Numerical study of a new construction sequence for railway viaducts utilizing a movable scaffolding system

Abstract

During last years a new constructive sequence of viaducts with movable scaffolding system (MSS) has been developed in Spain. This sequence is based on a self-supporting core that is formed by the bottom slab, webs and the cantilevers of the top slab so the MSS can advance to the next span and activities of the second casting phase can be performed out of crithical path. This current sequence has 2 related issues: the need of two prestressing stages per span and the need of long length splices between the self-supporting core and the second casting phase. The current paper studies if the number of prestressing stages per span can be reduced to only one. Two different solutions are proposed. Solution 1 consists in introducing 100% of the prestressing force at the self-supporting core. Solution 2 consists in introducing 50% of the prestressing force in a tendon that crosses two spans so when other 50% of the prestressing force is introduced at the self-supporting core, prestressing force reaches 100% at the previous span. As no viaducts have been constructed with Solution 1 and 2, Finite Element models have been carried out and suggest that Solutions 1 and 2 can be considered for construction.

Keywords

Bridges movable scaffolding system stresses viaducts concrete structures

1 Introduction

The first viaduct construction utilizing a movable scaffolding system (MSS) was at the Krahnember Viaduct in Germany. The Krahnember Viaduct was designed by Hans Wittfoht and constructed in 1961 [1]. During the seventies, the use of this construction technology spread in Europe. This technology has a number of advantages over other construction technologies. One of them is the environmental benefit as the use of MSS does not affect the ground. Moreover, this advantage permits to avoid complicated topography that must be overcome. Likewise, the construction with MSS is an advance in terms of safety [2, 3] as it is an industrialized process based on a provisional structure [4, 5] and allows the use of collective security measures. Operational risks are lower than with other constructive methods.

There are two different sequences in order to construct a viaduct with MSS. Both of them have been performed in Spain during last ten years [6, 7]. The traditional sequence consists in a first casting phase formed by the bottom slab and webs and a second casting phase that is formed by the top slab (Fig. 1). When the concrete of the whole section is hardened the whole prestressing force is introduced and the scaffolding can advance to the next span.

Fig.1

Traditional sequence. A) Phase 1. B) Phase 2.

The traditional sequence for one span per week can be longitudinally describe as follows (Fig. 2):

t = 0 days: the scaffolding supports the weight of the formworks and fresh concrete of the first casting phase.

t = 2 days: the concrete of the first casting phase has hardened and the fresh concrete of the top slab is placed. Though the whole weight of the first casting phase is supported by the scaffolding, the weight of the top slab is distributed between the scaffolding and the first casting phase [8].

t = 4 days: the concrete of the top slab has hardened and the whole prestressing force is introduced, the deck is self-supporting and the scaffolding can move to the next span.

t = 7 days: the scaffoldings hangs from the front of the completed span and transmits not only a part of its own weight but also a part of the first casting phase and top slab weights.

Fig.2

New construction sequence. A) Phase 1: self-supporting core. B) Phase 2.

Besides the traditional sequence, the new sequence, that henceforth will be named current sequence, has been used to construct viaducts in Spain since 2005 [7] (Fig. 3), it consists in a first casting phase that is formed by the bottom slab, webs and cantilevers of the top slab. This casting phase is partially prestressed when the concrete has hardened so a self-supporting core is formed and allows the MSS advance to the next span. The current sequence has the advantage of simplifying the constructive sequence. Moreover, the current sequence not only simplifies the distribution of the top slab weight between the first casting phase and the MSS but also reduces the auxiliary means that are needed and the number of activities at critical path, however it still requires night shifts [7, 9].

Fig.3

Longitudinal scheme of the bridge.

The current sequence presents several longitudinal phases (Fig. 4):

t = 0 days: the scaffolding supports the weight of the formworks and fresh concrete of the first casting phase.

t = 2 days: the concrete of the first casting phase has hardened and the first prestressing force (50–75%) is introduced.

t = 3 days: as the first casting phase is a self-supporting core, the scaffolding can move to the next span.

t = 4 days: the concrete of the central part of the top slab is placed. It is supported by the self-supporting core with a prestressing force of 50–75%.

t = 5 days: since the concrete of the central zone of the top slab has hardened so the rest of the prestressing force (50–25%) is introduced.

t = 7 days: the scaffolding hangs from the front of the deck. The scaffolding transmits a part of its own weight and a part of the weight of the fresh concrete of the first casting phase of the next span.

Fig.4

Standard section (m).

Nevertheless, the current sequence presents some issues as the need of two prestressing stages per span and the need of long splices between casting phases to provide long overlap lengths as Codes prescribe. In practice, this long length disrupts the extraction of the inner formwork. This last issue was already studied and a solution was proposed by using loop joints [10 –12]. In order to reduce the number of prestressing stages per span at railway viaducts, two solutions are proposed.

Solution 1 consists in introducing the 100% of the total prestressing force into the self-supporting core. Solution 1 consists of several stages (Fig. 5):

t = 0 days: the scaffolding supports the weight of the formworks and fresh concrete of the self-supporting core.

t = 2 days: the concrete of the self-supporting core has hardened and the 100% of the prestressing force is introduced.

t = 3 days: the scaffolding moves to its new position at the next span.

t = 4 days: the fresh concrete of the central part of the top slab is placed.

t = 5 days: the concrete of the central part of the top slab has hardened.

t = 7 days: the scaffolding hangs from the front of the deck and fresh concrete of the next self-supporting core is placed.

Fig.5

Beam elements of the deck.

Solution 2 consists in the use of tendons that cross two spans and that are partially prestressed at 50% when each self-supporting core is constructed. When the section is completed and the self-supporting core of the next span is constructed, the prestressing force of the section reaches 100% of the total prestressing force. The stages of this solution (Fig. 6) are:

t = 0 days: the scaffolding supports the weight of the formworks and fresh concrete of the self-supporting core.

t = 2 days: the concrete of the first casting span has hardened and a partial prestressing of 50% is introduced so that the self-supporting core is created.

t = 3 days: the scaffolding moves to its position at the next span.

t = 4 days: the fresh concrete of the central part of the top slab is placed.

t = 5 days: the concrete of the central part of the top slab has hardened.

t = 7 days: the scaffolding hangs from the front of the deck and fresh concrete of the next self-supporting core is placed.

t = 9 days: when the concrete of the next self-supporting core has hardened, a tendon that crosses the last two spans is prestressed at 50% of the total force, so that the previous span reaches 100% of prestressing force and the current self-supporting core reaches 50% of the total force.

Fig.6

Viaduct deck portion. Nodal equivalent forces of one tendon are displayed.

2 Comparison procedure

This paper is focused on studying what solution is the best to reduce the number of prestressing stages per span to only one keeping internal force and stress values limited. To carry out this study, Finite Element (F.E.) Models were carried out. Although the F.E. results do not show the actual behaviour of bridges, they allow comparing the theoretical levels of stress and internal forces at the sequences so that the best sequence among the current sequence, Solution 1 and Solution 2 can be determined. The F.E. results that have been compared are:

The global bending moments at different phases in both sequences (2D models. Ultimate Limit State, ULS), so they can be compared with the bending moment resistance of the sections.

The stresses at all sequences (3D models with shell elements. Service Limit State, SLS), so the best solution would be the one with lower stresses because it would require less passive reinforcement to limit crack opening.

A common railway bridge configuration contructed in Spain [7] has been selected to perform the numerical study. Bridge behaviour is very sensitive to rheological phenomena and induces to consider creep, shrinkage, variation of compressive strength and relaxation during the construction stages [13 –15]. Model Code 1990 [16] has been considered for time dependent effects as of most of viaducts that were constructed in Spain. Multifrontal Sparse Gaussian Analysis [17] was considered to carry out calculations. Tolerance for 2D models is 5%. Tolerance for 3D models is 1%.

3 Model description

3.1 Geometric and mechanical characterization of the viaduct

Five spans have been considered. The external span length was 45 m. while the internal span length was 60 m. The deck (Fig. 7) consisted in a box girder. The total height of the deck was 4 m. The wings were cantilevers of 4 meters and they had a variable thickness between 20 and 35 cm. The bottom slab width was 5 m. Total width was 14.2 m. Geometrical characteristics including the distance of the centroid to the bottom soffit are shown in Table 1. These characteristics depended on the constructive method because the sectional evolution is different at the traditional sequence. As the study mainly concerned the deck, it was the only element of the viaduct that has been modelled.

Fig.7

Load scheme of the schaffolding.

Table 1

Mechanical characteristics of each section type depending on the constructive sequence

Characteristics	Traditional	New seq/Sol.
	sequence	1/Sol. 2
1st phase area (m²)	4.5	8.8
Total area (m²)	9.9	9.9
1st phase inertia (m⁴)	5.2	19.2
Total inertia (m⁴)	21.1	21.1
Centroid 1st phase (m)	1.2	2.5
Centroid total (m)	2.6	2.6

2D models were constituted by standard Timoshenko beam elements of Midas Civil. The length of beam elements was about 0.5 m. The tendon layout over piers was over the centroid of the section in order to induce a positive moment to compensate the moments due to permanent and live loads. 3D models were constituted by standard Reissner-Mindlin shell elements. Dimensions of these were about 0.5×0.5 m, nevertheless, none dimension was 2.5 times higher than the other dimension. The shell elements were capable of taking into account in-plane and out-of-plane stresses.

3.2 Material characteristics and prestressing parameters

C50/60 concrete has been considered in numerical models. Tendon steel grade was Y 1860 S7. Like the viaduct already constructed in Spain with the current sequence, Model Code 1990 [16] has been taken into account to determine the rheological parameters that have been considered for creep characterization: f_ck = 50 MPa, Relative Humidity: 70%, “h”: 336 mm and rapid hardening concrete: β_SC = 8. The shrinkage has been supposed to start from the first day because many of the structural elements start resisting the loads from this early age.

The relaxation coefficient for the prestressing tendons at 2D models has been supposed at 5% at infinite time. The equivalent force was equal to the prestressing force at each constructive stage and it was introduced into the 3D models. The values of the equivalent force came from 2D models and already include relaxation, creep and shrinkage effects. In order to determine the instantaneous prestressing losses some considerations were adopted according to Eurocode 2 such as a curvature friction factor μ= 0.21, a wobble friction factor K = 0.00126, anchorage slip equal to 6 mm and elastic shortening.

3.3 Loads and boundary conditions

IAPF-07 Code has been considered to determine the loads and combinations [18]. The loads that have been considered in order to compare the different constructive sequences were dead loads (Fig. 8). Live loads were equal at all sequences and only induced an equal increment of internal forces values or stresses values:

Deck self-weight: 25 kN/m³.

Dead loads:

Ballast weight: 10 meters wide and 50 cm thick. Specific gravity: 18 kN/m³.

Concrete pavement: 10 meters wide and 12.5 cm thick. Specific gravity: 24 kN/m³.

Sidewalk weight: 4.3 meters wide and 15 cm thick. Specific weigth: 25 kN/m³.

Concrete blocks: 0.6 meters high and 0.3 m thick. Specific weight: 25 kN/m³.

Barriers weight: load of 34.5 kN/m.

Railway sleepers: 10 kN/m³.

Railway rails: 2.5 kN/m³.

Scaffolding loads (Table 2): the scaffolding transmits a point load 2.4 m behind the front of the last completed span.

Fig.8

Explanation of the conversion of tendon forces into equivalent loads.

Table 2

Loads transmited to the front of the previous span by the scaffolding

	New seq. Sol.	Traditional
	1/ Sol. 2 (kN)	seq. (kN)
MSS self-weight+Formwork weight+1st casting phase weight	6250	4320
Top slab weight (only transmitted in the traditional sequence)	–	830

External spans were supported by abutments and bents while internal spans were only supported by piers. Left extreme abutment was simulated considering constraints in X, Y, Z displacement and rotations about longitudinal axis (X axis). Right extreme abutment and piers were simulated considering constraints in Y and Z displacements and X axis rotations.

The current sequence, Solution 1 and Solution 2 have the advantage that the whole weight of the second casting phase is supported by the self-supporting core. Otherwise, the traditional constructive sequence implies that interaction between the scaffolding and the first casting phase must be taken into account in order to determine the percentage of the second casting phase that is supported by the scaffolding and by the first casting phase [8].

Prestressing load has been modelled as equivalent tendon at 2D models (beam element models). If the traditional sequence was considered two equivalent tendons were prestressed at 31400 kN when the section was completed. If the current sequence was considered four equivalent tendons were considered. Two of them (18840 kN each tendon) were acting over the self-supporting core and the other two appeared when the section was completed and each one increased the prestressing force at 12560 kN. On the other hand, the Solution 1 was calculated with two equivalent tendons (31400 kN each one). If Solution 2 was considered, four equivalent tendons crossed two spans and each tendon was prestressed with 15700 kN. In 2D-models prestressing forces were applied according to Midas Civil procedure. The Midas Civil program converts the prestress tendon loads into equivalent loads. It divides a beam element into 4 segments and calculates equivalent forces for each segment. It was assumed that the tendon is linear at each segment. Midas Civil obtains forces at the ends of each segment and distributed loads so that equilibrium can be stablished. Regarding 3D–models, prestressing forces were introduced as nodal and edge equivalent forces according to a procedure developed by the author and described in the next item. These equivalent forces included the effects of creep, shrinkage and relaxation.

3.4 Equivalent prestressing loads generation

In order to perform calculations in 3D Finite Element Models, a software in Matlab was developed. The software takes the tendon forces from 2D Models at each stage and converts them into nodal and edge equivalent forces (Fig. 9) for shell elements in 3D Models.

Fig.9

Bending moments at different sequences and phases.

S_i represents the different sections at the 2D model. One tendon crosses them at different coordinates and with different prestressing forces (P_i). The vertical dimension of the shell element has a “l” value. The tendon crosses a shell element at a distance “d” from the lower node of the shell element. Nodal equivalent forces (N_i) (Fig. 9) depend on the distance between the point where the tendon crosses the plate and the considered node of the shell. The closer the crossing point to the node, the higher the load at the node: N₄ = P₂×d₂/l, N₃ = P₂×(l–d₂)/l. The losses distribution (Fig. 9) along the tendon is r_i. The equivalent tendon losses at shell elements are edge forces (I_i–j). Edge forces values depend on the distance between the point where the tendon crosses the shell and the shell edge length. When the tendon crosses the two opposite edges, the edge load is uniform and equal at both edges. It must be noticed that horizontal edges take the horizontal component of the lossess of the prestressing force and vertical edges take the vertical component of the losses of the prestressing force.

4 Model results and discussion

The best solution to construct railway viaducts with MSS has been determined by a parametric comparison of internal forces and stresses with F.E. Models. Models show an approximate comparison among the sequences in which parameters related to the evolution of static scheme and prestressing force differ from one sequence to another. Results have been obtained both from Ultimate Limit State and from Service Limit State. Ultimate Limit State (U.L.S) has been applied to Beam element models (2D models) and Service Limit State (S.L.S) to Shell models (3D models).

4.1 2D Ultimate limit state: Bending moment global comparison

A study of different internal forces was carried out and bending moment appeared to be the critical internal force to be taken into account in order to compare the different sequences. As the static scheme evolution of each sequence is different from the others, bending moment resistance differs depending on the sequence that is considered. Only the active reinforcement has considered to calculate the bending moment resistance of the sections. Depending on the sequence that has been considered, the concrete area of the top slab differs because the traditional sequence is loaded when the whole top slab is completed, though the other sequences differ (current sequence, Solution 1 and Solution 2) because they are loaded first when the central part of the top slab is not yet completed. Nevertheless, the results show that the main factor to be taken into account to determine the bending moment resistance is the % of the prestressing force that is introduced when the deck is first loaded.

The traditional sequence and the Solution 1 imply a 100% of active reinforcement in every stage of the constructive process but the current sequence and Solution 2 do not, as the self-supporting core is only supported by a fraction of the total prestressing force (60% at the current sequence and 50% at Solution 2). The results show that, if none passive reinforcement is taken into account, the bending moment resistance of the traditional sequence and Solution 1 is about 60% higher than at the current sequence and about 100% higher than at Solution 2. This is the most restrictive parameter to be considered when designing is carried out.

The most critical sections regarding bending moment resistance are those over piers (Fig. 10). As it can be observed at the Fig. 10, the current sequence and Solution 2 the bending moment resistance over piers is quite tight and it would require passive reinforcement or an increase of decks height to resist it. Actually, as bridge decks are strongly reinforced with passive reinforcement [8] this issue is not a limitative factor but designers should take it into account if these two sequences are selected for construction.

Fig.10

Plate element numbers.

Table 3

Internal forces at selected elements of the 4 sequences

Element	a) Traditional sequence				Element	b) New sequence: 60%
	Max.	Max.	Min.	In-plane		Max.	Max.	Min.	In-plane
	Axial	Bending	Bending	shear		Axial	Bending	Bending	shear
	(kN)	moment (kNm)	moment (kNm)	force (kN)		(kN)	moment (kNm)	moment (kNm)	force (kN)
1	3.2	6.5	–3.8	34.1	1	9.2	5.7	–4.2	32.9
4	132.5	229.0	–56.8	373.5	4	217.9	196.9	–46.1	326.0
5	18.9	199.3	–11.1	1044.8	5	110.8	25.3	–36.6	1060.1
9	45.7	315.5	–6.4	1525.5	9	119.2	258.1	0.0	1237.8
10	82.4	468.5	–11.5	423.2	10	55.0	425.9	0.0	445.2
25	116.7	58.8	–34.2	106.8	25	73.7	82.3	–5.3	52.1
29	46.2	344.9	–106.3	457.7	29	258.2	345.4	–55.7	408.0
30	454.7	370.4	–76.7	341.6	30	657.0	332.3	–17.3	343.9
32	757.9	52.0	–81.6	195.7	32	446.3	64.7	–8.2	134.9
Element	c) Solution 1:100%				Element	d) Solution 2:50%
	Max.	Max.	Min.	In-plane		Max.	Max.	Min.	In-plane
	Axial	Bending	Bending	shear		Axial	Bending	Bending	shear
	(kN)	moment (kNm)	moment (kNm)	force (kN)		(kN)	moment (kNm)	moment (kNm)	force (kN)
1	6.4	5.5	–5.0	35.8	1	6.8	7.1	–2.0	25.0
4	175.0	192.1	–40.1	316.8	4	169.0	248.7	–79.8	279.2
5	100.7	23.0	–40.2	1041.5	5	177.9	29.9	–40.4	921.5
9	112.4	267.4	0.0	1313.9	9	81.8	244.7	–3.9	1254.2
10	61.3	443.1	0.0	452.5	10	106.0	472.8	0.0	425.6
25	78.7	89.4	–2.1	50.0	25	110.2	88.8	–6.0	42.3
29	137.8	346.8	–69.2	378.3	29	173.5	425.3	–48.9	276.3
30	656.0	361.9	0.0	234.6	30	812.2	376.2	–34.1	268.8
32	422.7	74.2	–5.1	128.9	32	492.7	73.6	–3.7	118.8

4.2 3D-Service limit state: crack opening and transversal deformation study

Durability [19, 20] is an aspect that must be held when a bridge is designed. The main issue regarding durability is crack opening and it depends on the stresses that appear at the concrete. Stress levels at external fibres have been calculated to compare them in order to determine what constructive sequence is the best to build viaducts. The lower the stresses are, the lower the crack opening is at the considered fibre. The results have been obtained at 5 different cross-sections in the viaduct (Fig. 11). Sections S-1.3, S-2.3 are placed over piers, section S-1.4 is placed at longitudinal construction joints, where the prestressing force is introduced, section S-2.1 correspond to the mid span and S-2.2 is placed at 0.2 L at the left of the central pier. Results are shown at Figs. 12 and Fig. 13 regard S.L.S. during constructive stages.

Fig.11

Sections whose internal forces have been studied.

Fig.12

Longitudinal stresses at different sequences.

Fig.13

Transverse stresses at different sequences.

Tensile strengths of C50/60 concrete for different concrete ages are: f_ctm,3 = 2.7 MPa; f_ctm,₇ = 3.3 MPa; f_ctm,₂₈ = 4.1 MPa. [16].

Regarding longitudinal stresses at the top slab, Fig. 12. D, E (elements 4, 30) shows that during construction (until stage 15) tensions at the Solution 2 appear (4 MPa) while the other sequences fibres remain comprised. Elements 4 and 30 correspond to the self-supporting core except at the traditional sequence. It can be explained at the traditional sequence as it is completed and fully prestressed when it is loaded. Otherwise, current sequence and Solution 1 are not completed during all constructive stages, but the percentage of prestressing force (60% and 100% repectively) that is introduced at the self-supporting core is higher than at the Solution 2 (50%), so they can reach compressive levels. If elements at the central part of the top slab are considered (elem. 32, Fig. 12 F), tensions appear in all sequences except at traditional sequence. This can be explained because of its different static scheme evolution. Moreover, the stress level is different among the current sequence and solutions 1 and 2. As the central part of the top slab is part of the second casting phase of each section, if the first casting phase is completely prestressed (Solution 1), no compressive force will be introduced at the central part of the top slab so when other loads appear, it will be tensioned (4 MPa). Otherwise, current sequence and Solution 2 introduce a part of the prestressing force at the central part of the top slab (50% and 40% respectively) so its tension levels are lower (2 MPa). The results show that, although Solution 1 results are lower than Solution 2 results regarding longitudinal tensions at the self-supporting core, tensions at the Solution 2 are lower than at Solution 1 if the second casting phase is considered. If longitudinal stresses at the lower slab of the deck are studied, it will be observed that the current sequence, Solution 1 and Solution 2 are compressed and no crack opening due to tensions can be predicted.

Regarding top slab transverse stresses (Fig. 13 B, C, D, E, F), none substantial differences can be highlighted between the current sequence, Solution 1 and Solution 2, although there are differences between these sequences and the traditional sequence that can be explained by the static scheme evolution differences during construction. Moreover, it can be observed that the highest tensional levels (2.5 MPa at element 32) are below the critical values needed to open cracks whatever the concrete age considered (f_ctm,3 = 2.7 MPa).

5 Conclusions

The solutions that have been obtained show that regarding U.L.S. bending moments, Solution 2 exceeds the bending moment resistance of the self-supporting core during construction due to the lack of active reinforcement (50%) until the next self-supporting core is prestressed. Regarding durability, Solution 2 shows high tension levels at the top slab of the self-supporting core, due to the insufficient prestressing force to compensate the deck self-weight. These tensional levels do not appear at the other sequences studied in this paper. Otherwise, Solution 1 shows the higher tensional values at the central part of the top slab (second casting phase) as the whole prestressing force is introduced at the self-supporting core, so no compressive force is introduced at this casting phase.

Although Solution 2 could be considered less suitable to construct railway viaducts, it should be pointed that regarding bending moment resistance, the lack of active reinforcement (50%) to resist negative bending moments over piers is compensated by the passive reinforcement quantities that are commonly placed at these viaducts [7]. Regarding tension levels that appear at the self-supporting core top slab, a similar comment can be made related to limit crack opening by adding passive reinforcement. Hence, Solution 2 can be considered if these issues are taking into account. Solution 1 seems to be more suitable than Solution 2, but stress levels that are reached at the central part of the top slab would require passive reinforcement. Nevertheless, the additional passive reinforcement that would be required does not interfere with the ducts od tendons because they are at the webs and not at the central part of the top slab.

Although none solution suits perfectly to construct viaducts, both Solution 1 and Solution 2 are available to design railway viaducts if passive reinforcement is properly placed in order to avoid the limitations of each sequence.

Footnotes

Acknowledgments

The authors would like to acknowledge the University of Sao Paulo and Conselho Nacional de Pesquisa (Goberment of Brazil), which funded this project.

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