Study on the parameters of steel plate reinforcement rib-deck crack considering local stress disturbances

Abstract

Local reinforcement will change the local stiffness distribution of the component, causing perturbation effects on the local stress of the fatigue detail. Only considering the reinforcement effect may lead to excessive strengthening and induce new fatigue-prone points. For the fatigue detail of the rib-deck weld, steel plate reinforcement test and numerical simulations were conducted. The stress changes of the deck weld toe and weld root before and after reinforcement were analyzed. The influence of parameters such as steel plate length, thickness, and width on the reinforcement effect of the weld toe crack and local stress disturbance was discussed, and reasonable parameters were recommended. The results show that after the cracking of the weld toe, the stress concentration locations at the weld toe and weld root of the deck shift from the center of the specimen to the crack tip. Steel plate reinforcement can effectively restrain the crack propagation, but can lead to an increase in the stress at the deck weld root within the reinforced area. A good reinforcement effect can be achieved while the steel plate covers the crack, and further increasing the steel plate length has limited improvement on the reinforcement effect but reduces the adverse effect of steel plate reinforcement on the stress of the deck weld root. Increasing the steel plate width will increase the adverse effect of steel plate reinforcement on the deck weld root stress, and it is recommended to use steel plates with a length greater than 120 mm and a length-to-width ratio greater than 4 for reinforcement. Increasing the width of the steel plate has a relatively small effect on the reinforcement effect and the stress at the deck weld root, and steel plates with the same thickness as the deck are recommended.

Keywords

steel bridge decks rib-deck weld fatigue crack local reinforcement steel plate reinforcement

Introduction

Steel bridge decks are widely used in the construction of long-span bridges due to their superior load-bearing performance and spanning capability. However, under the influence of adverse factors such as vehicular load cycles, welding residual stress, and welding defects, their fatigue problems are becoming increasingly severe (Chen et al., 2023; Fang et al., 2022). Among these, rib-deck weld toe (RDWT) cracks that initiate at the weld toe of the rib-deck weld and propagate in the thickness direction of the deck are one of the common fatigue cracks in real bridges. Once these cracks penetrate the deck, they can cause secondary problems such as water seepage and corrosion, severely affecting the service performance of the bridge. Addressing these issues has become one of the main focuses of steel bridge maintenance (Xu et al., 2011; Yang et al., 2022).

At present, reinforcement technology is the primary method used to maintain RDWT cracks. Based on the scope of reinforcement, it can be divided into overall reinforcement and local reinforcement (Qin et al., 2022; Xin et al., 2022). Overall reinforcement mainly involves replacing high-strength pavement to increase the overall rigidity of the steel bridge deck, thereby inhibiting crack propagation (Cheng et al., 2022). However, due to the performance degradation and difficulty of replacing, this method has not been widely adopted (Wang et al., 2019). Local reinforcement, on the other hand, involves attaching reinforcement components at the crack locations to increase local rigidity and thus inhibit crack propagation (Guo et al., 2019; Jiang et al., 2021). This method is mainly used for reinforcing RDWT cracks due to its ease of construction, replaceability, and the fact that it does not require traffic interruption. Among these methods, steel plate reinforcement is the mainstream method for RDWT crack reinforcement in real bridges due to its advantages of low cost, ease of processing, and high rigidity (Kawakami et al., 2015). Researchers have demonstrated the effectiveness of steel plate reinforcement for RDWT cracks through experiments, simulations, and practical bridge applications, and have established steel plate size parameters from the perspective of crack propagation inhibition (Yang et al., 2023; Zhou et al., 2021). However, attaching reinforcing steel plates inevitably alters the local rigidity at the crack locations, which affects the distribution of local stress in fatigue details (Gao et al., 2024). Li et al. (2017) found that although increasing the thickness of the reinforcement steel plate can achieve better reinforcement effects, overly thick reinforcement plates may lead to new fatigue-prone points outside the reinforced area. Zhang et al. (2018) conducted fatigue crack reinforcement tests on rib-diaphragm weld that bolted angle steel can effectively inhibit crack propagation on U-ribs but alters the local force transmission path, significantly increasing stress at the weld toe of the diaphragm. Fang et al. (2019) discovered through numerical simulation that reinforcing the right side crack of the diaphragm with a steel plate significantly reduces the stress at the weld on the left side of the diaphragm. Therefore, the disturbance to the original stress pattern in fatigue details caused by steel plate reinforcement is unavoidable. If the reinforcement effect of existing cracks is the only focus while ignoring the disturbance to local stress distribution caused by steel plate reinforcement, it may lead to a shift in cracking patterns and induce new fatigue cracks. Hence, for fatigue details with multiple cracking patterns like rib-deck welds, the existing parameter recommendations that only consider the crack reinforcement effectiveness need further verification.

Therefore, in view of the shortcomings of existing research, it is necessary to conduct further studies to investigate the impact of RDWT crack reinforcement with steel plates on the stress disturbance of the rib-deck weld. Based on a comprehensive evaluation of the reinforcement effect on existing cracks and the degree of local stress disturbance, reinforcement parameters should be established to ensure the effectiveness of crack reinforcement while avoiding more severe fatigue cracking problems such as fatigue cracks at the rib-deck weld root. In this paper, the local stress changes at the weld toe and weld root after reinforcing the RDWT crack with steel plates are analyzed by conducting reinforcement tests and numerical simulations. The impact of steel plate reinforcement on the local stress disturbance of the rib-deck weld is explored. The influence of steel plate length, width, and thickness on the reinforcement effect of the RDWT crack and the stress disturbance at the weld root are discussed. Reasonable steel plate reinforcement parameters are suggested after considering the treatment effect of weld toe cracks and the stress at the weld root. The study provides a reference for the formulation of fatigue crack treatment strategies for real bridges.

Reinforcement test

Specimens design

Five deck-rib weld local full-size test specimens were designed according to the actual bridge size. The deck has a width of 600 mm horizontally, 300 mm vertically, and a thickness of 14 mm. The U-rib has the same width as the deck, with a length of 200 mm and a thickness of 8 mm. The deck and U-rib are connected by single-side welding with an 80% penetration rate, and the inclination angle of the U-rib is 78°. The specific dimensions of the specimen are shown in Figure 1. The material of the specimen is Q345qD (Liao et al., 2020) consistent with that of the real bridge, and the material properties comply with the Chinese standard GB/T 714-2015.

Figure 1.

Size of specimens.

Test process and conditions

The test is divided into two stages, the pre-cracked stage (Stage 1) and the reinforcement test stage (Stage 2), as shown in Figure 2.

Figure 2.

Testing procedures.

Stage 1: Fabricate specimens and steel plates according to the Figure 1 and Table 1. Subsequently, polish the surface of the specimen and paste unidirectional strain gauges at nominal stress measuring points 10 mm away from the weld toe and weld root, perpendicular to the direction of the weld, and label them as Point1-Point7 (P1-P7) respectively. After the strain gauges are pasted, the deck on the weld root side is fixed to the steel base with high-strength bolts, and an eccentric motor is arranged on the weld toe side to apply bending cyclic loads (Wang et al., 2021). The magnitude of the applied load is controlled by adjusting the angle of the eccentric block in the motor, and the strain measured at Point 3 is controlled to be 790µε. Due to manual adjustment, there is a measurement error of ±6µε when loading. The actual strain after loading is shown in Table 1. This stage ends when the crack reaches the predetermined length, as shown in Table 1. To improve the efficiency of this stage, a 55 ± 3 mm long and 4 mm deep initial defect is pre-made at the weld toe using a handheld mini-cutting machine before the test.

Table 1.

Test conditions.

	Prefabricated crack length (mm)	Crack length before reinforcement (mm)	Strain ( $μ ε$ )	Parameters of steel plate (mm)
	Prefabricated crack length (mm)	Crack length before reinforcement (mm)	Strain ( $μ ε$ )	Length	Thickness	Width
SP1	58	74	795.72	100	8	50
SP2	50	75	787.97	120	8	50
SP3	58	75	783.21	140	8	50
SP4	58	73	789.76	120	6	50
SP5	55	75	795.42	120	10	50

Stage 2: In this stage, the specimen is reinforced with steel plates and then subjected to bending cyclic loads until the specimen fractures. The parameters of the steel plate are shown in Table 1. The steel plate is bonded to the deck and U-rib on the weld toe side of the specimen using room temperature-curing Grade A structural adhesive. The centerline of the steel plate coincides with the centerline of the crack. The thickness of the adhesive layer is controlled to be 2 ± 1 mm, and the performance of the structural adhesive meets the relevant requirements of Chinese standard JTG/T J22-2008 (CCCC First Highway Consultants Co., Ltd. 2008). Following the bonding of the steel plate, a curing period of 3 days is required before reloading. Subsequently, reload the specimen with the same loading magnitude as in Stage 1 until the specimen fractures.

Test results

Local strain and failure behavior

Taking SP2 as an example, the strain time history curves at various measurement points are drawn, as shown in Figure 3. Based on the changes in strain at each measurement point, the process can be roughly divided into three stages. In Stage 1, Fatigue damage accumulates continuously at the bottom of the prefabricated crack, but no new cracks initiate. There is no significant change in the strain at each measurement point. In Stage 2, After 1.48 million load cycles, new cracks initiate and propagate from the bottom of the prefabricated crack. During the crack propagation process, the strain at P6 and P7 gradually increases. This is likely because the crack propagation reduces the effective cross-section of the deck at the weld toe, decreasing the local load-bearing capacity and increasing the load borne by the uncracked areas. The strain at the weld root point P3 gradually decreases, while the strain at other points gradually increases, indicating that the stress at the weld root also changes with the crack propagation at the weld toe. In Stage 3, When the load reaches 3.12 million cycles, steel plates are applied to the cracked area and the strain at the weld toe points P6 and P7 decreases by approximately 12.6% and 9.2%, respectively, compared to before reinforcement. This shows that the steel plate reinforcement can increase the local stiffness at the weld toe and inhibit crack propagation. The strain at the weld root points P1 and P5 decreases, considering that the steel plate shared part of the load, thereby reducing the strain at points P1 and P5. However, the strain at the points P2-P4 within the reinforced area increases by approximately 2.2%, 11.5%, and 2.8%, respectively. This indicates that while the steel plate reinforcement increases the local stiffness at the weld toe crack, it also increases the strain at the weld root within the reinforced area, accelerating the accumulation of fatigue damage at the weld root.

Figure 3.

Strain curve of measured points on SP2.

Additionally, after reinforcement with the steel plates, the edge of the adhesive layer on the side of the deck cracked when the load reaches 4.12 million cycles, as shown in Figure 4. Subsequently, the strain growth rate at points P6 and P7 significantly increases. At 4.35 million cycles, the adhesive layer on one side of the deck almost completely fails. At this point, the crack extends past the P6 point on the right and 2 mm through the adhesive layer on the left, causing a rapid decrease in the strain at P6 and a further increase in the strain growth rate at P7. At 4.44 million cycles, the crack extends to the edge of the specimen, leading to specimen fracture and failure. The detached reinforcement component remains intact, with complete adhesive layers on both sides but missing adhesive at the weld seam, as shown in Figure 4. This indicates that once the adhesive layer cracks after steel plate reinforcement, the local strain increases rapidly, and the reinforcement effect quickly diminishes, making it difficult to effectively inhibit crack propagation. Long-term monitoring of steel plate reinforcement on the rib-deck weld of a certain kilometer-scale cable-stayed bridge in China revealed that most of the secondary expansion sites experienced varying degrees of adhesive layer damage at the steel plate edges, as shown in Figure 5. Therefore, after bridge reinforcement, it is necessary to closely monitor the cracking of the adhesive layer. If any cracking is observed, the situation should be closely monitored, or the steel plates should be replaced.

Figure 4.

Cracking of the adhesive layer.

Figure 5.

Adhesive failure in real bridge.

Crack reinforcement effect

The strain and average strain reduction of the measuring points on the weld toe side of each specimen after reinforcement with steel plates are shown in Figure 6. Comparing SP1, SP2, and SP3, it can be seen that after reinforcing the weld toe crack with different lengths of steel plates, there is a certain reduction in strain at each measuring point. The reduction increases gradually with the length of the steel plate. P6 decreased by approximately 7.3%, 9.2%, and 22.1%, respectively, while P7 decreased by approximately 6.0%, 12.6%, and 21.3%. Although there are certain differences in the strain reduction between the two measuring points in each specimen, they are all within 5%, which is considered to be due to asymmetric reinforcement. It can be seen that increasing the length of the steel plate can significantly enhance the local stiffness at the weld toe, reduce the strain at the weld toe, and inhibit crack propagation.

Figure 6.

Strain at weld toes before and after reinforcement.

Calculating the strain reduction at P6 and P7 before and after reinforcement with SP4, SP2, and SP5, the strain at P6 decreased by approximately 8.8%, 9.2%, and 9.4%, respectively, and the strain at P7 decreased by approximately 10.8%, 12.6%, and 13.0%, respectively. When the steel plate thickness is 10 mm, the strain reduction is only 2.2% greater than when the thickness is 6 mm. It can be seen that increasing the thickness of the steel plate can further reduce the strain at the weld toe, but the reduction is limited and less significant than the effect of increasing the steel plate length on crack reinforcement.

Strain at the weld root

To further demonstrate the adverse effects of crack propagation and steel plate reinforcement on the stress at the weld root, the strain distribution at the weld root of the deck during initial loading, before reinforcement, and after reinforcement for SP3 was drawn, as shown in Figure 7. During initial loading, the strain at the weld root roughly showed an “M” shape distribution. When the crack extends to 76 mm, the strain distribution at the weld root is basically the same as during initial loading. The strain at point P3, due to the further weakening of local stiffness at the cracked area caused by crack propagation, is approximately 5.67% lower than during initial loading. The strain at other measurement points (P1∼2, P3∼4) increases to varying degrees. It can be seen that the change in local stiffness during the propagation of the RDWT crack adversely affects the stress at the weld root, accelerating the accumulation rate of fatigue damage at the weld root.

Figure 7.

Strain of each measuring point on SP3.

After reinforcement with the steel plate, the strain at each measuring point within the reinforced area increased compared to before reinforcement. The strain at P3 increased by about 9.74%, while the strains at P2 and P4 increased by 2.22% and 1.86%, respectively. The strain at each measuring point is also higher than the initial strain at the beginning of loading. However, the strain at measurement points far from the reinforced area decreased compared to before the reinforcement. The strain at P1 and P5 decreased by 11.15% and 8.40%, respectively, which is considered to be due to the limited effect of the steel plate, affecting only the reinforced area and nearby points. For points far from the reinforced area, the overall strain on the original specimen decreased after the steel plate shared part of the load, resulting in reduced strain at P1 and P5. Combined with the analysis in section ‘Local strain and failure behavior', it can be seen that steel plate reinforcement of the RDWT crack inevitably adversely affects the stress at the weld root within the reinforced area.

From the above analysis, it is clear that steel plate reinforcement has the most significant impact on the strain at P3. Therefore, the strain at P3 after reinforcement of each specimen is extracted to further discuss the effect of steel plate parameters on the stress at the weld root, as shown in Figure 8. The strain at each measuring point at the weld root increased to varying degrees after steel plate reinforcement, with SP1-SP5 increasing by 13.21%, 11.54%, 10.32%, 11.59%, and 11.62%, respectively. Comparing SP1∼SP3, it can be found that as the length of the steel plate increases, the stress increase at the weld root gradually decreases, with the change range within 3%. It can be seen that increasing the length of the steel plate can somewhat mitigate the adverse effects of steel plate reinforcement on the stress at the root. Comparing SP4, SP2, and SP5, it can be found that as the thickness of the steel plate increases, the strain increase at the root slowly increases, with the change range within 0.1%. Therefore, the effect of steel plate thickness on the stress at the root is relatively small.

Figure 8.

Strain of P3 on each specimen.

In summary, while steel plate reinforcement can inhibit the propagation of the RDWT crack, it has an adverse effect on the stress at the weld root within the reinforced area. Moreover, the steel plate parameters affect the degree of this impact on the weld root stress. Therefore, it is necessary to comprehensively consider the effect of steel plate parameters on the weld root stress when formulating reinforcement parameters. Additionally, due to the need to avoid mutual interference between strain gauges during the experiment, not many strain gauges could be attached at the weld root. Therefore, further analysis of the effect of steel plate parameter changes on the reinforcement effect of the RDWT crack and the stress at the weld root will be conducted through numerical simulation to formulate steel plate reinforcement parameters.

Numerical simulation

Model

A rib-deck weld model was established using the ABAQUS finite element analysis software, as shown in Figure 9. The model dimensions are consistent with the specimen in the test. The elastic modulus of the specimen and the steel plate is 2.06 × 10⁵ MPa, with a Poisson’s ratio of 0.3. The elastic modulus of the adhesive layer is 5596 MPa, with a Poisson’s ratio of 0.26. Fixed constraints were applied to the deck on the weld root side, and loads were applied to the deck on the weld toe side, with the loading position and area consistent with the test. Static loading was used in the simulation, controlling the X-direction normal stress at P3 after loading to be half of the stress amplitude in the test. For example, for SP5, this translated to a surface load of 0.282 MPa in the model. ‘Tie’ connections were used to simulate the connections between the steel plate, adhesive layer, deck, and U-rib. C3D8R hexahedral elements were used for meshing, with a global mesh size of 10 mm. A 1 mm mesh refinement was applied to the deck and U-rib regions within 20 mm of the weld toe and weld root, with a hexahedral swept mesh transition between the refined and other regions. A 2 mm mesh refinement was applied to the steel plate and adhesive layer.

Figure 9.

Finite element model.

The crack was simplified to a semi-elliptical shape (Zhang et al., 2019) with its length (a) set at 76 mm, height (c) at 7 mm, and the crack center aligned with the rib-deck center longitudinally; transversely, the crack was 0.2 mm away from the weld toe edge as shown in Figure 11. The steel plate length (L) was set to 50 mm, 76 mm (just covering the crack), and 100 mm-280 mm (average 20 mm), the width (W) was set to 30 mm-60 mm (average 10 mm) and 80 mm, and the thickness (T) was set to 4 mm-14 mm (average 2 mm). The stress intensity factor at the crack tip and the local stress at the weld root were analyzed to evaluate the effect of steel plate length, thickness, width, and other parameters on the reinforcement effectiveness.

Model accuracy verification

Taking SP5 as an example, calculate the normal stress in the X direction at the weld root measurement points (Point1-Point5) after introducing prefabricated crack (crack length a = 55 mm, depth c = 4 mm) and compare it with the experimental data, as shown in Table 2. Except for the control measurement point (Point3), the error between the simulation and the experimental at each point is within 10%, with the stress at Point5 being 10.7%. This is considered to be due to the inability to achieve complete symmetry in the prefabricated defects during the experiment. However, the overall average error is 6.1%, indicating that the model has a certain degree of accuracy and can be used for subsequent analysis.

Table 2.

Nominal stress at measured points under simulation and test.

	Point1	Point2	Point3	Point4	Point5	Average
Simulation (MPa)	85.40	91.53	81.93	90.87	84.66	/
Test (MPa)	83.46	85.52	81.93	87.09	94.85	/
Relative rate (%)	2.3	7.0	0.0	4.2	−10.7	6.1

Analysis of local stress disturbance

Using a steel plate with a length of 120 mm, a width of 50 mm, and a thickness of 8 mm as an example, the nominal stress at the weld toe, and the weld root of the deck was extracted to further investigate the local stress disturbance at the fatigue-prone areas of the rib-deck weld after reinforcing the RDWT crack with the steel plate. As shown in Figure 10, when the weld toe is not cracked, the stress at the weld toe, and the weld root of the deck all exhibit a symmetrical arc-shaped distribution with higher stress in the middle and lower stress at the ends. After the weld toe cracking, the stress at each position undergoes redistribution, with a significant reduction in stress at the transverse center of the model, and the stress concentration shifts to the crack tip, with stress levels exceeding those before cracking. It is evident that the initiation of the RDWT crack not only affects the stress distribution at the weld toe but also influences the stress distribution at the weld root.

Figure 10.

Nominal stress at each extraction path. (a) Deck weld toe. (b) Deck weld root.

After reinforcing with the steel plate, the overall stress at the weld toe decreases, while the stress at the weld root significantly increases within the steel plate reinforcement area and gradually decrease towards both sides. Compared to the stress levels before cracking, the maximum increase at the weld root is about 16%. This indicates that although reinforcing the RDWT crack with the steel plate can reduce the stress at the weld toe and inhibit crack propagation, it adversely affects the stress at the weld root, accelerating fatigue damage accumulation in these areas and potentially inducing new fatigue cracking problems.

The influence of steel plate parameters

From the above analysis, it is clear that the formulation of steel plate reinforcement parameters requires a comprehensive evaluation of the reinforcement effect on RDWT cracks and the disturbance impact on the weld root stress. Therefore, the stress intensity factor K at the crack tip and the stress at the weld root under various reinforcement conditions will be extracted and analyzed to formulate the steel plate parameters.

Steel plate thickness

When the width of the steel plate is 50 mm, plot the K_I curve after steel plate reinforcement with the thickness of the steel plate as the horizontal axis, as shown in Figure 11. From the figure, it can be seen that for steel plates of different lengths and widths, when the length and width of the steel plates remain constant, K_I decreases slowly with the increase in the thickness of the steel plates. Moreover, the trend of K_I remains unchanged with the variation in the length and width of the steel plates. When the thickness of the steel plate exceeds the thickness of the deck, the decrease in K_I is within 2% compared to the reinforcement using the thickness of the deck. It is evident that increasing the thickness of the steel plate has a limited effect on the improvement of the reinforcement.

Figure 11.

K_I at crack tip under different reinforcement conditions.

Taking the condition of the steel plate with a length of 120 mm and a width of 50 mm as an example, the nominal stress at the weld root after reinforcement with different steel plate thicknesses is calculated, as shown in Figure 12. From Figure 12, it can be seen that as the thickness of the steel plate increases, the stress variation at the weld root is relatively small, with a maximum fluctuation of less than 3%, which is consistent with the experimental results. Increasing the thickness of the steel plate has little effect on the stress at the weld root. Additionally, considering that increasing the thickness of the steel plate will increase the weight of the steel plate, which is detrimental to the stress on the adhesive layer, it is advisable to use a steel plate with the same thickness as the deck for reinforcement.

Figure 12.

Nominal stress at weld root.

Steel plate length

Based on the above analysis, it can be seen that increasing the thickness of the steel plate has a minimal impact on the reinforcement effect. Therefore, in subsequent analyses, the thickness of the steel plate is taken as 8 mm. Setting the length of the steel plate as the horizontal axis, the curves of K_I after reinforcement with steel plates of different thicknesses and widths are drawn, as shown in Figure 13, when the steel plate length does not cover the crack, the K_I has significantly decreased. When the steel plate fully covers the crack, the reduction in K_I gradually decreases and stabilizes as the length of the steel plate increases. For steel plates of different widths, although there is some difference in the rate of the K_I decrease after reinforcement, when the steel plate length (L > 200) mm (about 120 mm beyond the crack length), the increase in the reduction rate of K_I is within 1% for every additional 20 mm of steel plate length. It can be seen that a certain reinforcement effect can be achieved when the steel plate covers the crack. When the steel plate length exceeds 120 mm beyond the crack length, increasing the steel plate length has a limited effect on improving the reinforcement effect.

Figure 13.

K_I at crack tip under different reinforcement conditions.

Using a steel plate width of 50 mm and a thickness of 8 mm as an example, the stress at the weld root after reinforcement with steel plates of different lengths is shown in Figure 14. The figure shows that after steel plate reinforcement, the stress at the weld root within the reinforced area increases compared to before reinforcement. When the steel plate length (L < 200) mm, the stress is even greater than before the specimen cracked. As the steel plate length increases, the stress at the weld root in the reinforced area gradually decreases, but some areas still have stress greater than before the specimen cracked, and the stress concentration area gradually shifts towards the edge of the steel plate.

Figure 14.

Nominal stress at weld root.

To further assess the impact of steel plate length on crack reinforcement effectiveness and weld root stress, the reduction in stress intensity factor at the crack tip and the maximum stress increase at the weld root after reinforcement with steel plates of different lengths are extracted, as shown in Figure 15. The figure shows that as the length of the reinforcing steel plate increases, the stress increase at the weld root approximately linearly decreases, while the reduction in stress intensity factor at the crack tip initially rapidly increases and then slowly increases. When the steel plate length reaches 200 mm, the stress increase at the weld root decreases to within 10%, and the reduction in stress intensity factor reaches 69%. Thereafter, with the increase in steel plate length, the change in the reduction of the stress intensity factor is less than 5%. Combining with Figure 13, it can be seen that when the steel plate covers the crack and its length exceeds 120 mm beyond the crack, the crack reinforcement effect can be ensured, and the adverse impact on the weld root stress can be minimized. Therefore, for real bridge reinforcement, steel plates with a length exceeding 120 mm beyond the crack tip is recommended.

Figure 15.

The change of the stress and SIF.

Steel plate width

Using the steel plate width as the horizontal axis, the curves of K_I after reinforcement for different widths and lengths of steel plates are plotted, as shown in Figure 16. From the figure, it can be seen that when the steel plate length (L ≤ 200) mm, K_I decreases first and then increases with the increase in steel plate width. When (L > 200) mm, K_I shows a trend of first decreasing, then increasing, and then decreasing again. For the same steel plate length, the minimum K_I value is reached when the steel plate thickness is 40 mm. When the steel plate width exceeds 40 mm, the variation range of K_I under different lengths of steel plates is within 15% compared to when the width is 40 mm, and the variation range gradually decreases with the increase in steel plate length. Therefore, it can be seen that when the steel plate width (W ≥ 40) mm, the reinforcing effect of the steel plate on the crack is influenced by both the length and width of the steel plate. This consideration is due to the impact of the length and width of the steel plate on the load distribution and its bending performance. Hence, to further explore the influence of the length and width of the steel plate on the reinforcing effect, the length-to-width ratio of the steel plate is used as a variable. The K_I at the crack tip after reinforcement with different length-to-width ratios when the width W ≥ 40 mm are analyzed, as shown in Figure 17.

Figure 16.

K_I at crack tip after being reinforced by steel plate with different size.

Figure 17.

Fit curve of K_I at crack tip.

From Figure 17, it can be seen that with the increase in the steel plate length-to-width ratio, K_I generally shows a trend of first rapidly decreasing and then slowly decreasing. By fitting the data with a cubic curve, it can be found that when the steel plate length-to-width ratio is less than 4, K_I rapidly decreases with the increase in the length-to-width ratio. When the length-to-width ratio exceeds 4, the decrease in K_I gradually diminishes. This is considered to be because the bending performance along the length direction of the steel plate increases with the increase in the length-to-width ratio, thus achieving a better reinforcement effect.

Taking a steel plate with a thickness of 8 mm and a length of 120 mm as an example, the stress at the weld root after reinforcement for different plate widths is shown in Figure 18. It can be seen from the figure that the stress at the weld root in the reinforced area gradually increases with the increase in the steel plate width. When the steel plate width (W ≥ 40) mm, the stress at the weld root in the reinforced area exceeds that before cracking, with the maximum stress increasing by approximately 7.1%, 16.0%, 21.1%, and 26.7%, respectively. This increases the risk of weld root cracking in the reinforced area. This is considered to be due to the increased bonding area between the steel plate and the specimen, which leads to increased local stiffness and mutual constraint between components, thereby increasing the stress at the weld root. In combination with the aforementioned crack reinforcement effects, it is recommended to use steel plates with a length-to-width ratio greater than 4 and relatively small widths for reinforcement.

Figure 18.

Nominal stress at weld root.

Conclusion

In this paper, the disturbance effect on local stress after reinforcing the RDWT cracks of the rib-deck weld with steel plates was explored by conducting reinforcement experiments and numerical simulations. The effects of steel plate length, width, and thickness on the reinforcement effect of the RDWT crack and the local stress disturbance were discussed, and reasonable parameters for steel plate reinforcement were suggested. The conclusions are as follows:

(1) Both the weld toe cracking of the rib-deck weld and the steel plate reinforcement will disturb the stress at the weld root. After the weld toe cracking, the stress concentration areas at the weld toe,and weld root all shift to the crack tips. After the steel plate reinforcement, the local stress at the weld toe decreases, while the stress at the weld root within the reinforced area increases, accelerating the accumulation of fatigue damage.

(2) Good reinforcement effects can be achieved when the steel plate length covers the crack. Once the steel plate length exceeds the crack length by 120 mm, further increasing the steel plate length has a limited improvement effect on the crack reinforcement but can reduce the adverse impact on the weld root stress disturbance. Increasing the steel plate width has limited improvement on the reinforcement effect and will exacerbate the adverse impact on the weld root stress disturbance. The steel plate with a length greater than 120 mm and a length-to-width ratio greater than 4 can be used to reinforce the RDWT cracks in real bridges.

(3) Increasing the steel plate thickness has limited improvement on the RDWT crack reinforcement effect and has a smaller impact on the stress disturbance at the weld root. Steel plates with the same thickness as the deck can be used to reinforce the RDWT cracks in real bridges.

(4) When adhesive is used to adhere the steel plate, the cracking of the adhesive layer at the steel plate edge indicates a basic loss of reinforcement effect, and the local stress will quickly return to the state before reinforcement. The reinforcement effect of the steel plate can be evaluated by tracking the adhesive layer condition in actual bridges. If the adhesive layer cracking is found, the steel plate should be re-adhered.

Footnotes

Acknowledgments

The research was supported by funding from a National Natural Science Foundation of China (Grant No. 52378153) and Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. KYCX24_0852). The writers thank the funding body for their support.

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: This work was supported by the National Natural Science Foundation of China (Grant No. 52378153).

ORCID iD

Bohai Ji

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