Parametric study on seismic performance of self-centering reinforced concrete column with bottom-placed rubber layer

Abstract

To realize seismic-resilient reinforced concrete (RC) moment-resisting frame structures, a novel self-centering RC column with a rubber layer placed at the bottom (SRRC column) is proposed herein. For the column, the longitudinal reinforcement dissipates seismic energy, the rubber layer allows the rocking of the column, and the unbonded prestressed tendon enables self-centering capacity. A refined finite element model of the SRRC column is developed, the effectiveness of which is validated based on experimental results. Results show that the SRRC column exhibits stable energy dissipation capacity and no strength degradation; additionally, it can significantly reduce permanent residual deformation and mitigate damage to concrete. Extensive parametric studies pertaining to SRRC columns have been conducted to investigate the critical factors affecting their seismic performance.

Graphical abstract

Keywords

seismic resilience / self-centering / rubber layer / flag-shaped hysteresis loop / parametric study

1 Introduction

The current seismic design method of building structures can prevent collapse and protect people’s lives during earthquakes. However, the most typically used frame structures do not provide satisfactory seismic performance, as indicated in previous earthquakes [1,2]. The observed undesirable seismic damage phenomena are due to the following reasons. (1) The intended “strong column and weak beam” mechanism does not function as intended because of plastic hinge failure at the end of the column; instead, “weak column and strong beam” occurs, which results in insufficient energy dissipation capacity, unsatisfactory seismic performance, and structural collapse. (2) Because of high plasticity, post-earthquake damage is severe, which necessitates a significant amount of time and economic cost for repair (or demolishment). In the 2011 Christchurch earthquake, structures constructed based on the classical aseismic design principle were destroyed significantly, which incurred approximately 40 billion NZD for restoration [3]. To reduce post-earthquake losses, modern building structures must demonstrate better performance. Therefore, new technologies to achieve seismic resilience are urgently required.

Investigations into damage caused by the 1960 Chilean earthquake, the 1952 Arvin Tehachapi earthquake in California, and the 1971 San Fernando earthquake show that the uplift of a column or pier base can mitigate damage and protect the members from critical failure under severe earthquakes [4–6]. Based on this finding and the concept of seismic resilience [7], researchers have proposed novel members and structures with rocking, self-centering, and replaceable mechanisms, which can ensure that the members and structures return to their initial positions with negligible residual deformation after earthquakes. Consequently, damage can be mitigated and avoided effectively, and repair costs and time can be significantly reduced [8,9].

Additionally, researchers have investigated the seismic performance of rocking or self-centering columns and piers via quasistatic tests, shaking table tests, and numerical simulation studies. Using unbonded post-tensioned prestressed tendons, disc springs, or shape memory alloys to enable self-centering, Chi and Liu [10], Kamperidis et al. [11], Freddi et al. [12], Chen et al. [13], and Wang et al. [14] proposed different forms of self-centering steel columns with rocking and replaceable mechanisms and analyzed their hysteresis behaviors under cyclic loading tests. Lu et al. [15] combined replaceable steel dampers with replaceable prefabricated blocks and proposed a novel rocking reinforced concrete (RC) column that can be repaired in situ after damage. Guo et al. [16] investigated a self-centering concrete frame with sliding infill walls under cyclic loading. Wang et al. [17] investigated a self-centering steel tube–concrete column via quasistatic tests. Yang et al. [18] performed cyclic loading tests to investigate the seismic behavior of a self-centering RC column base joint equipped with replaceable dampers. Similarly, to improve the seismic performance of bridge piers, experimental studies on the behaviors of different forms of self-centering segmental piers have been conducted [19–21]. RC frames with self-centering columns were investigated using shaking table tests [22–24]. In addition, other types of structural members equipped with different self-centering components and energy dissipation devices have been developed and investigated, such as various self-centering shear walls [25–27] and self-centering braces [28–30]. The studies above show that structures with rocking and self-centering mechanisms offer the advantages of less post-earthquake damage, small residual deformation, and easy repair, which are conducive to improving seismic resilience.

In terms of numerical simulation studies, Wang et al. [31] used the ABAQUS software and developed a refined finite element model of a self-centering steel column that uses shape memory alloy bolts. Elettore et al. [32] investigated a self-centering steel column with friction-type dampers at both member and structural system levels using OpenSees. Using ANSYS, Goshtaei et al. [33] analyzed the hysteresis performance of a self-centering steel column with shape memory alloy bolts developed by Wang et al. [14] and performed sensitivity analyses to evaluate the key factors affecting its behavior. Guo et al. [34] performed nonlinear time-history analyses of a self-centering prestressed concrete frame structure using OpenSees.

The aforementioned rocking or self-centering columns are primarily steel columns. Studies pertaining to self-centering RC columns are few, which is attributable to the complex detailing required. Moreover, particularly in self-centering RC columns, the rocking mechanism may reduce the compressive area at the bottom of the column, thus resulting in stress concentrations and consequently concrete damage. In contrast to the abovementioned rocking columns, Zhang et al. [35] proposed a cast-in-place RC column with a rubber layer placed at the bottom (RRC column) to mitigate damage in the plastic hinge region at the column bottom. The RRC column exploits the advantages of the small modulus and low stiffness of the rubber layer, which enables the members to exhibit behaviors similar to those yielded by the rocking mechanism. Results of quasi-static cyclic loading tests showed that the crack width, crack number, and damage degree of the plastic hinge region at the column bottom reduced significantly. The RRC column exhibited shuttle-shaped hysteresis curves, and its energy dissipation efficiency was better than that of the conventional RC column. Similar to the most typically used rocking or self-centering columns, RRC columns offer the advantages of low cost and easy construction. However, RRC columns indicate large and non-negligible residual deformations after unloading, and the column base exhibits a certain degree of damage, which is not conducive to the realization of seismic-resilient designs. Moreover, an appropriate numerical simulation method for RRC columns has yet to be developed.

Hence, a new type of self-centering RC column with a rubber layer placed at the bottom (SRRC column) is proposed herein. The self-centering capability of the SRRC column is enabled by unbonded prestressed tendons (UPTs), which allows the column to return to its original position after earthquakes, thus decreasing the permanent residual deformation. The energy dissipation capacity is primarily enabled by the bonded longitudinal reinforcement. A shear key is set at the bottom of the column to prevent potential horizontal slips at the column bottom. A comprehensive numerical simulation method for an SRRC column is developed to investigate the hysteretic behavior of the proposed column under cyclic loading. Additionally, extensive parametric studies are performed to investigate the critical factors affecting its seismic performance.

2 Working mechanism of SRRC column

Fig.1 shows the details of the proposed SRRC column. The RC foundation, RC column, rubber layer, steel plate layer, shear key, and UPTs are key components. The RC foundation features a slot, and steel plates are placed around and at the bottom of the slot. The RC column comprises a concrete portion, longitudinal reinforcements that extend into the foundation, and hoop reinforcements. The bottom of the column, comprises a rubber layer, steel plate layer, and shear key. Compared with the RRC column introduced in Ref. [35], the most distinctive feature of the proposed SRRC column is the use of UPTs and shear keys. The steel plate is embedded in the concrete portion through sufficient anchoring reinforcement and is connected to the rubber layer via vulcanization and sandblasting. The shear key is connected firmly to the steel plate. The middle of the rubber layer features an opening, through which the shear key passes and finally reaches the slot in the RC foundation, thus achieving high shear resistance and preventing large horizontal column slips. In practice, an RC column with an embedded polyvinyl chloride (PVC) duct is first prefabricated. The anchors for the steel strands should be arranged before the foundation concrete is cast, similarly for the longitudinal reinforcement. During assembly, the steel strands are passed through ungrouted PVC ducts to form UPTs. Finally, the UPTs are stretched to the required pretension force and then anchored securely. In particular, for multistory buildings, the steel strands can be inserted into the PVC ducts from top to bottom, after all columns, beams, and floor slabs of each story are placed in the intended positions. This guarantees reliable anchoring at both the top and bottom (particularly when the working space at the bottom must be reserved).

When subjected to earthquake excitation, the bottom of the column is lifted. Consequently, the longitudinal reinforcement elongates and dissipates seismic energy through plastic deformation. The UPTs exhibit high strength and remain elastic during service, thus providing self-centering capability and allowing them to return to their original position after an earthquake. The concrete portion of the RC column is almost free from tensile force; more importantly, the compressive damage to the concrete at the bottom is expected to be reduced significantly owing to the rubber layer at the bottom. By adopting the self-centering RC column proposed herein, concrete damage and permanent residual deformation are expected to be reduced significantly, thus allowing seismic resilience to be achieved.

3 Numerical modeling and validation

3.1 Element type and interaction

The proposed SRRC column was modeled using the ABAQUS software. The three-dimensional eight-node linear brick solid element with reduced integration and hourglass control was used for the concrete; the longitudinal reinforcement and hoop reinforcement were modeled using the T3D2 element; the UPTs were modeled using the two-node linear beam element; the three-dimensional eight-node linear brick solid element with incompatible modes is adopted for the steel plate layer; and the rubber layer is simulated using a three-dimensional eight-node linear brick solid element with the property of hybrid formulation, reduced integration, and hourglass control. Fig.2(a) shows a schematic illustration of the numerical model.

The interaction between the reinforcement cage and the concrete was defined as the “embedded region.” The reliable connections between the steel plate layer and each of the upper concrete, rubber layer, and shear key were simulated using the “tie” command. The top and bottom ends of the UPTs were connected to the column top and the bottom of the foundation using the “tie” command (node region-to-surface) to simulate reliable anchorage at both ends. “Surface-to-surface” contact was imposed to define the interface between the RC foundation and the rubber layer as well as between the pre-embedded steel plate in the foundation and the shear key. The “penalty” option with a friction coefficient was used to model the tangential behavior at the interface; the “hard” option was chosen to model the normal behavior, which implies that the contact interface cannot penetrate under compression and can be detached under tension. Meanwhile, the “kinematic” coupling constraint was imposed, where two areas at the top and side of the column were coupled to Reference Points 1 and 2 such that vertical and horizontal loads can be applied. Similarly, another controlling point denoted as Reference Point 3, was introduced to model the function of the shear key, as shown in Fig.2(b).

3.2 Material models

The concrete damage plasticity (CDP) model was used as the material constitutive model for concrete. The main parameters of the model were the compressive and tensile stress–strain, compressive plasticity damage–inelastic strain, and tensile plasticity damage–cracking strain relationships. Compressive and tensile plasticity damage factors were used to reflect the degradation characteristics of the elastic modulus of the concrete material due to damage [36], as presented in Fig.3, where E₀ is the initial elastic modulus of the concrete; ω_t and ω_c are the tensile and compressive weight factors respectively, which are the material parameters to describe the stiffness recovery under reverse loading.

Based on the calculation method of the energy equivalent principle, the tensile plastic damage factor d_t and compressive plastic damage factor d_c of concrete can be obtained as follows [37]:

(1)\{\begin{array}{rlr}& x_{\mathrm{t}}={\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{t}}}},& \\ & d_{\mathrm{t}}=0,& (x_{\mathrm{t}}⩽1),\\ \\ & d_{\mathrm{t}}=1-\sqrt{{\displaystyle \frac{1}{{\alpha }_{\mathrm{t}}{(x_{\mathrm{t}}-1)}^{1.7}+x_{\mathrm{t}}}}},& (x_{\mathrm{t}}>1),\end{array}

(2)

where ε is the strain of the concrete; ε_t and ε_c are the strains corresponding to the peak tensile and compressive stresses respectively; x_t is the ratio of the tensile strain to the peak tensile strain corresponding to the peak tensile stress; α_t is the descending parameter of the uniaxial tensile stress–strain curve; x_c is the ratio of the compressive strain to the peak compressive strain corresponding to the peak compressive stress; f_c is the axial compressive strength of the concrete; and α_a and α_d are the ascending and descending parameters of the uniaxial compressive stress–strain curve, respectively.

To reflect the bond slip behavior of the reinforcement and concrete, the hysteretic constitutive model of the rebar material proposed by Qu [38] was adopted, as shown in Fig.4(a), where E_s is the elastic modulus of the reinforcement; f_y is the yield strength of the reinforcement; α is the coefficient of post-yield stiffness; f_tmax and f_cmax are the maximum tensile and compressive stresses, respectively. The elastic modulus of the reinforcement and the Poisson’s ratio were set as 200 GPa and 0.3, respectively. The steel plate layer at the bottom of the member was simulated using a bilinear kinematic hardening model based on the von Mises yield criterion. The properties of the steel plate were as follows: initial elastic stiffness E, 206 GPa; Poisson’s ratio, 0.3; and secondary stiffness E′, 1% of the initial stiffness, as illustrated in Fig.4(b), where F_Y and ε_Y are the yield strength and yield strain of the steel plate, respectively.

The two-parameter Mooney–Rivlin model from the ABAQUS software was used as the material model of the rubber layer. It characterizes the mechanical properties of the rubber material based on its elastic strain energy W, which is expressed as follows:

(3)W=C_{10}(I_1-3)+C_{01}(I_2-3)+\frac{1}{D_1}(J-1{)}^2,

where C₁₀ and C₀₁ are the first and second Rivlin coefficients (MPa), respectively; D₁ is the material incompressibility coefficient, which is related to the bulk modulus of the material (MPa⁻¹); I₁ and I₂ are the first- and second-order Green strain invariants, respectively; and J is the volume ratio of the material before and after deformation.

The specific parameter values of the two-parameter Mooney–Rivlin model can be estimated using the following equations [39]:

(4)\{\begin{array}{c}{E}_{\mathrm{r}0}=6\left(C_{10}+C_{01}\right),\\ C_{01}=0.25C_{10},\\ D_1=\frac{2}{K},\end{array}

where E_r0 is the Young’s modulus of the rubber material (MPa) and K_r is the bulk modulus of the rubber material (MPa).

The UPTs were simulated using an elastic constitutive model with “isotropic” characteristics, and the expansion coefficient was used. The pretension force in the UPTs was applied using an equivalent temperature-reduction approach. The initial pre-tension force with a corresponding temperature reduction was achieved via the temperature field. The equivalent temperature reduction approach has been demonstrated to be effective and reasonable in previous studies [40,41].

3.3 Model validation and preliminary discussions

3.3.1 Model validation

To validate the finite element model proposed herein, three RRC columns subjected to cyclic loading in Ref. [35] were selected. Fig.5 shows the geometry and reinforcement parameters of test specimen RRC-1 in Ref. [35]. The other two specimens, RRC-2 and RRC-3, had the same configuration and reinforcement as specimen RRC-1, except for the thickness of the rubber layer. The thickness of the rubber layer at the bottom of the three test specimens was t = 30, 40, and 50 mm, respectively. The longitudinal reinforcement ratio of all three RRC column specimens was ρ₁= 1.5%. The steel plate layers of the specimens had a nominal yield strength of 345 MPa. The materials and test parameters of the specimens are listed in Tab.1, where f_c1 and f_c2 denote the axial compressive strength of concrete in the RC column and RC foundation, respectively; f_y1 and f_u1 are the yield strength and ultimate strength of the longitudinal reinforcement in the RC column, respectively; f_yv and f_uv are the yield strength and ultimate strength of the hoop reinforcement, respectively; f_y2 and f_u2 are the yield strength and ultimate strength of the longitudinal reinforcement in the RC foundation respectively; HA is the Shore hardness of the rubber layer; and n is the axial compression ratio, which can be defined as

(5)n=\frac{N}{A{f}_{\mathrm{c}}},

where N is the axial compression force (N); A is the cross-section area of the column (mm²); and f_c is the axial compressive strength of the concrete (MPa), respectively.

Similar to the SRRC column, the RRC column in Ref. [35] also featured a rubber layer at the bottom. However, the SRRC and RRC columns differed in the following aspects. (1) The rubber layer in the RRC column is connected firmly to the steel plates, which are embedded in the RC column and foundation via anchorage reinforcement; thus, the bottom interface of the RRC column cannot be uplifted under lateral force, whereas that of the SRRC column can be uplifted, as shown in Fig.6. (2) The RRC column does not contain unbonded prestressed strands, i.e., it does not offer self-centering.

In this study, a displacement-controlled cyclic loading protocol was adopted, as illustrated in Fig.7. Each amplitude was loaded once. Before loading an amplitude of 20 mm, the increment was 2 mm; beyond 20 mm, the increment was 4 mm until the amplitude reached 40 mm. Subsequently, the increment was 5 mm until a maximum amplitude of 50 mm was attained. The loading point was 200 mm from the top of the column, which resulted in a shear–span ratio of λ = 3.25.

For the two-parameter Mooney–Rivlin model in ABAQUS, Eqs. (3) and (4) were applied to simulate the rubber layer material. Detailed parameter values related to the mechanical properties of the rubber layer material are listed in Tab.2. Fig.8 shows a comparison of the simulated and experimental results, where the horizontal coordinate represents the displacement amplitude at the loading point and the vertical coordinate represents the horizontal reaction force at that point. For all three RRC column specimens, the simulated hysteresis curves agreed well with the test results and accurately reflected the load-bearing capacity, stiffness degradation, hysteresis energy dissipation, and residual deformation (see Fig.8(a)–Fig.8(c)). Therefore, the modeling method and finite element model proposed herein can be regarded as reasonable and effective.

Fig.8(d) shows a comparison of the backbone curves. The load-bearing capacity of the RRC column increased with the displacement loading amplitudes, which is not observed in conventional cast-in-place RC columns; furthermore, this shows that the load-bearing capacity of the RRC column does not degrade even under large displacements and that the column exhibits high ductility. A comparison of the results of specimens RRC-1/2/3 showed the load-bearing capacity, stiffness, and load capacity enhancement speed decreased as the rubber thickness increased. For each specimen, the calculated initial stiffness was slightly higher than the test results, which is attributable to a certain slip that occurred in the column base during the tests. Another potential reason is that the measured concrete elastic modulus is not provided in Ref. [35]; therefore, the concrete elastic modulus calculated in this study based on Ref. [36] may deviate slightly from its actual value.

Fig.9(a) shows the crack distribution of RRC-1 in the test and its tensile damage to concrete in the simulation, where the A- and B-plane are the column surfaces perpendicular and parallel to the loading direction, respectively. The result shows that the concrete tensile damage areas of RRC-1 obtained from the numerical simulation were consistent with the crack location in the test. Additionally, the compressive damage to RRC-1 obtained from the experimental tests and numerical simulation was compared, as shown in Fig.9(b). The numerical compressive damage agreed well with the experimental results.

3.3.2 Preliminary discussions

The RRC column specimen exhibited a plump shuttle-shaped hysteresis curve (see Fig.8), which demonstrates its superiority in dissipating energy. However, the RRC column exhibited non-negligible and large permanent residual deformations after unloading, and the concrete at the column bottom indicated unavoidable damage under tension and compression. The SRRC column proposed herein can address the issues above via the introduction of UPTs into the column to reduce the residual deformation, and the bottom interface of the column can be uplifted to mitigate concrete damage.

To compare the seismic performance of the RRC and SRRC columns, two models, i.e., RRC-0 (without UPTs) and SRRC-0 (with UPTs, an initial pretension force P₀ = 50 kN in each prestressed tendon with an elastic modulus of 196.5 GPa and a yield strength of 1860 MPa), were developed, and their hysteresis behaviors were compared through numerical simulation. The two models were developed based on test specimen RRC-2 (rubber thickness t = 40 mm) from Ref. [35]; the geometry and material parameters of the models are shown in Fig.5 and Tab.1, respectively. The axial compression ratios of the two models are listed in Tab.2. The axial compression ratio of the SRRC column is calculated using the following equation:

(6)n=\frac{N+N_{\mathrm{p}\mathrm{e}}}{A{f}_{\mathrm{c}}}=\frac{N}{A{f}_{\mathrm{c}}}+\frac{N_{\mathrm{p}\mathrm{e}}}{A{f}_{\mathrm{c}}}=n_1+n_2,

where N_pe is the effective value of the prestressing force provided by the UPTs (N); n₁ is the axial compression ratio caused by the applied vertical external load; and n₂ is the axial compression ratio caused by the prestressing force in the UPTs.

Fig.10 shows a comparison of the simulated results for RRC-0 and SRRC-0 in terms of the hysteresis responses, backbone curves, cumulative dissipation energy, equivalent damping ratio, residual deformation, and stiffness degradation. The cumulative energy dissipation E (kJ) was obtained by summing the areas of the hysteresis loops corresponding to different displacement amplitudes. The equivalent damping ratio {\zeta }_{\mathrm{e}\mathrm{q}} can be obtained as follows [42]:

(7){\zeta }_{\mathrm{e}\mathrm{q}}=\frac{1}{4\text{π}}\frac{E_{\mathrm{D}}}{E_{\mathrm{S}}},

where E_D (kJ) is the amount of energy dissipated by one cycle under each displacement amplitude; and E_S (kJ) is the amount of energy dissipated by the corresponding elastic system.

The residual deformation \delta (mm) is defined as the permanent displacement deformation of each loop under different displacement amplitudes after unloading. The stiffness coefficient K₁ (kN/mm) was adopted to evaluate the stiffness degradation trend of the models, which can be calculated as follows:

(8)K_1=\frac{P_i}{{\mathrm{\Delta }}_i},

where P_i (kN) is the peak load under different displacement amplitudes; and {\mathrm{\Delta }}_i (mm) is the horizontal displacement corresponding to the peak load P_i.

Based on a comparison of the hysteresis curves shown in Fig.10(a), unlike the shuttle-shaped hysteresis loops of Model RRC-0, Model SRRC-0 exhibited clear flag-shaped hysteresis loops. Compared with Model RRC-0, Model SRRC-0 exhibited a higher initial stiffness and load-bearing capacity owing to the addition of UPTs, as shown in Fig.10(b). Because both models were designed to exhibit identical longitudinal reinforcement ratios, their cumulative energy dissipation amounts were similar at each displacement amplitude, as shown in Fig.10(c). Fig.10(d) shows the comparison results for the equivalent damping ratio, i.e., Model RRC-0 exhibited a slightly larger equivalent damping ratio than Model SRRC-0. However, as the horizontal displacement increased, the equivalent damping ratio of Model RRC-0 increased and then decreased, whereas the equivalent damping ratio of Model SRRC-0 continued to increase. Based on a comparison of the residual deformation at each displacement amplitude shown in Fig.10(e), Model SRRC-0 indicated a smaller residual deformation, which is its distinct advantage. The stiffness of Model SRRC-0 was larger than that of Model RRC-0 at different displacement amplitudes, particularly for the initial stiffness at small displacements, although its stiffness degradation was also evident, as shown in Fig.10(f).

Fig.11 shows the concrete compressive damage in Models RRC-0 and SRRC-0 after the cyclic loading was completed. Based on Fig.11(a) and Fig.11(b), the concrete damage in both RRC-0 and SRRC-0 was concentrated in the bottom region of the columns. The compressive damage range of Model RRC-0 was distributed within 200 mm at the bottom of the column, and the maximum value of the damage factor was approximately 0.92. By contrast, the damage range of Model SRRC-0 was concentrated within only 50 mm at the bottom of the column, and the maximum value of the damage factor was only approximately 0.29. A comparison of the concrete compressive damage range and damage degree of the two models shows that the damage to Model SRRC-0 was less significant. Therefore, one may conclude that the new type of SRRC column proposed herein is conducive to controlling the location of column damage and reducing its damage degree.

Fig.12(a) shows the variation in the internal forces of the UPTs of Model SRRC-0, where the abscissa represents the loading displacement and the ordinate the stress ratio (f_p/f_py, where f_p is the stress value of the UPT, and f_py is its yield strength). For the UPTs on both the west and east sides, f_p/f_py (with a maximum value of 0.55) remained less than 1.0 during the loading process, which implies that the stress level in the steel strand is less than its yield strength. In other words, the UPTs were always in an elastic state. Fig.12(b) shows the variation in the uplift height h₀ at the bottom of Model SRRC-0. The maximum uplift of Model SRRC-0 was approximately 11 mm at the maximum loading displacement.

Fig.13 shows the stress distribution of the reinforcement in the two models under the peak load. The following conclusions were inferred based on comparative analysis. (1) The maximum stress of the tensile longitudinal reinforcement in Model SRRC-0 (von Mises stress of 467.7 MPa) exceeded that in Model RRC-0 (von Mises stress of 434.4 MPa), which implies that the uplift of the bottom opening is conducive to the maximum utilization of the tensile longitudinal reinforcement. (2) The maximum stress of the compressive longitudinal reinforcement in Model SRRC-0 (von Mises stress of 409.8 MPa) was smaller than that in Model RRC-0 (von Mises stress of 467.5 MPa), which indicates that the opening uplift reduces the stress level of the compressive longitudinal reinforcement and thus delays its compressive buckling. (3) The stress distribution of the hoop reinforcement in both models was relatively low, with a maximum value of 70–80 MPa.

The stress distribution of the rubber layer and steel plate in Model SRRC-0 under the peak load are shown in Fig.14. Based on Fig.14(a), the rubber layer was almost free from tensile stress owing to the column bottom uplift, and the maximum von Mises stress in the rubber layer on the compressive side was only approximately 0.48 MPa. Fig.14(b) shows the stress distribution of the steel plate and shear key in Model SRRC-0. The stress levels of the steel plate layer and shear key were low, with a maximum von Mises stress of approximately 150.5 MPa, which is significantly lower than the nominal yield strength of the steel (345 MPa). In general, the rubber layer, steel plate layer, and shear key in Model SRRC-0 remained elastic during the loading process; thus, their safety margins were sufficient

4 Parametric study

The proposed SRRC column exhibited flag-shaped hysteresis responses, as indicated by the results presented in the previous section. More importantly, the residual deformation of the SRRC column after unloading was small, and the damage degree of the column was effectively controlled and mitigated. To expand the investigation, other critical factors that affect the seismic performance of the SRRC column were determined using Model SRRC-0 presented in Section 3 as the reference model, which is denoted as Model S0. A series of finite element models denoted as Models S1–18 were designed to investigate the effects of different parameters (including the longitudinal reinforcement ratio ρ_l, longitudinal reinforcement yield strength f_y1, rubber thickness t, rubber hardness HA, initial pretension force P₀, and axial compression ratio n). Subsequently, numerical parametric studies were conducted to compare the hysteresis performances of the different models. Tab.3 lists the parameters of the model in detail. The axial compression ratios are listed in Tab.4. Tab.5 lists the detailed parameters related to the mechanical properties of rubber layers with different hardness values in the models.

4.1 Longitudinal reinforcement

4.1.1 Reinforcement ratio

Fig.15 presents a comparison of the SRRC columns with different levels of longitudinal reinforcements. Based on Fig.15(a), as the longitudinal reinforcement ratio increased, the hysteresis loops of the column models evolved gradually from flag shaped to shuttle shaped. For instance, Model S3 with the largest longitudinal reinforcement ratio exhibited the plumpest hysteresis curve and the least evident pinching characteristics, whereas Model S1 indicate the opposite results. The load-bearing capacity of each model increased with the horizontal displacement amplitude without strength degradation, and the models with large longitudinal reinforcement ratios indicated greater initial stiffness and peak load-bearing capacities, as shown in Fig.15(b). Fig.15(c) shows a comparison of the cumulative dissipated energy of the models under different displacement amplitudes. The cumulative energy dissipation amount of each model increased with the horizontal displacement amplitude and longitudinal reinforcement ratio. Based on Fig.15(d), the equivalent damping ratio of the model increased with the longitudinal reinforcement ratio under large displacement amplitudes, which resulted in higher energy dissipation efficiency. Fig.15(e) shows a comparison of the residual deformation for each model. The residual deformation of the model became significantly larger as the longitudinal reinforcement ratio increased, which occurred because more longitudinal reinforcements in the model underwent plasticity deformation and dissipated energy. Therefore, energy dissipation and residual deformation should be evaluated and matched closely during the design process. In addition, the stiffness degradation curves of the models shown in Fig.15(f) indicate that the horizontal stiffness improved significantly as the longitudinal reinforcement ratio increased, although the rate of stiffness degradation increased as well.

4.1.2 Yield strength

To evaluate the effect of the longitudinal reinforcement, Models S4–S6 were designed with different reinforcement yield strengths, whereas the other design parameters were fixed. Fig.16 shows the comparison results. Based on Fig.16(a), as the yield strength of the longitudinal reinforcement increased, the hysteresis loops became plumper. Model S6, which featured a longitudinal reinforcement with the highest yield strength, exhibited the plumpest hysteresis loops, whereas Model S4, which featured a longitudinal reinforcement with the lowest yield strength, showed the most evident pinching behavior. The load-bearing capacity of each model increased gradually with the displacement and the peak load-bearing capacity increased with the yield strength of the longitudinal reinforcement, whereas the initial horizontal stiffness remained almost constant, as shown in Fig.16(b). The cumulative energy dissipation increased with the longitudinal reinforcement yield strength, as shown in Fig.16(c). A comparison of the equivalent damping ratios is shown in Fig.16(d). The models with larger longitudinal reinforcement yield strengths indicated smaller equivalent damping ratios at small horizontal displacement amplitudes and larger equivalent damping ratios at large horizontal displacement amplitudes. In other words, increasing the longitudinal reinforcement yield strength improves the energy-dissipation efficiency at large displacements. Fig.16(e) shows the residual deformation of each model under different displacement amplitudes. The residual deformation of the model increased significantly with the longitudinal reinforcement yield strength, which indicates the necessity for a design that balances both energy dissipation and self-centering capacity. Based on Fig.16(f), the horizontal stiffness of the model increased as the longitudinal reinforcement yield strength increased, and the stiffness degradation can be delayed to a certain extent.

4.2 Rubber property

4.2.1 Thickness

Fig.17 shows a comparison among Models S7–S9, which featured different rubber layer thicknesses. Based on Fig.17(a), all models exhibited flag-shaped hysteresis curves, and the plumpness of their hysteresis loops was relatively similar. As the thickness of the rubber layer increased, the load-bearing capacity, post-yield stiffness, and strength increase rate of the model decreased, whereas the initial stiffness remained unchanged. For instance, Model S7, which featured the smallest rubber layer thickness, indicated the maximum load-bearing capacity, post-yield stiffness, and load capacity increase speed, as shown in Fig.17(b). Fig.17(c) shows a comparison of the cumulative energy dissipation, which was the same at each displacement amplitude, indicating that the effect of the rubber layer thickness on the cumulative energy dissipation of the model is negligible. A comparison of the equivalent damping ratios is shown in Fig.17(d). The larger thickness of the rubber layer corresponded to a larger equivalent damping ratio and higher energy dissipation efficiency. The results shown in Fig.17(e) indicate that the effect of the rubber layer thickness on the residual deformation of the model was insignificant because the models with different rubber layer thicknesses exhibited similar amounts of residual deformation at each displacement amplitude. Under large horizontal displacements, the stiffness degradation became more conspicuous as the rubber layer thickness increased, as shown in Fig.17(f).

4.2.2 Hardness

Models S10–S12 were designed with different rubber layer hardness values. Fig.18(a)–Fig.18(f) show comparisons of the hysteresis responses, backbone curves, cumulative energy dissipation, equivalent damping ratio, residual deformation, and stiffness degradation. The effect of the rubber layer hardness on the hysteresis performance of the SRRC column was insignificant and thus negligible since all models indicated similar responses.

4.3 Initial pretension force

The self-centering capacity of the SRRC column was realized using four UPTs. To investigate the effect of the initial pretension force provided by the UPTs, models with different levels of initial pretension forces (i.e., Models S13–S15) were developed and compared, as shown in Fig.19. Based on Fig.19(a), the plumpness of the hysteresis curve was similar for the different models, and pinching was particularly evident at the coordinate origin for the models with a large initial pretension force. As the initial pretension force increased, the load-bearing capacity and stiffness increased. For instance, Model S15 (P₀= 70 kN) indicated the highest load-bearing capacity and stiffness, as shown in Fig.19(b). Based on Fig.19(c), the cumulative energy dissipation of all models was similar, which indicates that the initial pretension force did not affect the cumulative energy dissipation. This can be explained by the fact that the UPTs remained elastic during loading. Fig.19(d) shows that a larger initial pretension force resulted in a smaller equivalent damping ratio and a lower energy dissipation efficiency. Fig.19(e) shows a comparison of the residual deformation. The initial pretension force significantly affected the residual deformation. The model with a large initial pretension force (e.g., Model S15) exhibited a small residual deformation at each displacement amplitude, whereas the model with a small initial pretension force (e.g., Model S13) exhibited a large residual deformation. The stiffness of the model increased slightly as the initial pretension force increased; however, the stiffness degradation remained almost unchanged, as shown in Fig.19(f).

4.4 Axial compression ratio

To investigate the effect of the axial compression ratio, Models S16–S18 were built. The results of the models were compared, as shown in Fig.20. Fig.20(a) shows that the axial compression ratio significantly affected the hysteresis performance. The load-bearing capacity of the models with a small axial compression ratio (e.g., Model S16) increased with the displacement amplitude, whereas the load-bearing capacity of the models with a large axial compression ratio (e.g., Model S18) first increased and then decreased as the displacement amplitude increased. In other words, the ductility decreased as the axial compression ratio increased. As the axial compression ratio increased, the load-bearing capacity and initial stiffness of the model increased, as shown in Fig.20(b). For the models with different axial compression ratios, the accumulated dissipated energy at different displacement amplitudes was similar, as shown in Fig.20(c). Fig.20(d) shows a comparison of the equivalent damping ratios. The larger the axial compression ratio was, the smaller the equivalent damping ratio was. The energy-dissipation efficiency decreased as the axial compression ratio increased. Fig.20(e) shows a comparison of the residual deformation. The residual deformation of the model decreased significantly as the axial compression ratio increased, which indicates that an appropriate increase in the axial compression ratio is conducive to improving the self-centering capability. As shown in Fig.20(f), the stiffness increased with the axial compression ratio, but the stiffness degradation was more pronounced.

Summarizing the parametric studies presented above, (1) the larger longitudinal reinforcement ratio and longitudinal reinforcement yield strength resulted in plumper hysteresis loops with greater load-bearing capacity, stiffness, and energy dissipation amount, whereas the effect of rubber hardness was negligible; (2) the larger rubber thickness resulted in less enhancement in the load-bearing capacity under large displacements but resulted in larger equivalent damping ratios; (3) the large initial pretension force and axial compression ratio increased the high strength and initial stiffness but reduced the equivalent damping ratio, and the large axial compression ratio was not conducive to ductility; (4) the large longitudinal reinforcement ratio, large longitudinal reinforcement yield strength, small initial pretension force, and small axial compression ratio significantly increased the permanent residual deformation, which is not conducive to achieving seismic resilience; therefore, these parameters should be evaluated meticulously in the design stage.

5 Conclusions

In this study, a novel SRRC column was developed. After validating the numerical simulation method, extensive parametric studies were conducted to investigate the critical factors affecting the seismic performance of SRRC columns. The primary findings are summarized as follows.

(1) The numerical simulation method proposed herein can accurately replicate the behaviors of the SRRC column in terms of load-bearing capacity, stiffness degradation, hysteretic energy dissipation, residual deformation, and damage degree.

(2) The SRRC column exhibited flag-shaped hysteresis responses with no strength degradation. Furthermore, it successfully mitigated damage to concrete and exhibited a small permanent residual deformation, which implies that the SRRC column possesses the satisfactory self-centering capability for realizing seismic resilience.

(3) The longitudinal reinforcement ratio and yield strength significantly affected the hysteretic behavior of the SRRC column, whereas the effects of rubber thickness and hardness were insignificant. As the longitudinal reinforcement ratio and yield strength increased, the load-bearing capacity and stiffness of the column increased significantly, the cumulative energy dissipation amount increased, the equivalent viscous damping coefficient decreased, and the residual deformation increased. Therefore, the energy dissipation and self-centering capacity of the SRRC column must be designed appropriately.

(4) A large initial pretension force and axial compression ratio provided a large load-bearing capacity, high initial stiffness, and small permanent residual deformation, but a small equivalent damping ratio. Moreover, a large axial compression ratio was not conducive to ductility.

This study provides ideas for enhancing the seismic resilience of RC frame structures. Nevertheless, the current study focused only on the numerical simulation investigation and parametric analysis of the proposed column at the member level. In future studies, the overall seismic performance of a structural system adopting the proposed self-centering column and the corresponding design method must be considered at the system level.

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