Methods to Increase Fatigue Life at Rib to Deck Connection in Orthotropic Steel Bridge Decks

Abstract

Orthotropic steel bridge decks (OSDs) are very popular all over the world because of the low dead load, high stiffness in the longitudinal direction, high strength ratio to weight, and can be used in various types of bridges. The life of these bridges is affected by fatigue cracks in different portions. One of major areas where the fatigue cracks appear in these bridges is rib-to-deck connection. In this research finite element analysis is carried out by using ABAQUS/CAE 2022 software to determine the ways to increase the fatigue life at rib to deck connection in OSDs. In the first part, smaller models are simulated; stress concentration is analyzed and hot spot stress (HSS) is calculated according to International Institute of Welding (IIW) and Det Norske Veritas (DNV) recommendations. In the second part, a parametric analysis is carried out to analyze the effect of weld penetration, thickness of deck, thickness of rib and rib to deck connection type. In the third part, simulation of models similar to the real field is carried out to determine whether the double welded connections are better than single welded connections. Different models are analyzed for different load cases like single wheel load, double wheel load and also the position of the wheels is changed. The boundary conditions are changed to analyze whether the boundary condition has any significant effect on the result obtained. It is found that thicker decks, thinner ribs, and low penetrated welded connections reduce the stress concentrations at rib to deck connections which ultimately increase fatigue life. Among the parameters examined, deck thickness is the most important parameter. It is found that the percentage of stress increase with percentage decrease in deck thickness follows a power relation. The overall fatigue life of double welded connection is excepted to be lower since the stress concentration is maximum at the weld toe at deck on the outer side of the closed stiffener; however, if the cracks initiate on the inner side of closed stiffener, the cracks at the weld root of single welded connection can propagate much rapidly than the cracks initiating on the inner side of the closed stiffener at the weld toe, thereby reducing the fatigue life of the single-welded specimen significantly.

1. Introduction

1.1. General Introduction

Orthotropic steel bridge decks are very popular. They are most economical in terms of the material used as a lesser amount of material is enough for the construction. Structurally they are complex, having longitudinal and transverse (diaphragm) stiffeners. As there are large numbers of members connected together by weld joints, the length of welding in OSD can be more than 10 times the actual length of the bridge. These bridges have been constructed since the 1930s in Germany but they became more common after the Second World War. The reason behind that is, after the World War, countries were suffering from the economic recession, so to sustain the weak economy, it was very necessary to save materials for civil construction. These bridges are constructed all over the world with Germany and Netherlands possessing the largest numbers [1]. With the improvement in these types of bridge decks and development of movable bridge systems the combination of these became very promising [2]. The trend of construction of these bridges has decreased after the 1990s. The decrease in their popularity is because of the fatigue problems [1].

Fatigue can be defined as slow progressive localized structural damage of a material due to cyclic or repetitive loading. According to American Society for Testing and Materials, fatigue is the process of progressive localized permanent structural change occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations [3]. The fusion of filler material, heating and subsequent cooling affects the material homogeneity and residual stresses are produced by welding [4,5]. It is also one of the concerning points that ideal weld is never possible; it always has defects like inclusions, pores, cavities, undercuts, etc. from where cracks initiate. Mathddox [6] reported that welding decreases the fatigue life of specimens from experimental study.

1.2. Researches on Fatigue at Rib to Deck Connections in OSD

Fatigue cracks develop if there is insufficient weld penetration [7]. To avoid the insufficient weld penetration and protect the structures from fatigue different codes have different provisions of weld penetration. American Association of State Highway and Transportation Official [8] specifies that it should be 80% of the rib wall thickness for the rib-to-deck welds. The Japan Road Association [9] species it to be at least 75% of the rib wall. The Chinese Code [10] specifies it to be 85% of the rib wall and Eurocode [11] specifies that the nominal penetration should be 80% and the minimum must be at least 50%.

** 18 mm as reference deck thickness.

Δσ is the increase in stress kee** the stress at 18 mm deck thickness as reference stress.

Table 6. Hot spot stress in rib at weld toe.

Thickness of		Welded Side	σhs	Δσ (%)	Δσr (%)
Deck (mm)	Rib (mm)
18	8	2	46.30	7.80	30.50
18	8	1	49.91		29.74
18	6	2	35.48	8.43
18	6	1	38.47
16	8	2	59.41	13.21	34.47
16	8	1	67.26		29.65
16	6	2	44.18	17.43
16	6	1	51.88
14	8	2	76.15	13.28	36.59
14	8	1	86.26		34.15
14	6	2	55.75	15.34
14	6	1	64.30
12	8	2	121.28	9.51	24.02
12	8	1	132.81		22.95
12	6	2	97.79	10.46
12	6	1	108.02

Table 6. Hot spot stress in rib at weld toe.

Thickness of		Welded Side	σhs	Δσ (%)	Δσr (%)
Deck (mm)	Rib (mm)
18	8	2	46.30	7.80	30.50
18	8	1	49.91		29.74
18	6	2	35.48	8.43
18	6	1	38.47
16	8	2	59.41	13.21	34.47
16	8	1	67.26		29.65
16	6	2	44.18	17.43
16	6	1	51.88
14	8	2	76.15	13.28	36.59
14	8	1	86.26		34.15
14	6	2	55.75	15.34
14	6	1	64.30
12	8	2	121.28	9.51	24.02
12	8	1	132.81		22.95
12	6	2	97.79	10.46
12	6	1	108.02

• σ_hs is the hotspot stress at the weld.
• Δσ is the percentage higher stress value in the single weld with reference to double weld.
• Δσr is the percentage higher stress in 8 mm ribbed specimens with reference to 6 mm ribbed specimens, taking all other parameters as constant.

Table 6 demonstrates that the stress concentration at the toe in the rib is higher in case of a single-welded connection, but the stress is much lower than at the weld toe in deck in

Table 5. Hot spot stress at weld toe in deck.

DT	RT	WS	σhs (MPa)	Δσw (%)	Δσr	Δσd4 (%)	Δσd2 (%)	Δd (%)	Δσ (%)
18	8	2	173.71	3.21	6.238	54.96	20.45	11.11	20.45
18	8	1	168.3		4.866	55.16	21.35	11.11	21.35
18	6	2	163.51	1.88		45.1	24.68	11.11	24.68
18	6	1	160.49			45.29	23.75	11.11	23.76
16	8	2	209.23	2.44	2.629	66.95	28.68	22.22	54.96
16	8	1	204.24		2.830	65.72	27.86	22.22	55.17
16	6	2	203.87	2.64		62.69	16.37	22.22	45.10
16	6	1	198.62			65.72	17.4	22.22	45.29
14	8	2	269.18	3.07	13.454		29.77	33.33	101.09
14	8	1	261.15		11.995		29.6	33.33	101.11
14	6	2	237.26	1.75			39.79	33.33	102.84
14	6	1	233.18				41.16	33.33	105.09
12	8	2	349.32	3.21	5.322
12	8	1	338.46		2.828
12	6	2	331.67	0.77
12	6	1	329.15

, where the stress concentration due to double welds is higher than the stress concentration due to a single weld, so the failure is more likely to occur at the deck than at the rib. Similarly, the stress concentrated by 8 mm ribs is always higher than stress concentrated by the 6 mm rib, as shown in Table 5 and Table 6.

4. Simulations of Models Similar to Field Structures

Obviously, the magnitude of concentrated stress depends on the magnitude of applied load and the size of the structure (i.e., dimension of the structure); but the pattern of stress concentration can be analyzed even with the models smaller than the actual structures in the field [17,24]. The accuracy of FEM results depends on the mesh size. The finer the mesh is the higher the accuracy obtained. In this study, the mesh size applied in FEM modeling was as small as 1 mm; therefore, it was extremely cumbersome to run the large models as in the real field with the mesh size employed. Therefore, models from 1 m to 3 m length were prepared in this section; however, the loading pattern and boundary conditions were similar to the real world structures.

4.1. Single Ribbed Model

The length of the model was 1 m and the width was 0.6 m, and a rib was placed at the center along the longitudinal direction, as presented in Figure 6. The rib and deck thicknesses were 18 mm and 8 mm, respectively. Among the two legs of rib, one was connected with double weld and the other was connected with a single weld of 80% penetration. The reason for choosing this model is that the model can give the idea of stress produced within the rib and outside of the rib when the wheel of the vehicle is in between the two legs of the closed ribs. Load case 1 was 30 kN, which was uniformly distributed throughout the surface of the deck as pressure, and load case 2 was 50 kN, distributed in the middle portion of area 0.3 × 0.3 square meters, as presented in Figure 6.

Stress was collected creating a path in post-processing module. For load case 1, the stress values were taken at the outer side of the ribs and inner side of the ribs, starting from the double-welded connection to single-welded connections. The stress profiles are illustrated in Figure 7 and Figure 8.

For load case 2, the extreme values of stress collected at different paths along the weld (Figure 9) are tabulated in

Table 7. Stress concentration at weld toes and roots of double and single-welded connections.

Connection	Stress	Stress Values in (MPa) Inner Side				Stress Values in (MPa) Outer Side
	Value	Mises	S11	S33	S13	Mises	S11	S33	S13
Double welded	Max	27.24	8.27	5.42	15.51	19.03	8.99	6.17	9.85
	Min	8.89	−12.12	−22.44	−15.51	7.16	−18.06	−19.17	−9.85
Single welded	Max	35.38	14.28	8.89	16.22	23.45	8.96	7.04	8.70
	Min	18.45	−19.53	−28.24	−16.22	6.45	−16.48	−26.05	−8.70

.

From Table 7, the stress concentration at the inner side of the single-welded connection (root) was higher than other locations.

4.2. Double-Ribbed Specimen

The specimen was 1.1 m wide and 3 m long; the reason for choosing this specimen was that two ribs of a 300 mm width can be adjusted with a 300 mm gap between them so that the stress condition can be analyzed when the load is in between the two ribs. The deck thickness was 16 mm; the rib thickness was 8 mm. The legs of ribs were alternatively connected with a single and double weld, as illustrated in Figure 10 and Figure 11. The maximum stress values at connection B (both toes) and connection C (inner root and outer toe) are tabulated in

Table 8. Extreme values of stresses for first loading condition.

Max Stresses	Stress for Double Tyre Loading (MPa) at				Stress for Single Tyre Loading (MPa) at
	1	2	3	4	1	2	3	4
S11(−ve)	−51.27	−55.23	−55.40	−42.58	−41.43	−46.10	−46.30	−43.12
S11(+ve)	23.12	25.19	22.04	12.78	17.91	19.36	15.94	9.18
S33(−ve)	−46.85	−45.63	−47.44	−45.50	−35.06	−34.13	−35.39	−33.82
S33(+ve)	14.90	15.32	14.54	11.14	11.17	11.43	10.48	7.87
Mises	42.74	46.04	48.83	39.42	36.29	39.12	37.53	35.11

and

Table 9. Extreme values of stresses for second loading.

Stresses	Stress (MPa) at		Stress (MPa) at
	1	2	3	4
S11(−ve)	32.73	31.09	39.89	28.76
S11(+ve)	31.56	33.47	29.75	15.38
S33(−ve)	10.38	11.97	67.18	67.97
S33(+ve)	19.87	19.76	17.38	17.38
Mises	66.41	66.23	76.71	62.17

, which were extracted by creating a path in the post-processing module. For simplicity toe and root of single welded connection at ‘C’ are referred to as 1 and 3, respectively; similarly, the outer toe and inner toe of the double welded connection at ‘B’ are referred to as 2 and 4.

The first loading was applied in two steps: in the first step the double tyre load was applied in the middle and then in second step the double tyre load was removed and single tyre load was applied in the middle, as illustrated in Figure 8. The single tyre load was 50 kN, distributed uniformly in the area of 0.2 × 0.3 m². The double tyre load was 75 kN uniformly distributed in the area of 0.2 × 0.6 m². The results of first loading are given in Table 8

In second loading the double tyres and single tyre were 1.4 m apart, as illustrated in Figure 9, and both of them were applied simultaneously. The extreme values of stresses are given in Table 9.

The stress profile S₁₁ at path 1, 2, 3 and 4 are illustrated in Figure 12 and Figure 13.

5. Validation of Simulation Results

For the validation of results from simulation, the results of S2a model f from simulation were compared with the stress generated from laboratory test results reported by Zhu et al. [24] and are plotted in Figure 14. The average percentage difference between the test results from simulation and test was 3.8%, which demonstrates that the simulated results were consistent with the test results.

Similarly, the results of S3a model from simulation were compared with the stress generated from laboratory test reported by K C [23] and are plotted in Figure 15. The average percentage difference between the test results from simulation and test was 2.9%, which demonstrated that the simulated results were consistent with the test results.

6. Analysis

The fatigue of life of structures can be determined by using SN curves or equations. With a Linear Elastic Facture Mechanics (LEFM) approach, Equation (1) can be used to calculate the fatigue life of structures.

$$N={\int }_{ai}^{af}\frac{da}{C·{(f\left(a\right)·\Delta \sigma ·\sqrt{\pi a})}^m}$$

(1)

where ‘N’ is the number of cycles, ‘a’ is the crack depth, ‘C’ is a constant which value is 3.1 × 10⁻¹³ N·mm. For old bridges, value of ‘C’ and ‘m’ can be taken as 4.1 × 10⁻¹³ and 3, respectively [29]. In Equation (1), when kee** all other parameters constant, if stress amplitude decreases the number of cycles (fatigue life) increases drastically.

The stress concentration increases a little due to double welds or increase in weld penetration, which can be seen in

Table 1. Hotspot stress.

	Stress (MPa) Produced at Different Loadings					Remark
	5 kN	20 kN	25 kN	35 kN	40 kN
HSS in S2a (MPa)	32.050	128.201	160.251	224.241	253.985	IIW [25]
	31.637	126.547	158.183	221.349	251.527	DNV [27]
HSS in S2b (MPa)	32.454	129.816	162.270	227.179	259.632	IIW [25]
	32.187	128.046	160.056	223.329	256.090	DNV [27]

,

Table 3. Stress at different weld penetration.

Penetration	σhs (MPa)	σ1 (MPa)	σ2 (MPa)	σ3 (MPa)	σ4 (MPa)
50%	164.65	208.43	187.67	135.87	75.69
80%	164.78	213. 50	189.88	134.12	75.34
100%	165.29	215.89	190.12	133.51	74.47
Double weld	166.96	218.47	185.51	128.47	63.35

σ_hs is hotspot stress at weld toe calculated as per IIW [25]. σ₁ is tress concentration at the toe of outer weld in the deck. σ₂ is stress concentration at root (for single weld) or toe (for double weld) at inner side of the rib. σ₃ is stress concentration at 10 mm away from root or toe in inner side. σ₄ is stress concentration at the toe in the rib.

and Table 5. In Table 8, the extreme values of stress is highest at ‘2’ which is the outer toe of the double welded connection. If we compare the stress at ‘3’ and ‘4’ in Table 8, the stress concentration at inner root (at ‘3’) seems higher; one of the reasons is that ‘3’ is closer to load proximity than ‘4’; however, ‘1’ and ‘2’ are at same proximity from load and support but stress concentration at ‘2’ significantly higher than at ‘1’. This demonstrates that double welds concentrate more stress, although stress concentration at the root of single weld is also significant. From

Table 4. Tabulation of maximum stress values.

Deck Thickness (mm)	Stress Concentration (MPa) at
	Deck	Rib
20	169.85	58.70
18	208.43	75.12
16	261.52	100.34
14	334.76	136.2
12	412.94	186.42

and Table 5, it is seen that stress concentration at the weld toe in deck decreases with an increase in the thickness of deck. From Table 5 and Table 6, it is clear that the stress decreases when rib thickness decreases. In Table 5, the stress is higher for double-welded connection and in Table 6 stress is higher for single-welded connection, but the magnitude of stress is higher in Table 5, which is the stress at toe in deck; therefore, failure is more likely to occur at the weld toe in the deck. A higher stress concentration means higher stress amplitude due to loading, so from Equation (1), the fatigue life of specimens’ decreases where the stress concentration is higher.

In Section 2 and Section 3, the models are supported on lateral sides of the rib/ribs (fixed supports are parallel to ribs) but in Section 4, the models are supported such that the direction of ribs and support is perpendicular. Although the boundary condition is different in Section 4 from Section 2 and Section 3 the results on single and double welds were consistent, which shows double welds concentrate higher stress.

7. Discussion and Limitations

From the extensive simulation of different models, it was found that the increase in weld penetration increases the stress concentration slightly, which is similar to the findings by Dung et al. [17] and Mori [18]. Double welds at rib to deck connection can increase stress concentration slightly, which is more dependent on the thickness of the rib and deck. In addition, it was found that the stress concentration on a double-welded connection is higher if the deck and rib thickness is higher. Furthermore, it was found that the increase in rib thickness increases the stress concentration and decrease in rib thickness decreases the stress concentration, which is similar to the findings by Nagy et al. [20]. Among the examined parameters, the most important component that influences the fatigue life of OSD at the rib-to-deck connection was deck thickness. Considering the standard thickness of deck as 20 mm, a power relationship of percentage increase in stress concentration (y) and percentage decrease in deck thickness (x) was determined. The mathematical relation is given in Equation (2) which has the coefficient of determination (R²) of 0.9959. The relationship of stress concentration with decrease in deck thickness is also illustrated in Figure 16.

y = 0.9214x^1.468

(2)

From the earlier studies, Kainuma et al. [14] and Sim et al. [15] reported the decrease in fatigue life with an increase in weld penetration. Hung et al. [17] reported higher fatigue life in a 100% weld-penetrated specimen than in a 75% weld-penetrated specimen. In recent study, Zhu et al. [24] reported the increase in fatigue life in double-welded specimens is longer than in single welded specimens, while Yang et al. [30] reported that there is no significant difference between fatigue life of single-welded and double-welded U-shaped ribs connection to deck in orthotropic steel bridge decks.

This study was focused on the groove weld on single and double welds through numerical simulations. The modification made in the weld toe during the welding process was not considered in this study. All fabrication procedures of welding are unknown and the induced residual stress which might have been induced due to welding were not considered. The welds always have some defects; for instance, the welding material may not have the same property as parent material, but they were considered the same in this study. The weld is never uniformly penetrated but, in the simulations, it was considered uniformly penetrated.

8. Conclusions

Orthotropic steel bridges gained immense popularity due to their straightforward construction techniques and cost-effectiveness. However, their prevalence waned after the 1990s, primarily due to fatigue-related issues. In this paper, we delve into numerical simulations aimed at identifying potential design solutions for enhancing fatigue resistance in these bridges. Specifically, the impact of various factors, including weld fusion, deck thickness, rib thickness, and the use of single and double welds was explored. The key findings of the of this study which involved forty-two simulations, include the following:

• The decks are the most important component influencing the fatigue life at rib to deck connection. The percentage of stress increase with percentage decrease in deck thickness follows a power relation with coefficient 0.9214 and exponent 1.468, with a coefficient of determination R² equal to 0.9959. Therefore, an increase in deck thickness increases the fatigue life significantly.
• Thicker ribs increase stress concentration which may be due to an increase in stiffness.
• The overall stress concentration on the outer side of the closed stiffener at toe at the deck of double welded connection is maximum; however, on the inner side of the closed stiffener, the tensile stress concentration at the weld root of single welded connection is significantly higher than weld toe of double welded connection. Therefore, in general the fatigue cracks are expected to initiate on the outer side of closed stiffener at the weld toe at deck and the fatigue life of double welded connection is expected to be shortest, but in situation when micro cracks or weld defects are present at the inner side of the rib or if the crack initiate on the inner side of the rib, the cracks at the weld root of single welded connections can propagate much faster than the double welded connections.
• An increase in weld penetration slightly increases stress concentration possibly due to increase in stiffness at the connection.
• Double welds concentrate more stress which decrease fatigue life; however, for deep weld penetration the degradation of parent material is more severe so lower weld penetration from both sides may reduce the flaws during welding hence reduce the probability of crack initiation.
• The position of load also plays role in stress concentration. In Table 7, stress concentration at root is highest when the load is located entirely in between the two legs of a closed stiffener. Therefore, in this case the fatigue cracks are likely to occur at weld root.