# Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## Featured Application

**The results of this work can be used in the evaluation of existing prestressed concrete slab-between-girder bridges for fatigue.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of Case Study Bridge

_{ck,cube}= 35 MPa) and B45 (f

_{ck,cube}= 45 MPa) for the girders. Testing of the cores taken from the deck slab resulted in an average f

_{cm,cube}= 98.8 MPa (f

_{ck,cube}= 84.6 MPa), as a result of the continued cement hydration. For the assessment calculations, we conservatively assumed that the mean compressive cylinder strength f

_{cm}= 65 MPa on the deck. The associated characteristic concrete compressive strength was f

_{ck}= 53 MPa.

#### 2.2. Live Load Models

_{Q}

_{1}× 300 kN in the first lane, α

_{Q}

_{2}× 200 kN in the second lane, and α

_{Q}

_{3}× 300 kN in the third lane [12]. For the Netherlands, the values of all the α

_{Qi}= 1, with i = 1 … 3. The uniformly distributed load acts over the full width of the notional lane of 3 m width, and it equals α

_{q}

_{1}× 9 kN/m

^{2}for the first lane, and α

_{qi}× 2.5 kN/m

^{2}for all the other lanes. In the Netherlands, for bridges with three or more notional lanes, the value of α

_{q}

_{1}= 1.15 and α

_{qi}= 1.4, with i > 1. Figure 2 shows a sketch of the live load model 1.

_{ik}for the axle loads, and 0.3q

_{ik}for the distributed lane loads. In other words, the axle load becomes 0.7 × 300 kN = 210 kN, and the load per wheel print becomes 105 kN. The distributed lane load is 0.3 × 1.15 × 9 kN/m

^{2}= 3.105 kN/m

^{2}. The fatigue load model has as a reference load of 2 million trucks per year. In the Netherlands, the guidelines for the assessment of bridges (RBK [32]) uses a higher number of passages: 2.5 million trucks per year. Over a lifespan of 100 years, the result is 250 million truck passages.

#### 2.3. Description of Experiments

_{cm,cube}= 75 MPa for the original slab in setup 1, f

_{cm,cube}= 68 MPa for the newly cast slab in setup 1, f

_{cm,cube}= 81 MPa for the first cast of setup 2, and f

_{cm,cube}= 79 MPa for the second cast of setup 2.

_{min}being 10% of the upper limit. A sine function was used with a frequency of 1 Hz. In the fatigue tests, the load was applied in a force-controlled way. If fatigue failure did not occur after a large number of cycles, the upper load level was increased (and the associated lower limit of 10% of the upper limit was adjusted as well).

## 3. Results

#### 3.1. Results of the Experiments

_{max}, the age of the concrete of the slab at the moment of testing, and the concrete cube compressive strength f

_{cm,cube}determined at the day of testing the slab.

_{max}(with P

_{max}from the static test) was given, as well as N, the number of cycles. For the variable amplitude fatigue tests, N was the number of cycles for the associated load level F/P

_{max}. After N cycles at load level F/P

_{max}, given in one row of Table 3, the test was continued with N cycles at another load level F/P

_{max}, given in the next row. The column “age” gives the age of the slab at the age of testing, and f

_{cm,cube}gives the associated cube concrete compressive strength. For fatigue tests that lasted several days, a range of ages was given in the column “age”, indicating the age of the concrete in the slab at the beginning of testing and at the end of testing. Similarly, a range of compressive strengths was given for f

_{cm,cube}, representing the strength determined at the beginning and the end of testing.

#### 3.2. Resulting Wöhler Curve

_{max}was plotted, see Figure 6. For this curve, we interpreted the variable amplitude loading tests as follows: if N

_{1}cycles at load level F

_{1}are applied, followed by N

_{2}cycles at load level F

_{2}, and then N

_{3}cycles to failure at F

_{3}, with increasing load levels F

_{1}< F

_{2}< F

_{3}, it is conservative to assume that the slab can withstand N

_{1}+ N

_{2}+ N

_{3}cycles at the load level F

_{1}, N

_{2}+ N

_{3}cycles at load level F

_{2}, and N

_{3}cycles at load level F

_{3}. This approach led to three datapoints for one variable amplitude fatigue test. As a result of this approach, we obtained 16 datapoints on the first setup and 28 datapoints on the second setup, resulting in 44 datapoints in Figure 6. The average value of the Wöhler curve is shown as “mean” in Figure 6, and it is described with the following expression, using S for the load ratio and N for the number of cycles to failure:

#### 3.3. Assessment of the Case Study Bridge for Punching

_{1}= 0.1, for C

_{Rd,c}= 0.18/γ

_{c}with γ

_{c}= 1.5, and for v

_{min}:

^{2}= 10.35 kN/m

^{2}. The contributions of the self-weight and asphalt were 25 kN/m

^{3}× 200 mm = 5 kN/m

^{2}and 23 kN/m

^{3}× 120 mm = 2.8 kN/m

^{2}, respectively. The area over which these loads were considered was the area within the punching perimeter, A

_{u}= (400 mm)

^{2}+ 4 × 162 mm × 400 mm + π(162 mm/2)

^{2}= 439,812 mm

^{2}= 0.4398 m

^{2}. The corresponding loads for the distributed lane load, self-weight, and asphalt then became 4.55 kN, 2.2 kN, and 1.23 kN, respectively, when the Eurocode wheel print was considered. For the smaller wheel print, the area within the punching perimeter became A

_{u}= 0.2613 m

^{2}, resulting in loads of 2.7 kN, 1.3 kN, and 0.7 kN, respectively, for the distributed lane load, the self-weight, and the asphalt.

_{Rd,c}, using the capacity obtained in the tests. To translate the capacity obtained in the test to a representative design capacity of the case study bridge, we had to consider the following (see Annex D of NEN-EN 1990:2002 [43]):

- The laboratory setup was a 1:2 scale of the case study bridge, resulting in a factor 2
^{2}; - Considering scaling laws, a scale factor of 1.2 [13] had to be included in the capacity;
- The partial factor derived from the experiments γ
_{T}had to be included.

_{T}. To calculate this factor, we compared the punching capacity obtained in the static experiments with the average punching stress capacity v

_{R,c}according to NEN-EN 1992-1-1:2005 [3]. The expression for v

_{R,c}was given in the background report of Eurocode 2 [44] as follows:

_{R,c}, the stress v

_{R,c}was then multiplied with u × d, where u was determined as shown in Figure 8, for the considered wheel print. Table 5 combines the experimental results V

_{exp}and the predicted capacities V

_{R,c}, as well as the ratio of the tested to predicted capacity V

_{exp}/V

_{R,c}. The average value of V

_{exp}/V

_{R,c}was 2.61, with a standard deviation of 0.296 and a coefficient of variation of 11%. This information led to the derivation of γ

_{T}as determined in Annex C of NEN-EN 1990:2002 [43]:

_{T}then becomes:

_{exp}could be scaled to the capacity of the bridge V

_{BB}as follows:

^{2}corrects for the 1:2 scale, and 1.2 is the scaling factor. The design capacity based on the test results is then:

_{BB}according to Equation (20) and V

_{BB,d}according to Equation (21), as well as the demand V

_{Ed}that corresponds to the wheel print in the experiment under consideration (see Table 4). The average value of V

_{BB,d}/V

_{Ed}= 3.06, which meant that the margin of safety was 3.23, or that the Unity Check was the inverse, UC = 0.33. When comparing this value based on the experiments to the values in Table 4, we observed the beneficial effect of compressive membrane action on the capacity of the thin, transversely prestressed concrete slabs.

#### 3.4. Assessment of Case Study Bridge for Fatigue

^{2}= 4, so that the concentrated load became 26.25 kN. The distributed lane load of the fatigue load model was 3.105 kN/m

^{2}. For the 1:2 scale model, the distributed lane load became 0.776 kN/m

^{2}.

_{eq}= 0.83 kN for a single wheel load, and F

_{eq}= 1.40 kN for a double wheel load. Then, the total load was F = 27.08 kN for a single wheel load and F = 27.65 kN for a double wheel load.

_{Rd}= 1.622. As such, the design capacity of the punching resistance with the punching perimeter around one wheel load, including the enhancing effect of compressive membrane action became 1.622 × 124.4 kN = 201.8 kN, for the most critical case (lowest capacity V

_{Rd,c}as a result of the lowest concrete compressive strength). To determine the capacity for punching with the case of a double wheel print, one could expect a double capacity. However, the results in Table 2 show that the capacity in the FAT8S2 was 1.64 times the capacity in FAT7S1. This ratio was used to determine the punching shear capacity. The capacity was now 1.64 × 201.8 kN = 331.0 kN.

_{char}= 0.348. For two wheel loads, using Equation (5) with N = 250 million cycles gave S

_{char}= 0.447. The outcome of the assessment was that the margin of safety for one wheel print was 0.348/0.134 = 2.60, or that inversely, the UC = 0.39. For the case with two wheel prints, the margin of safety was 0.447/0.167 = 2.68 or inversely UC = 0.37. Thus, the results for one and two wheel prints were very similar. The conclusion of the assessment was that based on the experimental results, we found that the case study bridge met the code requirements for fatigue.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## List of Notations

b | width |

c | concrete cover |

d | average effective depth |

d_{l} | effective depth to the longitudinal reinforcement |

d_{t} | effective depth to the transverse reinforcement |

f_{ck,cube} | characteristic cube concrete compressive strength |

f_{cm,cube} | average cube concrete compressive strength |

f_{ck} | characteristic cylinder concrete compressive strength |

f_{cm} | average cylinder concrete compressive strength |

h | height |

k | size effect factor |

k_{1} | factor on effect of axial stresses |

l | length |

l_{span} | span length |

q_{ik} | distributed lane load |

u | punching perimeter length |

v_{min} | lower bound of shear capacity |

v_{R,c} | mean capacity for punching shear |

v_{Rd,c} | design capacity for punching shear |

A_{s,l} | longitudinal reinforcement area |

A_{sp} | area of prestressing steel |

A_{s,t} | transverse reinforcement area |

A_{u} | area within punching perimeter |

B_{Rd} | design capacity derived from statistical results of experiments |

COV | coefficient of variation |

C_{Rd,c} | constant in punching capacity equation |

DL | dead load |

DW | superimposed dead load |

F | applied load |

F_{eq} | equivalent load |

F_{min} | lower limit of the load as used in the fatigue tests |

LL | live load |

M_{dist,1wheel} | bending moment caused by distributed lane load for influence area of one wheel load |

M_{dist,2wheel} | bending moment caused by distributed lane load for influence area of two wheel loads |

N | number of cycles |

P_{max} | load at failure |

Q_{ik} | axle load of design tandem |

S | load ratio |

S_{char} | characteristic value of load ratio (5% lower bound Wöhler curve) |

U | load combination |

UC | Unity Check |

V_{BB} | average capacity of deck of Van Brienenoord Bridge based on experiments |

V_{BB,d} | design capacity of deck of Van Brienenoord Bridge based on experiments |

V_{R,c} | mean value of the punching shear capacity |

V_{Rd,c} | design value of the punching shear capacity |

V_{Ed} | design value of punching shear demand |

V_{exp} | experimental punching capacity |

α | factor that considered effect of experiments |

α_{qi} | factor on distributed lane loads |

α_{Qi} | factor on design tandem |

β | reliability index |

γ_{T} | partial factor derived from experiments |

μ | mean value of experimental results |

ρ_{avg} | average reinforcement ratio |

ρ_{l} | longitudinal reinforcement ratio |

ρ_{t} | transverse reinforcement ratio |

σ_{cp} | average axial stress |

σ_{cx} | longitudinal axial stress |

σ_{cy} | transverse axial stress |

## References

- CEN. Eurocode 1: Actions on Structures—Part 2: Traffic Loads on Bridges; Nen-en 1991-2:2003; Comité Européen de Normalisation: Brussels, Belgium, 2003; p. 168. [Google Scholar]
- Code Committee 351001. NEN 6720 Technical Foundations for Building Codes, Concrete Provisions Tgb 1990—Structural Requirements and Calculation Methods (VBC 1995); Civil Engineering Center for Research and Regulation, Dutch Normalization Institute: Delft, The Netherlands, 1995; p. 245. (In Dutch) [Google Scholar]
- CEN. Eurocode 2: Design of Concrete Structures—Part 1-1 General Rules and Rules for Buildings; NEN-EN 1992-1-1:2005; Comité Européen de Normalisation: Brussels, Belgium, 2005; p. 229. [Google Scholar]
- Lantsoght, E.O.L.; van der Veen, C.; de Boer, A.; Walraven, J.C. Recommendations for the shear assessment of reinforced concrete slab bridges from experiments. Struct. Eng. Int.
**2013**, 23, 418–426. [Google Scholar] [CrossRef] - Amir, S.; Van der Veen, C.; Walraven, J.C.; de Boer, A. Experiments on punching shear behavior of prestressed concrete bridge decks. ACI Struct. J.
**2016**, 113, 627–636. [Google Scholar] [CrossRef] - Teworte, F.; Herbrand, M.; Hegger, J. Structural assessment of concrete bridges in germany—Shear resistance under static and fatigue loading. Struct. Eng. Int.
**2015**, 25, 266–274. [Google Scholar] [CrossRef] - Bagge, N.; Nilimaa, J.; Puurula, A.; Täljsten, B.; Blanksvärd, T.; Sas, G.; Elfgren, L.; Carolin, A. Full-scale tests to failure compared to assessments—Three concrete bridges. In High Tech Concrete: Where Technology and Engineering Meet; Springer: Cham, Switzerland, 2018. [Google Scholar]
- Brühwiler, E.; Vogel, T.; Lang, T.; Luechinger, P. Swiss standards for existing structures. Struct. Eng. Int.
**2012**, 22, 275–280. [Google Scholar] [CrossRef] - Kong, J.S.; Frangopol, D.M. Probabilistic optimization of aging structures considering maintenance and failure costs. J. Struct. Eng. ASCE
**2005**, 131, 600–616. [Google Scholar] [CrossRef] - Frangopol, D.M.; Sabatino, S.; Dong, Y. Bridge life-cycle performance and cost: Analysis, prediction, optimization and decision making. In Maintenance, Monitoring, Safety, Risk and Resilience of Bridges and Bridge Networks; Bittencourt, T.N., Frangopol, D.M., Beck, A., Eds.; CRC Press: Foz do Iguacu, Brazil, 2016; pp. 2–20. [Google Scholar]
- Vergoossen, R.; Naaktgeboren, M.; Hart, M.; De Boer, A.; Van Vugt, E. Quick scan on shear in existing slab type viaducts. In Proceedings of the International IABSE Conference, Assessment, Upgrading and Refurbishment of Infrastructures, Rotterdam, The Netherlands, 6–8 May 2013; p. 8. [Google Scholar]
- Lantsoght, E.O.L.; van der Veen, C.; de Boer, A.; Walraven, J. Using eurocodes and aashto for assessing shear in slab bridges. Proc. Inst. Civ. Eng. Bridge Eng.
**2016**, 169, 285–297. [Google Scholar] [CrossRef] - Amir, S. Compressive Membrane Action in Prestressed Concrete Deck Slabs. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands, 2014. [Google Scholar]
- Collings, D.; Sagaseta, J. A review of arching and compressive membrane action in concrete bridges. Inst. Civ. Eng. Bridge Eng.
**2015**, 169, 271–284. [Google Scholar] [CrossRef] - Eyre, J.R. Direct assessment of safe strengths of rc slabs under membrane action. J. Struct. Eng. ASCE
**1997**, 123, 1331–1338. [Google Scholar] [CrossRef] - Highways Agency. Corrections within Design Manual for Roads and Bridges, Use of Compressive Membrane Action in Bridge Decks; Highways Agency: London, UK, 2007; pp. 35–51.
- Kirkpatrick, J.; Rankin, G.I.B.; Long, A.E. The influence of compressive membrane action on the serviceability of beam and slab bridge decks. Struct. Eng.
**1986**, 64B, 6–9. [Google Scholar] - Kuang, J.S.; Morley, C.T. A plasticity model for punching shear of laterally restrained slabs with compressive membrane action. Int. J. Mech. Sci.
**1993**, 35, 371–385. [Google Scholar] [CrossRef] - Tong, P.Y.; Batchelor, B.V. Compressive membrane enhancement in two-way bridge slabs. SP 30-12
**1972**, 30, 271–286. [Google Scholar] - Hewitt, B.E.; de Batchelor, B.V. Punching shear strenght of restrained slabs. J. Struct. Div.
**1975**, 101, 1837–1853. [Google Scholar] - Lantsoght, E.O.L.; Van der Veen, C.; Koekkoek, R.T.; Sliedrecht, H. Capacity of prestressed concrete bridge decks under fatigue loading. In Proceedings of the FIB Symposium, Cracow, Poland, 27–29 May 2019. [Google Scholar]
- Bennett, E.W.; Muir, S.E.S.J. Some fatigue tests of high-strength concrete in axial compression. Mag. Concr. Res.
**1967**, 19, 113–117. [Google Scholar] [CrossRef] - Lantsoght, E.O.L.; van der Veen, C.; de Boer, A. Proposal for the fatigue strength of concrete under cycles of compression. Constr. Build. Mater.
**2016**, 107, 138–156. [Google Scholar] [CrossRef] - Isojeh, B.; El-Zeghayar, M.; Vecchio, F.J. Fatigue resistance of steel fiber-reinforced concrete deep beams. ACI Struct. J.
**2017**, 114, 1215–1226. [Google Scholar] [CrossRef] - Teng, S.; Ma, W.; Tan, K.H.; Kong, F.K. Fatigue tests of reinforced concrete deep beams. Struct. Eng.
**1998**, 76, 347–352. [Google Scholar] - Teworte, F.; Hegger, J. Shear fatigue of prestressed concrete beams. In Proceedings of the IABSE 2011, London, UK, 23 September 2011; p. 8. [Google Scholar]
- Muller, J.F.; Dux, P.F. Fatigue of prestressed concrete beams with inclined strands. J. Struct. Eng.
**1994**, 120, 1122–1139. [Google Scholar] [CrossRef] - Yuan, M.; Yan, D.; Zhong, H.; Liu, Y. Experimental investigation of high-cycle fatigue behavior for prestressed concrete box-girders. Constr. Build. Mater.
**2017**, 157, 424–437. [Google Scholar] [CrossRef] - Fujiyama, C.; Gebreyouhannes, E.; Maekawa, K. Present achievement and future possibility of fatigue life simulation technology for rc bridge deck slabs. Soc. Soc. Manag. Syst. Internet J.
**2008**, 4. [Google Scholar] - Harajli, M.H.; Naaman, A.E. Static and fatigue tests on partially prestressed beams. J. Struct. Eng.
**1985**, 111, 1602–1618. [Google Scholar] [CrossRef] - Xin, Q.; Dou, Y.; Chen, W. Load spectrum and fatigue life computer analysis of prestressed concrete bridges. Int. J. Secur. Appl.
**2015**, 9, 247–266. [Google Scholar] [CrossRef] - Rijkswaterstaat. Guidelines Assessment Bridges—Assessment of Structural Safety of an Existing Bridge at Reconstruction, Usage and Disapproval; RTD 1006:2013 1.1; Rijkswaterstaat: Utrecht, The Netherlands, 2013; p. 117. (In Dutch) [Google Scholar]
- Van der Veen, C.; Bosman, A. Vermoeiingssterkte Voorgespannen Tussenstort; Stevin Report nr. 25.5-14-06; Delft University of Technology: Delft, The Netherlands, 2014; p. 65. [Google Scholar]
- Lantsoght, E.O.L.; Van der Veen, C.; Koekkoek, R.T.; Sliedrecht, H. Fatigue testing of transversely prestressed concrete decks. ACI Struct. J.
**2019**, in press. [Google Scholar] [CrossRef] - Koekkoek, R.T.; van der Veen, C.; de Boer, A. Fatigue Tests on Post-Tensioned Bridge Decks; Springer International Publishing: Cham, Switzerland, 2018; pp. 912–920. [Google Scholar]
- Koekkoek, R.T.; van der Veen, C. Measurement Report Fatigue Tests on Slabs Cast in-between Prestressed Concrete Beams; Stevin Report 25.5-17-14; Delft University of Technology: Delft, the Netherlands, 2017; p. 196. [Google Scholar]
- Lantsoght, E.O.L.; Van der Veen, C.; Koekkoek, R.T.; Sliedrecht, H. Punching capacity of prestressed concrete bridge decks under fatigue. ACI Struct. J.
**2019**, in press. [Google Scholar] [CrossRef] - Castillo, E.; Fernandez-Canteli, A. A Unified Statistical Methodology for Modeling Fatigue Damage; Springer: Dordrecht, The Netherlands, 2009; p. 189. [Google Scholar]
- Hanif, A.; Usman, M.; Lu, Z.; Cheng, Y.; Li, Z. Flexural fatigue behavior of thin laminated cementitious composites incorporating cenosphere fillers. Mater. Des.
**2018**, 140, 267–277. [Google Scholar] [CrossRef] - Hanif, A.; Kim, Y.; Park, C. Numerical validation of two-parameter weibull model for assessing failure fatigue lives of laminated cementitious composites—Comparative assessment of modeling approaches. Materials
**2018**, 12, 110. [Google Scholar] [CrossRef] [PubMed] - Lu, C.; Dong, B.; Pan, J.; Shan, Q.; Hanif, A.; Yin, W. An investigation on the behavior of a new connection for precast structures under reverse cyclic loading. Eng. Struct.
**2018**, 169, 131–140. [Google Scholar] [CrossRef] - Code Committee 351001. Assessement of Structural Safety of an Existing Structure at Repair or Unfit for Use—Basic Requirements; NEN 8700:2011; Civil Center for the Execution of Research and Standard, Dutch Normalisation Institute: Delft, The Netherlands, 2011; p. 56. (In Dutch) [Google Scholar]
- CEN. Eurocode—Basis of Structural Design; NEN-EN 1990:2002; Comité Européen de Normalisation: Brussels, Belgium, 2002; p. 103. [Google Scholar]
- Walraven, J.C. Background Document for EC-2, Chapter 6.4 Punching Shear; Delft University of Technology: Delft, The Netherlands, 2002; pp. 1–16. [Google Scholar]

**Figure 1.**Van Brienenoord Bridge: (

**a**) sketch of the elevation of the entire bridge structure, showing the approach slabs, as well as the steel arch; (

**b**) cross-section of the slab-between-girder approach bridge. Dimensions in cm.

**Figure 3.**Dimensions of first 1:2 scale model: (

**a**) top view; (

**b**) cross-section view. Figure adapted from Reference [34]. Reprinted with permission. This figure was originally published in Vol. 116 of the ACI Structural Journal.

**Figure 4.**Overview of the second 1:2 scale setup: (

**a**) top view; (

**b**) cross-section view. Figure adapted from Reference [37]. Reprinted with permission. This figure was originally published in Vol. 116 of the ACI Structural Journal.

**Figure 6.**Relation between the number of cycles N and the applied load ratio F/P

_{max}in all the fatigue experiments, adapted from Reference [37]. Reprinted with permission. This figure was originally published in Vol. 116 of the ACI Structural Journal.

**Figure 7.**Relation between the number of cycles N and applied load level F/P

_{max}for (

**a**) a single wheel load; and (

**b**) a double wheel load, from Reference [37]. Reprinted with permission. This figure was originally published in Vol. 116 of the ACI Structural Journal.

Dimension | Value |
---|---|

Thickness h | 200 mm |

Concrete cover c | 30 mm |

Longitudinal reinforcement | ϕ8 mm–250 mm |

Effective depth longitudinal d_{l} | 166 mm |

Area of longitudinal reinforcement A_{s,l} | 201.1 mm^{2}/m |

Longitudinal reinforcement ratio ρ_{l} | 0.12% |

Transverse reinforcement | ϕ8 mm–200 mm |

Effective depth transverse d_{t} | 158 mm |

Area of transverse reinforcement A_{s,t} | 251.3 mm^{2}/m |

Transverse reinforcement ratio ρ_{t} | 0.16% |

Average effective depth d | 162 mm |

Average reinforcement ratio ρ_{avg} | 0.14% |

Prestressing reinforcement | 462 mm^{2}–800 mm |

Area of prestressing steel A_{sp} | 0.5775 mm^{2}/mm |

Test Number | Size Load (mm × mm) | P_{max}(kN) | Age (days) | f_{cm,cube}(MPa) |
---|---|---|---|---|

BB1 | 200 × 200 | 348.7 | 96 | 80.0 |

BB2 | 200 × 200 | 321.4 | 99 | 79.7 |

BB7 | 200 × 200 | 345.9 | 127 | 80.8 |

BB19 | 200 × 200 | 317.8 | 223 | 79.9 |

FAT1S1 | 150 × 115 | 347.8 | 94 | 82.2 |

FAT7S1 | 150 × 115 | 393.7 | 240 | 88.8 |

FAT8S2 | 2 of 150 × 115 | 646.1 | 245 | 88.6 |

Test Number | Setup | Size Load (mm × mm) | Wheel | F/P_{max} | N | Age (days) | f_{cm,cube}(MPa) |
---|---|---|---|---|---|---|---|

BB17 | 1 | 200 × 200 | S | 0.80 | 13 | 147 | 82.6 |

BB18 | 1 | 200 × 200 | S | 0.85 | 16 | 56 | 82.6 |

BB23 | 1 | 200 × 200 | S | 0.60 | 24,800 | 301 | 79.9 |

BB24 | 1 | 200 × 200 | S | 0.45 | 1,500,000 | 307–326 | 79.9 |

BB26 | 1, new | 150 × 115 | S | 0.48 | 1,405,337 | 35–59 | 70.5–76.7 |

BB28 | 1, new | 150 × 115 | S | 0.48 | 1,500,000 | 68–97 | 76.8–77.1 |

0.58 | 1,000,000 | 97–113 | 77.1–77.3 | ||||

0.70 | 7144 | 113 | 77.3 | ||||

BB29 | 1, new | 150 × 115 | S | 0.58 | 1,500,000 | 117–136 | 77.3–77.5 |

0.64 | 264,840 | 136–139 | 77.5–77.6 | ||||

BB30 | 1, new | 150 × 115 | D | 0.58 | 100,000 | 143–144 | 77.6 |

0.50 | 1,400,000 | 144–162 | 77.6–77.8 | ||||

0.58 | 750,000 | 162–171 | 77.8–77.9 | ||||

0.67 | 500,000 | 171–177 | 77.9–78.0 | ||||

0.75 | 32,643 | 177 | 78.0 | ||||

BB32 | 1, new | 150 × 115 | S | 0.70 | 10,000 | 184 | 78.1 |

0.58 | 272,548 | 185–187 | 78.1 | ||||

FAT2D1 | 2 | 150 × 115 | S | 0.69 | 100,000 | 102–144 | 82.6–84.6 |

0.58 | 2,915,123 | ||||||

0.69 | 100,000 | ||||||

0.75 | 150,000 | ||||||

0.81 | 20,094 | ||||||

FAT3D1 | 2 | 150 × 115 | S | 0.69 | 200,000 | 149–168 | 84.9–85.8 |

0.58 | 1,000,000 | ||||||

0.69 | 100,000 | ||||||

0.75 | 300,000 | ||||||

0.81 | 6114 | ||||||

FAT4D1 | 2 | 150 × 115 | S | 0.58 | 1,000,000 | 169–190 | 85.8–86.8 |

0.69 | 200,000 | ||||||

0.75 | 100,000 | ||||||

0.81 | 63,473 | ||||||

FAT5D1 | 2 | 150 × 115 | S | 0.71 | 10,000 | 192–217 | 91.6–89.6 |

0.51 | 1,000,000 | ||||||

0.61 | 100,000 | ||||||

0.66 | 1,000,000 | ||||||

0.71 | 1424 | ||||||

FAT6D1 | 2 | 150 × 115 | S | 0.71 | 10,000 | 219–239 | 89.6–88.8 |

0.51 | 1,000,000 | ||||||

0.61 | 100,000 | ||||||

0.71 | 160,000 | ||||||

0.51 | 410,000 | ||||||

0.71 | 26,865 | ||||||

FAT9D2 | 2 | 150 × 115 | D | 0.59 | 500,000 | 246–255 | 88.5–88.2 |

0.65 | 209,800 | ||||||

FAT10D2 | 2 | 150 × 115 | D | 0.63 | 100,000 | 260–284 | 90.2–91.3 |

0.56 | 1,000,000 | ||||||

0.63 | 950,928 | ||||||

FAT11D2 | 2 | 150 × 115 | D | 0.67 | 100,000 | 288–315 | 91.5–92.8 |

0.60 | 1,000,000 | ||||||

0.67 | 1,100,000 | ||||||

0.75 | 1720 | ||||||

FAT12D1 | 2 | 150 × 115 | S | 0.89 | 30 | 318 | 85.9 |

FAT13D1 | 2 | 150 × 115 | S | 0.86 | 38 | 319 | 85.8 |

Wheel Print | V_{Ed} (kN) | V_{Rd,c} (kN) | Unity Check |
---|---|---|---|

400 mm × 400 mm | 236 | 337 | 0.70 |

230 mm × 300 mm | 232 | 287 | 0.81 |

**Table 5.**Comparison between the mean predicted punching capacity and punching capacity in experiment.

Test Number | Wheel Print (mm × mm) | V_{exp}(kN) | V_{R,c}(kN) | V_{exp}/V_{R,c} |
---|---|---|---|---|

BB1 | 200 × 200 | 348.7 | 141.9 | 2.458 |

BB2 | 200 × 200 | 321.4 | 141.9 | 2.266 |

BB7 | 200 × 200 | 345.9 | 141.9 | 2.438 |

BB19 | 115 × 150 | 317.8 | 121.6 | 2.613 |

FAT1S1 | 115 × 150 | 347.8 | 124.4 | 2.795 |

FAT7S1 | 115 × 150 | 393.7 | 127.4 | 3.091 |

Test Number | V_{exp}(kN) | V_{BB}(kN) | V_{BB,d}(kN) | V_{Ed}(kN) | V_{BB,d}/V_{Ed} |
---|---|---|---|---|---|

BB1 | 348.7 | 1162.3 | 721.9 | 236.0 | 3.06 |

BB2 | 321.4 | 1071.3 | 665.4 | 236.0 | 2.82 |

BB7 | 345.9 | 1153.0 | 716.1 | 236.0 | 3.03 |

BB19 | 317.8 | 1059.3 | 658.0 | 232.0 | 2.84 |

FAT1S1 | 347.8 | 1159.3 | 720.1 | 232.0 | 3.10 |

FAT7S1 | 393.7 | 1312.3 | 815.1 | 232.0 | 3.51 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lantsoght, E.O.L.; Koekkoek, R.; van der Veen, C.; Sliedrecht, H. Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges. *Appl. Sci.* **2019**, *9*, 2312.
https://doi.org/10.3390/app9112312

**AMA Style**

Lantsoght EOL, Koekkoek R, van der Veen C, Sliedrecht H. Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges. *Applied Sciences*. 2019; 9(11):2312.
https://doi.org/10.3390/app9112312

**Chicago/Turabian Style**

Lantsoght, Eva O.L., Rutger Koekkoek, Cor van der Veen, and Henk Sliedrecht. 2019. "Fatigue Assessment of Prestressed Concrete Slab-Between-Girder Bridges" *Applied Sciences* 9, no. 11: 2312.
https://doi.org/10.3390/app9112312