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Master s Thesis ECTS Department of Mathematical Sciences and Technology Buried Flexible Structures Modeling and Field Behavior Andrea Fæste MTech Construction and Architecture Preface Seven years

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Master s Thesis ECTS Department of Mathematical Sciences and Technology Buried Flexible Structures Modeling and Field Behavior Andrea Fæste MTech Construction and Architecture Preface Seven years in higher education has come to its end, and its time to grow up. With me I bring three good years at NTNU and four even better years at NMBU. I was lucky to get a summer job at Statens Vegvesen in 2012, which lead me into the right course and the right educational pathway. With this I deliver my final assignment, all good times must come to an end. First I would like to give tanks to my supervisor Jan Vaslestad for guidance and motivation during my work. I would like to thank the guys at Statens Vegvesen for helping me with PLAXIS 2D, especially Girum Yimer Yesuf and Murad Sani Sayd. Also a big thanks to Tor Helge Johansen which together with my supervisor brought me along on field trips to perform measurements on both the Dovre structure and Furulund bru. All gratitude to Magnhild Skattebu for teaching me the word the and proof-reading. To my mother and father for encouraging and supporting me, and for picking up the phone at 5 am. To my brother for always having my back and to my little sister for being my Baluba. Last but not least, to my fiancé Torfinn Belbo for feeding me, reading me to sleep and always bringing me morning coffee. I Abstract The future utilization of long-span buried structures requires improved theoretical understanding of the constructions. The physical dimensions are increasing and the mechanical features grow more complex. FEM modeling serves as a good tool to explore the earth pressure and the internal forces in the steel structure. The main goal of t his thesis is to investigate the reliability of FEM modeling compared to short- and long- term measurements, with a main focus on the the pressure distribution and internal forces in the steel structure. To perform the study two existing buried structures in Norway were examined; a horizontal ellipse and an arch footed in concrete. Measurements on the horizontal ellipse included earth pressure and deformation, and measurements on the arch included earth pressure, axial force and moment. The model was contrived in PLAXIS 2D based on theoretical material properties and structure geometry. The earth pressure on the steel structure will increase in a long-term perspective. It is therefore preferred that the modelled earth pressure coincide this accretion. The results show overall good correspondence. At the ellipse structure the modelled arching effect was higher than measured. Laboratory tests are required in order to achieve a more accurate soil model, thereby improving the results. The modelled axial stress was inverted from the measured axial stress. The measured axial force and moment were also higher than the modelled values. The measurements are based on five locations in the steel structure and it remains unclear whether or not they represent the total stress distribution. It is likely that the modelled values present a better estimation on the stress distribution. However, further investigation and additional measurements are necessary to investigate this assumption. The measurements on deformation suggested that peaking occurred during construction. Controlled peaking in buried structures is desired when the internal stress caused by deformation don t exceed the yield point. The modelled deformation estimated that the span increased. An alternative solution for obtaining a better estimate is to insert a line-load on each backfill layer in order to imitate the compression performed during backfill. Overall the model in PLAXIS 2D produced adequate estimations of the earth pressure and internal forces. The detailed monitoring of the construction presented in the model could prove useful in future soil-steel structures. Obtaining a representative model of the selected structures will however require some additional adjustments. III Sammendrag For å imøtekomme utfordringer knyttet til fremtidige korrugerte stålkonstruksjoner kreves økt teoretisk forståelse. Dimensjonene blir stadig større og med det blir det byggetekniske mer innviklet. FEM modellering gir et godt verktøy til utforsking av jordtrykk og kraftpåkjenning på stålstrukturen. Målet med denne masteroppgaven er å teste relabiliteten til FEM modellering sammenlignet med målte verdier. Det er fokusert på interaksjon mellom stålrør og friksjonsmassene og kraftpåkjenningen dette medfører. To eksisterende kulverter i Norge er testet; en kulvert med horisontal ellipse og en med bueform. Målingene på ellipsen inkluderer jordtrykk og deformasjon, og på kulvert med bueform inkluderer jordtrykk, aksialkraft og moment. Modelleringen er utført i PLAXIS 2D. Modellen er basert på teoretiske verdier og geometri. Målingene viste at jordtrykket økte over tid. Det modellert jordtrykket viste god korrelasjon opp mot de målte verdiene. I kulverten med ellipse viste modellerte verdier høyere Arching effekt enn i de målte resultatene. Dette kan være grunnet de valgte parameterne i friksjonsmassene. Tester utført på friksjonsmassene kan forbedre modellen og derav forbedre resultatene. Den modellerte aksialkrafta og moment samsvarte ikke med de målte verdiene. De målte verdiene representerer spesifiserte korrugeringer i stålkonstruksjonen og det kan diskuteres om dette gir et godt bilde på total kraftdistribusjon. For å undersøke om dette er tilfelle må flere målinger utføres på et større antall korrugeringer. Den målte deformasjonen viser at det var peaking i konstruksjonen under bygging. Det er ønskelig med peaking så fremt ikke deformasjonen fører til flyt i stålet. Den modellerte deformasjonen samsvarte ikke med de målte verdiene. For å bedre modellen foreslås det at at det tilføres linjelast i hvert lag for å imitere tilbakefylling. Alt i alt ga modellen i PLAXIS 2D gode estimater. Programmet er bygget opp slik at endringer under byggeprosess kan følges, dette gir god kontroll. For å forbedre modellen til de presenterte strukturene kreves enkelte forbedringer som nevnt. V Table of Contents 1. Introduction General Aims, Goals and Restrictions 1 2. Theory Buried Structures Long Span Flexible Metal Culverts Considerations during Construction and Completion Recent Developments Construction of a Corrugated Steel Culvert Steel Structure and Fundament Backfill and Cover Finite Element Method Fundamental Theories Challenges with FEM Modeling Method of Calculation SCI-Method Machelski, Michalski & Janusz Pettersson and Sundquist Structures Dovre Description Instrumentation Furulund Bru Description Instrumentation Procedure of measurement Earth Pressure Cells Strain Gauges Deformation Method Measurements Earth Pressure Axial Stress and Moment Deformation PLAXIS 2D Material Properties Geometry Staged Construction and Calculation Hand calculations Estimated Axial Force and Moment Estimated Deformation Results Dovre Measurements Modeling with PLAXIS 2D 29 VII Final Results Furulund bru Measurements Modeling with PLAXIS 2D Final Results Discussion Earth Pressure Axial Stress and Moment in the Steel Structure Deformations in the Steel Structure Conclusions Bibliography Appendix Appendix Appendix Appendix 3 55 VIII List of Figures All unreferenced figures in chapter 2, 3, 4 and Appendix 2 are designed by Andrea Fæste in the student versions of Vectorworks 2016 and ArchiCAD 19, with basis in associated references. All unreferenced photographs are taken by the author in the field. All figures in chapter 5 is produced by the author in Microsoft Excel and PLAXIS 2D. Figure 2.1. General description of a buried steel-soil structure Figure 2.2. The inside of a soil-steel buried structure... 3 Figure 2.3.Cross sections of various steel structures Figure 2.4. The difference between steel plates with corrugation 380x140 mm and 200x55 mm Figure 2.5. Vertical deflection w in the steel structure caused by soil compression... 6 Figure 2.6. Template used to form the bedding into a desired curved form (Vaslestad 1985).. 7 Figure 2.7. The base structure lifted with crane into the pre-formed soil (Vaslestad 1985) Figure 2.8. The side plates bolted together with the base plates in situ (Vaslestad 1985) Figure 2.9. Installation of steel plates in concrete footing (Vaslestad 1997) Figure Compaction of backfill with manual labour and a plate compacter (Vaslestad 1985) Figure Compaction of backfill with a vibration roller (Vaslestad 1985) Figure The final step of construction (Vaslestad 1985) Figure The function Kw(κ, λ) (Machelski et al. 2009) Figure 2.14 Parameters and as a function of geometric parameters and shape (Machelski et al. 2009) Figure The arching coefficient Sar in relation to the relative cover ratio hc,red/d and the angle of internal friction tan( cover,d) (Pettersson & Sundquist 2007) Figure 3.1. Presentation of the Dovre structure Figure 3.2. Cross section of the Dovre structure including description of the soil geometry 1: Figure 3.3. Location of earth pressure cells at the Dovre structure Figure 3.4. Presentation of Furulund bru Figure 3.5 Cross section of Furulund bru including description of soils 1: Figure 3.6. Location of the earth pressure cells at Furulund bru Figure 3.7 Location of the strain gauges situated at Furulund bru Figure 5.1. Measurements of earth pressure in cell 3 on the Dovre structure Figure 5.2. Measurements of earth pressure in cell 6 on the Dovre structure Figure 5.3. Measurements of earth pressure in cell 5 on the Dovre structure Figure 5.4. Measurements of earth pressure in cell 1 on the Dovre structure Figure 5.5. Horizontal deformation in the Dovre structure, measured inside the steel structure Figure 5.6. Final geometry of the Dovre structure modelled in PLAXIS 2D Figure 5.7. The Dovre structure after completed calculations, including deformed mesh IX Figure 5.8. Modelled axial force in the Dovre structure...30 Figure 5.9. Modelled moment in the Dovre structure Figure Modelled vertical deformation in the Dovre structure. Scaled up 50 times...31 Figure Modelled horizontal deformation in the Dovre structure. Scaled up 50 times Figure Measurements of earth pressure in cell 2 on the Furulund bru structure Figure Measurements of earth pressure in cell 1 on the Furulund bru structure Figure 5.14 Measurements of earth pressure in cell 1 on the Furulund bru structure Figure Measurements of earth pressure in cell 3 on the Furulund bru structure Figure 5.16 Axial force measured in strain gauge 3 in the Furulund bru structure Figure Axial force measured in strain gauge 2 and 4 in the Furulund bru structure Figur 5.18 Axial force measured in strain gauge 1 and 5 in the Furulund bru structure Figure Moment measured in strain gauge 3 in the Furulund bru structure Figure 5.20 Moment measured in strain gauge 2 and 4 in the Furulund bru structure Figure 5.21 Moment measured in strain gauge 1 and 5 in the Furulund bru structure Figure Final geometry of the Furulund bru structure modelled in PLAXIS 2D Figure Furulund bru with 1.2 m cover after completed calculation. Deformation is scaled up 50 times Figure 5.24 Modelled Axial force in the Furulund bru structure with 1.2 m cover Figure 5.25 Modelled moment in the Furulund bru structure with 1.2 m cover Figure Modelled vertical deformation in the Furulund bru structure with 1.2 m cover. Scaled up 50 times Figure 5.27 Modelled horizontal deformation in the structure Furulund bru with 1.2 m cover. Scaled up 50 times Figure 9.1 Measurements of earth pressure in cell 2 on the Dovre structure Figure 9.2 Measurements of earth pressure in cell 4 on the Dovre structure Figure 9.3 Measurements of earth pressure in cell 7 on the Dovre structure Figure 9.4 Measurements of earth pressure in cell 8 on the Dovre structure Figure 9.5 Cross section of the Dovre structure including description of the soil geometry 1: Figure 9.6 Cross section of the Dovre structure including description of the soil geometry 1: Figure 9.2 Cross section of Furulund bru including description of soils 1: X List of Tables Table 1 Modelled earth pressure in the Dovre structure...30 Table 2 Systematisation of result for the Dovre structure Table 3. Modelled earth pressure on the Furulund bru structure Table 4 Modelled axial force and moment in the Furulund bru structure Table 5 Systematisation of result for the structure Furulund bru Table 6 Material properties used in the PLAXIS 2D model...51 Table 7 Material properties for steel used in the PLAXIS 2D model...52 Table 8 Parameters, assumptions and calculated results from the methods based on Pettersson and Sundquist (2007) and Machelski et. al (2009) XI List of parameters A Area of cross section [m 2 /m] D Span of the structure [m] Eb Young s modulus for soil [kn/m 2 ] Es Young s modulus for steel [kn/m 2 ] F Calibration factor Is Moment of inertia, steel [m 4 /m] Kw Shape parameter MC Calculated moment with completed backfill and cover [knm/m] MM Measured moment [knm/m] NC Calculated axial force with completed backfill and cover [kn/m] NM Measured axial force [kn/m] P0 Oil circulation pressure [kn/m 2 ] PA Calliper pressure [kn/m 2 ] PB The difference in height between cell and pressure pump [m] PC Correlation for temperature Q External load from engineered soil [kn/m] RP Compression grade, Standard Proctor % Rs Side radius, dependent on cross section of steel pipe [m] Rt Top radius, dependent on cross section of steel pipe [m] Sar The arching coefficient W Moment of resistance [m3/m] a Length of corrugation [m] f1 Function associated with the equation MC f2 Function associated with the equation MC f3 Function associated with the equation MC hc Height of cover [m] hc,red Reduced height of cover, with consideration due to peaking [m] hd Vertical distance between the crown and the line of maximum diameter [m] hrel Relative height of structure [m] u Horizontal deflection [m] w Vertical deflection [m] Shape parameter for vertical deflection Shape parameter for horizontal deflection b Measured strain at the base of corrugation [kn/m 2 ] t Measured strain at the top of corrugation [kn/m 2 ] Unit weight of the backfill soil b XII c Unit weight of the cover soil [kn/m 3 ] Safety factor m n Safety factor Parameter describing shape of the corrugated structure Global stiffness of the soil steel structure σb Tension at the base of corrugation [kn/m 2 ] σep Earth pressure [kn/m 2 ] σt Tension at the top of corrugation [kn/m 2 ] σc Soil stress at the crown [kn/m 2 ] XIII XIV 1. Introduction 1.1. General Despite more than a hundred years of experience, corrugated steel pipes still remain an underestimated structural shape. Experience indicates that flexible culverts correctly installed require less maintenance and are more cost-effective than similar rigid structures (Peck & Peck 1948). In general, there are two types of steel pipes: closed pipes moulded in one piece, and pipes build up by corrugated plates. The larger structures are built up by plates (Abdel-Sayed et al. 1993). Soil-steel structures in the road sector are predominantly used as crossings and passages for trains, animals, bicycles, and agriculture. In Norway, such structures are also commonly used for avalanche protection. Long-span flexible culverts undergo changes in stress distribution and structural deformations over time. The greatest changes occur during the first six months after construction has been finalized (Vaslestad 1990). The structural dimensions of long-span flexible metal culverts are continuously increasing and the mechanical features are growing more complex. In order to accommodate these challenges, it is necessary to strengthen the theoretical understanding and awareness during the construction process Aims, Goals and Restrictions The main goal of this paper is to compare measured results to theoretical results. Measurements were performed on two existing structures, a train passage in Sjoa and an agricultural crossing in Dovre. The modeling was performed in PLAXIS 2D. Selected hand calculations are included in order to provide a basis for comparison when measurements are absent. Deflection calculations are based on Machelski et al. (2009) and calculations on axial force and moment are based on Pettersson and Sundquist (2007). The main focus of this study is on the soil-steel interaction, and the effect on the steel structure. The model in PLAXIS was developed by the use of material properties and geometry of selected structures. The goal is to test whether the software can produce consistent accurate estimates of earth pressure, deformations and forces in the steel structures compared to short- and long-term measurements. 1 2. Theory 2.1. Buried Structures Buried corrugated steel structures can be used as an alternative to conventional bridges and concrete culverts. The main advantages for building soil-steel structures include a shorter construction period, as well as the structures large load-bearing capacity. In relation to avalanche protection the flexibility of the steel has proven favourable due to its ability to absorb the transient pressure from snow slides (Vegdirektoratet 2015) Long Span Flexible Metal Culverts A visual description of how the structures are constructed is shown in Figure 2.1. The bedding is made up from loose filling which is contoured to invert the shape of the steel pipe. Curved steel plates compose the pipe, and an example from inside the structure is shown in Figure 2.2. The steel plates can either be bolted together one at a time, be set up by rigging the base, side and top shell, or by setting up the rings independently before installation. Following the pipe construction, the dike is filled with backfill on both sides at equal pace. The final step is the cover. The thickness of the cover is determined by the vertical distance from pipe crown to the surface (Abdel-Sayed et al. 1993). Surface Depth of cover Crown Fill, normally local material Engineered soil Backfill Steel pipe Bedding Foundation, natural ground Figure 2.1. General description of a buried steel-soil structure. 2 Figure 2.2. The inside of a soil-steel buried structure The cross section of the steel structure varies according to the different areas of application. Various cross sections are illustrated in Figure 2.3. The shapes are divided into two groups; open profiles and arches. Different radii determine the structural shape. The circular pipe (2.3a) has a constant radius R. The horizontal and vertical ellipses (2.3b and 2.3c) usually have two radii, equivalent base radius Rb and top radius Rt, and a second radius on the sides Rs. A pipe arch (2.3d) have three or four different radii, one top radius Rt, on base radius Rb, and a corner radius Rc. Some pipe arches also have an additional side radius Rs. Arches can have a single radius R (2.3e) or three radii Rt, Rs and Rb (2.3d). A box culvert has a top radius Rt, a side radius Rs and a straight section instead of a base radius (Pettersson & Sundquist 2007). 3 R hc hc hd R hd h h D D Figure 2.3a Circular pipe Figure 2.3e Arch, single radius Rt hc Rt hc Rs hd Rs hd h Rb Rb D D Figure 2.3b Horizontal ellipse Figure 2.3f Arch, multiple radii Rt hd hc hc Rs h Rs Rt hd h Rb D Straight section D Figure 2.3c Vertical ellipse Figure 2.3g Box culvert Rt hc hd Rc h D Rb Figure 2.3d Pipe arch Figure 2.3. Cross sections of various steel structures. 4 The curved steel plates building the structure has a corrugation with a certain length and amplitude. The quality of the steel is S235J2 or higher. Steel plates used in Norway normally have 200x55 mm corrugation on structures smaller than 11 m in diameter, and 380x140 mm on larger ones. Corrugation is shown in Figure 2.4. The difference between steel plates with corrugation 380x140 mm and 200x55 mm. When corrugation is this deep, the structures can span up to 24 m. Plates interfacing the soil are refaced with corrosion protection in or

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