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Soil-steel composite bridges
A soil-steel composite bridge is a structure comprised of corrugated steel plates, which are joined with bolted connections, enclosed in friction soil material on both sides and on the top. The corrugated plates can be assembled into different cross sectional shapes. Some typical shapes are circular sections, elliptical sections and arched sections.
Once the steel plates have been installed, on for example concrete foundation slabs if needed, granular backfill is applied on both sides. The backfill is applied in sequential steps, each step involving compaction of the soil, which is a necessity for the construction to accumulate the required bearing capacity. The bearing capacity is thus a direct result of the interaction between the steel plates of the pipe and the friction soil surrounding it, and is also dependent upon the fill height at the crown of the conduit and the thickness of the plate itself [1]. As the structure is loaded, the deformation of the steel section is checked by the soil through the development of earth pressure as the steel is pressed against the backfill.
Soil-steel composite bridges are an attractive option as compared with other more customary bridge types owing to the lower construction time and building cost involved. This is particularly true in cases where gaps in the form of minor watercourses, roads or railways must be bridged [2]. One example demonstrating the relative ease with which this type of structure is assembled is the soil-steel composite bridge that transverses the stream Skivarpsån in southern Sweden [3]. The plates were fabricated in Canada and pieced together into an arched section with a span of about 11 m on location. The process of installing the concrete footings and the culvert and subsequently applying and compacting the backfill was completed over the course of only two days. Figure 1.1 shows the bridge being installed.
Design and dynamics
Bridges are affected by dynamic loads through the passing of traffic in the form of vehicles and trains [5]. These dynamic loads affect the initial static stresses and deformations, either decreasing or increasing them. If certain conditions are met, these dynamic loads can result in a situation where they and the structure are in resonance. This means that the frequency of the excitation coincides with the natural frequency of the structure and amplifies the static stresses and deformations considerably. Other factors which can increase or decrease the static stresses and deformations are the fast frequency of loading and disparities in the load from the vehicle wheels caused for instance by flaws in the track or vehicle itself.
How the structure reacts when exposed to a dynamic load is affected by many factors [5]. Some of these are; the mass of the structure itself, the span of the bridge, the speed at which the traffic crossing it travels at, the damping inherent to the bridge, the loads in each axle along with the number and spacing of the axles and the natural frequencies of the bridge.
The effects of the dynamic loading are taken into account in the design of railway bridges according to the Eurocodes in one of two ways. Either a static analysis is carried out and the results multiplied by a dynamic factor as defined in section 6.4.5 of EN 1991-2, or a more demanding dynamic analysis is required, as specified in section 6.4.6 of the same Eurocode.
Whether a static or a dynamic analysis is required is determined with the aid of figure 6.9 (see Figure 1.2) in section 6.4.4 of EN 1991-2.
According to the Eurocode, note one in the chart above is “Valid for simply supported bridges with only longitudinal line beam or simple plate behavior with negligible skew effects on rigid supports.”
Section 6.4.3 of EN 1991-2 states the following general design rules concerning a dynamic analysis:
• The additional load cases for the dynamic analysis shall be in accordance with 6.4.6.1.2.
• Maximum peak deck acceleration shall be checked in accordance with 6.4.6.5.
• The results of the dynamic analysis shall be compared with the results of the static analysis multiplied by the dynamic factor Φ in 6.4.5 (and if required multiplied by α in accordance with 6.3.2). The most unfavourable values of the load effects shall be used for the bridge design in accordance with 6.4.6.5.
• A check shall be carried out according to 6.4.6.6 to ensure that the additional fatigue loading at high speeds and at resonance is covered by consideration of the stresses derived from the results of the static analysis multiplied by the dynamic factor Φ.
According to EN 1991-2 6.4.6.5 the maximum permitted peak acceleration must be lower than values given in annex A2 in EN 1990 (A2.4.4.2.1). A2.4.4.1 specifies limits of deformation and vibration when designing railway bridges. Vertical deck acceleration shall be checked to avoid instability in the ballast and to avoid excessive losses in contact forces between wheel and rail. A2.4.4.2 further specifies that the peak values in bridge deck acceleration shall not exceed 3,5 m/s2 for ballasted tracks and 5 m/s2 for direct fastened tracks with track and structural elements designed for high speed traffic. Frequencies shall be considered in these checks up the greater of one of three frequencies:
• 30 Hz
• 1,5 times the frequency of the fundamental mode of vibration of the member being considered
• The frequency of the third mode of vibration of the member
Note that these are recommended values and may be otherwise defined in the National Annex.
Furthermore, it is stated in EN 1991-2 6.4.3 that:
All bridges where the Maximum Line Speed at the Site is greater than 200 km/h or where a dynamic analysis is required should be designed for characteristic values of Load Model 71 (and where required Load Model SW/0) or classified vertical loads with α ≥ 1 in accordance with 6.3.2.
And:
For passenger trains the allowances for dynamic effects in 6.4.4 to 6.4.6 are valid for Maximum Permitted Vehicle Speeds up to 350 km/h.
Furthermore, where a dynamic analysis is required, it shall according to the flow chart be performed in conformity with the specifications of EN 1991-2 6.4.6. Section 6.4.6 regulates among other things the load combinations which shall be taken into consideration. These include Load Models HSLM, which consists of the HSLM-A and HSLM-B, the twelve Train Types specified in annex D and Real Trains specified.
Due to the complex nature of the behaviour of soil-steel composite bridges when they are subjected to loading, further insight and knowledge in how to model them in finite element software is needed in order to capture the real behaviour. Such knowledge is needed in order to produce models with which reliable dynamic analyses can be performed. One important reason for this is that soil-steel composite structures operate in a way that diverges from the less complicated model of vibrating beams that is the basis for much of the norms that EN 1990 contains regarding high speed trains and dynamics [6].
Previous studies
The literature which has been read consists mainly of papers, articles and reports on full scale testing, (static and dynamic) on soil-steel composite structures, analysis of testing results and FEM-analysis of soil-steel composite bridges. In some cases only field-testing and analysis of test results have been performed, in others numerical analysis has been performed without any prior field-testing, and in some cases field-testing with subsequent numerical analysis and comparison has been done.
In [7], static and dynamic truck loading is performed on four soil-steel composite bridges with different sections (two box culverts and two pipe-arch culverts), spans and backfill heights. Dynamic amplification factors were calculated for these four culverts with two methods, with the difference in these two methods being how the static response was obtained. In the first method, the static response was a result of direct static testing, and in the second method the static response was in essence back-calculated using the dynamic response and filtering.
Several conclusions were made by Beben in this study. Dynamic response was higher than static response, and maximum response was observed in the conduit crown. Dynamic amplification factors (DAF) in the range of 1,105-1,293 for strains and 1,116-1,260 for displacements were calculated. Several important factors that influence the DAF were pointed out. Foremost among these were the culvert span, which causes higher DAFs as it increases. Also significant are crown soil cover height, the connection between the crown fill height and the culvert span, and the radii of the pipe. The dynamic tests were performed at speeds between 10 and 70 km/h, and it was noted that higher speeds yield higher DAFs, but with the maximum DAF acquired for a speed of 60 km/h. Another important conclusion was that the calculation of DAF by using the filtered dynamic response in order to calculate static response yields small errors. This is helpful in that such a method can be used in cases where it is not possible to perform static tests in an appropriate manner.
In [8], Beben models a soil-steel composite bridge with a box section located in Gimån, Sweden in FLAC 2D. Model calculations were compared with measured strains and deflections during the backfilling process and subsequent static vehicle loading. The model was created to mimic the construction process in that the backfill layers, all in all 20 layers, were added separately one at a time until the process was complete.
In [9], static loading with trucks was performed on an arc soil-steel composite bridge with a span of 10 m and a clear height of 4,02 m. Deflections and strains were measured in different points and compared to strains and deflections calculated with Cosmos/M and Robot Millenium. The measured response of the bridge was for all points lower than the calculated deflections and strains.
In [10] Kunecki and Korusiewicz perform full scale laboratory testing on a box culvert with a span of 3,55 m and a height of 1,42 m using different cover heights and load magnitudes. What they found through their testing was that the strains and displacements in the culvert were low, that the structure was very rigid and that the crown fill height had very little effect on the stiffness of the structure.
In [11], El-Sawy uses ANSYS FE-software to model two existing soil-steel culverts with the aim of comparing the results from the finite element modelling with measurement data collected by Bakht and theoretical analysis performed by Moore and Brachman for the same structures. The culverts are located in Ontario, Canada and were tested using heavy truckloads. One culvert is located in the Deux Rivieres and is circular, with a diameter of 7,77 m and a crown fill height of 2,6 m. The second culvert is located in Adelaide and has a horizontal ellipse section with a maximum width of 7,24 m and a maximum height of 4,08 m. The crown fill height is 1,35 m.
According to El-Sawy, Moore and Bachman modelled the circular culvert, which is located in the Deux Rivieres, in 2D and 3D, modelling the culvert as both orthotropic and isotropic in 3D, and using plane strain and equivalent line loads to model the truckloads in 2D. The 3D models provided results for circumferential thrust, which were in line with the behaviour shown in measurements, but with overestimated values in many locations. The results from their 2D model differed from measured data and from the results of the 3D models.
El-Sawy models the Deux Rivieres culvert in two ways, once with the actual geography and once through sweeping of a 2D mesh along the longitudinal direction of the culvert. The Adelaide culvert is modelled only by the second method. The truckloads in both cases are modelled as concentrated point loads.
Equivalent thicknesses and stiffnesses in the circumferential direction are calculated based on the bending stiffness of the steel plate. For the isotropic case, the calculated equivalent thickness and Young’s modulus was the same in the longitudinal direction of the conduit, and for the orthotropic case the equivalent Young’s modulus is calculated through equating the true axial stiffness in the longitudinal direction for the corrugated plate with the equivalent stiffness in the longitudinal direction for the orthotropic plate, which according to El-Sawy satisfies both the axial and bending longitudinal stiffness’s, as opposed to the method used by Moore and Brachman, where only the axial longitudinal stiffness was satisfied.
Both soil and culvert materials are modelled as linear elastic, with two magnitudes, 30 MPa and 80 MPa, used for the soil modulus. Conclusions were made by El-Sawy that the orthotropic conduit yields results which are more in line with measurement data than does the isotropic conduit. The isotropic conduit shows values which are too high for longitudinal thrust whereas the orthotropic conduit shows negligible values, which is more in line with real behaviour. Further conclusions were made that the soil modulus does not have very strong influence on the circumferential thrusts for the orthotropic case, whereas it has more of an effect on the isotropic conduit. In both cases, the soil modulus has a significant influence on circumferential bending moments.
Some of the literature read concerned testing and some finite element modelling and comparing of results with measurement data. In some literature both these things were done. No literature was found that dealt specifically with soil-steel composite bridges and high speed railways, other than [12] where Mellat has performed dynamic calculations for high speed trains in the FE-software Abaqus, based on the same field-testing measurements as this study. The literature read was about further understanding the behaviour of soil-steel composite bridges, in reality and in modelling, and the extension of the knowledge we have about this kind of structure; also in connection with design norms. In this study, we, the authors, try to continue on this track in order to make some small contribution.
Aim and scope
The objective of this master thesis is the modelling of an existing soil-steel composite railway bridge in Märsta, Sweden with the finite element software Plaxis. A 3D model is created and calibrated for crown deflection against measurement data collected by the Division of Structural Engineering and Bridges of the Royal Institute of Technology (KTH) in Stockholm, Sweden.
Once the 3D model is calibrated for crown deflection, two 2D models with different properties are created in much the same way. In one the full axle load is used and the soil stiffness varied using different effective widths, and in the other the soil stiffness acquired in the 3D model is used and the external load varied using different effective widths. The results are compared to measurement data.
The results from the 3D model and the 2D model are compared and commented upon.
Aside from this, parametric studies are performed in order to analyse the effect of certain input parameters upon output results, and in order to analyse influence line lengths.
The purpose of these analyses is to gain more insight in how to create a 2D model in order to capture the three-dimensional behaviour of the structure, using effective widths for the soil stiffness and for the external load. In addition, one objective is to evaluate the Plaxis software as a tool in modelling of soil-steel composite bridges, in 2D as well as 3D.
Table of contents :
1 Introduction
1.1 Soil-steel composite bridges
1.2 Design and dynamics
1.3 Previous studies
1.4 Aim and scope
1.5 Structure of the thesis
2 The soil-steel composite bridge in Märsta
2.1 Bridge location and traffic
2.2 Bridge specifications
2.3 Instrumentation and measurement
3 FE- modelling in Plaxis
3.1 About Plaxis
3.2 Model properties
3.3 Creating soil layers
3.3.1 Soil materials
3.3.2 Boreholes
3.4 Creating plates and beams
3.4.1 Creating plates in 3D
3.4.2 Creating beams in 3D
3.4.3 Creating plates in 2D
3.5 Creating interfaces
3.6 Creating point loads and load multipliers
3.6.1 3D
3.6.2 2D
3.7 Mesh
3.7.1 3D
3.7.2 2D
3.8 Staged construction
4 Results and discussion
4.1 Results from 3D-modelling
4.1.1 Influence lines
4.1.2 3D-results versus measurement data
4.1.3 The effect of soil stiffness on pipe behaviour
4.1.4 The effect of friction on pipe behaviour
4.2 Results from 2D-modelling
4.2.1 Influence lines
4.2.2 2D-results versus measurement data
4.2.3 The effect of soil stiffness on pipe behaviour, model 1
4.2.4 The effect of friction on pipe behaviour, model 1
4.2.5 The effect of load on pipe behaviour, model 2
4.3 Comparison of results from 3D and 2D-modelling
5 Conclusions and future research
5.1 Conclusions
5.2 Future research
Bibliography
