Description and Structural Analysis of a Marine Bridge for the Digernessund crossing Elise Hellvik Marine Technology Submission date: June 2018 Supervisor: Bernt Johan Leira, IMT Norwegian University of Science and Technology Department of Marine Technology NTNU Norwegian University of Science and Technology Department of Marine Technology Master Thesis, Spring 2018 for Master Student Elise Hellvik Description and Structural Analysis of a Marine Bridge for the Digernessundet crossing Beskrivelse og strukturanalyse av et marint brukonsept for kryssing av Digernessundet Marine bridges (i.e. floating bridges, submerged tunnels and more traditional bridge types with floating foundations) are relevant for crossing of very deep and wide lakes or fjord systems. In order to compute the static and dynamic response of these bridges, the joint properties of the entire hydro-elastic system need to be accounted for. The objective of the present project is to outline methods for response analysis and illustrate the calculation procedure for a particular bridge concept. The following subjects are to be addressed as part of this work: 1. Review of existing marine bridges and future plans for such bridges. Similarities and differences between the different bridge types are to be highlighted. Loads acting on such bridges are described together with associated structural models. Methods for both static and dynamic response analysis are elaborated and relevant numerical algorithms are described. 2. A global model of a particular bridge (Submerged tunnel for Digernessundet) is to be established in SESAM. Static response analyses are performed. Sensitivity studies of bending moment and axial forces with respect to current direction and profile are performed. 3. Concrete stresses for the most critical sections are to be controlled. The influence of post- tension cables on the stresses is to be investigated. 4. Natural frequencies (and mode shapes) are to be computed. 5. Dynamic response analysis is to be performed for the case of swell sea. 6. Parametric studies are performed with respect to curve height. Static response analyses with different curve heights are performed, and associated natural frequencies are investigated. The objective is to find the curve height where the first horisontal mode shape consists of two halfwaves. 1 iv Abstract The relevance of marine bridges have increased during the past years due to the plans of renewing route E39. Different types of marine bridges have been described in this thesis, with focus on the concepts proposed for the fjord-crossings along route E39. The existing bridge over the Digernesund does not meet the new requirements for the new E39, and a submerged floating tunnel (SFT) has therefore been proposed as a replacement. The proposed SFT, given in the technical report provided by dr. Techn. Olav Olsen, has been investigated in this thesis with respect to its structural behaviour. The SFT proposed by dr. Techn. Olav Olsen is a reinforced concrete structure with post-tension cables. The cross-section used in this thesis is rectangular, and the bridge has one single span including both driving directions. There are no intermediate sup- ports, meaning the bridge is only supported by buoyancy and the connections to rocks tunnels at the two ends. The model and structural analysis of the SFT were estab- lished and conducted in the Sesam package. The bridge was modeled as an assemble of straight 2-node beam elements creating an arc. The influence of reinforcements and post-tension cables were accounted for in the bending stiffness of the structure, in the stress calculations and in the eigenvalue analysis. The average increase of moments of inertia is 3.89% for Iz and 3.24% for Iy. The axial compression from the PT-cables was calculated 5.75% of the Euler buckling load. Thus, global buckling was not considered a problem for the base case configuration of the bridge. Buoyancy was found as the dominating load in the vertical direction for the base case. The results from static analysis showed high reaction forces to be transferred to the abutments and high bending moments. The stress calculations showed that the max- imal total compressive stresses were below the allowable limit. However, the tensile stresses from the characteristic loads exceeds the tensile strength of concrete. Thus, the weight should be increased to balance the buoyancy. A full calculation of the amount of reinforcements should be carried out and its contribution included in the weight calculations. An alternative could be to increase the ballast chamber fill percentage to increase the weight. The transverse reactions are dependent on the current direction and profile. Different directions and profiles were investigated with respect to static response. The cases of applying uniformly distributed current loads to the full length of the bridge, in either the positive or negative transverse direction, gave the highest bending moments and axial forces in the structure. It was found that the contribu- tions in stress from axial forces and bending moments due to current loads are small compared to the contributions from PT-cables and the net vertical forces. Eigenvalue analyses were conducted using Sestra and Abaqus, and the results were compared to results from analytical calculations. The resulting mode shapes were sim- v vi ilar to those given in the technical report established by dr. Techn. Olav Olsen. The eigenperiods calculated by Sestra and Abaqus deviates from the calculations by the NPRA by about 10-20%. It is assumed that this deviations can be a result of differ- ences in modeling and assumptions for the eigenvalue analysis. The eigenfrequency for the first mode is multiplied by a reduction factor to account for the influence of the compression force from the PT-cables. The first eigenperiod for the base case was thus calculated 9.14s. The second eigenperiod, corresponding to a horizontal mode with one half-wave, was calculated 5.16s by Sestra. The third and forth eigenperiod, corresponding to vertical and horizontal mode with two half-waves respectively, were calculated 3.34s and 3.00s by Sestra. For increasing mode number, the eigenfrequencies were closely spaced. A parameter study of the curve height in the transverse direction were also carried out. Increasing curve height influences the static response, the eigenfrequencies and the mode shapes. The main findings were that the transverse loading is carried by axial forces and bending moments, as expected. Increasing the curve height results in reduced bending moments due to transverse loads. However, it also results in in- creased torsion moments due to the translation of centre of gravity along the y-axis. For eigenvalue analysis, the first horizontal mode is of interest when introducing a curve height. The result is reduced eigenfrequency for increasing curve height. At one curve height, it was expected that the first and second horizontal mode shape changes place. The curve height corresponding to the changing point was calculated 49m analytically, 53m in Sestra and 56m in Abaqus. Swell sea was the dominating wave type at the depth of the SFT. The submergence of the tunnel provides shelter from the wave loads as the wave action at the depth of the SFT is 35.8% of the wave action at the free surface. Wave loads due to swell sea were calculated using deterministic wave load calculation in Wajac. The dynamic response was calculated using direct time domain analysis in Sestra. However, the dynamic response due to swell waves was found to be of second importance compared to the response from static loads. Displacements due to the swell waves investigated in this thesis were found negligible compared to the results from static analysis. The bending moments due to swell waves were calculated 6% of the bending moment from net static loads. To ensure conservatism in stress calculations, the bending moments from wave loads should be included. Sammendrag Interessen for marine broer har økt de siste årene som et resultat av planene om en fornyet E39. Ulike typer marine broer har blitt presentert i denne oppgaven, med fokus på et konsept foreslått for en fjord-krysning langs E39. Den eksisterende broen over Di- gernessundet møter ikke dagens krav til nye E39 og en rørbro har derfor blitt foreslått som erstatning. Den foreslåtte broen, gitt i teknisk raport av dr. Techn. Olav Olsen, har blitt undersøkt i denne oppgaven med fokus på konstruksjonens oppførsel. Rørbroen foreslått av dr. Techn Olav Olsen er en armert betongkonstruksjon med et- teroppspenning. Tverrsnittet brukt i denne oppgaven er rektangulært. Broen har ett enkelt spenn som inneholder begge kjøreretninger. Den har ingen mellomliggende støtter, og bæres av oppdrift og endeforbindelser til fjelltunneller. Elementmodell og strukturanalyse av rørbroen har blitt utført i programvaren Sesam pakken. Broen ble modelert som en kurve, sammensatt av rette 2-nodede bjelkeelementer. Innflytelse av armering og spennkabler ble tatt hensyn til i bøyestivheten til broen, i spennings- beregninger og i egenverdianalysen. Gjennomsnittlig økning av treghetsmomentene ble beregnet til 3.89% for Iz og 3.24% for Iy. Trykk-kraften fra spennkablene ble bereg- net til 5.75% av Euler knekklasten. Global knekking ble derfor ikke sett på som et problem for konseptet brukt i denne oppgaven. Oppdrift ble observert som den dominerende lasten i vertikal retning for konseptet brukt i oppgaven. Resultatene fra statisk analyse viste høye reaksjonskrefter og bøye- momenter. Spenningsberegningene viste at de maksimale trykk-spenningene i be- tongen var innenfor tillatte verdier, men strekkspenningene fra karakterisiske laster overgikk karakteristisk strekkfasthet til betongen. Det er derfor viktig at vekten økes for å balansere oppdriften. Beregning av nødvendig armering og spennkabler må utar- beides og inkluderes i vektberegningen. Alternativt kan også prosent av fyllmasser i ballastkammerne økes. Tverr-reaksjonene er avhengig av strømretning og profil. Forskjellige strømretninger og profiler ble derfor undersøkt mot statisk respons. Jevnt fordelt strømlast påsatt over hele lengden av broen ga høyeste aksialkrefter og bøye- momenter i konstruksjonen.