Seismic performance and hysteretic model of corroded steel frame columns in offshore atmospheric environment

Abstract

Previous studies show that the offshore atmospheric environment corrosion gradually reduces the physical and mechanical properties of steel and eventually deteriorate the seismic performance of steel structures. This paper presents a comprehensive study on the seismic performance of corroded steel frame columns in offshore atmospheric environment. Artificial climate accelerated corrosion tests and cyclic loading tests were carried out on six steel frame columns. The effects of corrosion level and axial compression ratio on the failure mechanism and seismic performance of the columns were investigated in details. The test results indicate that with an increase in corrosion level or axial compression ratio, the displacements associated with plate local buckling, plastic hinge formation and final failure tend to reduce gradually. The bending capacity, ductility and energy dissipation capacity of columns also significantly decrease, and the strength and stiffness degradation effect intensify. Furthermore, a moment-rotation hysteretic model in plastic hinge zone for corroded steel frame columns, considering the cyclic deterioration in strength and stiffness, was established by introducing a two-parameter seismic damage model. The predicted moment-rotation curves and energy dissipations coincided well with the experimental results, verifying the rationality and applicability of the proposed hysteretic model. The research results provide theoretical support for elastic-plastic time history analysis and seismic risk assessment of existing steel frame structures in offshore atmospheric environment.

Keywords

seismic performance corroded steel frame column cyclic loading test hysteretic model corrosion level axial compression ratio

Introduction

Corrosion is one of the main reasons that affect the durability of steel structures. It may reduce the mechanical properties of steel, weaken the cross-sectional areas of components, and eventually result in a significant deterioration of the bearing capacity of steel structure (Karina et al., 2017; Pidaparti and Rao, 2008; Shahabi and Narmashiri, 2018; Sultana et al., 2015). The offshore atmospheric environment, due to its high relative humidity, high chloride ion concentration and obvious wet-dry cycle effect, accelerates the corrosion rate of steel, and thus greatly reduces the safe service life of steel structures (Apostolopoulos et al., 2013; Wang et al., 2014). Despite many anti-corrosion measures, the aging steel frames exposed in an aggressive corrosion environment still suffer serious corrosion, especially the exterior components (Karagah et al., 2015; Xu et al., 2019). If the structure suffers from corrosion damage and is in high intensity seismic zone, its seismic performance after corrosion is an urgent problem to be solved.

At present, researchers at home and abroad have carried out comprehensive studies on the corrosion mechanism of steel (Albrecht and Hall, 2003; Duquesnay et al., 2003; Xu and Wang, 2015), mechanical properties of corroded steel (Garbatov et al., 2014; Huang et al., 2010; Khedmati et al., 2011), performance degradation of corroded steel member and structure (Albrecht and Lenwari, 2008; Beaulieu et al., 2010; Han et al., 2014; Kim et al., 2013; Takahashi and Andoa, 2007; Zhang et al., 2020) in the offshore atmospheric environment. Xu and Wang (2015) estimated the effects of corrosion pits on the fatigue life of Q235 steel plates based on the 3D profile measurements. Khedmati et al. (2011) investigated the strength characteristics of the both-sides randomly corroded steel plates using a series of elastic-plastic finite element analysis. Kim et al. (2013) conducted the static tests for corroded H-shaped steel beams and then obtained the degradation law of web shear buckling. Beaulieu et al. (2010) carried out salt-spray accelerated corrosion and compression tests on 16 angle steel members, studied the effects of corrosion degree on the compressive properties, and then evaluated the residual compressive bearing capacity of corroded angle steel members based on the average residual thickness. Zhang et al. (2020) conducted quasi-static tests on four plane steel frames in chloride environment, revealed the failure mechanism of corroded steel frames, and studied the effects of corrosion level on the bearing capacity, deformation capacity and energy dissipation capacity of steel frames. However, studies on the degradation laws of seismic performance for corroded steel members and structures under low cyclic loading are still quite rare.

In addition, the hysteretic model of members is an important basis for elastic-plastic seismic response analysis of structures. In recent years, copious studies have been carried out on the hysteretic models of steel structure members. Kumar and Usami (1996) presented an evolutionary-degrading (E-D) hysteretic model for thin-walled steel structures, based on a comprehensive damage index considering the effect of large deformation, low cycle fatigue and the loading history. Subsequently, they adopted the same theory to establish the E-D hysteretic model for steel bridge piers (Usami and Kumar, 1998). Shen and Astanehasl (2000) presented a realistic hysteresis model for bolted angle connection based on the combined experimental and analytical results. Lignos and Krawinkler (2009) provided the modified Ibarra-Krawinkler (IK) model, which can capture asymmetric component hysteretic behavior. Subsequently, they also proposed empirical equations of the deterioration modeling parameters for steel beams and columns (Lignos and Krawinkler, 2011; Lignos et al. 2019). Shi et al. (2012) developed a simplified constitutive model of high-strength structural steel Q460D under cyclic loading, which could be implemented in ABAQUS software for seismic analysis. Wang et al. (2014) proposed a trilinear hysteretic model in terms of the normalized moment–curvature relationship for Q460C high strength steel (HSS) beam-columns.

However, researching on the hysteretic models of corroded steel members is rarely involved. Corrosion damage could reduce the bearing and deformation capacity, accelerate the cyclic degradation of strength and stiffness, and then lead to significant differences in hysteretic curves between corroded and uncorroded members (Zheng et al., 2018). Therefore, to truly reflect the hysteretic behavior of corroded steel members, and accurately analyze the seismic response of existing steel structures, it is necessary to establish a hysteretic model for corroded steel members.

The steel frame column is the main load-bearing member, whose mechanical behavior has a significant impact on the safety of the whole structure. Hence, in this research, artificial climatic accelerated corrosion and lateral cyclic loading tests were carried out on six steel frame columns. The effects of corrosion level and axial compression ratio on the failure mode, bearing capacity, deformation capacity and energy dissipation capacity of columns were discussed in detail. Furthermore, a hysteretic model of corroded steel frame columns that can reflect the deterioration in strength and stiffness was established.

Test program

Test specimens

According to the mechanical characteristics of steel frame columns under horizontal earthquake action, one half of the column bent in double curvature was selected as the research object, as shown in Figure 1. Reference to the Chinese codes (GB 50017, 2017; GB 50011, 2010), practical engineering size and limited test conditions, six 1:2 scale steel frame column specimens were designed. The specimen configuration and detailed dimensions are depicted in Figure 2. All specimens were manufactured using a Chinese standard Grade Q235B H-shaped steel (f_y = 235 MPa) with a section profile of HW250 × 250 × 9× 14 mm. For guaranteeing the fixed boundary condition, a relatively rigid support beam with a section profile of HW390 ×3 00 × 10 × 16 mm was welded at the column bottom. The main test parameters included corrosion level and axial compression ratio (see Table 1). Four corrosion levels of 0%, 3.06%, 5.33% and 8.02% were chosen for test columns, which were quantized by average mass loss rate of its constituent plates with different thickness. The mass loss rate index η is defined as:

η = (m_{0} - m_{1}) / m_{0}

(1)

where m₀ and m₁ are the uncorroded and corroded sample mass, respectively. And three design axial compression ratio levels of 0.2, 0.3 and 0.4 were selected, which can be calculated as follows:

n = N / f_{y} A

(2)

where N is the design axial load applied to specimens; f_y is the design yield strength of Q235B steel (f_y = 235 MPa); and A is the cross-sectional area.

Figure 1.

Research object.

Figure 2.

Details of specimen (Unit: mm).

Table 1.

Design parameters of test specimens.

ID	Section profile	Design axial compression ratio n	Accelerated corrosion time (h)	Mass loss rateη (%)
SC-1	HW250 × 250 ×9 × 14	0.2	1920	5.33
SC-2	HW250 × 25 0× 9 × 14	0.3	0	0
SC-3	HW250 × 250 × 9 × 14	0.3	960	3.06
SC-4	HW250 × 250 × 9 × 14	0.3	1920	5.33
SC-5	HW250 × 250 × 9 ×14	0.3	2880	8.02
SC-6	HW250 × 250 × 9 × 14	0.4	1920	5.33

Artificial climate accelerated corrosion test

The neutral salt spray (NSS) test is usually adopted to simulate offshore atmospheric environment (Sutter et al., 2014). Thus, the test columns were subjected to neutral salt spray accelerated corrosion using ZHT/W2300 climate simulation system, as shown in Figure 3. According to the standard of ISO 9227 (2012), Table 2 lists the system environment parameters. The specimens were sprayed with a NaCl solution (50 ± 5 g/L, pH = 6.5–7.2). The inner system temperature and relative humidity were 35 ± 2°C and 95%, respectively. The spraying scheme of 5-min spray and following 5-min interval was adopted. And after 24 h of continuous spraying, the condensation rate of salt spray was 1.0–2.0 mL/80 cm² h. The accelerated corrosion time for specimens SC-1 to SC-6 was set as 0, 960, 1920 and 2880 h respectively, which corresponded with four corrosion levels.

Figure 3.

Photos of accelerated corrosion testing process: (a) exterior of the climatic simulation system; (b) interior of the system; (c) test columns in the system; and (d) steel tensile samples in the system.

Table 2.

Environment parameters of the climate simulation system.

NaCl solution	50 g/L ± 5 g/L
pH	6.5∼7.2
Temperature	35°C ± 2°C
Humidity	≥95% RH
Spraying scheme	5-Minu te spray, 5-min interval
Condensation rate of salt spray	1.0–2.0 mL/80 cm² h

Materials

Based on the Chinese Standards (GB/T 2975, 2018; GB/T 228.1, 2010), steel tensile samples with thicknesses of 9 mm and 14 mm were made, and then subjected to accelerated corrosion and tensile failure tests. Table 3 lists the measured mechanical properties of corroded Q235B steel, in which three identical coupons were for each test condition. Note that the cross-sectional area of the uncorroded sample was used here to obtain nominal mechanical performance indexes. It can be seen that with the increase of mass loss rate, the yield strength, tensile strength, elongation and elastic modulus all decrease gradually. Moreover, through linear fitting, the relationships of relative mechanical properties with mass loss rate for Q235B steel are plotted in Figure 4. The fitting formulas are described as follows:

{\begin{cases} \frac{f_{y}^{'}}{f_{y}} = 1 - 0.9833 η R^{2} = 0.98 \\ \frac{f_{u}^{'}}{f_{u}} = 1 - 0.8791 η R^{2} = 0.94 \\ \frac{δ^{'}}{δ} = 1 - 1.7780 η R^{2} = 0.96 \\ \frac{E_{s}^{'}}{E_{s}} = 1 - 0.9312 η R^{2} = 0.83 \end{cases}

(3)

where f'_y, f'_u, δ' and E'_s are the yield strength, tensile strength, elongation and elastic modulus of corroded samples, respectively; while f_y, f_u, δ and E_s are the corresponding ones of uncorroded samples; and η is the mass loss rate, less than 10%.

Table 3.

Mechanical properties of corroded Q235B steel.

Thickness (Mm)	Accelerated corrosion time T (hour)	Mass loss rate η (%)	Yield strength f_y (MPa)	Tensile strength f_u (MPa)	Elongation δ (%)	Elastic modulus E_s (MPa)
9	0	0.00	282.0	420.0	26.09	205,881
	240	0.93	280.4	414.7	25.86	204,111
	480	1.81	276.1	409.9	25.62	200,684
	960	3.72	271.2	403.9	24.89	199,844
	1440	5.02	266.5	401.8	24.12	192,336
	1920	6.49	263.3	392.6	23.81	191,558
	2400	8.24	259.4	386.8	22.35	188,955
	2800	9.76	255.9	384.4	21.30	185,684
14	0	0.00	268.0	412.7	28.96	204,768
	240	0.59	266.8	407.1	28.67	201,335
	480	1.13	264.3	403.4	28.20	202,351
	960	2.39	262.9	398.3	27.81	190,667
	1440	3.19	258.9	394.3	27.31	197,684
	1920	4.17	256.4	391.2	26.96	195,558
	2400	5.26	253.3	389.7	25.99	194,668
	2800	6.27	251.6	383.0	25.71	193,336

Figure 4.

Fitting curves of mechanical properties for corroded Q235B steel: (a) yield strength; (b) tensile strength; (c) elongation; and (d) elastic modulus.

Test setup and instrumentations

Figure 5 shows the loading setup, which enabled the column specimens to bear both lateral cyclic load and vertical load. The column base was fixed to the laboratory floor by the rigid pressure beams and anchor bolts. The lateral cyclic load was applied to the loading point using a 50-t capacity MTS electrohydraulic servo actuator. The vertical axial load was imposed on the column top and kept constant using a 100-t capacity hydraulic jack. Meanwhile, the lateral braces were employed to prevent out-of-plane instability of the column specimens.

Figure 5.

Test setup: (a) scheme; and (b) on-site photo.

Figure 6 shows the loading protocol recommended in ANSI/AISC 341 (2010). As shown, two cycles were imposed at 0.375%, 0.5%, 0.75%, 1%, 1.5%, 2%, 3%, 4%, etc. drift ratio levels, until obvious damage or the lateral load fell by more than 15% of the maximum. The drift ratio θ is defined as:

θ = Δ / L

(4)

where Δ is the lateral displacement at loading point, and L is the calculated length of the column (i.e., 1200 mm). Furthermore, the pushing and pulling direction of the actuator were stipulated as positive and negative value, respectively.

Figure 6.

Loading protocol.

Figure 7 illustrates the measurement configuration. The lateral displacement at the loading point and the possible sliding of the support beam were monitored by the linear variable displacement transducers LVDT-1 and LVDT-2, respectively. The rotation of plastic hinge region at column end was measured by LVDT-3 and LVDT-4. In addition, a considerable number of strain gauges were arranged to record the strain variation in the potential plastic hinge region.

Figure 7.

Instrumentation: (a) strain gauges; and (b) displacement transducers (unit: mm).

Test results and discussion

Behavior and failure modes

Similar failure process was observed for test columns SC-1∼SC-6, which having experienced the elastic stage, elastic-plastic stage and plastic failure stage during the whole loading period. At the beginning of loading, the steel stress was less than the yield strength, all specimens remained at the elastic stage without notable damage, and the lateral load on column top increased with the displacement linearly. At the drift ratio level of 1.5%, the steel stress at column end exceeded the yield strength, and the lateral load-displacement curves successively exhibited significant nonlinear behavior due to different levels of corrosion and axial compression ratio, indicating that the specimens reached the elastic-plastic stage. At the drift ratio level of 2%∼3%, slight local buckling of both flanges was observed at column end due to the stress exceeding the critical buckling stress of plates, as shown in Figure 8(a). At the drift ratio level of 3%∼4%, local buckling of flanges became apparent, and the lateral load reached the maximum. Meanwhile, local buckling also occurred in the web, indicating the formation of plastic hinge at column end, as shown in Figure 8(b). Continuous loading, the plastic deformation of specimens increased while the lateral load declined gradually, which indicates that the specimens entered into the plastic failure stage. When the drift ratio level increased to 4%∼5%, the test was halted owing to the sufficient development of plastic hinge at column end and more than 15% reduction in lateral load.

Figure 8.

Typical failure modes of specimens: (a) slight local buckling of flanges; (b) slight local buckling of web; (c) overall column failure; (d) failure mode of SC-1; (e) failure mode of SC-2; (f) failure mode of SC-3; (g) failure mode of SC-4; (h) failure mode of SC-5; and (i) failure mode of SC-6.

While with the increase in corrosion level, the drift ratio levels corresponding to plate local buckling, plastic hinge formation and final failure tended to reduce, and the bearing capacity decreased gradually. This was mainly because the corrosion damage reduced the sectional size of columns and caused stress concentration in the corrosion pits, thereby accelerating the development of accumulated plastic strain and local buckling of plates. Additionally, the higher the axial compression ratio was, the earlier the local buckling occurred, and the faster the late bearing capacity decreased. This was largely due to the more prominent P-Δ second order effect, which was more likely to cause local buckling of plates. The failure modes of all test columns are displayed in Figure 8, and the main test observations are recorded in Table 4.

Table 4.

Main test observations of specimens.

ID	Drift ratio level of flange local buckling	Drift ratio level of web local buckling	Drift ratio level of maximum strength	Drift ratio level of failure	Plastic hinge length (mm)
SC-1	3% (2)	4% (2)	4% (1)	5% (2)	330
SC-2	3% (2)	4% (2)	4% (1)	5% (2)	340
SC-3	3% (2)	4% (1)	3% (2)	5% (1)	325
SC-4	3% (1)	4% (1)	3% (2)	5% (1)	315
SC-5	2% (2)	3% (1)	3% (1)	4% (2)	330
SC-6	2% (2)	3% (2)	3% (1)	4% (2)	280

Hysteretic curves

Figure 9 shows the hysteretic curves of the bending moment (M) versus chord rotation (θ) for all test columns. Herein, the bending moment M and chord rotation θ are calculated according to Equation (4) and (5), respectively.

M = P L + N Δ

(5)

where P is the lateral load; and N is the axial load.

Figure 9.

Hysteretic curves: (a) SC-1; (b) SC-2; (c) SC-3; (d) SC-4; (e) SC-5; and (f) SC-6.

The occurrences of flange and web local buckling are also marked in Figure 9. As shown, all curves are plump in shapes with no pinching effect. When the drift ratio level was less than 1%, all specimens behaved elastically without any visual signs of damage, and the slope of hysteresis curves changed little. Beyond the drift ratio level of 1.5%, the specimens yielded, the area of hysteresis loops increased and the residual deformation occurred. At this moment, due to the small plastic deformation and light cumulative damage of specimens, the loading and unloading curves for two cycles at the same drift ratio level basically coincided. When the drift ratio level exceeded 3% ∼ 4% (i.e., after reaching the peak load), both the strength and stiffness gradually deteriorated owing to the obvious flange and web local buckling and great cumulative damage, thus leading to the separation of the loading and unloading curves for two cycles at the same drift ratio level.

With an increase in corrosion level, the nominal strength of steel decreased, and the plate local buckling occurred easily owing to a reduction in plate thickness. Thus the bending capacity of columns decreased, the hysteresis loop area reduced, and the strength and stiffness degradation effect after peak load got increasingly notable. Additionally, rising axial compression ratio in some degree could reduce the lateral stiffness and bending capacity of columns, and accelerate the strength and stiffness degradation rate due to more severe P-Δ effect.

Characteristic parameters of skeleton curves

For better comparison, the skeleton curves constructed from the hysteretic curves by connecting the peak point for each drift ratio level are shown in Figure 10. Table 5 summarizes the major test results, including the yield moment M_y, maximum moment M_max, ultimate moment M_u and the corresponding rotation θ_y, θ_m and θ_u, and the ductility coefficient μ = θ_u/θ_y. Note that the yield point is defined by the energy equivalent method (see Figure 11) (Hu et al., 2017).

Figure 10.

Comparison of skeleton curves: (a) corrosion level; and (b) axial compression ratio.

Table 5.

Summary of the experimental results.

ID	Direction	Yield point		Maximum point		Ultimate point		Ductility coefficientµ	M_max/M_p	θ_p (% rad)	θ_r (% rad)
ID	Direction	M_y (kN·m)	θ_y (% rad)	M_max (kN·m)	θ_max (% rad)	M_u (kN·m)	θ_u (% rad)	Ductility coefficientµ	M_max/M_p	θ_p (% rad)	θ_r (% rad)
SC-1	Positive	260.12	1.60	307.69	4.00	269.51	4.97	3.10	1.44	2.40	0.97
	Negative	−268.38	−1.68	−344.14	−4.00	−305.97	−5.00	2.98	−1.61	−2.32	−1.00
	Average	264.25	1.64	325.91	4.00	287.74	4.99	3.04	1.52	2.36	0.99
SC-2	Positive	266.42	1.54	329.87	3.25	296.12	4.83	3.14	1.46	1.71	1.58
	Negative	−276.02	−1.67	−340.49	−3.00	−306.12	−4.75	2.84	−1.51	−1.33	−1.75
	Average	271.22	1.60	335.18	3.13	301.12	4.79	2.99	1.48	1.53	1.66
SC-3	Positive	263.17	1.51	315.61	3.00	283.09	4.50	2.99	1.41	1.49	1.50
	Negative	−267.74	−1.58	−330.69	−3.00	−295.84	−4.49	2.85	−1.47	−1.42	−1.49
	Average	265.46	1.54	323.15	3.00	289.46	4.49	2.92	1.44	1.46	1.49
SC-4	Positive	259.13	1.43	304.77	2.99	271.71	4.21	2.93	1.42	1.56	1.20
	Negative	−264.08	−1.50	−324.49	-2.99	−284.78	−3.72	2.48	−1.51	-1.49	−0.73
	Average	261.61	1.47	314.63	2.99	278.24	3.96	2.71	1.46	1.52	0.96
SC-5	Positive	243.36	1.30	288.95	2.80	255.98	3.74	2.87	1.44	1.50	0.94
	Negative	−242.69	−1.44	−281.46	−2.93	−247.64	−3.60	2.49	−1.40	−1.49	−0.67
	Average	243.03	1.37	285.21	2.86	251.81	3.67	2.68	1.42	1.49	0.81
SC-6	Positive	252.18	1.43	303.04	2.92	273.85	4.09	2.85	1.42	1.49	1.17
	Negative	−258.96	−1.41	−302.54	−2.95	−267.81	-3.56	2.53	−1.42	−1.54	−0.61
	Average	255.57	1.42	302.79	2.94	270.83	3.82	2.69	1.42	1.52	0.88

Figure 11.

Definition of yield point: (a) energy equivalent method; and (b) a hysteretic loop.

(1) Ductility and rotation capacity

As can be seen from Figure 10 and Table 5, the deformation capacity of steel frame columns decreases with the increase of corrosion level or axial compression ratio. When the mass loss rate increased from 0% to 8.02%, the average yield rotation, ultimate rotation and ductility coefficient decreased by 14.38%, 23.38% and 10.37%, respectively. When the axial compression ratio increased from 0.2 to 0.4, the average yield rotation, ultimate rotation and ductility coefficient decreased by 13.41%, 23.45% and 11.51%, respectively. Columns with a lower axial compression ratio (n ≤ 0.2) or corrosion level (η ≤ 3.06%), accommodated a maximum story drift angle larger than 0.04 rad, satisfying the requirements for special moment frames (SMFs) in ANSI/AISC 341 (2010). While columns with a higher axial compression ratio (n > 0.2) or corrosion level (η > 3.06%), though not meeting this requirement, could still achieve a story drift angle greater than 0.02 rad, satisfying the specifications for intermediate moment frames (IMFs).

(2) Strength

When the mass loss rate increased from 0% to 8.02%, the average yield moment and maximum moment decreased by 10.39% and 14.91%, respectively. When the axial compression ratio increased from 0.2 to 0.4, the average yield moment and maximum moment decreased by 3.28% and 7.10%, respectively. These indicate that the corrosion level and axial compression ratio have significant influence on the bending capacity of steel frame columns. Thus, an overall and perfect anti-corrosion measure and appropriate axial compression ratio must be introduced in the seismic designs of steel frame columns in structural engineering.

Strength degradation

Strength degradation coefficient λ at ith drift ratio level, can be defined as the ratio of peak loads in the last cycle to that in the first cycle (Yang et al., 2016). Figure 12 depicts the strength degradation curves for test columns. It is clearly seen that before peak load (2%∼3% drift ratio level), the strength degradation coefficients λ of all specimens are greater than or equal to 1, which is attributed to the cyclic hardening effect of steel. After that, the strength degradation coefficients λ decrease dramatically owing to the occurrence of plate local buckling and the increasing damage accumulation. Moreover, as the axial compression ratio or corrosion level increases, the strength degradation becomes more serious, which is due to the early occurrence of plate local buckling in the presence of high corrosion level or axial compression ratio.

Figure 12.

Comparison of strength degradation curves: (a) corrosion level; and (b) axial compression ratio.

Stiffness degradation

The stiffness of specimens can be expressed in terms of the secant stiffness K_i, which is defined as (Cai et al., 2016):

K_{i +} = \frac{+ P_{i}}{+ Δ_{i}} and K_{i -} = \frac{- P_{i}}{- Δ_{i}}

(6)

where ±P_i are the peak load at ith drift ratio level in two reversal directions, respectively; and ±Δ_i are the displacement corresponding to ±P_i.

Thus, the variation of the secant stiffness can be used to reflect the stiffness degradation of specimens, as shown in Figure 13. It can be seen that all specimens experience a nearly identical stiffness degradation law of “significant followed by moderate trend”. At the early loading stage, the plastic strain at column end accumulated rapidly, plate local buckling developed fast, and the stiffness degraded quickly. At the late loading stage, the plastic deformation at column end developed fully and tended to stabilize, and thus the stiffness degradation slowed down. In addition, Figure 13(a) shows that the corrosion damage could reduce the initial stiffness and accelerate stiffness degradation of steel columns. As the axial compression ratio increases within a certain range, the initial stiffness enhances somewhat, while the later stiffness degradation aggravates due to more severe P-Δ effect, as shown in Figure 13(b).

Figure 13.

Comparison of stiffness degradation curves: (a) corrosion level; and (b) axial compression ratio.

Energy dissipation capacity

Figure 14 illustrates the cumulative energy dissipation E_total for all specimens. As it shows, when the mass loss rate increased from 0% to 8.02%, the cumulative energy dissipation decreased from 141.41 to 115.05 kJ with a reduction of 18.64%. Meanwhile, when the axial compression ratio increased from 0.2 to 0.4, the cumulative energy dissipation decreased from 129.18 to 105.15 kJ with a reduction of 18.60%. These indicate that an increase in the corrosion level or axial compression ratio may significantly decrease the energy dissipation capacity of steel frame columns.

Figure 14.

Cumulative energy dissipation.

In order to further analyze the energy dissipation capacity of test columns, equivalent viscous damping coefficient h_e is also utilized here, which is defined as (Fang et al., 2014):

h_{e} = \frac{1}{2 π} \frac{S_{ABCDA}}{S_{OBE} + S_{OFD}}

(7)

where S_ABCDA, S_OBE and S_OFD are the areas of hysteresis loop ABCDA, triangle OBE and OFD, respectively, see Figure 11(b).

Figure 15 presents the equivalent viscous damping coefficient versus drift ratio level of each specimen. It is evident that the equivalent viscous damping coefficient of all specimens increases gradually as the drift ratio level increases. Furthermore, the equivalent viscous damping coefficient decreases with the increase of corrosion level or axial compression ratio within a certain range.

Figure 15.

Comparison of equivalent viscous damping coefficients: (a) corrosion level; and (b) axial compression ratio.

Strain analysis

Figure 16 depicts the strain-drift ratio relationships of flange and web maximum strain measuring points for all specimens. As shown, during the initial loading period, the strain at each measuring point developed linearly with the drift ratio, indicating that the specimen was in the elastic stage. When the drift ratio level increased to 1.5%∼2%, the strains at flanges and web successively exceeded the test yield strain of steel (ε_y = f_y/E), and exhibited nonlinear characteristics, indicating that the specimen had entered into elastic-plastic stage. Afterward, owing to the plate local buckling, a leap of the strains could be found at all measuring points.

Figure 16.

Strain analysis: (a) SC-1; (b) SC-2; (c) SC-3; (d) SC-4; (e) SC-5; and (f) SC-6.

Figure 17 presents the strain distribution of the plastic hinge central section at column end in the positive loading, where h' is the distance between strain measuring point and compressed flange, and h is the section height. It is illustrated that:

(1) Under the combined effect of lateral cyclic load and constant axial load, the compression flange at column end yielded firstly and entered into the elastic-plastic state. Subsequently, the tension flange yielded due to the fact that the strain increasing rate of flanges was greater than that of web. Finally, the web yielded and the whole section entered into the plastic state, indicating the formation of plastic hinge at column end. These all coincided with the preceding test phenome non.

(2) Before yielding (1.5% drift ratio level), the section strains along height varied linearly for all specimens, indicating that the deformation basically satisfied plane-section assumption. Meanwhile, the strain of each measuring point at the same drift ratio level increased with the increase of corrosion level or axial compression ratio. At the drift ratio level of 2%, the section reached a fully plastic state, and the strains along section height presented nonlinear change trends. At the drift ratio level of 3%∼4%, the strain at each measuring point exhibited an obvious jump, and the plane-section assumption was no longer valid. Moreover, owing to the local buckling of flanges and web, the section strains were distributed asymmetrically.

(3) Note that the strain development law in the negative loading was basically similar to that in the positive loading.

Figure 17.

Strain distribution of plastic hinge central section in positive loading: (a) SC-1; (b) SC-2; (c) SC-3; (d) SC-4; (e) SC-5; and (f) SC-6.

Hysteretic model

Hysteretic model of members is an important basis for the elastic-plastic seismic response analysis of structures. The above experimental results show that the corrosion damage can reduce the bearing and deformation capacity of steel columns, accelerate the cyclic degradation effect in strength and stiffness, while cannot change the overall trends of hysteretic curves. By modifying the hysteretic model parameters of uncorroded ones, the hysteretic model of steel columns considering the influence of corrosion can be established. Thus, based on the ModIK-Bilin model (Lignos and Krawinkler, 2009, 2011) and statistical regression idea, a moment-rotation hysteretic model in plastic hinge zone for corroded steel frame column was proposed, which contained mainly two parts: backbone curve and cyclic deterioration rules, as described next.

Data supplement of finite element analysis

Due to the limited test data, the finite element analysis was applied to expand the statistical dataset, so as to obtain a reliable hysteretic model of corroded steel frame columns.

Based on ABAQUS general software, a three-dimensional finite element model for steel frame columns considering corrosion damage was established, as shown in Figure 18. The material properties were characterized by the deteriorated steel mechanical performance indexes (see Table 3 and equation (3)), as well as a mixed-hardening constitutive model considering the Bauschinger effect. All components of the model adopted C3D8R solid elements with a minimum size of 3 mm. The binding constraints (“Tie” command) were used to simulate the welding action among components. The boundary and loading conditions of the model were consistent with the test. Meanwhile, an initial defect based on the first-order buckling mode was introduced to accurately simulate the local buckling phenomenon at column end.

Figure 18.

Finite element model of corroded steel frame columns (Zheng et al., 2018; Zhang et al., 2023).

The FEA results were in good agreement with the test results in terms of failure modes and hysteresis behavior, which could truly reflect the bearing and deformation performance of corroded steel frame columns under low cyclic loading. Detailed modeling information and validation can be found in the author's published article (Zheng et al., 2018; Zhang et al., 2023). On this basis, the parameter analysis of corrosion level (mass loss rate η) and axial compression ratio n was presented. The mass loss rate was taken as 0%, 3%, 6%, 9%, 12%, 15%, 18%, 21%, 24%, and the axial compression ratio was taken as 0, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5.

Backbone curve

The backbone curve of moment-rotation hysteretic model in plastic hinge zone was defined by three strength parameters (the effective yield moment M_y, maximum moment M_max and residual moment M_r = κM_y) and four deformation parameters (the effective yield rotation θ_y, pre-capping plastic rotation θ_p, post-capping plastic rotation θ_pc and failure rotation θ_f), as shown in Figure 19.

Figure 19.

Backbone curve.

Effective yield moment and rotation

ASCE/SEI 41-06 (2007) recommends that the effective yield point of steel columns is characterized by the full-section yielding state, that is, the effective yield moment M_y and effective yield rotation θ_y can be calculated by Equations (8) and (9), respectively:

M_{y} = M_{P} = 1.18 (1 - \frac{N}{A_{n} f_{y}}) W_{P} f_{y}

(8)

θ_{y} = θ_{ye} = \frac{W_{P} f_{y} L}{3 E I} (1 - \frac{N}{A_{n} f_{y}})

(9)

where M_P is the expected plastic bending moment; N is the axial force; A_nf_y is the expected axial yield force; W_P is the plastic section modulus; f_y is the expected yield strength of the material; E is the Young’s modulus of elasticity; I is the moment of inertia; and L is the column length.

Due to the different definitions and determination methods of yield point, the elastic stiffness of columns varies widely. In this hysteretic model, the effective yield point represents that the section has formed the plastic region on both tension and compression sides. Given this, combined with the test results and the suggested values by ASCE/SEI 41-06 (2007), OpenSEES website (2010) and Lignos and Krawinkler (2011), the effective yield moment M_y and yield rotation θ_y are recommended as follows:

M_{y} = 1.3 M_{P} = 1.53 (1 - \frac{N}{A_{n} f_{y}}) W_{P} f_{y}

(10)

θ_{y} = 3 θ_{ye} = \frac{W_{P} f_{y} L}{E I} (1 - \frac{N}{A_{n} f_{y}})

(11)

Moreover, Figures 20 and 21 depict the relationships of the yield moment and yield rotation with corrosion level and axial compression ratio for all test and FEA columns, respectively. It can be seen that the yield moment and yield rotation both decrease with the increase of corrosion level or axial compression ratio. Through dualistic linear regression analysis, the expressions for the yield moment M'_y and yield rotation θ'_y considering the effect of corrosion level η and axial compression ratio n, are given by:

M_{y}^{'} = (1.059 - 0.295 n - 1.568 η) M_{y}

(12)

θ_{y}^{'} = (1.129 - 0.595 n - 0.964 η) θ_{y}

(13)

Figure 20.

Relationships of yield moment M_y with test parameters: (a) corrosion level η; (b) axial compression ratio n; and (c) corrosion level η and axial compression ratio n.

Figure 21.

Relationships of yield rotation θ_y with test parameters: (a) corrosion level η; (b) axial compression ratio n; and (c) corrosion level η and axial compression ratio n.

Maximum moment and pre-capping plastic rotation

Owing to the strain hardening performance of steel, the test maximum moment will necessarily exceed the full plastic moment M_P (see Table 5), and the plane-section assumption is no longer valid. By this time, it is difficult to theoretically deduce the maximum moment. Figure 22 shows the relationships of M_max/M_y ratio with corrosion level η and axial compression ratio n for all test and FEA columns. It can be seen that within a certain range, the ratio of the maximum moment to the yield moment M_max/M_y reduces as the increase of corrosion level η or axial compression ratio n. Using dualistic nonlinear regression analysis, the equation for M_max/M_y ratio is given by:

\frac{M_{\max}}{M_{y}} = 1.221 + 0.041 e^{- 8.185 n} - 0.380 η

(14)

Figure 22.

Relationships between the ratio of the maximum moment to the yield moment M_max/M_y and test parameters: (a) corrosion level η; (b) axial compression ratio n; and (c) corrosion level η and axial compression ratio n.

Simultaneously, Lignos et al. (2019) proposed the empirical equation for pre-capping plastic rotation θ_p:

θ_{p} = 294 \cdot {(\frac{h}{t_{w}})}^{- 1.7} \cdot {(\frac{L_{b}}{r_{y}})}^{- 0.7} \cdot {(1 - \frac{P_{g}}{P_{ye}})}^{1.6} \leq 0.20 rad

(15)

where h/t_w is the web slenderness ratio; L_b/d is the member slenderness ratio; P_g/P_ye is the gravity-induced compressive axial load ratio.

Furthermore, Figure 23 depicts the relationships of the pre-capping plastic rotation with corrosion level and axial compression ratio for all test and FEA columns. As shown, the pre-capping plastic rotation decreases with the increase of corrosion level or axial compression ratio. The regressed equation for pre-capping plastic rotation θ'_p considering the effect of corrosion level η and axial compression ratio n, is given by:

θ_{p}^{'} = (0.523 + 1.373 e^{- 5.596 n} - 2.318 η) θ_{p}

(16)

Figure 23.

Relationships of pre-capping plastic rotation θ_p with test parameters: (a) corrosion level η; (b) axial compression ratio n; and (c) corrosion level η and axial compression ratio n.

Residual moment and post-capping plastic rotation

Based on the test and FEA results and the suggested values by OpenSEES website (2010), Lignos and Krawinkler (2011) and Lignos et al. (2019), the residual moment M_r can be taken as 34% of the effective yield moment M_y, i.e.,

M_{r} = 0.34 M_{\max}

(17)

Simultaneously, the empirical equation for post-capping plastic rotation θ_pc is given by Lignos et al. (2019):

θ_{pc} = 90 \cdot {(\frac{h}{t_{w}})}^{- 0.8} \cdot {(\frac{L_{b}}{r_{y}})}^{- 0.8} \cdot {(1 - \frac{P_{g}}{P_{ye}})}^{2.5} \leq 0.30 rad

(18)

It is clear from Figure 19 that the change law of the post-capping plastic rotation θ_pc is consistent with that of the plastic rotation θ_r (θ_r = θ_u - θ_max). Moreover, Figure 24 displays the relationships of the plastic rotation with corrosion level and axial compression ratio for all specimens. As shown, the plastic rotation decreases with the increase of corrosion level or axial compression ratio. Using dualistic nonlinear regression analysis, the equation for plastic rotation θ'_r considering the effect of corrosion level η and axial compression ratio n, is given by equation (19). Thereby combined with Equation (18) and Equation (19), the calculation formula of post-capping plastic rotation θ_pc for corroded steel frame columns can be determined.

θ_{r}^{'} = (- 0.107 + 0.742 e^{- 3.813 n} + 0.706 e^{- 7.938 η}) θ_{r}

(19)

Figure 24.

Relationships of plastic rotation θ_r with test parameters: (a) corrosion level η; (b) axial compression ratio n; and (c) corrosion level η and axial compression ratio n.

Cyclic deterioration rules

Based on the backbone curve, three cyclic deterioration rules are defined: basic strength deterioration, post-capping strength deterioration and unloading stiffness deterioration, which are specifically described as follows.

Cyclic deterioration index

The ModIK-Bilin model is able to capture member deterioration in strength and stiffness. And the cyclic deterioration rates are controlled based on the hysteretic energy dissipated (Rahnama and Krawinkler, 1993), which is defined as:

β_{i} = {[E_{i} / (E_{t} - \sum_{j = 1}^{i} E_{j})]}^{c}

(20)

where β_i is the cyclic deterioration index; E_i is the hysteretic energy dissipation in the ith cycle; ∑E_j is total energy dissipation in past cycles; E_t is the reference hysteretic energy dissipation capacity; and c is empirical parameter, usually taken as 1.0. But it assumes that every member possesses an inherent hysteretic energy dissipation, regardless of the loading history. Given this, a two-parameter seismic damage model based on displacement and energy was presented (Usami and Kumar, 1998), i.e.,

D = (1 - γ) {\sum_{j = 1}^{N_{1}} (\frac{δ_{\max, j} - δ_{y}}{δ_{u} - δ_{y}})}^{c} + γ {\sum_{i = 1}^{N} (\frac{E_{i}}{E_{u}})}^{c}

(21)

where N₁ is the cycle number producing δ_max,j for the first time such that δ_max,j >(δ_max,j-1+δ_y); N is the total cycle number; δ_y and δ_u are yield displacement and ultimate displacement under monotonic loading, respectively; E_i is the hysteretic energy dissipation in the ith cycle; E_u is the ultimate hysteretic energy dissipation under monotonic loading; γ is the combination parameter; and c is the test parameter.

Thus, the cyclic deterioration index is redefined as follows:

β_{i} = {[Δ D_{i} / (1 - D_{i - 1})]}^{φ}

(22)

where ΔD_i is the damage increment in the ith cycle; D_i-1 is the cumulative damage before the ith cycle; and φ is the correlation coefficient, taken as 1.0 using a trial-and-error approach. This proposed cyclic deterioration index adopted member damage degree to describe the cyclic deterioration effects, and what’s more, the loading history was considered. Note that β_i must be within the limits 0<β_i≤1. If β_i≤0 or β_i>1, the damage increment in a certain cycle exceeds the residual damage value and the failure is assumed to take place. Mathematically,

1 - D_{i - 1} < Δ D_{i}

(23)

The damage model (see equation (21)) assumed that there was no damage to member before yielding, while beginning development after yielding. Test parameter c mainly considered the effects of corrosion level η and axial compression ratio n. Meanwhile, the test results under cyclic loading were approximately substituted for the corresponding values under monotonic loading. Kumar and Usami (1996) suggested that for steel structures, discreteness of parameter c was smaller when parameter γ= 0.15. So, this paper took γ= 0.15, and then determined c by D= 1 when complete failure for test specimens. Figure 25 shows the relationships of parameter c with corrosion level η and axial compression ratio n for all test and FEA columns. It can be seen that parameter c decreases with the increase of corrosion level or axial compression ratio. Using dualistic nonlinear regression analysis, the equation for parameter c is given by:

c = 2.466 + 1.638 e^{- 5.104 n} - 5.284 η

(24)

Figure 25.

Relationships of parameter c with test parameters: (a) corrosion level; (b) axial compression ratio; and (c) corrosion level and axial compression ratio.

Basic strength deterioration

Figure 26(a) illustrates the basic strength deterioration rule, which characterizes the phenomenon that the yield strength and strain-hardening stiffness of members gradually decrease with the increase of cycle numbers at the elastic-plastic stage. The yield strength and strain-hardening stiffness deterioration could be expressed as follows:

M_{y, i}^{\pm} = (1 - β_{i}) M_{y, i - 1}^{\pm}

(25)

K_{s, i}^{\pm} = (1 - β_{i}) K_{s, i - 1}^{\pm}

(26)

where M±y,i and M±y,i-1 are the deteriorated yield strength after and before the ith cycle respectively; K±s,i and K±s,i-1 are the deteriorated strain-hardening stiffness after and before the ith cycle respectively. Note that the yield strength and strain-hardening stiffness deteriorate independently in both directions.

Figure 26.

Cyclic deterioration rules: (a) basic strength deterioration; (b) post-capping strength deterioration; and (c) unloading stiffness deterioration.

As shown in Figure 26(a), after loading in the positive direction for a half cycle, the yield strength on the negative side reduces from M-y,0 to M-y,1, and the strain-hardening stiffness decreases from K-s,0 to K-s,1 (i.e., point 4). After continue loading in the negative direction for a half cycle, the positive yield strength reduces from M+y,0 to M+y,1, and the strain-hardening stiffness decreases from K+s,0 to K+s,1 (i.e., point 8).

Post-capping strength deterioration

Figure 26(b) illustrates the post-capping strength deterioration rule. As shown, after the peak, the strength gradually degenerates but the slope of the post-capping branch remains unchanged. The post-capping strength deterioration is modeled by:

M_{ref, i}^{\pm} = (1 - β_{i}) M_{ref, i - 1}^{\pm}

(27)

where M±ref,i and M±ref,i-1 are the intersection of the vertical axis with the projection of the post-capping branch after and before the ith cycle respectively. The post-capping strength deteriorates independently in both directions.

In Figure 26(b), after loading in the positive direction for a half cycle, the post-capping strength on the negative side reduces from M-ref,0 to M-ref,1 (i.e., point 5). After continue loading in the negative direction for a half cycle, the positive yield strength is modified from M+ref,0 to M+ref,1 (i.e., point 9). Note that post-capping stiffness K_n is kept constant.

Unloading stiffness deterioration

Under cyclic loading, the unloading stiffness deterioration is governed by:

K_{u, i} = (1 - β_{i}) K_{u, i - 1}

(28)

where K_u,i and K_u,i-1 are the deteriorated unloading stiffness after and before the ith cycle respectively. Note that the unloading stiffness deteriorates simultaneously in both directions.

Figure 26(c) shows unloading stiffness deterioration rule. At point 2 the first reversal in the inelastic range takes place and the unloading stiffness deteriorates from K_e to K_u,1. At point 5 the first reversal on the negative side occurs and K_u,2 is calculated based on the updated K_u,1.

Verification of hysteretic model

According to the determined backbone curve and cyclic deterioration rules, a moment-rotation hysteretic model in plastic hinge zone for corroded steel frame column was established. Based on the Software OpenSees, the predicted hysteretic curves were obtained and then compared with the test results, as shown in Figure 27. Moreover, Figure 28 illustrates the comparisons of energy dissipation between the test and predicted results. It can be seen from Figures 27 and 28 that the predicted hysteretic curves and energy dissipation are in relatively good agreement with the test results. In terms of average maximum moment, ductility coefficient and accumulated energy dissipation, the maximum difference between the predicted and test results is less than 7%, 11% and 13%, respectively. This indicates that the proposed hysteretic model could reasonably predict the hysteretic behavior of corroded steel frame columns, such as the bending capacity, deformation, energy dissipation and deterioration effect in strength and stiffness.

Figure 27.

Comparison of hysteretic curves between test and predicted results: (a) SC-1; (b) SC-2; (c) SC-3; (d) SC-4; (e) SC-5.

Figure 28.

Comparison of energy dissipation between test and predicted results: (a) SC-1; (b) SC-2; (c) SC-3; (d) SC-4; (e) SC-5 and (f) SC-6.

Conclusions

Based on the experimental and modeling results for corroded steel frame columns in offshore atmospheric environment, the following conclusions can be drawn:

(1) An attenuation model of mechanical properties (such as yield strength, tensile strength, elongation and elastic modulus) with mass loss rate for corroded Q235B steel was established.

(2) The corrosion damage has a considerable influence on the seismic performance deterioration of steel frame columns. With an increase in corrosion level, the displacements associated with plate local buckling, maximum strength and final failure tend to reduce gradually, the bending capacity and energy dissipation also decrease, and the strength and stiffness degradation intensify. When the mass loss rate increased from 0% to 8.02%, the maximum moment, ultimate rotation, ductility coefficient and cumulative energy dissipation of steel frame columns decreased by 14.91%, 23.38%, 10.37% and 18.64%, respectively. Hence an overall and perfect anti-corrosion measure should be introduced in practical engineering design.

(3) In a certain range, the higher the axial compression ratio is, the earlier the plate local buckling occurs, the significant the cyclic deterioration effect is, and the more serious the seismic damage of columns is. Meanwhile, with the increase of axial compression ratio, the bending capacity, deformation and energy dissipation of steel frame columns all decrease gradually. Therefore, an appropriate axial compression ratio should be controlled in seismic design.

(4) Through introducing the two-parameter seismic damage model based on displacement and energy, a moment-rotation hysteretic model in plastic hinge zone for corroded steel frame columns was established, which could consider the cyclic deterioration effect in strength and stiffness. The predicted hysteretic curves and the energy dissipation are in relatively good agreement with the test results, indicating that the proposed hysteretic model can well describe the hysteretic behavior of corroded steel frame columns. The research results provide a theoretical basis for elastic-plastic seismic response analysis of existing steel frame structures in offshore atmospheric environment.

Footnotes

Author contributions

Xiaohui Zhang: Conceptualization, Methodology, Data curation, Funding acquisition, Investigation, Writing - original draft, Writing - review & editing. Shansuo Zheng: Resources, Supervision, Funding acquisition, Writing - review & editing. Xuran Zhao: Writing - original draft, Software, Formal analysis, Validation. Qian Yang: Writing - review & editing.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research described in this paper was financially supported by the National Key Research and Development Program of China (Grant No. 2019YFC1509302), the Key Research and Development Program of Shaanxi Province (Grant No. 2021ZDLSF06-10), and the Scientific Research Foundation of Shaanxi Polytechnic Institute (Grant No. BSJ2022-03 and 2023YKZD-009). The support is gratefully acknowledged.

ORCID iD

Xiaohui Zhang

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