Degradation Behavior of the Preload Force of High-Strength Bolts after Corrosion

Abstract

Corrosion significantly affects the structural behavior of members in a connection (i.e., the thickness of steel plates, the preload force of bolts, and the friction factor of steel plates). Safety assessment of corroded steel frames (i.e., beam-to-column connection, beams, or columns) has been a major concern in engineering. In this work, an experiment of accelerated corrosion testing is carried out to obtain corroded specimens connected with high-strength bolts, and the preload force of high-strength bolts (PF-HSB) is monitored throughout the whole stage of the corrosion testing. Before the corrosion testing, the PF-HSB caused by the stress relaxation is also recorded. The PF-HSB decreases rapidly in the first five hours after the final screwing of bolts and it keeps stable after 100 h. The PF-HSB is seriously affected by corrosion, which decreases by 30.0% of the original preload force when the corrosion rate of steel plate reaches 3.5%. A finite element method for predicting the PF-HSB after corrosion is proposed. An estimation model for the PF-HSB considering the stress relaxation is established. A degradation model for predicting the PF-HSB after corrosion is also suggested, and is in good agreement with experimental data. The results of this research are of great significance for the safety assessment of in-service steel structures.

1. Introduction

Due to the advantages of high stiffness, good seismic resistance, and convenient assembly, high-strength bolted connections have been extensively utilized in steel structures [1,2]. Generally, high-strength bolted connections can be divided into friction-type connections and bearing-type connections. Friction-type connections include multiple bolts with the preload force and the relative sliding of steel plates is taken as the ultimate state of this type of connections [3]. As a result, the preload force is a very important parameter affecting the mechanical behavior of friction-type connections [4,5,6,7]. Details for the preload force of high-strength bolts (PF-HSB) are provided for guiding the construction of buildings in AISC 360-16 [8], Eurocode 3 [9], and GB 50017-2017 [10]. For example, the value for the preload force in GB 50017-2017 [10] is suggested as 0.61 f_ub where f_ub is the tensile strength of high-strength bolts and the value suggested in AISC 360-16 [8] and Eurocode 3 [9] is 0.70 f_ub.

In conventional design of a building, the PF-HSB is considered as constant in service. However, several factors (i.e., friction and creep deformation) can affect the stress relaxation of high-strength bolts, which is no negligible problem in engineering [11]. Previously, Shi et al. [12,13] experimentally investigated the variation law of the PF-HSB and they found that the PF-HSB gradually decreased with the increase in time after the final screwing of bolts. After 45 h of the final screwing of high-strength bolts, the preload force decreased slowly and it was stable after 100 h of the final screwing of high-strength bolts [12,13]. Cavallaro et al. [14], Zhang [15], and Hu [16] discussed the effects of multiple-pass tightening methods on the preload force. By introducing nodal spring elements, Li and Liu et al. [17] proposed a model for the preload force considering the stress relaxation based on Saint Venant’s principle. Wang et al. [18] analyzed the influence of twisting sequence and ways of surface clearance on the PF-HSB. Caccess et al. [19] investigated the influences of environment (i.e., temperature and humidity) on the PF-HSB and they proposed a model of the PF-HSB.

As described above, there are some investigations on the PF-HSB. However, these investigations only consider the PF-HSB without corrosion. In fact, corrosion is normal in engineering and it significantly influences the structural behavior of steel structures [20,21], even leads to serious engineering accidents, for example, the corrosion on the interior of the gondola leaded to the catastrophic failure of the ride in KMG Fireball in 2017. Therefore, it is necessary and important to monitor and assess in-service corroded steel structures. Connections, an important part in a steel frame, influence the structural behavior of a building. The assessment of an in-service corroded steel structure needs the estimation of the structural performance of corroded connections. As far as the author knows, only Zhang [22] carried out the experiment to research the performance of corroded friction-type connections by accelerated corrosion testing. However, the loss of the preload force is not considered in this study, which may not reflect the real situation of connections. Ahn et al. [23] simulated the sectional loss of nuts after corrosion by cutting parts of nuts and analyzed the loss of PF-HSB. The PF-HSB decreases by 50% when the volume loss ratio of bolts head reaches 12%. From Wang et al.’s experiment [24], the PF-HSB is mainly dependent on the corrosion rate of specimens, and the value for the PF-HSB is 50% of the original value of the preload force when the corrosion rate reaches 20%. Jiang et al. [25] found the loss of PF-HSB reached 41.2% when the weight loss ratio is 10%.

Though a big step forward has been made regarding the PF-HSB in corroded connections, the experimental data on the PF-HSB after corrosion are limited. To evaluate the mechanical behavior of in-service friction-type connections, the accurate estimation for the PF-HSB in corroded connections is important, which is the objective of this paper. The experiment of accelerated corrosion testing is performed, and the PF-HSB is monitored in the whole stage of the corrosion testing. A finite element method validated by experimental results is developed to predict the PF-HSB after corrosion using Abaqus. Empirical models for estimating the PF-HSB considering the effects of stress relaxation and corrosion are proposed, and the models make good agreement with experimental data.

2. Experimental Program

2.1. Assembly of High-Strength Bolted Connections

According to GB50017-2017 [10] and JGJ82-2011 [26], two different types of high-strength bolted connections (TX Series and TY Series) with double friction surfaces were considered, as shown in Figure 1 and Figure 2. The bolts with diameter of 20 mm was used, and the diameter of bolt holes was 22 mm. Torsional shear high-strength bolts with Grade 10.9, normally utilized in engineering, were adopted. In TX Series (Figure 1), all steel plates including two cover plates and two inner plates were fabricated from Q235 with 8 mm thickness. The length and width of the cover plate were 185 × 180 mm, and the inner plate was 240 × 180 mm. In TY Series (Figure 2), Q345 steel with 12 mm thickness was utilized for all steel plates. The width and length of steel plates and the diameter bolts were same with those in TX. All surfaces of these steel plates in TX Series and TY Series kept original status and phosphating was used to treat bolts. The yield strength and the ultimate strength of Grade 10.9 high-strength bolts were 940 MPa and 1040 MPa according to the coupon testing, respectively. The yield and ultimate strengths of Q235 were 288 MPa and 434 MPa, respectively, and the yield and ultimate strengths of Q345 were 389 MPa and 533 MPa, respectively.

For monitoring the strain variation of bolts, strain gauges were arranged in bolts. First, a 2 mm diameter circular hole was drilled at the center of the nut. Then, BTM strain gauges were embedded in the hole using epoxy resin, as shown in Figure 3a. Figure 3b shows high-strength bolts with embedded BTM strain gauges. After that, the calibration process was carried out to establish the relation between the preload force and the value of strain using a tensile testing machine, as depicted in Figure 4, and

Table 1. Calibration parameters of high-strength bolts.

Applied Force (kN)	0	3	6	9	12	15	Calibration Coefficient (kN/μ)
Bolt I	0	25	48	76	118	154	0.098
Bolt II	0	32	68	106	142	176	0.084
Bolt III	0	32	68	102	142	180	0.081
Bolt IV	0	50	94	142	186	236	0.065

lists the values of calibration coefficient for each bolt. Finally, the preload force was applied and high-strength bolted connections were assembled. According to JGJ82-2011 [26], the preload force of 50% of the design value (155 kN) of high-strength bolts was firstly applied using a pointer torque wrench (Figure 5). Then, an electric torque wrench (Figure 6) was utilized to apply the preload force and the screwing of the preload force was finished when the plum blossom-shaped head of the twist-off tension-control high-strength bolts fractured. After the assembly of connections, they were arranged in salt-spray chamber. In order to avoid the failure of wires connected to strain gauges in the corrosion testing, all wires were surrounded by the epoxy resin, as shown in Figure 7.

2.2. Monitoring of the Preload Force

To monitor the strain variation of the preload force, a DH3818Y static strain sensor before the screwing was connected to the wires, as shown in Figure 8. After stress relaxation of bolts was finished, which was exhibited by the stable status of the preload force, all connections were placed in the salt-spray chamber to perform the accelerated corrosion testing, as described in Section 2.3.

Table 2. Monitoring scheme of the PF-HSB.

Specimen Number	Bolt Grade	Diameter of Bolt (mm)	Steel Plate	Numbers of Bolts in Monitoring
S235-1	10.9S	20	Q235	2 (Bolt I and Bolt II)
S355-1	10.9S	20	Q355	2 (Bolt III and Bolt IV)

presents the details for the PF-HSB.

2.3. Accelerated Corrosion Testing

In this study, two types of specimens with different corrosion levels were obtained by accelerated corrosion testing. As the copper accelerated spray can simulate natural corrosion condition and it can obtain specimens with high corrosion rate in a short time, it was employed to investigate the PF-HSB in corroded connections in this work. According to GB/T 10125-2012 [27], 500 g NaCl was firstly added to each 9.5 L distilled water, and the salt solution with the concentration of 50 g/L ± 5 g/L was prepared. After stirring evenly, 2.47 g copper chloride (CuCl₂·2H₂O) was added to the salt solution. The concentration for the copper chloride was 0.26 g/L ± 0.02 g/L. Finally, pH value of the solution was adjusted by glacial acetic acid and it kept between 3.0 and 3.1. According to GB/T 10125-2012 [27], the pH value of the collected solution varies from 3.1 to 3.3. More details can be found in authors’ previous study [28]. Note that accelerated corrosion testing started after the PF-HSB had stabilized. Figure 9 shows specimens in the accelerated corrosion testing in the salt-spray chamber.

3. Experimental Results and Discussion

3.1. Corrosion Degree

The accelerated corrosion testing lasted six months, and a batch of specimens were taken out to get the corrosion rate every two months. The mass of the steel plates and bolts were measured and recorded prior to the accelerated corrosion testing. After being taken out, the yellow and black corrosion product on the surface of specimens was found, as depicted in Figure 10. The corrosion product on the surface of steel plates and bolts were then cleared using physical method, as shown in Figure 11. The mass of each sample was then measured and recorded again. Finally, the corrosion degree (the mass loss ratio) for each sample was established, as shown in Equation (1), and

Table 3. Corrosion rate of high-strength bolts.

Bolts Number	Corrosion Time (h)	Mass before Corrosion(g)	Mass after Corrosion(g)	Corrosion Rate (%)	Average Corrosion Rate (%)
MZ11	1440	263.50	254.50	3.42	3.55
MZ12		263.50	254.00	3.61
MZ13		263.50	254.00	3.61
MZ21	2880	263.50	245.00	7.02	6.78
MZ22		262.00	246.00	6.11
MZ23		263.00	244.00	7.22
MZ31	4320	262.00	224.50	14.31	17.05
MZ32		263.50	217.50	17.46
MZ33		263.00	212.00	19.39

and

Table 4. Corrosion rate of steel plates.

Specimen Number	Corrosion Time (h)	Mass before Corrosion (g)	Mass after Corrosion (g)	Corrosion Rate (%)	Average Corrosion Rate (%)	Average Thickness Loss of Steel Plate (mm)
MX11	1440	441.50	428.50	2.94	2.97	0.22
MX12		444.00	430.50	3.04
MX13		442.50	429.50	2.94
MY11		706.50	686.00	2.90	2.91	0.35
MY12		697.50	676.50	3.01
MY13		711.00	691.00	2.81
MX21	2880	440.00	401.00	8.86	8.91	0.67
MX22		443.00	404.50	8.69
MX23		442.00	401.50	9.16
MY21		712.00	665.00	6.60	6.62	0.80
MY22		706.50	659.50	6.65
MY23		704.50	658.00	6.60
MX31	4320	444.00	375.00	15.54	15.56	1.17
MX32		441.00	373.00	15.42
MX33		445.50	375.50	15.71
MY31		706.00	588.00	16.71	17.17	2.07
MY32		716.00	590.00	17.60
MY33		706.50	585.00	17.20

.

$$\eta =\frac{m_0-m}{m_0}\times 100\%$$

(1)

where m₀ is the primitive mass of samples; m is the mass of samples after clearing the rust; and η is the corrosion rate of samples. Corrosion rate for high-strength bolts and steel plates is shown in Table 3 and Table 4.

According to Xia et al.’s investigations [29], the average thickness loss of Q235 steel is 2.35 mm/a, which corresponds to the thickness loss of Q235 steel in 6.5 years in Beijing, China. In contrast, the average thickness loss of Q345 steel is 4.15 mm/a, which is 19 times of that in natural atmospheric corrosion environment of Beijing, China.

3.2. Degradation of the Preload Force

3.2.1. Stress Relaxation

Similar to Shi et al.’s experimental results [12], the stress relaxation of high-strength bolts is found after the final screwing of the preload force, as shown in Figure 12 and

Table 5. Stress relaxation of high-strength bolts in real-time.

Time	Bolt I	Bolt II	Bolt III	Bolt IV	Average
0 h	100.00%	100.00%	100.00%	100.00%	100.00%
5 h	81.41%	75.89%	84.56%	86.16%	82.01%
10 h	79.66%	73.53%	83.55%	84.42%	80.29%
15 h	78.79%	72.69%	82.82%	83.76%	79.52%
20 h	78.05%	72.33%	81.74%	83.41%	78.88%
25 h	77.02%	71.37%	80.98%	82.66%	78.01%
30 h	76.04%	70.12%	80.71%	81.71%	77.15%
35 h	75.52%	69.38%	80.48%	81.21%	76.65%
40 h	75.23%	69.24%	80.06%	80.99%	76.38%
45 h	74.93%	69.47%	79.22%	81.11%	76.18%
50 h	74.03%	68.60%	78.80%	80.45%	75.47%
60 h	72.92%	67.18%	78.34%	79.38%	74.46%
70 h	72.34%	66.66%	77.81%	78.96%	73.94%
88 h	71.17%	65.68%	76.74%	78.18%	72.94%
90 h	71.34%	66.06%	76.74%	78.36%	73.13%
100 h	70.45%	65.17%	76.32%	77.68%	72.41%

. Here,$P_0$ is the applied PF-HSB, and $P$ is the real-time PF-HSB. Clearly, the PF-HSB decreased rapidly in the first five hours after the final screwing of the preload force. For example, the preload force of Bolt I decreased to 81.4%, and that of Bolt III decreased by 15.4%. After 45 h of the final screwing of the preload force, it gradually became stable. The average loss of the preload force in TX Series was 27.8%, and that of the preload force in TY Series wass 19.8%. After 100 h, the process of stress relaxation was finished and the preload force became stable. A similar conclusion was also reached by Shi et al. [12].

3.2.2. Effect of Corrosion on the Preload Force

According to the test results, the relations between the PF-HSB and corrosion time are obtained, as depicted in Figure 13. Here, $P_c$ is the real-time PF-HSB and $P_{c0}$ is the PF-HSB after stress relaxation. Note that values of strain gauges at Bolt I, Bolt II, and Bolt III were not effective after 1600 h, so only the PF-HSB in 1600 h are shown in Figure 13. As the wire connected to Bolt IV was broken in the accelerated corrosion testing, the strain variation of Bolt IV is not captured. From the results of test, corrosion had significant influences on the PF-HSB, as reflected in Figure 13 and

Table 6. Details of specimens in test.

Specimens	Material of Plates	Corrosion Rate η (%)	Test Data Pc/Pc0	Group
TX Series	Q235	0.075	0.930	Predicting group
	Q235	0.123	0.915
	Q235	0.183	0.906
	Q235	0.250	0.894
	Q235	0.485	0.894
	Q235	1.733	0.814
	Q235	0.714	0.864	Verifying group
	Q235	1.363	0.829
	Q235	2.129	0.796
	Q235	2.768	0.765
	Q235	3.537	0.747
TY Series	Q355	0.047	0.874	Predicting group
	Q355	0.120	0.865
	Q355	0.208	0.836
	Q355	0.347	0.816
	Q355	0.522	0.809
	Q355	0.734	0.800	Verifying group
	Q355	0.983	0.790
	Q355	1.428	0.764
	Q355	2.022	0.676

. The PF-HSB decreased by 30.0% when the corrosion degree of steel plates reached 3.5%. This may be mainly attributed to the softness of corrosion product on steel plates.

4. Finite Element Analysis

4.1. Finite Element Method

In order to investigate the loss of PF-HSB caused by corrosion, a three-dimensional finite element method was developed using Abaqus [30]. All members for high-strength bolted connections were simulated using C3D8R Element [31,32,33]. All contacts (i.e., bolt heads and steel plates, bolt nuts and steel plates, bolt shanks and bolt holes, and contacts between steel plates) were simulated, and surface-to-surface contact with hard contact was selected. The influences of corrosion was considered in three aspects: the friction factor of steel plates after corrosion, the constitutive model of steel plate after corrosion, and the stiffness reduction in cover plates. The friction factor for the contact was adopted according to Hong’s test [34]. The influences of corrosion on mechanical properties of steel plate were considered, and the corresponding constitutive model of steel plate after corrosion was adopted according to authors’ previous study [28]. The “Predefined filed” was used to control the variation of mechanical properties of steel before and after corrosion. As the surface of the bolts was treated by the phosphating method, the corrosion extent of bolts was not serious in this work. As a result, the effect of corrosion on bolts was not considered in the finite element analysis. Mesh sizes for the steel plates and bolts were 8 mm and 2 mm, respectively, as shown in Figure 14. The reason for the choice of the mesh sizes is that they can accurately predict the behavior of connections, as discussed in Section 3.2 in this work.

Note that the preload force loss caused by stress relaxation was not considered. As discussed in Section 3.2.1, the preload force will keep stable after 100 h of the final screwing of the preload force. Therefore, the stable preload force (124 kN for TX Series and 121 kN for TY Series) was considered as the initial value for the PF-HSB in the finite element analysis. The preload force was applied by “Bolt load” on each bolt, as shown in Figure 15. To handle the difficulties of convergence, the whole process is composed of a series of different analysis steps [35,36,37]. Firstly, each bolt was subjected to a tensile load of 10 N, so that all the parts could contact with each other. Secondly, all the preload force was applied to each bolt in accordance with JGJ 82-2011 [26]. Thirdly, all bolts were fixed at current length [38]. On the basis of the corrosion rate in the test, the corrosion depth (the thickness loss of steel plates) can be obtained. As shown in Figure 15, the surface of steel plate became soft after the accumulation of the corrosion product. For this reason, a stiffness reduction method was employed to consider the corrosion damage on the high-strength bolt. The corrosion depth is firstly calculated according to corrosion degree, and reduced field variable method, which is considered by the reduction in elasticity modulus, is then applied to the corrosion depth of the cover plates. To solve the converge problem, the process of reducing stiffness is divided into several steps, and the corrosion depth for each step is less than 0.5 mm.

4.2. Validation of Finite Element Analysis

Based on the stiffness reduction method, the PF-HSB at different corrosion rates was obtained. To verify the reliability of the stiffness reduction method, the test data in this study were utilized as listed in

Table 7. Comparison of PF-HSB after corrosion between test and FEM.

Specimens	$\mathbf{Corrosion} \mathbf{Rate} \mathit{\eta }$ (%)	Test Results		FEM Results		Error (%)	Average Error (%)
		Preload Force (kN)	Pc/Pc0	Preload Force (kN)	Pc/Pc0
TX1	0.7137	107.11	0.864	114.20	0.921	6.60%	3.36%
TX2	1.363	102.73	0.828	106.91	0.862	4.10%
TX3	2.129	98.64	0.796	99.18	0.800	0.50%
TX4	2.768	94.80	0.765	93.99	0.758	0.92%
TX5	3.537	92.68	0.747	83.31	0.712	4.69%
TY1	0.734	96.76	0.800	103.46	0.855	6.92%	3.45%
TY2	0.983	95.62	0.790	98.81	0.817	3.33%
TY3	1.428	92.41	0.764	91.33	0.755	1.17%
TY4	2.022	81.83	0.676	83.71	0.692	2.37%

. Clearly, the developed stiffness reduction method accurately captured the PF-HSB after corrosion as the average error between results from the stiffness reduction method and experimental results is only 3.52% (TX Series) and 3.58% (TY Series).

4.3. Parametric Study

As the corrosion rate in the experiment only reached 3.537%, a parametric study is carried out to investigate the PF-HSB of specimens with relatively large corrosion rate, as listed in

Table 8. Details of specimens in FEM.

Specimens	Material of Plates	Plate Thickness (mm)	$\mathbf{Corrosion} \mathbf{Rate} \mathit{\eta }$ (%)	Corrosion Depth (mm)	Young’s Modulus (Gpa)	Poisson’s Ratio
TX0	Q235	8	0.000	0.000	206	0.3
TX1	Q235	8	0.714	0.053	204.7	0.3
TX2	Q235	8	1.363	0.101	203.54	0.3
TX3	Q235	8	2.129	0.158	202.16	0.3
TX4	Q235	8	2.768	0.206	201.01	0.3
TX5	Q235	8	3.537	0.263	200.65	0.3
TX 6	Q235	8	2.97	0.220	199.62	0.3
TX 7	Q235	8	5.500	0.408	196.08	0.3
TX 8	Q235	8	7.000	0.520	193.38	0.3
TX 9	Q235	8	8.910	0.670	189.94	0.3
TX 10	Q235	8	12.000	0.891	184.37	0.3
TX 11	Q235	8	15.560	1.175	177.95	0.3
TY0	Q355	12	0.000	0.000	206	0.3
TY1	Q355	12	0.734	0.090	204.21	0.3
TY2	Q355	12	0.983	0.120	203.02	0.3
TY3	Q355	12	1.428	0.175	201.02	0.3
TY4	Q355	12	2.022	0.247	198.59	0.3
TY 5	Q355	12	2.910	0.350	195.40	0.3
TY 6	Q355	12	6.620	0.800	186.48	0.3
TY 7	Q355	12	9.000	1.101	183.21	0.3
TY 8	Q355	12	11.000	1.346	181.38	0.3
TY 9	Q355	12	14.000	1.713	179.61	0.3
TY 10	Q355	12	17.170	2.070	178.54	0.3

. The maximum corrosion rates for TX series and TY series in the finite element analysis are identical with those in the experiment, as shown in Table 4. From Zhang et al.’s investigations [39], the value of 15.56% for the corrosion rate of Q235 steel corresponds to the corrosion rate of specimens after exposure at ambient environment in Shanghai, China for 65 years. For this reason, the maximum corrosion rate in the analysis may be enough to envelope the corrosion extent of in-service steel structures.

Figure 16 shows the stress distribution in high-strength bolted connections before and after corrosion. Clearly, the maximum stress distributed on the connection decreased from 527.6 Mpa to 207.7 Mpa when the corrosion rate reached 15.15% for TX series. In contrast, the maximum stress on the connection decreased by 75% after the corrosion rate increased to 17.17%.

5. Model for the PF-HSB

5.1. Stress Relaxation of High-Strength Bolts

For predicting the stress relaxation of high-strength bolts after final screwing, models for the stress relaxation are suggested based on the results of the monitoring test, as shown in Equations (2) and (3) and Figure 17.

$$\frac{P}{P_0}=-0.32t^{0.10}+1.00 \left(R^2=0.95\right) \mathrm{for} \mathrm{TX} \mathrm{series}$$

(2)

$$\frac{P}{P_0}=-0.19t^{0.11}+1.00 \left(R^2=0.96\right) \mathrm{for} \mathrm{TY} \mathrm{series}$$

(3)

where $P_0$ is the applied PF-HSB according to JGJ82-2011 [26], and $P$ is the real-time PF-HSB.

5.2. Degradation Model for the Preload Force of Corroded High-Strength Bolts

To estimate the PF-HSB after corrosion, the experimental and numerical results are employed, as shown in Equations (4) and (5) and Figure 18. Here, the experimental results are divided into two groups: predicting group and verifying group, as shown in Table 6. The predicting group is incorporated with numerical results to develop the degradation model of corroded high-strength bolts, and the verifying group is utilized to validate the veracity of the degradation model, as discussed in Section 5.3.

$$\frac{P_c}{P_{c0}}=-0.144{\eta }^{0.535}+1.00 \left(R^2=0.976\right) \mathrm{for} \mathrm{TX} \mathrm{Series}$$

(4)

$$\frac{P_c}{P_{c0}}=-0.235{\eta }^{0.436}+1.00 \left(R^2=0.974\right) \mathrm{for} \mathrm{TY} \mathrm{Series}$$

(5)

where $P_c$ is the real-time PF-HSB after corrosion, $\eta$ is the corrosion rate, and $P_{c0}$ is the PF-HSB after stress relaxation, which is 124 kN for TX Series and 121 kN for TY Series, respectively.

As depicted in Figure 19, the loss of PF-HSB in TX Series reaches 65% when the corrosion rate is 15.56%, while the loss of PF-HSB in TY Series reaches 80% when the corrosion rate is 17.17%.

5.3. Evaluation of the Proposed Model

To assess the accuracy of the proposed models, the other group of experimental results is utilized, as shown in

Table 9. Comparison of the PF-HSB after corrosion between the proposed model and test data.

Specimens	$\mathbf{Corrosion} \mathbf{Rate} \mathit{\eta }$ (%)	Test Data Pc/Pc0	Proposed Model Pc/Pc0	Error (%)	Average Error (%)
TX1	0.714	0.864	0.880	1.85%	1.12%
TX2	1.363	0.828	0.831	0.36%
TX3	2.129	0.796	0.7857	1.29%
TX4	2.768	0.764	0.752	1.57%
TX5	3.537	0.747	0.743	0.54%
TY1	0.734	0.800	0.794	0.75%	2.34%
TY2	0.983	0.790	0.767	2.91%
TY3	1.428	0.764	0.725	5.10%
TY4	2.022	0.676	0.680	0.59%

. Clearly, the proposed degradation model can accurately estimate the PF-HSB after corrosion as the average error between the proposed model and test data in TX series is 1.97%, and the average error in TY series is 2.97%.

6. Conclusions

In this study, the degradation behavior of the PF-HSB after corrosion was investigated. The accelerated corrosion testing and the monitoring test for the PF-HSB were performed. The finite element method for estimating the loss of PF-HSB after corrosion was developed using ABAQUS. The main conclusions are made as follows:

(1)

The PF-HSB decreases rapidly in the first five hours after the final screwing, and it tends to be stable after 45 h. A model that can predicts the stress relaxation of high-strength bolts after final screwing is suggested.

(2)

Corrosion has significant influences on the PF-HSB. The PF-HSB decreases by 30.0% when the corrosion degree of steel plates reaches 3.5%.

(3)

A finite element method is developed to predict the loss of PF-HSB after corrosion.

(4)

Accurate models for predicting the loss of PF-HSB after corrosion are proposed.