An investigation was performed for live load forces applied to soil-steel structures under shallow backfill depths, specifically a long span deeply corrugated box culvert. The work was also relevant to other types of flexible buried structures and loading scenarios. The investigation involved the application of both a robust experimental testing process and the development of 3-D finite element models. Full scale live load tests, performed in Dorchester NB, were executed to obtain a large sample of experimental data. The testing program was designed specifically to fully characterize the structural response of a long span box culvert to CHBDC design truck live loads. The program included live load testing at six different backfill depths with 21 unique truck positions per lift, with instrumentation at four separate rings. The experimental data was used to assess and calibrate the finite element models being developed to predict structural effects. The finite element software package ADINA was used to model the test structure in 3-D. The basics of model development, such as element types, boundary conditions, loads, and other analysis options were discussed. An orthotropic shell modeling approach to accurately describe the corrugated plate properties was developed. A number of soil constitutive models, both linear and nonlinear, were examined and evaluated. The data obtained from experimental testing was compared to the results obtained by the finite element modeling and the various soil models were evaluated. A parametric study was performed examining the sensitivity of modeling parameters. The impact of various assumptions made regarding the model was quantitatively established. The thesis provided guidance on the 3-D modeling of soil-steel structures allowing future researchers to study the factors which were significant to their design and field applications.

This research aims to analyse the dynamic behaviour of Soil-Steel Composite Bridges when subjected by high-speed trains. the analyses of the dynamic response for these structures are needed since there is little research performed in the present field of knowledge. Since there is also in need to perform separate dynamic analysis for these structures to verify their dynamic response, the dynamic behaviour must be analysed. The research are performed in 2D FE-models in the commercial FE-program Brigade/PLUS since there is of interest to analyse if simplified 2D-models can predict the dynamic behaviour for these structures and verify against design criterions in regulatory documents. The research is performed by calibrating a reference model against collected field measurements from a constructed Soil-Steel Composite Bridge, SSCB, located in Märsta, Sweden, Märsta Bridge. The calibration process was made to ensure satisfactory results before continuing the research by analysing a future planned SSCB in a case study that is known to in the future be subjected by high-speed trains. The future planned bridge is the Björnbo Bridge located in Skutskär, Sweden. A static structural design is first made with existing methods to verify Björnbo Bridge for static load cases. Attempts is made to verify the Björnbo Bridge against dynamic criterions available in Eurocode documents and Swedish Transport Administration regulatory documents, which includes verifying accelerations limits for 10 different high-speed trains. Smaller analysis of fatigue for the Märsta Bridge and the Björnbo Bridge was also made to verify dynamic stresses from giving fatigue damages. Since the research is limited for SSCB for dynamic cases, parametric studies are performed for certain parameters identified from an international literature review of earlier studies in both static and dynamic analysis. The studied parameters are: Soil cover depth, Young's modulus for engineered backfill and different profiles impact. These parametric studies are made to be able to understand influence and sensitivities from the analysed parameters with the long-term goal to develop analysis methods and verifications for SSCB for dynamic load situations. The calibrated reference model showed that there are difficulties in calibrating acceleration levels that agrees with the field measurements from Märsta Bridge. The expected result from the analysis of the Björnbo bridge was to fulfil static structural design criterions and that the acceleration limits were below serviceability criterions for dynamic analysis according to Eurocode documents. Moreover, that the stresses did not give fatigue damages. From parametric studies, it has shown that the governing parameter is the Young's modulus for engineered backfill, which affects estimated accelerations in a fashion that was not expected in the beginning. The presumption to perform dynamic analysis with 2D FE-models has shown that all aspects that is needed to verify cannot be performed, such as bending in two directions or twisting mode shapes. Thus, there is in need to find ways to perform dynamic analysis for SSCB with efficient 3D-models. / Denna avhandling syftar till att undersöka det dynamiska beteendet hos rörbroar när dem belastas med höghastighetståg. Analyser av den dynamiska responsen för dessa konstruktioner är behövlig då det finns lite forskning som utförts inom kunskapsområdet. Då man även behöver genomföra separata dynamiska analyser för dessa konstruktioner för att verifiera  deras dynamiska beteende, så är det ett behov av att dess dynamiska beteende analyseras. Undersökningen är genomförd med FE-modeller i 2D i det kommersiella FE-programmet Brigade/PLUS då det är av intresse att analysera om förenklade 2D-modeller kan forutse det dynamiska beteendet för dessa konstruktioner och verifiera konstruktionen mot kriterier ställda i styrande dokument. Undersökningen genomförs genom att kalibrera en referens modell mot insamlade fältmätningar från en konstruerad rörbro i Märsta, Sverige, Märsta rörbro. Kalibreringsprocessen genomförs för att försäkra att godtagbara resultat erhålls innan undersökningen fortsätter med att analysera en planerad rörbro i en fallstudie som kommer belastas av höghastighetståg. Den planerade rörbron är Björnbo rörbro som skall konstrueras i Skutskär, Sverige. En statisk konstruktionsberäkning med befintliga metoder är först utförd för att erhålla dimensioner och verifiera Björnbo rörbro för ett statiskt lastfall. Därefter utförs försök att verifiera Björnbo rörbro mot dynamiska villkor tillgängliga i Eurokod och Trafikverkets styrande dokument, detta inkluderar att verifiera accelerationsnivåer för 10 olika höghastighetståg. Mindre analyser genomförs även för utmattning för Märsta rörbro och Björnbo rörbro för att verifiera den dynamiska spänningshistoriken inte orsakar utmattningsskador. Då forskningen är begränsad gällande dynamiska studier för rörbroar, så utförs även parametriska studier för parametrar identifierade från en internationell litteraturinventering av tidigare studerade fall för rörbroar gällande både statiska och dynamiska analyser. Dom studerade parametrarna är: Överfyllnadshöjd, Jordmodul för kringfyllning och olika profilers inverkan. Dessa parametriska studier är utförda för att förstå influensen och känsligheten i dessa parametrar med det långsiktiga målet att utveckla analysmetoder för att verifiera rörbroar även för dynamiska situationer. Den kalibrerade modellen visade att det var svårigheter att kalibrera in accelerationsnivåer som överensstämde med fältmätningar från Märsta rörbro. Det förväntade resultatet från Björnbo rörbro var att uppfylla statiska konstruktionsvillkor och att uppfylla accelerationskrav för bruksgränstillståndet för konstruktionen. Samt att kunna verifiera att utmattningen inte skulle utgöra ett problem. Från dom parametriska studierna så har det visat att den styrande parametern är jordmodulen för kringfyllningen, den påverkar accelerationsnivåer som inte var förväntat vid undersökningens påbörjan. Antagandet att utföra de dynamiska analyserna med 2D FE-modeller har visat att alla aspekter som ska verifierasinte kan utföras, så som böjande moment i två riktningar eller vridande mod former. Således, så finns ett behov av att finna vägar att utföra dynamiska analyser för rörbroar i effektiva 3D-modeller

Soil-steel composite bridge refers to structures where a buried flexible corrugated steel pipe works in composite action with the surrounding soil. These structures are being increasingly used in road and railway projects as an alternative to standard type bridges, e.g. short- and medium span concrete beam- and portal frame bridges. On account of their economic advantage and short and easy construction operation, soil-steel composite bridges are getting more popular as railway crossings located far from the cities at the heart of the nature. In this research, the dynamic behaviour of soil-steel composite bridges under high-speed train passages is studied. The studied case is a short span soil-steel composite railway bridge located in Märsta close to Stockholm. The behaviour of the bridge is first observed through field measurements in terms of deflections, stresses, and accelerations at several locations on the bridge. The measured responses are then analysed in order to predict the properties of the soil and steel material working in composite action. Subsequently, 2D and 3D finite element models are developed in order to simulate the behaviour of the bridge. The models are calibrated using the field measurements through several parametric studies. The 3D-model also enables estimation of the load distribution, which is found to increase at higher train speeds. An effective width to be used in 2D analyses is proposed. Finally, the response of the bridge is studied under high-speed train models according to Eurocode.

The need of exploring efficient solutions to today’s engineering problems is becoming essential in the current market development. Soil Steel composite bridges (SSCB) are considered well competitive in terms of their feasibility and constructability. The primary objective of this study is to provide a comprehensive comparison study for two known design methods of SSCB, which are the Pettersson-Sundquist design method (developed in Sweden) and the Klöppel & Glock design method (developed in Germany). Moreover, in the goal of having better behaviour understanding for SSCBs, the study also include finite element modelling (FEM) using PLAXIS 2D of three case studies and compare model results with field measurements.   The design comparison deals with the design concepts, assumptions and limitations for both design methods, where full design procedures are implemented and compared for a defined case study.   The results of the FEM analysis show rational outcome to the field measurements for structural response during backfilling and close results for ordinary loading as well. While the design comparison shows how the different approach in both design methods in limitations and design assumptions has important impact on the results, where soil failure in the Klöppel & Glock design method can be controlling the design for low heights of cover, whereas formation of crown plastic hinge is more controlling in the Pettersson-Sundquist design method. However, and in general, the Pettersson-Sundquist design method require more steel in low heights of cover while it is less demanding for higher soil covers compared to the Klöppel & Glock design method.

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 surrounding friction soil material, or 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. 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. 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 deflection, two 2D models with different properties are created in much the same way. In model 1, the full axle load is used and the soil stiffness varied, and in model 2 the soil stiffness acquired in the 3D model is used and the external load varied. The results are compared to measurement data. In 2D model 1 an efficient width of 1,46 m for the soil stiffness is used in combination with the full axle load, and in 2D model 2 an efficient width of 2,85 m is used for the external load, in combination with the soil stiffness acquired in the 3D model. 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. Recreating the accelerations and stresses in the existing bridge using finite element models is complicated, and the results reflect this. Below are shown the discrepancies between model results and measurement data for the pipe crown. The scatter in the measurement data has not been taken into consideration for this; these specific numbers are valid only for one particular train passage. For crown deflection, the 3D model shows a discrepancy of 4%, 2D model 1 5% and 2D model 2 8% compared with measurement data. For crown acceleration, in the same order, the discrepancy with measurements is 1%, 71% and 21% for maximum acceleration, and 46%, 35% and 28% for minimum acceleration. For maximum crown tensile stress, the discrepancy is 95%, 263% and 13%. For maximum crown compressive stress, the discrepancy is 70%, 16% and 46%.

Nowadays, many different efficient solutions are being studied to solve engineering problems. Inside this group of solutions we can find the Soil Steel Composite Bridges (SSCB) as an alternative to traditional bridges. SSCB are being used more often every day and they are showing themselves as competitive structures in terms of feasibility and constructability. This project was started to achieve two different goals. The first one was to create a general database of SSCB including few selected tests all around the world and the second one was to compare and discuss full scale tests using the Pettersson-Sundquist design method. To create the database and the following comparisons, twenty-five different full scale tests were used. From this tests all the necessary information was extracted and used to create the database. After creating the database, the project continued with the discussion and comparison of the full scale tests. Specifically those discussions and comparisons were related to the resistance of the soil (the soil modulus) used in the construction of the SSCB. All the values of the different soil modulus of each full scale test used in the comparisons were calculated using the Swedish Design Manual (SDM). Two different types of soil modulus were calculated in this project using SDM, ones are the soil modulus back calculated using the values reported from the live load tests performed on the culverts and the others are theoretical soil modulus calculated using the detailed information of the soil. The report continues with the explanation of the different conclusions ended up with during this project. It can be highlighted within this group of conclusions, the one related to the importance of reporting all the necessary information from the full scale tests including the soil parameters, the measures of the culvert, the cross sectional parameters and the vehicle dimensions among others. Another important conclusions are the effect of using the slabs over the top of the culvert and how it would effect to the sectional forces over the culvert and also the limitations using method B of the SDM regarding the type of soil used as backfilling Finally, the project finishes explaining some proposals for future research about other fields of the study of SSCB.

Although the construction of flexible culverts involves simplicity in comparison to similar concrete structures, the complexity of the beneficial interaction between soil and steel materials requires good understanding for their composite action and performance. Current design methods have certain validity limitations with regard to applicable slopes above the structures. Given the short construction time of flexible culverts, there is an urge to explore the feasibility and the constructability of such as cost-effective structures in sloping terrain, where they may function as an avalanche protection structure for a given road, a culvert under a ski slope, or even as a protection canopy for tunnel entrances. This report compiles the efforts carried out toward gaining knowledge about the different factors that may affect the behaviour of flexible culverts in sloping environment. The report includes an extended summary of the investigation, which is mainly presented in two appended papers. The study involved numerical simulation of three case studies to investigate their performances with regard to soil loading and avalanche loads as well. The height of cover, surface slope intensity, slope stability, soil support conditions, and avalanche proximity, were studied and discussed. The study results allowed realizing the susceptibility of flexible culverts to low heights of soil cover when built in sloping terrain, which is reflected in the deformation response and the incremental change in sectional forces, especially the bending moments. It is also found that increasing the depth of soil cover may feasibly improve the structural performance under asymmetrical soil loading and avalanche loads, where it subsequently help in reducing the bending moments in the wall conduit. The presence of a flexible culvert may affect adversely the soil stability in sloping terrain and thus need to be addressed in design. Furthermore, the flexural response of a flexible culvert is directly influenced by the soil support configuration at the downhill side of the structure. In addition, the report also attempts to highlight some general guidelines about the design aspects of flexible culverts in sloping terrain, and seeks to reflect some of the findings on the design methodology for flexible culverts used in Sweden. / <p>QC 20151130</p>

This master thesis covers the dynamic soil structure interaction of soil-steel culverts applyinga methodology based on the frequency domain response. At the first stage of this masterthesis, field tests were performed on one bridge using controlled excitation. Then, themethodology followed uses previous research, the field tests, finite element models (FEM)and perfectly matched layer (PML) elements.Firstly, a 2D model of the analysed bridge, Hårestorp, was made to compare the frequencyresponse functions (FRF) with the ones obtained from the field tests. Simultaneously, a 3Dmodel of the bridge is created for the following purposes: compare it against the 2D modeland the field tests, and to implement a model updating procedure with the particle swarmalgorithm to calibrate the model parameters. Both models use PML elements, which areverified against previous solution from the literature. The verification concludes that thePML behave correctly except for extreme parameter values.In the course of this master thesis, relatively advanced computation techniques were requiredto ensure the computational feasibility of the problem with the resources available.To do that, a literature review of theoretical aspects of parallel computing was performed, aswell as the practical aspects in Comsol. Then, in collaboration with Comsol Support and thehelp given by PDC at KTH it was possible to reduce the computational time to a feasiblepoint of around two weeks for the model updating of the 3D model.The results are inconclusive, in terms of searching for a perfectly fitting model. Therefore,further research is required to adequately face the problem. Nevertheless, there are some accelerometerswhich show a considerable level of agreement. This thesis concludes to discardthe 2D models due to their incapability of facing the reality correctly, and establishes a modeloptimisation methodology using Comsol in connection with Matlab.

In this thesis, parametric studies have been performed for a soil-steel compositebridge to determine and investigate the most influential parameters on the dynamicresponse.High-speed railways are currently being planned in Sweden by the Swedish TransportAdministration with train speeds up to 320 km/h. According to the European designcodes, bridges must be verified with respect to dynamic resonance behaviour for trainspeeds exceeding 200 km/h. However, there are no guidelines or design criterion forperforming dynamic verifications of soil-steel composite bridges. The aim of thisthesis has therefore been to investigate the influence of the geometry and materialproperties of soil-steel composite bridges on their dynamic response.This thesis is based upon the frequency domain approach for dynamic analysis ofa soil-steel composite bridge using finite element software. In 2018, field measurementswere performed on a soil-steel composite bridge in Hårestorp, Sweden. Areference finite element model was developed based on previous research and wasverified against these field measurements. Parametric studies where performed byextrapolating the geometry of the reference model, focusing primarily on the crownheight, culvert span width and the location of the bedrock. Sensitivity analyses ofthe density- and stiffness of the soil was also performed.The parametric studies showed that the crown height was the most influential parameterwith respect to the amplitude of the resonance peak. Increasing it from 1 mto 3 m reduced the amplitude by approximately 70 %. An increased span width ofthe culvert was found to reduce the frequency and amplitude of the resonance peak,however increasing the stiffness of the culvert increased the resonance frequency.The position of the rock layer also reduced the amplitude of the resonance peak iflowered, likely because of lessened wave reflection. The lowest rock level investigatedshowed a significant decrease of more than 70 % in amplitude. However, the modelused to calculate this response was heavily extrapolated and thus difficult to verify.The sensitivity analyses showed that the soil density- and stiffness was negativelyand positively correlated with the resonance frequency, respectively. Additionally,the soil density lowered the amplitude of the resonance peak if increased.

Soil-steel composite bridges are for many reasons very favorable bridges to build. Up to a certain span length they are economical, practical to transport and simple and quick to build. Especially in remote places, with unfavorable sloping terrain, this can be of great interest when the transport of material can be difficult and costly. The swedish manual for design of soil steel composite bridges was presented by Lars Pettersson and Håkan Sundquist in the year 2000. It is today used in Sweden and other neighboring countries as the main manual for the design of soil-steel composite bridges. The design manual is however only valid for longitudinal slopes up to 10%, which is low in comparison to natural sloping hillsides. The purpose of this thesis is to study the structural behavior of soil steel composite bridges in sloping terrain, with the use of the finite element software PLAXIS 2D. Two case studies of one low arch culvert bridge and one pipe arch culvert are studied and later modeled in PLAXIS. The two case studies does not have sloping terrain, but are used to assure that the FEM-models behaves correctly during the backfilling process in PLAXIS. The analysis studies the change in sectional forces in the bridges during an increase inslope above the structures. The values from the FEM-models are compared to field measurements from the case studies, as well as to values calculated in accordance to the swedish design manual. This is done to see how well the different approaches compare to each other, and, since the design manual does not consider slopes exceeding 10%, it is interesting to investigate if the SDM-calculated values still appear valid for slopes larger than 10%. In addition to sectional forces, the slope stability of the FEM-models is also evaluated and compared to analytical values calculated using the ordinary method of slices. This slope stability study focuses on if the bridges affect the slope stability safety factor. The thesis also investigates if these bridges are more sensitive to increasing slopes from a slope stability or sectional forces point of view. I.e if the slope inclination magnitude will be determined based on the sectional forces in the structure or the slope stability of the soil surrounding the structure. The criteria that are researched to come to this conclusion are for example the slope stability safety factor, or the possible yielding of the culvert wall due to too large sectional forces in the structure. The results show that for low cover depths, the slope stability safety factor decreases slightly when a structure is introduced to the slope. For larger cover depths, read 3 meters or more, the slope stability seems unaffectedby the structure. The results also shows that the sectional forces in the structures compares well to both measured and calculated values for slope inclinations up to 30% for rather small cover depths, i.e 1 meter. For slopes larger than 30% the sectional forces grows and no longer reflect the measured and calculated values. However, since only two case studies are performed, these conclusions might not be valid for different profile shapes. Additionally there are indications that the low arch bridge is more sensitive to slopes than the pipearch culvert. / Rörbroar, eller “soil-steel composite bridges”, är av många anledningar fördelaktiga att bygga. Upp till en viss spännvidd är de ekonomiska, praktiska att transportera samt enkla och snabba att konstruera. Särskilt vid vissa svåråtkomliga platser, med ofördelaktigt sluttande terräng, kan det vara av stort intresse när materialtransport annars kan vara både komplicerat och kostsamt. Den svenska manualen för dimensionering av rörbroar presenterades av Lars Pettersson och Håkan Sundquiståret 2000. Manualen används idag i Sverige samt angränsande länder som den huvudsakliga dimensioneringsmanualen för rörbroar. Dock är den svenska manualen enbart giltig för lutningar upp till 10%, vilket ären låg lutning i jämförese med många naturliga sluttningar. Syftet för detta arbete är att studera det statiska beteendet hos kringfyllda rörbroar i lutande terräng,med hjälp av det finita element programmet PLAXIS 2D. Två fallstudier av dels en låg bågbro, dels en sluten kulvertbro, studeras och modelleras senare i PLAXIS. De två fallstudierna har inte sluttande terräng, men används för att säkerställa att FEM-modellerna beter sig korrekt under återfyllnadsfasen I PLAXIS. Analysen studerar förändringen av tvärsnittskrafter i broarna när sluttningen de belastas av ökar. Värdena från FEM-modellerna jämförs mot mätdata från fallstudierna, samt mot värden beräknade enligt den svenska manualen. Detta utförs för att se hur väl de olika metoderna överensstämmer med varandra, och, eftersom dimensioneringsmanualen inte tar hänsyn till lutningar överstigande 10%, är det intressant att se om deSDM-beräknade värdena fortfarande gäller för lutningar större än 10%. Utöver tvärsnittskrafter utvärderas släntstabiliteten hos FEM-modellerna, och dessa resultat jämförs sen mot analytiska värden beräknade enligt lamellmetoden, eller “the ordinary method of slices”. Släntstabilitetsstudien fokuserar på hur broarna påverkar säkerhetsfaktorn för släntstabilitet. Avhandlingen undersöker även om dessa broar är mer känsliga för ökande lutningar från en släntstabilitets- eller tvärsnittskrafts-synvinkel, dvs. om lutningens största storlek kommer att avgöras baserat på de tvärsnittskrafter som uppstår i konstruktionen eller på släntstabiliteten i marken runt konstruktionen. För att bilda oss en uppfattning om detta jämförs exempelvis säkerhetsfaktorn för släntabilitet mot ett eventuellt brott i stålprofilen orsakat av för stora tvärsnittskrafter i konstruktionen. Resultaten visar att säkerhetsfaktorn för släntstabilitet, vid liten överfyllnadshöjd över hjässan, minskar något när en bro byggs i en sluttning. För större överfyllnadshöjder, läs 3 meter och högre, verkar släntstabiliteten vara oförändrad vid introducering av en bro. Resultaten visar även att tvärsnittskrafterna i konstruktionerna överensstämmer bra både mot mätdata samt beräknade värden, för lutningar upp till 30% och små överfyllnadshöjder på exampelvis 1 meter. För lutningar större än 30% växer tvärsnittskrafterna och är inte längre jämförbara mot varken mätdata eller beräknade värden. Dock bör det tilläggas att eftersom endast två fall har studerats utförs så behöver dessa slutsatser inte gälla för andra profiltyper. Utöver detta finns indikationer på att den låga rörbron är mer känslig för en ökning i släntlutning i jämförelse mot denandra bron när det gäller tvärsnittskrafter.