Modelling of Tunnels in 2D & 3D

MIDAS Geotechnical Know-how Sharing Series November 28 th, 2017 (Tue) 10:00 ~ 11:00 AM (CET) Session 3. Modelling of Tunnels in 2D & 3D JaeSeok Yang Principal Geotechnical Engineer, MIDAS IT Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering

01 Tunnel Construction 02 Simulation of the Sequential Excavation 03 Case Study 04 Conclusion Integrated Solver Optimized for the next generation 64-bit platform Finite Element Solutions for Geotechnical Engineering

Tunnel Construction Most common tunnel excavation techniques Open faced shield tunnelling Tunnel Boring Machines (TBM), including slurry shield and Earth Pressure Balance (EPB) tunnelling The sprayed concrete lining (SCL) method 3

Tunnel Construction Open faced shield tunnelling Schematic view of shielding during tunnel excavation 4

Tunnel Construction Tunnel Boring Machines (TBM) Schematic view of TBM 5

Tunnel Construction Sprayed concrete lining (SCL) method Schematic view of SCL method 6

Tunnel Construction Ground response to tunnel construction Sources of volume loss (example of TBM) 7

Simulation of the Sequential Excavation Introduction Axi-symmetric geometry Plane strain geometry 9

Simulation of the Sequential Excavation Modelling of tunnels in 3D 3D stress transfer at tunnel face 10

Simulation of the Sequential Excavation Setting up the initial conditions If it is known: Modelling the complete geological history of the site If it is not known: Input the conditions appropriate to a greenfield site (by means of the material unit weight, the pore water pressure profile and the coefficient of earth pressure at rest, K 0 ) Simulating any previous construction activities that have occurred at the site 11

Simulation of the Sequential Excavation Important boundary conditions The boundary displacement conditions, required to represent the far field conditions or any symmetry of the problem Any surface traction The excavation of solid soil elements The construction of structural shell elements The hydraulic conditions at the far field boundaries, the soil strata interfaces (if an interface is between consolidating and non-consolidating elements) and the tunnel lining itself 12

Simulation of the Sequential Excavation Gap method Gap method for modelling tunnel excavation 13

Simulation of the Sequential Excavation Contraction Engineering example: Contraction of shield TBM 14

Simulation of the Sequential Excavation Convergence-confinement method Convergence-confinement method 15

Simulation of the Sequential Excavation Modelling tunnel excavation Transient Seepage Analysis Control Drag & Drop Tree Structure Initial & Construction Excavation Load Distribution Factors 16

Simulation of the Sequential Excavation Progressive softening method Progressive softening method 17

Simulation of the Sequential Excavation Volume loss control method Volume loss method 18

Simulation of the Sequential Excavation Modelling tunnel lining The use of solid elements Allows the analyst a very wide range of constitutive models Maintain an acceptable element shape (defined by the aspect ratio of length to width) The use of shell elements Removes the problem of aspect ratio control Allows more flexibility in the mesh definition A structural nature (i.e. shear force, hoop force, and bending moment) 19

Simulation of the Sequential Excavation Gauging element Gauging Element Generation Gauging Element Results 20

Simulation of the Sequential Excavation Modelling the connections between lining segments Modelling segment connection as a moment-free joint Unrolled and rolled tunnel lining 21

Simulation of the Sequential Excavation Shell interface element Input properties of the shell interface element Input dialog for user-defined shell interface behaviour 22

Simulation of the Sequential Excavation Shell interface element Example of shell interface element creation 23

Introduction - Two single tracks (TBM diameter Ø 5.8m), total length of 15.5km - Totally automatic, driverless, lightweight rail system 17 Underground Stations Total travel time: 23 min Maximum depth ~ 35m Completed in 2018 25

Introduction - Two single tracks (TBM diameter Ø 5.8m), total length of 15.5km - Totally automatic, driverless, lightweight rail system 26

Introduction 27

Description of sites and its specifics Copenhagen Central Station 28

Description of sites and its specifics Kongens Nytorv Station Magasin Du Nord 29

Description of sites and its specifics Magasin Du Nord 30

Description of sites and its specifics Magasin Du Nord 31

Description of sites and its specifics Sand till Limestone Magasin Du Nord 32

Description of sites and its specifics 1930 s basement and ground floor 1960 s first floor and above 1960 s colonned r.c. costr. 1954 r.c. constr. 1914 Concrete encased steel costr. 1857 Mansory construction 1962 R.C.. car park Main 1893 Magasin building Medieval Part Early 20th century 1990 s r.c. construction 33

Description of sites and its specifics Tunnel 1 alignment Tunnel 2 alignment 34

Geotechnical Characterization Tunnel 1 35

Geotechnical Characterization Tunnel 2 36

Geotechnical Characterization Nomenclature Layer No. FY Age Deposition environment Soil type Recent Re Fi/Ts Fill PG2 Postglacial Pg Ma Gravel Solifluction/meltwater clay, silt and SL/SI/SS Lateglacial Lg Ss/Mw sand Quaternary ML1/MS1 Gl Upper clay and sand till DS2/DG2 Mw Middle meltwater sand and gravel Glacial Gc ML2/MS2 Gl Lower clay and sand till DS3/DG3 Mw Lower meltwater sand and gravel UCL Upper Copenhagen Limestone MCL Palaeogene Danian Da Ma Middle Copenhagen Limestone LCL Lower Copenhagen Limestone Nomenclature Layer No. Model γ sat [kn/m 3 ] ф c [kpa] K 0 E [MPa] FY EL 17 - - - 2 0.3 DS / DG / MS MC 21.25 38 0 0.52 50/100 * 0.25 UCL (HP) MC 21.5 45 100 0.77 800 0.3 UCL / MCL MC 21.5 45 100 0.725 1500 0.3 Input parameters in modelling v 37

Definition of objectives Input Evaluation of the class of damage that the structure may bring back Identification of the characteristics of the materials of the structural elements Calibration of the rigidity of the structural elements Definition of permanent and accidental loads on the existing structure Discretization of the coupled ground-structure model for interaction analysis (fully coupled soil-structure interaction analysis) Tunnel steps and sequences Output Evaluation of structural stress under ordinary conditions Evaluation of absolute and differential settlements during tunnel excavation sequences Evaluation of structural stresses during the tunnel excavation sequence and comparison with stresses under ordinary conditions Evaluation of the class of damage and comparison with the allowable damage class Determination of threshold levels Finding any mitigation actions Check in with the monitoring data 38

Modelling Geometry of the structure model - First floor 39

Modelling Geometry of the structure model - Type plane 40

Modelling Numerical model of 3D structure 41

Modelling Material Modulus of Elasticity Weight density Masonry 1500 MPa 18 kn/m 3 Cast Iron 120000 MPa 73 kn/m 3 Wrought Iron 190000 MPa 75 kn/m 3 Concrete C25/30 Concrete C25/30 floor 30500 MPa 25 kn/m 3 30500 MPa 25 kn/m 3 Steel S275 210000 MPa 78.5 kn/m 3 Concrete encased steel columns Composite section: Steel S275 +concrete C25/30 Composite section: Steel S275 +concrete C25/30 Numerical model of 3D structure 42

Modelling Numerical model of 3D structure - Solicitations in cond. ordinary 43

Modelling Numerical model of 3D structure - Solicitations in cond. ordinary 44

Modelling Numerical model of 3D fully coupled soil-structure interaction 45

Modelling Numerical model of 3D fully coupled soil-structure interaction 46

Modelling Numerical model of 3D fully coupled soil-structure interaction 47

Modelling Numerical model of 3D fully coupled soil-structure interaction 48

Modelling Numerical model of 3D fully coupled soil-structure interaction 49

Modelling Numerical model of 3D fully coupled soil-structure interaction 50

Modelling Applied load conditions 51

Modelling TBM construction phases 52

Modelling TBM construction phases 53

Modelling TBM EPB face pressure Face pressure TBM construction phases 54

Modelling TBM construction phases 55

Modelling Lining TBM construction phases 56

Modelling Shield Face pressure Lining Jack pressure Lining Solid grouting Lining + Solid grouting Steel Shield Face pressure TBM construction phases 57

Modelling TBM construction phases 58

Analysis implemented scenarios and details For each scenario, you have been determined: cuts (absolute and differential) stress on structures level of potential damage c (%) DR [cm] V loss (%) SC 3 E1 1.15 3.31 0.50 SC 4 - E1 2.76 8.12 1.04 SC 3 E2 1.38 4.03 0.52 SC 4 E2 3.06 8.87 1.02 59

Case Study Results and final considerations Evolution of the settlement 60

Results and final considerations Deformation of the structure 61

Settlement of scenario 4-E2, V loss 1% 62

Results and final considerations Settlement of scenario 3-E2, V loss 0.5% Settlement of scenario 4-E2, V loss 1% 63

Conclusion Summary A three dimensional engineering process Methods of simulating tunnel construction in plane strain: the volume loss to be expected; the percentage of load removal prior to lining construction; or the actual displacement of the tunnel boundary Segmental linings to open or rotate at their joints, or sprayed concrete linings to crack View any prediction of intermediate and long term behaviour Select constitutive models capable of reproducing field behaviour FEM can be used to quickly assess the impact of different influences on tunnelling-induced ground movements Numerical analysis can incorporate adjacent influences 65

Q & A 66