between PCFV and RCFV. The experimental results show that PCFV specimens exhibited flexural failure at the beam ends and column bases, while RCFV specimens experienced a combination of flexural and shear failure at the column bases. This section provides a theoretical discussion of how the viscous damper influences collapse mechanisms. In the PCFV specimen, the damper contributed additional lateral resistance and energy dissipation, which delayed the development of plastic hinges in both the beams and columns. Because the damper acts as a velocity-dependent force element, it effectively reduces peak displacements and redistributes internal forces, leading to more localized and ductile failure patterns. This explains the smaller plastic hinge zones and limited damage observed in PCFV.

In contrast, in the RCFV specimen, although similar dampers were used, the CIP construction offered higher global integrity and stiffness. As a result, the stress was more efficiently transferred to the column bases, leading to larger plastic hinge regions and the development of shear cracks. The higher stiffness of the CIP system, combined with the strong energy dissipation of the damper, caused a more complex interaction between flexural and shear mechanisms. These findings underscore the importance of accounting for damping-induced force redistribution in failure mode prediction and structural design when implementing nonlinear viscous dampers.

4.7 Limitations and future work

This study focuses on the seismic performance of single-story, single-span frame specimens. While the results provide meaningful insight into the influence of viscous dampers on precast and CIP concrete structures, their applicability to multi-story or irregular buildings requires further investigation. In particular, the effects of higher mode contributions, cumulative damage over multiple stories, and interstory interaction have not been addressed in this work. Additionally, this work provides experimental evidence but does not yet incorporate detailed numerical simulations or performance-based seismic design implications. Future work will involve nonlinear time-history analysis and design optimization. These limitations point toward future directions for validating the findings in broader structural contexts and incorporating them into engineering practice.

5 Conclusions

Based on the experimental data, an analysis was conducted on the PCFV, which was then compared to the RCFV and the PCF. The primary objective was to assess the seismic performance, focusing on factors such as failure modes, hysteresis characteristics, displacement ductility, deformation capacity, stiffness degradation, energy dissipation ability, and lateral resistance. From this analysis, several key conclusions can be drawn.

1) Beams of all frames experienced flexural failure near the beam-column joints. In the case of precast specimens PCF and PCFV, column failure occurred predominantly as flexural failure at the bottom of the column, concentrated within the grout layer, exhibiting a limited plastic hinge region, and substantial slip at the column base. In contrast, RCFV columns experienced flexural-shear failure, featuring a larger plastic hinge region and significant shear deformations observed at the column base.

2) The hysteresis curves of PC frames equipped with viscous dampers were relatively plump, resembling those of corresponding CIP specimens, but both were superior to PC specimens without viscous dampers. As the loading frequency increased, the hysteresis curves of all specimens became plumper. PC frames with dampers exhibited similar hysteresis characteristics to their corresponding CIP specimens, but the hysteresis characteristics were more pronounced compared to PC specimens without viscous dampers.

3) The displacement ductility of PC frames with viscous dampers was approximately 1.3% and 11.3% lower than that of corresponding CIP frames and PC frames without dampers, respectively. The corresponding initial stiffnesses were higher by 4.0% and 9.2%, and the lateral resistances were higher by 0.3% and lower by 7.7%, respectively. Furthermore, with increasing displacement, the stiffness of PC frames with viscous dampers decreased more rapidly in the positive direction compared to PC frames without viscous dampers.

4) The inclusion of a viscous damper significantly improved the energy dissipation capacity of concrete frames under single-cycle loading. As the loading frequency rose, energy dissipation also increased, with the frames equipped with viscous dampers demonstrating a more pronounced enhancement. Furthermore, the equivalent viscous damping ratio of PC frames with dampers was marginally higher than that of the corresponding CIP frames, and considerably greater than that of the PC frames without dampers.

These conclusions support the integration of viscous dampers into PC systems and provide a valuable reference for improving seismic resilience in modern structural design. However, this research was limited to single-story frame specimens without vertical axial loads. The influence of higher-mode effects, interstory dynamics, and gravity loads was not considered. Therefore, the applicability of these findings to multi-story buildings requires further investigation. Future research will extend this study to multi-story frame systems and include detailed numerical simulations to explore dynamic response mechanisms under realistic seismic loading.

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