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Numerical analysis of a soil-steel bridge during backfilling using various shell models
Engineering Structures 196 (2019) 109358
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Numerical analysis of a soil-steel bridge during backfilling using various shell models Tomasz Maleska, Damian Beben
T
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Faculty of Civil Engineering and Architecture, Opole University of Technology, Katowicka 48, 46-061 Opole, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Backfilling Soil-steel bridge Corrugated steel plate Steel ribs Shell model Stiffening
Soil-steel bridges are becoming increasingly popular in various parts of the world, and are often built with a span of 3–25 m. Those with a span greater than 12 m are usually equipped with additional stiffening elements, e.g. ribs, relieving slabs, longitudinal beams, steel ribs and steel ribs filled with concrete. This paper examines the necessity of using these additional stiffening elements, using the example of a soil-steel bridge with a span of over 17 m. Stiffening steel ribs filled with concrete were used in this bridge, and the behaviour of the corrugated steel shell of the bridge was then analysed under backfilling loads. The DIANA program with the finite element method was used for the numerical analysis. The maximum displacements, bending moments and axial forces for the three numerical models of corrugated steel shell were considered, and the displacements obtained from numerical calculations were compared with measured results. In addition, the bending moments and axial forces obtained using finite element analysis were compared with results based on the relevant standards and design methods.
1. Introduction Soil-steel bridges consisting of a corrugated steel plate (CSP) and backfill have been used for many years to build transportation structures around the world. In Europe, this type of structure began to become more popular in the 1980s, and the subsequent years saw a rapid growth in further investments based on the use of CSPs. The reasons for such a rapid increase in the number of structures involving a CSP include (i) the simplicity of construction; (ii) their relatively low construction costs; (iii) the short construction period; and (iv) the low expenditure related to maintenance of the object. Soil-steel bridges usually have a span in the range 3–25 m, and are used to construct bridges, culverts, railway passes, etc. Currently, a soil-steel bridge with a span of 32.5 m was built in the United Arab Emirates, and this is the world’s largest span for this type of bridge structure. During the construction process and service period of such a large soil-steel bridge, new problems may arise that have not previously been identified. The durability of soil-steel bridges determines the resistance of the steel to corrosion, the backfill quality and the soil-structure interaction. Due to the nature of the behaviour of soil-steel bridges, recognised procedures for their design and for the selection and execution of the backfill are very important for the safe operation of the entire structure. This is especially true during the backfilling process (compaction of the backfill). Suitable characteristics of the backfill, such as its density ⁎
index, aggregate grain size, density intensity, the thickness of the compacted layers, backfill range, type of soil and soil cover height, are basic elements that affect the strength of soil-steel bridges. The following factors also need to be checked: (i) the weight of the construction equipment near the structure; (ii) the size of the structural deformations during backfilling; and (iii) tightening of the connecting bolts. Strict observance to the technological regime and control over the construction processes are required, as is the application of appropriate enforcement procedures. Even a well designed structure can be damaged as a result of an incorrect compaction procedure (Fig. 1a), the use of unsuitable backfill, lack of appropriate equipment, or lack of control over the structure during backfilling [1–3]. Thus far, several attempts have been made to analyse the impact of backfilling on soil-steel bridges [4,5]. It has been found that during backfilling, the displacements and bending moments are relatively high, especially in the initial layers of backfilling of the CSP structure. Koruszewicz and Kunecki [6] analysed the backfill densities under laboratory conditions and the results obtained were compared with numerical results. The difference between the experimental and numerical results was at the level of 16%, which can be considered an acceptable error. Sanaeiha et al. [7] presented a field test of a soil-steel bridge during backfilling. Their case study involved a CSP that was stiffened by concrete rings, and test results showed that both the maximum
Corresponding author. E-mail addresses: [email protected] (T. Maleska), [email protected] (D. Beben).
https://doi.org/10.1016/j.engstruct.2019.109358 Received 3 January 2019; Received in revised form 24 June 2019; Accepted 28 June 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
Engineering Structures 196 (2019) 109358
T. Maleska and D. Beben
and for strains 13%). The highest discrepancies, reaching 40%, occurred in the bending moments. Numerical 2D studies of soil-steel bridges during backfilling have also been presented by Taleb and Moore [15], Beben [16] and Kunecki [17]. The results were reasonable, although they did not describe the behaviour of the entire bridge structure. Maleska and Beben [18] analysed the impact of backfill on the shell of a soil-steel bridge, using a corrugated shell that was modelled using orthotropic characteristics. Finite element method (FEM) results obtained using DIANA software were compared with measured ones. A special function of the DIANA FEA program to model the interface (Coulomb friction) was used, which allowed the authors to better describe the interaction between two different materials (steel and backfill). Borana et al. [19] also analysed the importance of this problem, in which the impact of the roughness of particular materials on the values of shear forces was examined. Some design methods, such as those of Sundquist-Pettersson [20] and the Canadian Highway Bridge Design Code (CHBDC) [12], also allow calculation of the maximum internal forces in these structures during the backfilling process. However, these methods give appropriate results only for bridges with small spans of up to 8.0 m. Soil-steel bridges with a span of over 12 m are usually equipped with additional stiffening elements, e.g. ribs, relieving slabs, longitudinal beams, steel ribs filled with concrete, etc. In most cases, the use of these additional stiffening elements is required by regulations published in the patents of these structural solutions, although there are some examples of small bridges where the designer did not foresee the need for stiffening and the contractor for the construction works was forced to apply them [21]. This stiffening causes a significant increase in construction costs, and the question therefore arises of whether the use of additional stiffening is necessary from the point of view of the safety of the soil-steel structure. This paper shows this problem using the example of a soil-steel bridge (Fig. 1b) with a large span (over 17 m), where stiffening ribs were used and were also filled with concrete. Three different models of a corrugated steel shell were analysed: without stiffening ribs (model I), with steel ribs (model II) and with steel ribs filled with concrete (model III). The maximum displacements, bending moments, axial forces and stresses during the backfilling process are presented for these three numerical models. The numerically calculated displacements are compared with measured values, and the bending moments and axial forces obtained from numerical calculations are compared with results from standards and design methods (the Sundquist-Pettersson method [20] and CHBDC [12]). This study can aid in the design and construction of large soil-steel bridges, and the results presented here can form the basis for large financial savings (due to a reduced consumption of steel and concrete).
Fig. 1. Front view of soil-steel bridge: (a) shell dislocation resulting from improper backfilling; (b) shell during correct backfilling.
deflection and the maximum bending moment occurred at the crown, at the point where the soil reached the crown level. Conversely, the maximum axial force occurred at the bottom of the arch where the soil reached its maximum level above the arch. The influence of the backfill quality and the use of RC relieving slab on soil-steel bridges were analysed by Beben [8] and Beben and Stryczek [9], respectively, while Meguid et al. [10] examined the effect of soil pressure on the side walls of the box-culvert. In order to reduce the soil pressure on the sidewalls, expanded polystyrene was used. The design of this type of bridge structure has also been verified using the relevant standards, and various soil cover heights (in the range 0.45–1.5 m) were considered [11]. Significant differences in the bending moments of up to 70% were observed between values obtained using the Canadian standard [12] and measured results. These results were also compared with values obtained using finite element analysis (FEA), and the difference was found to be a few percent. Bayoglu Flener [13] analysed the Canadian standard in comparison with FEA, where the backfill height over the shell crown was in the range 2.5–4.08 m. Significant discrepancies were observed that reached more than 50%. Brachaman and Elshimi [14] investigated the influence of the CSP modelling types (orthotropic and corrugated), and their results were compared to measured values. They showed that the difference between the simplified model (an orthotropic steel plate) and the results obtained in the tests was a few percent (for displacements, this was 4%,
2. Short description of the soil-steel bridge The soil-steel bridge analysed acts as an overpass for animals, and is located in Trzebaw, Poland over National Road no. 5 in Wielkopolski National Park. This soil-steel bridge is one of the largest object of this type in Europe. The load-carrying structure was constructed as a shell assembled from CSPs. The shell structure has a span of 17.67 m and a vertical height of 6.05 m (Fig. 2). The length of the shell structure at the top is 40.39 m, while that of the lower part of the structure is 53.83 m. The predicted depth of soil cover at the shell crown is 1.80 m, which makes it possible to plant various types of vegetation. This backfill depth also results in effective damping of the shell structure and a reduction of the noise level from the vehicles travelling under the bridge. The shell structure was made from CSP with depth of 0.14 m, a pitch of 0.38 m and a plate thickness of 0.007 m (Fig. 3a). The CSP sheets were joined together on the span using high-strength bolts. The CSP shell was reinforced using additional ribs of the same corrugated plates, with an axial spacing of 1.524 m (Fig. 3b). Additional steel ribs consisted of two waves over the entire length of the bridge (Figs. 2a and 2
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Fig. 2. The analysed soil-steel bridge: (a) longitudinal section; (b) cross section.
Fig. 3. Analysed models: (a) model I (shell made of CSPs); (b) model II (shell made of CSPs with additional CSP ribs); (c) model III (shell made of CSPs with CSP ribs and filling with C25/30 concrete). 3
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Table 1 Weight and thickness of backfill layers used for numerical analyses and tests. Number of backfill layers
Thickness* (m)
Weight (kN/m2)
1 2 3 4 5 6
2.82 4.21 5.20 6.16 6.96 7.46
57.8 86.3 106.6 126.3 142.7 153.0
* Thickness of backfill is counted from top level of foundation (please see Fig. 2b).
•
•
Fig. 4. A view of additional stiffeners of CSP shell: (a) during backfilling process; (b) bridge model in the DIANA program.
•
4b). The interior of the ribs was filled with a C25/30 concrete mix without bars (Fig. 3c). The stiffening was applied to the entire shell circuit, in order to ensure a higher transversal rigidity of the bridge span. The assembled shell structure was backfilled with layers of soil of thickness between 0.2 and 0.3 m, which were then compacted (ID = 0.97). Both ends of the shell structure (the inlet and outlet sides) were secured and reinforced using RC collars with dimensions of 0.40 × 0.60 m. The collars were made with a C25/30 concrete mix. The CSP structure was based on two massive footings with a base width of 4.00 m and a length of 57.83 m, made of C30/37 concrete. The basic dimensions of the soil-steel bridge are shown in Fig. 2.
• •
3. Numerical modelling
plate thicknesses of both the shell and ribs were was 0.007 m. The steel shell and additional stiffeners (ribs) were modelled as corrugated. The backfill was modelled as solid elements (TE12L) using the Duncan-Chang nonlinear elastic hyperbolic model. The backfill parameters were a Poisson’s ratio of 0.2, dilation angle 5°, angle of internal friction 39°, cohesion 3 kPa, failure ratio 0.7, unloadingreloading stiffness 1000 N/m2, reference pressure 101350 N/m2, exponent for the unloading-reloading curve 0.25, exponent for the backbone curve 1.1, minimum compressive stress 350 N/m2, and minimum tangential stiffness of the backbone curve 1200 N/m3. Table 1 and Fig. 2b present the thicknesses and weight of the backfill for the numerical analyses and field measurements conducted here. The C25/30 concrete used for filling the additional stiffeners (ribs) was modelled as solid elements (TE12L) according to EC 1992-1-1 [23]. The parameters for the concrete were a Poisson’s ratio of 0.2, characteristic cylinder compressive strength 25 MPa, mean compressive strength 33 MPa, mean tensile strength 2.56 MPa, elastic modulus 31476 MPa, design compressive strength 16.67 MPa (for αcc = 1.00), design compressive strength 14.17 MPa (for αcc = 0.85), design tensile strength 1.20 MPa (for αct = 1.00), minimum longitudinal tension reinforcement ratio 0.133%, and minimum shear reinforcement ratio 0.08%. The connection between the backfill and shell steel was modelled as an automatic interface using a “Coulomb friction” function with angle of internal friction 39°, dilation angle 5°, rigidity 100,000 kN/ m3, and cohesion 3 kPa. The connection between the steel ribs and filling concrete was modelled as a fixed connection, i.e. an interface function was not used. The boundary conditions were modelled as hinged supports for the base of the bridge model (foundations and backfill) in the x, y, z directions. The outlet and inlet of the steel shell were also modelled as hinged supports in the x, y, z directions (Fig. 5a). The finite elements were modelled as triangular elements with maximum dimensions of 0.50 × 0.50 m for backfill, CSP shell and concrete. In the contact areas between the steel shell and the backfill, and in the places where maximum values are expected (crown, haunches), the finite element mesh was denser (Fig. 5b).
Numerical analyses were conducted for three types of shell structure: (i) a CSP shell with no reinforcements (Fig. 3a); (ii) a CSP shell with additional CSP ribs (Fig. 3b); and (iii) a CSP shell with additional CSP ribs filled with C25/30 concrete (Fig. 3c).
The DIANA software program [22], based on FEM, was used for numerical analysis of the soil-steel bridge. The bridge was modelled as a 3D object, using curved shell elements for the shell structure and solid elements for the soil (backfill) medium, as follows:
• The corrugated steel plates (primary steel shell and additional stif-
4. Experimental testing
feners (ribs) – Fig. 4a) were modelled (Fig. 4b) as curved shell elements (T15SH) with a Young’s modulus of 205 GPa, a Poisson’s ratio 0.3, an elastic-plastic model with a density of 7850 kg/m2, a yield strength of steel of 235 MPa. Values for the moment of inertia of 21897.45 mm4/mm and 28736.81 mm4/mm, and for the cross-sectional area of 8.867 mm2/mm and 11.64 mm2/mm were used for the primary shell and the shell with additional ribs, respectively. The
Four Leica self-levelling levels with a reading accuracy of 0.01 m were used for the displacement measurements of the shell structure during backfilling. Due to the relatively long shell structure (about 60 m), four measuring stations were set up (Fig. 6). This approach allowed at least two independent measuring instruments to be controlled at each measuring point. 4
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Fig. 5. Numerical model of a soil-steel bridge in DIANA: (a) division into six backfill layers; (b) FE mesh.
Three transverse cross sections and four longitudinal cross sections were selected to provide accurate information about the displacements of the CSP shell structure (Fig. 6). Measurement points were stabilised from the bottom of the shell structure to allow the exact measurements to be made. Measurements of the height network of benchmarks # 101, 102, 103 and 104 were performed by geometric levelling in the main and return directions. An assessment of the constancy of the benchmarks was also conducted. Displacement and strain measurements were made between 6 pm and 10 pm (i.e. after completion of all building work on the facility) to obtain the actual deformation of the shell structure after a full day of loading and compacting of the backfill around the structure. The testing was started with the output measurements, i.e. an analysis of the state of the structure before loading (without backfill) to obtain the so-called measurement base (comparative). The vertical displacements of the examined points were calculated on the basis of changes in altitude differences. Fig. 6. Location of measurement points and testing sections.
5. Results analysis backfill on the CSP shell, modelled using three variants. It should be added that (−) or (+) for displacements mean move down or up the CSP shell, respectively. In the case of stresses, bending moments and axial forces, (−) or (+) mean compressive or tensile values in the CSP shell, respectively.
5.1. General remarks It is very important to implement the backfill correctly in order to ensure a proper connection and interaction with the CSP shell. In extreme cases, improper execution of the backfill can lead to damage or destruction of the CSP shell. It is worth noting that the load due to the backfill compacted around the CSP shell and the technological loads are the first that need to be transferred by the structure during backfilling. This paper does not analyse the impact of technological loads (the effects of compaction equipment), and focuses on the influence of the
5.2. Displacements The largest displacements for the shell models analysed here were observed in model I (Fig. 7a), and were equal to −20.20 mm. For model II (Figs. 7b and 8), the displacements were lower, about 30% less than 5
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Fig. 7. Maximum displacements of the CSP shell in: (a) model I; (b) model II; (c) model III.
in model I, and were −14.03 mm. However, the smallest displacement was obtained for model III (Fig. 7c), where the value was −9.32 mm, constituting about 46% of that for model I. The maximum displacements for shell models (I, II and III) were directed downwards, and these were obtained for the six backfill layers (i.e. the CSP shell was already completely backfilled, and the soil cover above the shell was 1.80 m). In addition, the maximum displacements for the shell models occurred in the same places, that is, at the shell crown. It should be emphasised that despite the visible differences in displacements for the different shell models, the maximum displacements for model I were relatively small, and did not pose a threat to the safety of the bridge (either in the construction process or the later service period). It should be noted that the CSP shell does not always shift downwards, and this can be seen in the different shell models. In model II, the maximum displacements were equal to −1.3 mm and −0.62 mm during compacting of backfill layers #1 and 2, respectively. In this case, the CSP shell lifted upwards by 0.68 mm, i.e. by 48% in relation to the displacement caused by backfill #1. For the next backfill layers, successive deflections of the CSP shell were observed, as shown in Fig. 8. A change in the character of the displacements could also be seen at around 2/3 of the height of the shell. Based on the displacement results shown in Fig. 9, it can be seen that during compacting of the first backfill layers (#1–3), the shell displacements in models I, II and III are relatively similar to each other. However, when comparing the calculated values with the measured ones, a slightly different behaviour of the CSP shell (layer #1) was noticed. It is noticeable that the shell is lifted up, contrary to the numerical results. This may be the result of the impact of the compaction machines. In the numerical models (I, II, III), the steel shell always deflects downwards. Fig. 9 also shows the impact of the additional stiffeners used in the construction of the soil-steel bridge. The maximum displacements obtained from the numerical calculations (different shell models) are generally smaller than the values measured at the construction site (Fig. 9). The measurements were
conducted for the CSP shell with stiffening that only uses additional ribs (numerical model II). This is because the ribs were filled with concrete when the shell was completely backfilled. The maximum measured displacement for the soil-steel bridge was −29 mm, a value about 44% higher than that in model I, 107% higher than in model II and 211% than in model III. In a similar way to the numerical models, the maximum displacements occurred at the shell crown, and were recorded during the compaction of the fifth backfill layer. 5.3. Stresses The highest stresses in the shell of the soil-steel bridge were observed for model II, and reached −178 MPa (Fig. 10b). These stresses were compressive, and were 8% greater than the stress in model I, which reached −165 MPa (Fig. 10a). The smallest compression stresses were obtained for model III, and had a value of −100 MPa (Fig. 10c). This constitutes approximately 43% of the maximum stresses in model II. The maximum stresses were observed in the Szz direction (Fig. 10). It is worth noting that these occurred near the connection between the CSP shell and the foundation. It should also be noted that in most parts of the shell (and especially around the shell crown, e.g. in model II), the stresses in the shell were significantly lower (Fig. 11) and were at the level of −10 MPa, about 5% of the maximum stress for this model. The stresses in the steel shell for numerical models I and III typically did not exceed −20 MPa and −15 MPa, respectively. The most significant stresses were obtained during backfilling of soil layers #4, 5 and 6 (Fig. 11). Initial compaction of the backfill around the steel shell (layers #1–3) caused much lower stresses for certain shell models. In model I, the maximum stresses during backfilling of the first three layers ranged from −8 MPa (#1) to −39 MPa (# 3), that is, between 5% and 24% of the maximum stresses in model I (−165 MPa). However, in the case of model II, the influence of the first backfill layers (#1–3) caused stresses in the CSP shell of between −11.5 MPa (#1) and −33 MPa (#3). In model III, the stresses in the steel shell ranged from −11 MPa (#1) to −21.5 MPa (#3). It should be pointed out that all of 6
Engineering Structures 196 (2019) 109358
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Fig. 8. Maximum displacement of the CSP shell for each backfill layer in model II.
addition, slightly higher bending moments can be observed at the shell crown in all three models. Fig. 14 presents the distribution of bending moments in the CSP shell of the bridge. As in the case of stresses and displacements, there are no significant differences in the bending moments at the shell when backfilling the initial backfill layers (#1–3). However, the variable nature of the bending moments caused by the compaction of backfill layer #2 was observed, in which the moments changed from compressive to tension (model III). While compacting the other backfill layers, the differences between the numerical models start to become more apparent, but the overall level of the bending moment is small. It can therefore be concluded that there are no significant advantages to the use of additional CSP shell stiffening. 5.5. Axial forces Fig. 9. Maximum displacements of the CSP shell for each backfill layer, obtained from numerical models and measurements.
The largest axial forces in the CSP shell of the soil-steel bridge were noted for the II model, and amounted to −1256 kN/m (Fig. 15b). This value was slightly higher (about 5%) than the axial force obtained for model I, which was −1201 kN/m (Fig. 15a). In model III, the maximum axial force was −696 kN/m (Fig. 15c), which was 44% less than the value in model II. In all of the models, the axial forces were compressive and occurred at the CSP shell near the foundation. In the other parts of the CSP shell, the axial forces were much smaller (Fig. 15). In the same way as for the stresses and bending moments, the most important axial forces were obtained during the compaction of backfill layers #4, 5 and 6 (Fig. 16). However, the initial backfilling of the soil (layers #1–3) caused significantly lower axial forces in the shell for particular models. The influence of the stiffeners in the CSP shell is well illustrated in Fig. 17, which shows that the first two backfill layers cause almost identical axial forces. Compaction of the successive backfill layers causes increasingly large differences in axial forces. However, it should also be noted that the axial forces in models I and II differ slightly. Therefore, the use of stiffener ribs does not affect the reduction in the axial forces on the CSP shell.
the maximum stresses for particular shell models were compressive. The stresses resulting from compaction of the first backfill layers can be considered relatively small in relation to the maximum stresses obtained in the particular numerical models. Fig. 12 shows the course of the maximum stresses obtained in the numerical models. It should be noted that the stiffeners used in the bridge structure influenced the obtained stresses, and that during compaction of the first two backfill layers, the stresses were very similar for all three numerical models. Larger differences were only visible during compaction of the subsequent backfill layers. In addition, it is very important to note that the use of stiffening ribs (model II) does not reduce the stress in the shell (model I). 5.4. Bending moments The bending moments in the CSP shell were relatively small. The highest value was obtained for model I (Fig. 13a), and was −0.14 kNm/m. For the other shell models, the bending moments were −0.0795 kNm/m (Fig. 13b) for model II (57% of the value for model I) and −0.0612 kNm/m (Fig. 13c) for model III (44% of the value for model I). The maximum bending moments were obtained near the shell support, at the foundation, and occurred during backfilling of the last backfill layer (#6). In the remaining parts of the CSP shell, the bending moments were significantly lower for all the analysed models (Fig. 13). The initial compaction of the backfill (layers #1–3) resulted in much lower bending moments in the CSP shell than the backfilling of layers #4–6. These values were found above the shell support at around 1/6 (model III), 1/5 (model II) and 1/4 (model I) of the CSP shell height. In
5.6. Summary of numerical analysis It should be clearly emphasised that in the case of model I (without any additional stiffening) the allowable stresses and displacements were not exceeded, i.e. the CSP shell is able to carry the loads due to the backfilling process. In addition, the steel ribs do not offer significant advantages in terms of reducing the response of the shell, and even causes stresses to increase (model II + 8%) in relation to the model without the steel ribs. Moreover, the use of steel ribs filled with concrete is hazardous (model III), since during the use of the bridge, there is a risk of damage 7
Engineering Structures 196 (2019) 109358
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Fig. 10. Maximum stresses of CSP structure in numerical models: (a) I; (b) II; (c) III.
shell in the form of steel ribs (model II). The results are shown in Table 2. The values obtained using the Sundquist-Pettersson analytical method [20] and the CHBDC standard [12] differ significantly from the values calculated using the DIANA numerical program. The largest differences were observed in bending moments for model II. In this case, the moments calculated using the Sundquist-Pettersson method [20] are 179 times greater than those derived from FEM calculations. In contrast, the bending moments obtained with the CHBDC standard [12] are 97 times larger than those obtained from the numerical model. For model I, where the CSP shell was not stiffened with steel ribs, the moments calculated using the Sundquist-Pettersson method [20] are almost 102 times larger than those obtained from the FEM calculations. In turn, the bending moments obtained with the CHBDC standard [12] are 62 times higher than those of the numerical model. In the case of the axial forces, smaller differences were found between the analytical approach and FEM models. The axial forces for
to the concrete in the ribs as a result of cyclic loading and unloading of the structure. The standards do not indicate how to apply these additional steel ribs filled with concrete. However, the most important issue is the fact that the use of additional stiffening elements significantly increases the cost of the construction process of soil-steel bridges, and the advantages gained in terms of a higher bearing capacity of the bridge are not necessary from a practical point of view. 5.7. Analytical solution 5.7.1. Bending moments and axial forces The results obtained from numerical analysis were compared with the results of analytical methods, i.e. the Sundquist-Pettersson method [20] and the CHBDC [12]. These methods are intended to dimension the structures of the so-called Super-Span, an object with a large span. Verification was carried out for shell models I and II, which used the CSP shell without stiffening (model I) and with strengthening of the
Fig. 11. Maximum stresses on the CSP shell for each backfill layer in model II. 8
Engineering Structures 196 (2019) 109358
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Fig. 14. Maximum bending moments of the CSP shell for each backfill layer, obtained from numerical analyses.
[12,20]. In addition, it is relatively difficult to correctly image the interaction between the backfill and CSP shell in the analytical methods; they also use an imaginary cross section of the bridge for the calculation. In the case of 3D numerical calculations, the spatial response of the whole bridge is obtained.
Fig. 12. Maximum stresses on the CSP shell for each backfill layer.
model II calculated using the Sundquist-Pettersson method [20] are almost six times larger than those obtained from calculations using the DIANA FEA program. However, in the case of the CHBDC standard [12], the axial forces were slightly more than twice as great as those calculated using the Sundquist-Pettersson method [20]. Larger differences were observed for model I, where the axial forces computed based on the Sundquist-Pettersson method [20] were six times larger than those obtained in the numerical model. However, in the case of CHBDC [12], the axial forces were over three times higher than those calculated using the Sundquist-Pettersson analytical method [20]. This shows that the CHBDC [12] standard allows to obtain more reasonable bending moments and axial forces than those computed using the Sundquist-Pettersson method [20]. Such large differences in bending moments and axial forces indicate a conservative approach to the calculation of internal forces in these bridges, and the use of relatively high safety factors and arching factor in the analytical methods
5.7.2. Stresses The stresses obtained from numerical models I and II were compared with results that were previously calculated using the SundquistPettersson [20] and CHBDC methods [12]. The bending moments and axial forces were substituted into the Navier Eq. (1). The axial forces and bending moments in equation (1) can be positive or negative depending on the side of the cross-section or the loading/moment direction. In model I, stresses of −81 and −45 MPa were obtained using the Sundquist-Pettersson [20] and CHBDC methods [12], respectively. The calculated stresses were significantly smaller than those obtained using the numerical approach (−165 MPa). The relative differences between the numerically calculated values and those obtained based on
Fig. 13. Maximum bending moment of the CSP shell for models: (a) I; (b) II; (c) III. 9
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Fig. 15. Maximum axial forces on the CSP shell for numerical models: (a) I; (b) II; (c) III.
analytical methods were 51% and 73% for Sundquist-Pettersson [20] and CHBDC [12], respectively. A similar situation occurred in the case of model II, where the stresses were equal to −61 and −26 MPa using the Sundquist-Pettersson [20] and CHBDC methods [12], respectively. The obtained stresses were also significantly lower than those obtained from numerical computations (−178 MPa). The relative differences between the numerical values and those obtained using analytical methods were 65% and 86% for Sundquist-Pettersson [20] and CHBDC [12], respectively.
σ=
Nd, s Md, s + As1 W1
(1)
σ - maximum stresses in the CSP shell [MPa], Nd,S - axial force due to backfilling [kN/m], Md,S - bending moment due to backfilling [kNm/m], AS1 - area of the cross section of the CSP shell [m2],
Fig. 17. Influence of backfill layers on maximal axial forces in CSP shell.
Fig. 16. Maximum axial forces on the CSP structure for each layer of model II. 10
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Table 2 Comparing values of numerical models and analytical solutions.
Model I Bending moments [kNm/m] Axial forces [kN/m] Model II Bending moments [kNm/m] Axial forces [kN/m]
Numerical values (XCal)
Sundquist-Pettersson [20] values (XS-P)
Canadian standard [12] values (XCHBDC)
≈XS-P/XCal
≈XCHBDC/XCal
−0.14 −1201
−14 −7154
−9 −3952
102 6
62 3
−0.0795 −1256
−14 −7154
−7.73 −2971
179 6
97 2
W1- section modulus [mm3/mm].
The comparison of the analytical solutions (Sundquist-Pettersson [20], CHBDC [12] methods and CSPI [24]) and the numerical approach allows to formulate the following notes:
It should be added that for the CSP shell as a whole, the stresses obtained using FEM calculations were much smaller than those from analytical methods. The latter allow to calculate the maximum stresses but without determining where they occur. In the case of FEM, the locations of the maximum values can be accurately defined (in this case, these were on the side walls of the shell, at the support). A comparison of these values therefore gives only a general view of the load-carrying capacity of the CSP shell.
• the CHBDC standard gives values that are closer to the FEM results than the Sundquist-Pettersson method, • the bending moments and axial forces obtained using FEM (models I •
5.7.3. Displacements The maximum design displacement is determined as the allowable vertical displacement of the bridge, which should not exceed the value calculated based on the following conditions:
•
• 0.5% of the bridge span, i.e. in this case, ∼88 mm (CHBDC [12]); • 2% of the bridge span, i.e. ∼ 353 mm (Corrugated Steel Plate
and II) were significantly smaller than those from the analytical methods, significant differences between the stresses calculated using analytical methods and FEM were also observed. The analytical values were much smaller than those from FEM, although over the whole shell, the trend was opposite. This shows that there is a need for further improvement in design methods, especially in terms of load distribution and safety factors, regarding the shell displacement, it should be noted that the numerical values (models I and II) and measured results were much smaller than those obtained using the CHBDC and CSPI standards.
Institute [24]).
Based on a numerical analysis, the use of an analytical approach and experimental measurements of a CSP shell, it can be concluded that further studies should be carried out to develop appropriate design methods, especially for large-span soil-steel bridges (over 15 m). The primary issue is the use of additional stiffeners in the CSP shell (steel ribs and steel ribs filled with concrete).
The maximum displacements of the CSP shell obtained from numerical analysis during the backfilling process do not exceed 20.2 mm and 14.03 mm for models I and II, respectively. Thus, it can be seen that the values obtained from measurements and FEM calculations are much smaller than those obtained based on the abovementioned CHBDC [12] and CSPI standards [24]. The smallest difference in shell displacement obtained from the analytical solutions (CHBDC and CSPI) and numerical solutions was about 43%. It is therefore necessary to consider verification of the standard provisions. A direct comparison of the results obtained using analytical methods and FEM models does not give a full response to the behaviour of soil-steel bridges. In the case of FEM, each individual finite element node is analysed, while analytical methods allow to consider a particular fragment (a section 1.0 m in width) of the bridge.
References [1] Machelski C. Construction of soil-shell structures. Wroclaw: The Lower Silesian Educational Publishers; 2013. [2] Machelski C. Steel plate curvatures of soil-steel structures during construction and exploitation. Roads and Bridges - Drogi i Mosty 2016;15(3):207–20. [3] Janusz L, Madaj A. Engineering structures from corrugated plates. Design and construction. Warsaw: Transport and Communication Publishers; 2009. [4] Pittino G, Gosler J. Structural plate steel underpasses during backfilling - how to minimize the bending moment. In: Varona P, Hart RD, editors. 4th International FLAC symposium on numerical modeling in geomechanics. Madrid; 2006. p. 5–10. [5] Manko Z, Beben D. Research on steel shell of a road bridge made of corrugated plates during backfilling. J Bridge Eng 2005;10(5):592–603. [6] Koruszewicz L, Kunecki B. Behaviour of steel box-type culvert during backfilling. Arch Civ Mech Eng 2011;11(3):637–50. [7] Sanaeiha A, Rahimian M, Marefat SM. Field test of a large-span soil-steel bridge stiffened by concrete rings during backfilling. J Bridge Eng 2017;22(10). [8] Beben D. The role of backfill quality on corrugated steel plate culvert behaviour. Baltic J Road Bridge Eng 2017;12(1):1–11. [9] Beben D, Stryczek A. Numerical analysis of corrugated steel plate bridge with reinforced concrete relieving slab. J Civ Eng Manag 2016;22(5):585–96. [10] Meguid MA, Hussein MG, Ahmed MR, Omeman Z, Whalen J. Investigation of soilgeosynthetic-structure interaction associated with induced trench installation. J Geotext Geomemb 2017;45:320–30. [11] Elshimi TM, Mak AC, Brachman RWI, Moore ID. Behaviour of a deep-corrugated large-span box culvert during backfilling. In: Gibson group association management. Pan-American conference on teaching and learning of geotechnical engineering. Toronto; 2011. [12] CHBDC. Canadian highway bridge design code. CAN/CSA-S6-06, Canadian Standards Association International. Mississauga, Ontario; 2006. [13] Bayoglu Flener E. Soil-steel interaction of long-span box culverts-performance during backfilling. J Geotech Geoenviron Eng 2010;136:823–32. [14] Brachman RWI, Elshimi AC. Testing and analysis of a deep-corrugated large-span box culvert prior to burial. J Bridge Eng 2012;17:81–8. [15] Taleb B, Moore ID. Metal culvert response to earth loading. Performance of twodimensional analysis. Transportation Res Rec. J Transp Res Board 1999;1656:25–36.
6. Conclusions As a result of both numerical analysis and measurements, it can be concluded that the additional stiffening elements (steel ribs and steel ribs filled with concrete) of the CSP shell in a soil-steel bridge primarily affect the displacement and internal forces. The additional stiffening has the following effects:
• a reduction of the maximum displacement of the CSP shell. In the • • •
case of FEM calculations, the displacement of the shell in model III was −9.32 mm, approximately 54% and 34% lower than in models I and II, respectively, a reduction in the stresses on the CSP shell, and in particular the shear stress. The value is about 44% lower in model III than in model I, a reduction in the bending moments by about 43% and 56% for models II and III, respectively, a reduction in the axial forces of 44% for model III compared to model I.
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[20] Pettersson L, Sundquist H. Design of soil-steel composite bridges. Royal Institute of Technology. Stockholm: TRITA-BKN; 2014. p. 112. [21] Beben D, Manko Z. Dynamic testing of a soil-steel bridge. Struct Eng Mech 2010;35(3):301–14. [22] DIANA FEA. 2017. Available online from URL: www.dianafea.com/. [23] EC 1992-1-1. Design of concrete structures. General rules and rules for buildings. European Committee for Standardization. Brussels; 2008. [24] CSPI. Handbook of steel drainage & highway construction products. American Iron and Steel Institute, Corrugated Steel Plate Institute. Canadian Edition. Ontario; 2007.
[16] Beben D. Numerical study of performance of soil-steel bridge during soil backfilling. Struct Eng Mech 2012;42(4):571–87. [17] Kunecki B. Field test and three-dimensional numerical analysis of soil-steel tunnel during backfilling. J Transp Res Board 2014;2462:55–60. [18] Maleska T, Beben D. Study on soil-steel bridge response during backfilling. In: Powers N, Frangopol DM, Al-Mahaidi R, Caprani C, editors. 9th International conference on bridge maintenance, safety and management. Melbourne; 2018. p. 548–54. [19] Borana L, Yin JH, Signh DN, Shukla SK. Influence of Matric Suction and Counter face Roughness on Shearing Behavior of Completely Decomposed Granit Soil and Steel Interface. J Indian Geotech 2017;47(2):150–60.
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Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Numerical analysis of a soil-steel bridge during backfilling using various shell models Tomasz Maleska, Damian Beben
T
⁎
Faculty of Civil Engineering and Architecture, Opole University of Technology, Katowicka 48, 46-061 Opole, Poland
A R T I C LE I N FO
A B S T R A C T
Keywords: Backfilling Soil-steel bridge Corrugated steel plate Steel ribs Shell model Stiffening
Soil-steel bridges are becoming increasingly popular in various parts of the world, and are often built with a span of 3–25 m. Those with a span greater than 12 m are usually equipped with additional stiffening elements, e.g. ribs, relieving slabs, longitudinal beams, steel ribs and steel ribs filled with concrete. This paper examines the necessity of using these additional stiffening elements, using the example of a soil-steel bridge with a span of over 17 m. Stiffening steel ribs filled with concrete were used in this bridge, and the behaviour of the corrugated steel shell of the bridge was then analysed under backfilling loads. The DIANA program with the finite element method was used for the numerical analysis. The maximum displacements, bending moments and axial forces for the three numerical models of corrugated steel shell were considered, and the displacements obtained from numerical calculations were compared with measured results. In addition, the bending moments and axial forces obtained using finite element analysis were compared with results based on the relevant standards and design methods.
1. Introduction Soil-steel bridges consisting of a corrugated steel plate (CSP) and backfill have been used for many years to build transportation structures around the world. In Europe, this type of structure began to become more popular in the 1980s, and the subsequent years saw a rapid growth in further investments based on the use of CSPs. The reasons for such a rapid increase in the number of structures involving a CSP include (i) the simplicity of construction; (ii) their relatively low construction costs; (iii) the short construction period; and (iv) the low expenditure related to maintenance of the object. Soil-steel bridges usually have a span in the range 3–25 m, and are used to construct bridges, culverts, railway passes, etc. Currently, a soil-steel bridge with a span of 32.5 m was built in the United Arab Emirates, and this is the world’s largest span for this type of bridge structure. During the construction process and service period of such a large soil-steel bridge, new problems may arise that have not previously been identified. The durability of soil-steel bridges determines the resistance of the steel to corrosion, the backfill quality and the soil-structure interaction. Due to the nature of the behaviour of soil-steel bridges, recognised procedures for their design and for the selection and execution of the backfill are very important for the safe operation of the entire structure. This is especially true during the backfilling process (compaction of the backfill). Suitable characteristics of the backfill, such as its density ⁎
index, aggregate grain size, density intensity, the thickness of the compacted layers, backfill range, type of soil and soil cover height, are basic elements that affect the strength of soil-steel bridges. The following factors also need to be checked: (i) the weight of the construction equipment near the structure; (ii) the size of the structural deformations during backfilling; and (iii) tightening of the connecting bolts. Strict observance to the technological regime and control over the construction processes are required, as is the application of appropriate enforcement procedures. Even a well designed structure can be damaged as a result of an incorrect compaction procedure (Fig. 1a), the use of unsuitable backfill, lack of appropriate equipment, or lack of control over the structure during backfilling [1–3]. Thus far, several attempts have been made to analyse the impact of backfilling on soil-steel bridges [4,5]. It has been found that during backfilling, the displacements and bending moments are relatively high, especially in the initial layers of backfilling of the CSP structure. Koruszewicz and Kunecki [6] analysed the backfill densities under laboratory conditions and the results obtained were compared with numerical results. The difference between the experimental and numerical results was at the level of 16%, which can be considered an acceptable error. Sanaeiha et al. [7] presented a field test of a soil-steel bridge during backfilling. Their case study involved a CSP that was stiffened by concrete rings, and test results showed that both the maximum
Corresponding author. E-mail addresses: [email protected] (T. Maleska), [email protected] (D. Beben).
https://doi.org/10.1016/j.engstruct.2019.109358 Received 3 January 2019; Received in revised form 24 June 2019; Accepted 28 June 2019 0141-0296/ © 2019 Elsevier Ltd. All rights reserved.
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and for strains 13%). The highest discrepancies, reaching 40%, occurred in the bending moments. Numerical 2D studies of soil-steel bridges during backfilling have also been presented by Taleb and Moore [15], Beben [16] and Kunecki [17]. The results were reasonable, although they did not describe the behaviour of the entire bridge structure. Maleska and Beben [18] analysed the impact of backfill on the shell of a soil-steel bridge, using a corrugated shell that was modelled using orthotropic characteristics. Finite element method (FEM) results obtained using DIANA software were compared with measured ones. A special function of the DIANA FEA program to model the interface (Coulomb friction) was used, which allowed the authors to better describe the interaction between two different materials (steel and backfill). Borana et al. [19] also analysed the importance of this problem, in which the impact of the roughness of particular materials on the values of shear forces was examined. Some design methods, such as those of Sundquist-Pettersson [20] and the Canadian Highway Bridge Design Code (CHBDC) [12], also allow calculation of the maximum internal forces in these structures during the backfilling process. However, these methods give appropriate results only for bridges with small spans of up to 8.0 m. Soil-steel bridges with a span of over 12 m are usually equipped with additional stiffening elements, e.g. ribs, relieving slabs, longitudinal beams, steel ribs filled with concrete, etc. In most cases, the use of these additional stiffening elements is required by regulations published in the patents of these structural solutions, although there are some examples of small bridges where the designer did not foresee the need for stiffening and the contractor for the construction works was forced to apply them [21]. This stiffening causes a significant increase in construction costs, and the question therefore arises of whether the use of additional stiffening is necessary from the point of view of the safety of the soil-steel structure. This paper shows this problem using the example of a soil-steel bridge (Fig. 1b) with a large span (over 17 m), where stiffening ribs were used and were also filled with concrete. Three different models of a corrugated steel shell were analysed: without stiffening ribs (model I), with steel ribs (model II) and with steel ribs filled with concrete (model III). The maximum displacements, bending moments, axial forces and stresses during the backfilling process are presented for these three numerical models. The numerically calculated displacements are compared with measured values, and the bending moments and axial forces obtained from numerical calculations are compared with results from standards and design methods (the Sundquist-Pettersson method [20] and CHBDC [12]). This study can aid in the design and construction of large soil-steel bridges, and the results presented here can form the basis for large financial savings (due to a reduced consumption of steel and concrete).
Fig. 1. Front view of soil-steel bridge: (a) shell dislocation resulting from improper backfilling; (b) shell during correct backfilling.
deflection and the maximum bending moment occurred at the crown, at the point where the soil reached the crown level. Conversely, the maximum axial force occurred at the bottom of the arch where the soil reached its maximum level above the arch. The influence of the backfill quality and the use of RC relieving slab on soil-steel bridges were analysed by Beben [8] and Beben and Stryczek [9], respectively, while Meguid et al. [10] examined the effect of soil pressure on the side walls of the box-culvert. In order to reduce the soil pressure on the sidewalls, expanded polystyrene was used. The design of this type of bridge structure has also been verified using the relevant standards, and various soil cover heights (in the range 0.45–1.5 m) were considered [11]. Significant differences in the bending moments of up to 70% were observed between values obtained using the Canadian standard [12] and measured results. These results were also compared with values obtained using finite element analysis (FEA), and the difference was found to be a few percent. Bayoglu Flener [13] analysed the Canadian standard in comparison with FEA, where the backfill height over the shell crown was in the range 2.5–4.08 m. Significant discrepancies were observed that reached more than 50%. Brachaman and Elshimi [14] investigated the influence of the CSP modelling types (orthotropic and corrugated), and their results were compared to measured values. They showed that the difference between the simplified model (an orthotropic steel plate) and the results obtained in the tests was a few percent (for displacements, this was 4%,
2. Short description of the soil-steel bridge The soil-steel bridge analysed acts as an overpass for animals, and is located in Trzebaw, Poland over National Road no. 5 in Wielkopolski National Park. This soil-steel bridge is one of the largest object of this type in Europe. The load-carrying structure was constructed as a shell assembled from CSPs. The shell structure has a span of 17.67 m and a vertical height of 6.05 m (Fig. 2). The length of the shell structure at the top is 40.39 m, while that of the lower part of the structure is 53.83 m. The predicted depth of soil cover at the shell crown is 1.80 m, which makes it possible to plant various types of vegetation. This backfill depth also results in effective damping of the shell structure and a reduction of the noise level from the vehicles travelling under the bridge. The shell structure was made from CSP with depth of 0.14 m, a pitch of 0.38 m and a plate thickness of 0.007 m (Fig. 3a). The CSP sheets were joined together on the span using high-strength bolts. The CSP shell was reinforced using additional ribs of the same corrugated plates, with an axial spacing of 1.524 m (Fig. 3b). Additional steel ribs consisted of two waves over the entire length of the bridge (Figs. 2a and 2
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Fig. 2. The analysed soil-steel bridge: (a) longitudinal section; (b) cross section.
Fig. 3. Analysed models: (a) model I (shell made of CSPs); (b) model II (shell made of CSPs with additional CSP ribs); (c) model III (shell made of CSPs with CSP ribs and filling with C25/30 concrete). 3
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Table 1 Weight and thickness of backfill layers used for numerical analyses and tests. Number of backfill layers
Thickness* (m)
Weight (kN/m2)
1 2 3 4 5 6
2.82 4.21 5.20 6.16 6.96 7.46
57.8 86.3 106.6 126.3 142.7 153.0
* Thickness of backfill is counted from top level of foundation (please see Fig. 2b).
•
•
Fig. 4. A view of additional stiffeners of CSP shell: (a) during backfilling process; (b) bridge model in the DIANA program.
•
4b). The interior of the ribs was filled with a C25/30 concrete mix without bars (Fig. 3c). The stiffening was applied to the entire shell circuit, in order to ensure a higher transversal rigidity of the bridge span. The assembled shell structure was backfilled with layers of soil of thickness between 0.2 and 0.3 m, which were then compacted (ID = 0.97). Both ends of the shell structure (the inlet and outlet sides) were secured and reinforced using RC collars with dimensions of 0.40 × 0.60 m. The collars were made with a C25/30 concrete mix. The CSP structure was based on two massive footings with a base width of 4.00 m and a length of 57.83 m, made of C30/37 concrete. The basic dimensions of the soil-steel bridge are shown in Fig. 2.
• •
3. Numerical modelling
plate thicknesses of both the shell and ribs were was 0.007 m. The steel shell and additional stiffeners (ribs) were modelled as corrugated. The backfill was modelled as solid elements (TE12L) using the Duncan-Chang nonlinear elastic hyperbolic model. The backfill parameters were a Poisson’s ratio of 0.2, dilation angle 5°, angle of internal friction 39°, cohesion 3 kPa, failure ratio 0.7, unloadingreloading stiffness 1000 N/m2, reference pressure 101350 N/m2, exponent for the unloading-reloading curve 0.25, exponent for the backbone curve 1.1, minimum compressive stress 350 N/m2, and minimum tangential stiffness of the backbone curve 1200 N/m3. Table 1 and Fig. 2b present the thicknesses and weight of the backfill for the numerical analyses and field measurements conducted here. The C25/30 concrete used for filling the additional stiffeners (ribs) was modelled as solid elements (TE12L) according to EC 1992-1-1 [23]. The parameters for the concrete were a Poisson’s ratio of 0.2, characteristic cylinder compressive strength 25 MPa, mean compressive strength 33 MPa, mean tensile strength 2.56 MPa, elastic modulus 31476 MPa, design compressive strength 16.67 MPa (for αcc = 1.00), design compressive strength 14.17 MPa (for αcc = 0.85), design tensile strength 1.20 MPa (for αct = 1.00), minimum longitudinal tension reinforcement ratio 0.133%, and minimum shear reinforcement ratio 0.08%. The connection between the backfill and shell steel was modelled as an automatic interface using a “Coulomb friction” function with angle of internal friction 39°, dilation angle 5°, rigidity 100,000 kN/ m3, and cohesion 3 kPa. The connection between the steel ribs and filling concrete was modelled as a fixed connection, i.e. an interface function was not used. The boundary conditions were modelled as hinged supports for the base of the bridge model (foundations and backfill) in the x, y, z directions. The outlet and inlet of the steel shell were also modelled as hinged supports in the x, y, z directions (Fig. 5a). The finite elements were modelled as triangular elements with maximum dimensions of 0.50 × 0.50 m for backfill, CSP shell and concrete. In the contact areas between the steel shell and the backfill, and in the places where maximum values are expected (crown, haunches), the finite element mesh was denser (Fig. 5b).
Numerical analyses were conducted for three types of shell structure: (i) a CSP shell with no reinforcements (Fig. 3a); (ii) a CSP shell with additional CSP ribs (Fig. 3b); and (iii) a CSP shell with additional CSP ribs filled with C25/30 concrete (Fig. 3c).
The DIANA software program [22], based on FEM, was used for numerical analysis of the soil-steel bridge. The bridge was modelled as a 3D object, using curved shell elements for the shell structure and solid elements for the soil (backfill) medium, as follows:
• The corrugated steel plates (primary steel shell and additional stif-
4. Experimental testing
feners (ribs) – Fig. 4a) were modelled (Fig. 4b) as curved shell elements (T15SH) with a Young’s modulus of 205 GPa, a Poisson’s ratio 0.3, an elastic-plastic model with a density of 7850 kg/m2, a yield strength of steel of 235 MPa. Values for the moment of inertia of 21897.45 mm4/mm and 28736.81 mm4/mm, and for the cross-sectional area of 8.867 mm2/mm and 11.64 mm2/mm were used for the primary shell and the shell with additional ribs, respectively. The
Four Leica self-levelling levels with a reading accuracy of 0.01 m were used for the displacement measurements of the shell structure during backfilling. Due to the relatively long shell structure (about 60 m), four measuring stations were set up (Fig. 6). This approach allowed at least two independent measuring instruments to be controlled at each measuring point. 4
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Fig. 5. Numerical model of a soil-steel bridge in DIANA: (a) division into six backfill layers; (b) FE mesh.
Three transverse cross sections and four longitudinal cross sections were selected to provide accurate information about the displacements of the CSP shell structure (Fig. 6). Measurement points were stabilised from the bottom of the shell structure to allow the exact measurements to be made. Measurements of the height network of benchmarks # 101, 102, 103 and 104 were performed by geometric levelling in the main and return directions. An assessment of the constancy of the benchmarks was also conducted. Displacement and strain measurements were made between 6 pm and 10 pm (i.e. after completion of all building work on the facility) to obtain the actual deformation of the shell structure after a full day of loading and compacting of the backfill around the structure. The testing was started with the output measurements, i.e. an analysis of the state of the structure before loading (without backfill) to obtain the so-called measurement base (comparative). The vertical displacements of the examined points were calculated on the basis of changes in altitude differences. Fig. 6. Location of measurement points and testing sections.
5. Results analysis backfill on the CSP shell, modelled using three variants. It should be added that (−) or (+) for displacements mean move down or up the CSP shell, respectively. In the case of stresses, bending moments and axial forces, (−) or (+) mean compressive or tensile values in the CSP shell, respectively.
5.1. General remarks It is very important to implement the backfill correctly in order to ensure a proper connection and interaction with the CSP shell. In extreme cases, improper execution of the backfill can lead to damage or destruction of the CSP shell. It is worth noting that the load due to the backfill compacted around the CSP shell and the technological loads are the first that need to be transferred by the structure during backfilling. This paper does not analyse the impact of technological loads (the effects of compaction equipment), and focuses on the influence of the
5.2. Displacements The largest displacements for the shell models analysed here were observed in model I (Fig. 7a), and were equal to −20.20 mm. For model II (Figs. 7b and 8), the displacements were lower, about 30% less than 5
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Fig. 7. Maximum displacements of the CSP shell in: (a) model I; (b) model II; (c) model III.
in model I, and were −14.03 mm. However, the smallest displacement was obtained for model III (Fig. 7c), where the value was −9.32 mm, constituting about 46% of that for model I. The maximum displacements for shell models (I, II and III) were directed downwards, and these were obtained for the six backfill layers (i.e. the CSP shell was already completely backfilled, and the soil cover above the shell was 1.80 m). In addition, the maximum displacements for the shell models occurred in the same places, that is, at the shell crown. It should be emphasised that despite the visible differences in displacements for the different shell models, the maximum displacements for model I were relatively small, and did not pose a threat to the safety of the bridge (either in the construction process or the later service period). It should be noted that the CSP shell does not always shift downwards, and this can be seen in the different shell models. In model II, the maximum displacements were equal to −1.3 mm and −0.62 mm during compacting of backfill layers #1 and 2, respectively. In this case, the CSP shell lifted upwards by 0.68 mm, i.e. by 48% in relation to the displacement caused by backfill #1. For the next backfill layers, successive deflections of the CSP shell were observed, as shown in Fig. 8. A change in the character of the displacements could also be seen at around 2/3 of the height of the shell. Based on the displacement results shown in Fig. 9, it can be seen that during compacting of the first backfill layers (#1–3), the shell displacements in models I, II and III are relatively similar to each other. However, when comparing the calculated values with the measured ones, a slightly different behaviour of the CSP shell (layer #1) was noticed. It is noticeable that the shell is lifted up, contrary to the numerical results. This may be the result of the impact of the compaction machines. In the numerical models (I, II, III), the steel shell always deflects downwards. Fig. 9 also shows the impact of the additional stiffeners used in the construction of the soil-steel bridge. The maximum displacements obtained from the numerical calculations (different shell models) are generally smaller than the values measured at the construction site (Fig. 9). The measurements were
conducted for the CSP shell with stiffening that only uses additional ribs (numerical model II). This is because the ribs were filled with concrete when the shell was completely backfilled. The maximum measured displacement for the soil-steel bridge was −29 mm, a value about 44% higher than that in model I, 107% higher than in model II and 211% than in model III. In a similar way to the numerical models, the maximum displacements occurred at the shell crown, and were recorded during the compaction of the fifth backfill layer. 5.3. Stresses The highest stresses in the shell of the soil-steel bridge were observed for model II, and reached −178 MPa (Fig. 10b). These stresses were compressive, and were 8% greater than the stress in model I, which reached −165 MPa (Fig. 10a). The smallest compression stresses were obtained for model III, and had a value of −100 MPa (Fig. 10c). This constitutes approximately 43% of the maximum stresses in model II. The maximum stresses were observed in the Szz direction (Fig. 10). It is worth noting that these occurred near the connection between the CSP shell and the foundation. It should also be noted that in most parts of the shell (and especially around the shell crown, e.g. in model II), the stresses in the shell were significantly lower (Fig. 11) and were at the level of −10 MPa, about 5% of the maximum stress for this model. The stresses in the steel shell for numerical models I and III typically did not exceed −20 MPa and −15 MPa, respectively. The most significant stresses were obtained during backfilling of soil layers #4, 5 and 6 (Fig. 11). Initial compaction of the backfill around the steel shell (layers #1–3) caused much lower stresses for certain shell models. In model I, the maximum stresses during backfilling of the first three layers ranged from −8 MPa (#1) to −39 MPa (# 3), that is, between 5% and 24% of the maximum stresses in model I (−165 MPa). However, in the case of model II, the influence of the first backfill layers (#1–3) caused stresses in the CSP shell of between −11.5 MPa (#1) and −33 MPa (#3). In model III, the stresses in the steel shell ranged from −11 MPa (#1) to −21.5 MPa (#3). It should be pointed out that all of 6
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Fig. 8. Maximum displacement of the CSP shell for each backfill layer in model II.
addition, slightly higher bending moments can be observed at the shell crown in all three models. Fig. 14 presents the distribution of bending moments in the CSP shell of the bridge. As in the case of stresses and displacements, there are no significant differences in the bending moments at the shell when backfilling the initial backfill layers (#1–3). However, the variable nature of the bending moments caused by the compaction of backfill layer #2 was observed, in which the moments changed from compressive to tension (model III). While compacting the other backfill layers, the differences between the numerical models start to become more apparent, but the overall level of the bending moment is small. It can therefore be concluded that there are no significant advantages to the use of additional CSP shell stiffening. 5.5. Axial forces Fig. 9. Maximum displacements of the CSP shell for each backfill layer, obtained from numerical models and measurements.
The largest axial forces in the CSP shell of the soil-steel bridge were noted for the II model, and amounted to −1256 kN/m (Fig. 15b). This value was slightly higher (about 5%) than the axial force obtained for model I, which was −1201 kN/m (Fig. 15a). In model III, the maximum axial force was −696 kN/m (Fig. 15c), which was 44% less than the value in model II. In all of the models, the axial forces were compressive and occurred at the CSP shell near the foundation. In the other parts of the CSP shell, the axial forces were much smaller (Fig. 15). In the same way as for the stresses and bending moments, the most important axial forces were obtained during the compaction of backfill layers #4, 5 and 6 (Fig. 16). However, the initial backfilling of the soil (layers #1–3) caused significantly lower axial forces in the shell for particular models. The influence of the stiffeners in the CSP shell is well illustrated in Fig. 17, which shows that the first two backfill layers cause almost identical axial forces. Compaction of the successive backfill layers causes increasingly large differences in axial forces. However, it should also be noted that the axial forces in models I and II differ slightly. Therefore, the use of stiffener ribs does not affect the reduction in the axial forces on the CSP shell.
the maximum stresses for particular shell models were compressive. The stresses resulting from compaction of the first backfill layers can be considered relatively small in relation to the maximum stresses obtained in the particular numerical models. Fig. 12 shows the course of the maximum stresses obtained in the numerical models. It should be noted that the stiffeners used in the bridge structure influenced the obtained stresses, and that during compaction of the first two backfill layers, the stresses were very similar for all three numerical models. Larger differences were only visible during compaction of the subsequent backfill layers. In addition, it is very important to note that the use of stiffening ribs (model II) does not reduce the stress in the shell (model I). 5.4. Bending moments The bending moments in the CSP shell were relatively small. The highest value was obtained for model I (Fig. 13a), and was −0.14 kNm/m. For the other shell models, the bending moments were −0.0795 kNm/m (Fig. 13b) for model II (57% of the value for model I) and −0.0612 kNm/m (Fig. 13c) for model III (44% of the value for model I). The maximum bending moments were obtained near the shell support, at the foundation, and occurred during backfilling of the last backfill layer (#6). In the remaining parts of the CSP shell, the bending moments were significantly lower for all the analysed models (Fig. 13). The initial compaction of the backfill (layers #1–3) resulted in much lower bending moments in the CSP shell than the backfilling of layers #4–6. These values were found above the shell support at around 1/6 (model III), 1/5 (model II) and 1/4 (model I) of the CSP shell height. In
5.6. Summary of numerical analysis It should be clearly emphasised that in the case of model I (without any additional stiffening) the allowable stresses and displacements were not exceeded, i.e. the CSP shell is able to carry the loads due to the backfilling process. In addition, the steel ribs do not offer significant advantages in terms of reducing the response of the shell, and even causes stresses to increase (model II + 8%) in relation to the model without the steel ribs. Moreover, the use of steel ribs filled with concrete is hazardous (model III), since during the use of the bridge, there is a risk of damage 7
Engineering Structures 196 (2019) 109358
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Fig. 10. Maximum stresses of CSP structure in numerical models: (a) I; (b) II; (c) III.
shell in the form of steel ribs (model II). The results are shown in Table 2. The values obtained using the Sundquist-Pettersson analytical method [20] and the CHBDC standard [12] differ significantly from the values calculated using the DIANA numerical program. The largest differences were observed in bending moments for model II. In this case, the moments calculated using the Sundquist-Pettersson method [20] are 179 times greater than those derived from FEM calculations. In contrast, the bending moments obtained with the CHBDC standard [12] are 97 times larger than those obtained from the numerical model. For model I, where the CSP shell was not stiffened with steel ribs, the moments calculated using the Sundquist-Pettersson method [20] are almost 102 times larger than those obtained from the FEM calculations. In turn, the bending moments obtained with the CHBDC standard [12] are 62 times higher than those of the numerical model. In the case of the axial forces, smaller differences were found between the analytical approach and FEM models. The axial forces for
to the concrete in the ribs as a result of cyclic loading and unloading of the structure. The standards do not indicate how to apply these additional steel ribs filled with concrete. However, the most important issue is the fact that the use of additional stiffening elements significantly increases the cost of the construction process of soil-steel bridges, and the advantages gained in terms of a higher bearing capacity of the bridge are not necessary from a practical point of view. 5.7. Analytical solution 5.7.1. Bending moments and axial forces The results obtained from numerical analysis were compared with the results of analytical methods, i.e. the Sundquist-Pettersson method [20] and the CHBDC [12]. These methods are intended to dimension the structures of the so-called Super-Span, an object with a large span. Verification was carried out for shell models I and II, which used the CSP shell without stiffening (model I) and with strengthening of the
Fig. 11. Maximum stresses on the CSP shell for each backfill layer in model II. 8
Engineering Structures 196 (2019) 109358
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Fig. 14. Maximum bending moments of the CSP shell for each backfill layer, obtained from numerical analyses.
[12,20]. In addition, it is relatively difficult to correctly image the interaction between the backfill and CSP shell in the analytical methods; they also use an imaginary cross section of the bridge for the calculation. In the case of 3D numerical calculations, the spatial response of the whole bridge is obtained.
Fig. 12. Maximum stresses on the CSP shell for each backfill layer.
model II calculated using the Sundquist-Pettersson method [20] are almost six times larger than those obtained from calculations using the DIANA FEA program. However, in the case of the CHBDC standard [12], the axial forces were slightly more than twice as great as those calculated using the Sundquist-Pettersson method [20]. Larger differences were observed for model I, where the axial forces computed based on the Sundquist-Pettersson method [20] were six times larger than those obtained in the numerical model. However, in the case of CHBDC [12], the axial forces were over three times higher than those calculated using the Sundquist-Pettersson analytical method [20]. This shows that the CHBDC [12] standard allows to obtain more reasonable bending moments and axial forces than those computed using the Sundquist-Pettersson method [20]. Such large differences in bending moments and axial forces indicate a conservative approach to the calculation of internal forces in these bridges, and the use of relatively high safety factors and arching factor in the analytical methods
5.7.2. Stresses The stresses obtained from numerical models I and II were compared with results that were previously calculated using the SundquistPettersson [20] and CHBDC methods [12]. The bending moments and axial forces were substituted into the Navier Eq. (1). The axial forces and bending moments in equation (1) can be positive or negative depending on the side of the cross-section or the loading/moment direction. In model I, stresses of −81 and −45 MPa were obtained using the Sundquist-Pettersson [20] and CHBDC methods [12], respectively. The calculated stresses were significantly smaller than those obtained using the numerical approach (−165 MPa). The relative differences between the numerically calculated values and those obtained based on
Fig. 13. Maximum bending moment of the CSP shell for models: (a) I; (b) II; (c) III. 9
Engineering Structures 196 (2019) 109358
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Fig. 15. Maximum axial forces on the CSP shell for numerical models: (a) I; (b) II; (c) III.
analytical methods were 51% and 73% for Sundquist-Pettersson [20] and CHBDC [12], respectively. A similar situation occurred in the case of model II, where the stresses were equal to −61 and −26 MPa using the Sundquist-Pettersson [20] and CHBDC methods [12], respectively. The obtained stresses were also significantly lower than those obtained from numerical computations (−178 MPa). The relative differences between the numerical values and those obtained using analytical methods were 65% and 86% for Sundquist-Pettersson [20] and CHBDC [12], respectively.
σ=
Nd, s Md, s + As1 W1
(1)
σ - maximum stresses in the CSP shell [MPa], Nd,S - axial force due to backfilling [kN/m], Md,S - bending moment due to backfilling [kNm/m], AS1 - area of the cross section of the CSP shell [m2],
Fig. 17. Influence of backfill layers on maximal axial forces in CSP shell.
Fig. 16. Maximum axial forces on the CSP structure for each layer of model II. 10
Engineering Structures 196 (2019) 109358
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Table 2 Comparing values of numerical models and analytical solutions.
Model I Bending moments [kNm/m] Axial forces [kN/m] Model II Bending moments [kNm/m] Axial forces [kN/m]
Numerical values (XCal)
Sundquist-Pettersson [20] values (XS-P)
Canadian standard [12] values (XCHBDC)
≈XS-P/XCal
≈XCHBDC/XCal
−0.14 −1201
−14 −7154
−9 −3952
102 6
62 3
−0.0795 −1256
−14 −7154
−7.73 −2971
179 6
97 2
W1- section modulus [mm3/mm].
The comparison of the analytical solutions (Sundquist-Pettersson [20], CHBDC [12] methods and CSPI [24]) and the numerical approach allows to formulate the following notes:
It should be added that for the CSP shell as a whole, the stresses obtained using FEM calculations were much smaller than those from analytical methods. The latter allow to calculate the maximum stresses but without determining where they occur. In the case of FEM, the locations of the maximum values can be accurately defined (in this case, these were on the side walls of the shell, at the support). A comparison of these values therefore gives only a general view of the load-carrying capacity of the CSP shell.
• the CHBDC standard gives values that are closer to the FEM results than the Sundquist-Pettersson method, • the bending moments and axial forces obtained using FEM (models I •
5.7.3. Displacements The maximum design displacement is determined as the allowable vertical displacement of the bridge, which should not exceed the value calculated based on the following conditions:
•
• 0.5% of the bridge span, i.e. in this case, ∼88 mm (CHBDC [12]); • 2% of the bridge span, i.e. ∼ 353 mm (Corrugated Steel Plate
and II) were significantly smaller than those from the analytical methods, significant differences between the stresses calculated using analytical methods and FEM were also observed. The analytical values were much smaller than those from FEM, although over the whole shell, the trend was opposite. This shows that there is a need for further improvement in design methods, especially in terms of load distribution and safety factors, regarding the shell displacement, it should be noted that the numerical values (models I and II) and measured results were much smaller than those obtained using the CHBDC and CSPI standards.
Institute [24]).
Based on a numerical analysis, the use of an analytical approach and experimental measurements of a CSP shell, it can be concluded that further studies should be carried out to develop appropriate design methods, especially for large-span soil-steel bridges (over 15 m). The primary issue is the use of additional stiffeners in the CSP shell (steel ribs and steel ribs filled with concrete).
The maximum displacements of the CSP shell obtained from numerical analysis during the backfilling process do not exceed 20.2 mm and 14.03 mm for models I and II, respectively. Thus, it can be seen that the values obtained from measurements and FEM calculations are much smaller than those obtained based on the abovementioned CHBDC [12] and CSPI standards [24]. The smallest difference in shell displacement obtained from the analytical solutions (CHBDC and CSPI) and numerical solutions was about 43%. It is therefore necessary to consider verification of the standard provisions. A direct comparison of the results obtained using analytical methods and FEM models does not give a full response to the behaviour of soil-steel bridges. In the case of FEM, each individual finite element node is analysed, while analytical methods allow to consider a particular fragment (a section 1.0 m in width) of the bridge.
References [1] Machelski C. Construction of soil-shell structures. Wroclaw: The Lower Silesian Educational Publishers; 2013. [2] Machelski C. Steel plate curvatures of soil-steel structures during construction and exploitation. Roads and Bridges - Drogi i Mosty 2016;15(3):207–20. [3] Janusz L, Madaj A. Engineering structures from corrugated plates. Design and construction. Warsaw: Transport and Communication Publishers; 2009. [4] Pittino G, Gosler J. Structural plate steel underpasses during backfilling - how to minimize the bending moment. In: Varona P, Hart RD, editors. 4th International FLAC symposium on numerical modeling in geomechanics. Madrid; 2006. p. 5–10. [5] Manko Z, Beben D. Research on steel shell of a road bridge made of corrugated plates during backfilling. J Bridge Eng 2005;10(5):592–603. [6] Koruszewicz L, Kunecki B. Behaviour of steel box-type culvert during backfilling. Arch Civ Mech Eng 2011;11(3):637–50. [7] Sanaeiha A, Rahimian M, Marefat SM. Field test of a large-span soil-steel bridge stiffened by concrete rings during backfilling. J Bridge Eng 2017;22(10). [8] Beben D. The role of backfill quality on corrugated steel plate culvert behaviour. Baltic J Road Bridge Eng 2017;12(1):1–11. [9] Beben D, Stryczek A. Numerical analysis of corrugated steel plate bridge with reinforced concrete relieving slab. J Civ Eng Manag 2016;22(5):585–96. [10] Meguid MA, Hussein MG, Ahmed MR, Omeman Z, Whalen J. Investigation of soilgeosynthetic-structure interaction associated with induced trench installation. J Geotext Geomemb 2017;45:320–30. [11] Elshimi TM, Mak AC, Brachman RWI, Moore ID. Behaviour of a deep-corrugated large-span box culvert during backfilling. In: Gibson group association management. Pan-American conference on teaching and learning of geotechnical engineering. Toronto; 2011. [12] CHBDC. Canadian highway bridge design code. CAN/CSA-S6-06, Canadian Standards Association International. Mississauga, Ontario; 2006. [13] Bayoglu Flener E. Soil-steel interaction of long-span box culverts-performance during backfilling. J Geotech Geoenviron Eng 2010;136:823–32. [14] Brachman RWI, Elshimi AC. Testing and analysis of a deep-corrugated large-span box culvert prior to burial. J Bridge Eng 2012;17:81–8. [15] Taleb B, Moore ID. Metal culvert response to earth loading. Performance of twodimensional analysis. Transportation Res Rec. J Transp Res Board 1999;1656:25–36.
6. Conclusions As a result of both numerical analysis and measurements, it can be concluded that the additional stiffening elements (steel ribs and steel ribs filled with concrete) of the CSP shell in a soil-steel bridge primarily affect the displacement and internal forces. The additional stiffening has the following effects:
• a reduction of the maximum displacement of the CSP shell. In the • • •
case of FEM calculations, the displacement of the shell in model III was −9.32 mm, approximately 54% and 34% lower than in models I and II, respectively, a reduction in the stresses on the CSP shell, and in particular the shear stress. The value is about 44% lower in model III than in model I, a reduction in the bending moments by about 43% and 56% for models II and III, respectively, a reduction in the axial forces of 44% for model III compared to model I.
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[20] Pettersson L, Sundquist H. Design of soil-steel composite bridges. Royal Institute of Technology. Stockholm: TRITA-BKN; 2014. p. 112. [21] Beben D, Manko Z. Dynamic testing of a soil-steel bridge. Struct Eng Mech 2010;35(3):301–14. [22] DIANA FEA. 2017. Available online from URL: www.dianafea.com/. [23] EC 1992-1-1. Design of concrete structures. General rules and rules for buildings. European Committee for Standardization. Brussels; 2008. [24] CSPI. Handbook of steel drainage & highway construction products. American Iron and Steel Institute, Corrugated Steel Plate Institute. Canadian Edition. Ontario; 2007.
[16] Beben D. Numerical study of performance of soil-steel bridge during soil backfilling. Struct Eng Mech 2012;42(4):571–87. [17] Kunecki B. Field test and three-dimensional numerical analysis of soil-steel tunnel during backfilling. J Transp Res Board 2014;2462:55–60. [18] Maleska T, Beben D. Study on soil-steel bridge response during backfilling. In: Powers N, Frangopol DM, Al-Mahaidi R, Caprani C, editors. 9th International conference on bridge maintenance, safety and management. Melbourne; 2018. p. 548–54. [19] Borana L, Yin JH, Signh DN, Shukla SK. Influence of Matric Suction and Counter face Roughness on Shearing Behavior of Completely Decomposed Granit Soil and Steel Interface. J Indian Geotech 2017;47(2):150–60.
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