AUTh TUC ΕΠΙΧΕΙΡΗΣΙΑΚΟ ΠΡΟΓΡΑΜΜΑ «ΕΚΠΑΙΔΕΥΣΗ ΚΑΙ ΔΙΑ ΒΙΟΥ ΜΑΘΗΣΗ» Πρόγραμμα Δια Βίου Μάθησης ΑΕΙ για την Επικαιροποίηση Γνώσεων Αποφοίτων ΑΕΙ Χρονική Περίοδος: 2014 2016 ΠΕΓΑ: ΣΥΓΧΡΟΝΕΣ ΕΞΕΛΙΞΕΙΣ ΣΤΙΣ ΘΑΛΑΣΣΙΕΣ ΚΑΤΑΣΚΕΥΕΣ SECTION 8: ANALYSIS AND DESIGN OF MARINE STRUCTURES 8.4 Submerged tunnels (Υποθαλάσσιες σήραγγες) 8.4.4: Στατική και Δυναμική Ανάλυση Συστήματος NSRF 2007-2013 / SECTION 8.2 / GDM 1
Operational Programme: Education and Lifelong Learning Subject: Modern Development in Offshore Structures Lecture Notes: Dynamic Analysis in the Half space Supporting Pipelines or Buried Tunnels George D. Manolis, Professor Department of Civil Engineering Aristotle University, Thessaloniki GR 54124, Greece Tel: (+30 2310) 99 5663, Fax: (+30 2310) 99 5769 E mail: gdm@civil.auth.gr NSRF 2007-2013 / SECTION 8.2 / GDM 2
Figure 1: 3D Tunnel buried at seabed modeled as a poroelastic medium NSRF 2007 2013 / SECTION 8.2 / GDM 3
Figure 2: Buried pipeline viewed as a continuous beam on elastic foundation (1D representation) NSRF 2007 2013 / SECTION 8.2 / GDM 4
Figure 3: Tunnel cross section viewed as a cavity under plane strain conditions (2D representation) NSRF 2007 2013 / SECTION 8.2 / GDM 5
PART I: SOIL STRUCTURE INTERACTION (SSI) PHENOMENA FOR A PIPELINE RESTING ON THE SEAFLOOR A. GENERAL OVERVIEW OF SSI: THE ATC CODE B. STRUCTURE FOUNDATION SOIL MODELLING C. MULTI DEGREE OF FREEDOM (MDOF) REPRESENTATION FOR SSI D. SOIL IMPEDANCES E. FEM MODELS FOR SSI F. SUBSTRUCTURING TECHNIQUES NSRF 2007 2013 / SECTION 8.2 / GDM 6
PART I: SOIL STRUCTURE INTERACTION FOR A PIPELINE RESTING ON THE SEAFLOOR NSRF 2007 2013 / SECTION 8.2 / GDM 7
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ΦΑΣΜΑΤΑ ΑΠΟΚΡΙΣΗΣ ΓΙΑ ΕΠΙΤΑΧΥΝΣΕΙΣ ΠΡΙΣΜΑΤΙΚΗΣ ΚΑΤΑΣΚΕΥΗΣ ΣΕ ΕΥΚΑΜΠΤΟ ΕΔΑΦΟΣ ΥΠΟ ΤΗΝ ΕΠΙΔΡΑΣΗ ΣΕΙΣΜΙΚΩΝ ΚΥΜΑΤΩΝ ΤΥΠΟΥ SH ΚΑΙ RAYLEIGH NSRF 2007 2013 / SECTION 8.2 / GDM 13
ΕΛΑΣΤΙΚΗ ΘΕΜΕΛΙΩΣΗ ΕΠΙ ΕΔΑΦΟΥΣ EΠΙΡΡΟΗ ΤΗΣ ΜΑΖΑΣ NSRF 2007 2013 / SECTION 8.2 / GDM 14
ΜΕΤΑΣΧΗΜΑΤΙΣΜΟΙ FOURIER NSRF 2007 2013 / SECTION 8.2 / GDM 15
ΜΕΤΑΣΧΗΜΑΤΙΣΜΟΙ FOURIER NSRF 2007 2013 / SECTION 8.2 / GDM 16
ANALYSIS METHODS I. COMPLETE MODEL NSRF 2007 2013 / SECTION 8.2 / GDM 17
ANALYSIS METODS II. SUBSTRUCTURING NSRF 2007 2013 / SECTION 8.2 / GDM 18
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ΜΕΘΟΔΟΙ ΑΝΑΛΥΣΗΣ NSRF 2007 2013 / SECTION 8.2 / GDM 21
ΜΕΘΟΔΟΙ ΑΝΑΛΥΣΗΣ NSRF 2007 2013 / SECTION 8.2 / GDM 22
PART II: SOIL-STRUCTURE INTERACTION FOR A BURIED TUNNEL FEM Analysis: Static Application of Loads for Finite Domains Containing a Buried Structure (Note: All problem parameters are dimensionless) Y p=10 X E=10, ν=0.2 10 10 These loads can be applied at the edges (boundaries ) of the domain NSRF 2007-2013 / SECTION 8.2 / GDM 23
FEM Analysis: Application of Loads at Infinity Infinite Domains for Modelling the Surrounding Seabed Deposits Y p=10 X E=10, ν=0.2 10 10 Now the load cannot be applied at the boundaries of the domain NSRF 2007-2013 / SECTION 8.2 / GDM 24
FEM Analysis: Application of Loads at Infinity The domain is infinte E=10, ν=0.2 Y p=10 X p p u x, v y E E p p x, y, xy 0 E E p, 0 x Exact solution (Uniaxial Tension) Now the load cannot be applied at the edges of the domain, but we know the solution (stress and displacement fields) from such load in the absence of a cavity or inclusion Note that this solution does not depend on the size of the domain. y NSRF 2007-2013 / SECTION 8.2 / GDM 25
Application of Scattered Tractions along the Perimeter t Exact solution (incident): p, 0, 0 x y xy Relation between tractions and stresses in Cartesian coordinates: 1 11 1 12 2 11 1 2 21 1 22 2 0 sc inc 1 1 1 sc inc 1 t2 0 t t pn t n i ij j t n n n t n n NSRF 2007-2013 / SECTION 8.2 / GDM 26
FEM Analysis: Implicit Application of Loads at Infinity Wave field is decomposed into incident and scattered fields Exact solution (for homogeneous plate without hole)=incident Y p=10 Unknown solution=scattered Y X + X 10 Known stress and displcement fields at the fictitious interface 10 total Because t 0 Superposition (using equilibrium and compatibility conditions) of these two solutions gives the complete (total) solution NSRF 2007-2013 / SECTION 8.2 / GDM 27
FEM Analysis: Implicit Application of Loads at Infinity Solution of scattered problem by implicit application of the load Y t sc t inc X 10 10 total Because t 0 NSRF 2007-2013 / SECTION 8.2 / GDM 28
Second Part of Solution: Scattered Field We can use the same model. First we have to delete the line pressure (uniform tractions) ANSYS Main Menu > Preprocessor Loads Define Loads Delete Structural Pressure On lines 29
Application of Scattered Tractions as Nodal Forces sc inc 1 1 1 sc inc 1 t2 0 t t pn t Nodes from the FEM model Length of FE edges -L (n) i Calculated nodal tractions t1 sc F i Lt sc 1 NSRF 2007-2013 / SECTION 8.2 / GDM 30
Second Part of Solution: Scattered Field Application of scattered tractions as nodal forces 31
Deformed Shape ANSYS Main Menu > General Postproc Plot Results Deformed shape NSRF 2007-2013 / SECTION 8.2 / GDM 32
Time Harmonic Analysis of Tunnel: In-plane Stress State Dimensionless frequency η E=10, ν=0.2, =1 Y 10 p=0.1e i t 10 X f 4 4 V 1 f f SV 10 / 2 1 0, 2 1 4 E / 2 1 4 4 f 0,51031Hz NSRF 2007-2013 / SECTION 8.2 / GDM 33
Damping Definition N m 2 2 K i C M u F ; C j j j 1 K NSRF 2007-2013 / SECTION 8.2 / GDM 34
Displacement Amplitudes versus Frequency ANSYS Main Menu > TimeHist Postpro 35
Displacement Amplitudes versus Frequency 36
REFERENCES ANSYS (2008), Structural Mechanics Finite Element Software, Version 10.0, Canonsburg, Pennsylvania. S. K. Chakrabarti, Dynamics of Floating Offshore Structures, World Scientific Publishing, Oxon, UK, 2014. Johnson, J.J.: Soil Structure Interaction: The Status of Current Analysis Methods and Research, Nuclear Regulatory Commission Research Report NUREG CR 1780, Washington D.C.,1981. Y.C. Kim, Handbook of Coastal and Ocean Engineering, World Scientific Publishing, Oxon, UK, 2009. B. M. Sumer, Liquefaction around Marine Structures, World Scientific Publishing, Oxon, UK, 2014. NSRF 2007-2013 / SECTION 8.2 / GDM 37