CONCEPCIÓN, CASTILLO DE LA

6.3.1 Introduction

Many components have been involved in the fatigue tests on composite beams: The UHPFRC layer, the rebars of the UHPFRC layer, the rebars of the reinforced concrete and the concrete that partially works in tension and finally the concrete working in compression. The relevant

Table 11: Comparison between a reinforced concrete and a composite beam for the same fatigue loading

Loading ΔM / Msup Reinforcement stress Inertia moment / stiffness 80 MPa (< Δσs,D) 200 MPa (> Δσs,D) maintained at 75 % of the initial value

strong decrease down to 25 % of the initial value

Composite section Original RC- section (entirely cracked) stiffness N ≥ 500’000 (stable behaviour) - hU =30 mm 3 ∅ 12 5 ∅ 16 ∅ 8@140 28 kNm (test result) 24 kNm (calculated)

Ultimate resistance MULS

range Δσs 9 / 12 kNm 18 0 300 18 0 300 [mm] ΔM ΔM

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parameter that has to be controlled for a fatigue safe design is the strain in the UHPFRC layer.

6.3.2 Dimensioning of the UHPFRC - layer a) Relation between strains and stresses

The thickness of the UHPFRC layer should be large enough in order to allow the maximum stresses to be below a given threshold under cyclic loading. The stress in the UHPFRC layer is a function of its deformation state and the rebar section in the UHPFRC and in the reinforced concrete. In the fatigue tests, most beam segments with maximum calculated tensile stresses up to 5 MPa showed no macro cracks. However, in few segments a visible crack appeared. This is due to the variability of the material properties. This variability is attenuated when the element has a larger extension perpendicular to the load-carrying axis [Wuest 2007].

b) Design criterion

The UHPFRC layer has both a load carrying and a protection function. In order to guarantee both functions, the strain under cyclic loading has to be limited.

The strain should remain below a threshold during cyclic loading. With this strain, the stress under maximum service load should also remain below an admissible value. The thickness of the UHPFRC layer should be chosen large enough and/or a steel reinforcement should be laid in the UHPFRC layer. [Charron 2006] has shown that the tightening function of the UHPFRC is guaranteed for strains up to 1.3 o_/

oo. Stable fatigue behaviour has been observed for strains

up to 1.0 o_/ oo.

Figure 88 schematically shows a) the stress-strain curve of the uniaxial quasi-static fracture test of UHPFRC as stability criterion for stable behaviour under cyclic loading, and b) the de- velopment of stresses and strains in the UHPFRC layer (average values for the UHPFRC layer cross section) of the composite cross section under cyclic bending loading with stabilisation at εU = 1 o/oo. 0 5 10 0 1 2 εU [o /oo] σU,max ΔσU σU [MPa] 15 εU,max,cycl characteristic values for stable strain a)

b)

σU,r

strain hardening

Figure 88: a) Stress strain curve of the uniaxial quasi-static fracture test of UHPFRC as stability criterion for stable behaviour under cyclic loading. b) Stresses and strains in the UHPFRC layer of the composite

cross section under cyclic bending loading. σU,r: residual stress due to restrained deformation of

Chapter 6: Fatigue strengthening with UHPFRC

The design procedure is as follows: first, a strain of 1o_/

oo corresponding to the threshold for

the durability is imposed on the UHPFRC layer of the composite cross section. Then the stress under the maximum bending moment is calculated and compared with the admissible stress for a stable strain under cyclic loading. The UHPFRC layer is sufficiently thick if the stress in the UHPFRC layer is below the admissible stress.

b) Example

The following example is introduced to illustrate the design process. The action effect of the subsequent example is related to the loading characteristic of bridge elements. A cross sec- tion with a negative moment is considered that represents a slab strip of a continuous slab

bridge over an intermediate support. The moment due to the self weight is MG = 306 kNm,

the moment due to the weight of the railway superstructure is Mg = 230 kNm and the maxi-

mum moment due to traffic loads is M(Qfat) = 740 kNm.

The stability criterion requests a strain under cyclic loading equal or below εU,max,cycl = 1 o/oo

in the UHPFRC layer. The maximum allowed (average) stress then is equal to σU,max, which is

about 4 MPa (calculated value of the fatigue tests for stable fatigue behaviour). Thus, the thickness and the reinforcement content of the UHPFRC layer have to be chosen large enough that both criteria be fulfilled. Due to geometrical reasons, the maximum possible thickness of the UHPFRC layer is 100 mm when the cover concrete of 30 mm is cleared away (Figure 89b). Therefore, the design consists in the choice of the reinforcement of the UHPFRC layer.

It is assumed that the effect of the self-weight of the structure (MG) is taken by the rein-

forced concrete cross section only, as this loading act already on the structure during the execution of the UHPFRC layer and therefore cannot be taken by the UHPFRC layer. The ef- fect of the weight of the railway track superstructure (Mg) and the traffic (M(Qfat) are taken

by the entire composite cross section.

Figure 90 shows the relation εU – σU (Qfat) for the cross section in Figure 89b for three differ-

ent reinforcement contents in the UHPFRC layer (curves a). σU is the average stress in the

UHPFRC layer for Msup = Mg + M(Qfat). This relation is obtained by the establishment of the

equilibrium between external and internal moments, plane section assumed, for different val- ues of εU.

With 10 ∅ 18 in the UHPFRC layer the average stress in the UHPFRC layer under maximum traffic load is just below the allowable stress of σU,max (Figure 90).

a) b)

As,ct = 8 ∅ 30, ρ = 0. 87 % _{M M}

mortar layer

polymer bitumen UHPFRC

hRC = 7 00 70 67 0 1 00 1000 1000 As,U As,ct = 8 ∅ 30

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The stress range of the reinforcement in the concrete is equal to Δσs,ct = 110 MPa which is

below the nominal fatigue limit according to [SIA 262 2003] instead of Δσs,ct = 210 MPa with-

out UHPFRC layer.

Remark: In order to be able to establish this example, numerical values that are based on the measured strains and calculated stresses of the fatigue tests for stable load carrying behav- iour have been chosen. These numerical values are conservative, as they are based on rela- tively high stress ranges compared to the loading condition of bridge elements with higher dead load part. These numerical values should be determined more exactly for typical loading conditions for railway bridges by future research works.

c) Discussion and future work

According to the test results on the composite beams (Chapter 6.2), strains (until 1 o_/

oo) can

be allowed for a fatigue resistant design and stresses up to 10 MPa for good fibre orientation. Even macro cracks of w = 0.1 mm opening supported stress ranges up to 10 MPa without failure (supplementary three point fatigue test of beam P9).

For the development of a damage model for UHPFRC under cyclic loading fatigue tests with specimen of UHPFRC are necessary. However, also empirical relations based on tests between the deformation (that will be dictated by the durability criterion at the design of a new