Dynamic Behavior of Shallow Rectangular Underground Structures in Soft Soils

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1 SERIES Concluding Workshop Joint with US-NEES "Earthquake Engineering Research Infrastructures" Ispra, May 28-3, 213 Dynamic Behavior of Shallow Rectangular Underground Structures in Soft Soils TA Project: DRESBUS II Investigation of the Seismic Behaviour of Shallow Rectangular Underground Structures in Soft Soils Using Centrifuge Experiments Tsinidis G., Rovithis E., Pitilakis K., Chazelas J. L. TA Project: TUNNELSEIS Investigation of Several Aspects Affecting the Seismic Behaviour of Shallow Rectangular Underground Structures in Soft Soils Tsinidis G., Heron C., Madabhushi S.P.G., Pitilakis K., Stringer M. 1

2 Scope Seismic behavior of shallow rectangular underground structures in soft soils in transversal direction Racking deformations Dynamic earth pressures Seismic shear stresses soil tunnel interface characteristics Dynamic internal forces Soil structure relative flexibility 2

3 Seismic performance Several cases of extensive damage and collapses Daikai station, Kobe Earthquake, st embedded structure to be collapsed under seismic shaking d s Vs 1.72m 2.19m Column 1 3

Soil to structure flexural stiffness (flexibility ratio) Soil tunnel interface conditions (rough

4 Seismic behavior Imposed seismic ground deformations rather than inertial forces dominate the structure s seismic response Crucial parameters controlling the soil structure system behavior: Soil to structure flexural stiffness (flexibility ratio) Soil tunnel interface conditions (rough or smooth interface separation) M max =444kNm α max =.62g M max =683kNm α max ==.37g α max =.2g α max =.2g 4

5 Important Open Issues Input motion intensity and characteristics Transversal seismic behavior and analysis Complex deformation modes (i.e. rocking, inward deformations) Estimation of seismic earth pressures Estimation of seismic shear stresses along the perimeter Estimation of impedance functions Effect of the soil structure relative flexibility Effect of the soil structure interface characteristics Longitudinal seismic behavior and analysis Estimation of the asynchronous seismic motion Estimation of impedance functions Several other issues coming from the design and construction point of view Joints performance, design and construction, in case of segmented underground structures (e.g. immersed tunnels) 5

6 Experimental research within SERIES A substantial advancement to the above topics may be accomplished by means of well constrained experimental data allowing investigation of crucial response parameters SERIES TA projects: DRESBUS II Investigation of the seismic behavior of shallow rectangular underground structures in soft soils using centrifuge experiments IFSTTAR, Nantes, FR TUNNELSEIS Investigation of several aspects affecting the seismic behavior of shallow rectangular underground structures in soft soils Schofield Centre, University of Cambridge, UK 6

7 TA Project: DRESBUS II 7

8 Project partners and research team TA User team Manos Rovithis (Researcher, EPPO ITSAK) Lead User Grigoris Tsinidis (Civil Engineer MSc, PhD candidate AUTH) Kyriazis Pitilakis (Professor, AUTH) Emmanouil Kirtas (Assistant Professor, TEI SERRES) Dimitris Pitilakis (Assistant Professor, AUTH) Anastasios Anastasiadis (Assistant Professor, AUTH) Konstantia Makra (Researcher, EPPO ITSAK) Roberto Paolucci (Professor, POLITECNICO DI MILANO) Access Provider: IFSTTAR, Nantes, FR Jean Louis Chazelas (Researcher, IFSTTAR) 8

9 Dynamic centrifuge tests Dynamic centrifuge tests on rectangular tunnels embedded in dry and saturated sands, under centrifuge acceleration of 4g The program extends the DRESBUS program (METU) posing a series of original issues Investigation of salient parameters affecting the tunnel response Tunnel flexibility Tunnel external face rugosity Soil saturation Input motion 9

10 Centrifuge facility IFSTTAR geotechnical centrifuge Actidyn QS8 actuator (sine wavelets, real records) Large Equivalent Shear Box (ESB) container 1

11 Materials Sand Fontainebleau sand NE34 D5 =.2 mm, of relative density of about 7% Tunnel models Material: 217 A aluminum alloy Model 1 47mm Model 2 54mm 2 pairs of models: flexible and rigid tunnels 5mm 6mm 1.5mm 1.5mm 5mm 5mm 6mm 5mm 2 levels of rugosity: smooth and rough tunnels 6mm 6mm flexible rigid t w / t s Flexibility ratio smooth Rough δ δ alum. φ R R R AR AR AR 11

12 Models preparation Automatic pluvation device During the construction, the tunnel and all the embedded transducers are positioned in the model 12

13 Models preparation saturated tests Saturation liquid of increased viscosity (N times) similitude laws Water + Hydroxy methyl propylcellulose (HPMC) 13

14 Tunnel boundaries Provide sufficient support and waterproof without jeopardizing the plane strain behavior of the tunnel Dry tests Saturated tests (a) Teflon plate ESB container aluminum frame (c) Teflon plate Waterproof rubber membrane ESB container aluminum frame Aluminum plate Tunnel ESB container rubber layer Aluminum plate Soft silicon joint Tunnel ESB container rubber layer Soft rubber foam PVC cap Soft rubber foam 14

15 Models layout instrumentation scheme Accelerometers Displacement sensors Extensometers Pore pressure cells 36mm A1 36mm 326mm 25mm S1 P2 P1 Dry Fontainebleau Sand (Dr=7%) 4mm 24mm 18mm S2 Model S3 P6 A11 A5 A15 A1 A8 A14 A7 P4 P5 A9 A6 A13 P3 A27 A2 A4 A3 A2 14mm 8mm 1mm 13mm 13mm A12 2mm y A19 A18 A17 A16 z x Accelerometer Laser displacement sensor Diagonal extensiometer Transversal "fork" extensiometer Pore pressure sensor 5mm 54mm A26 A23 A25 A22 A21 5.mm 6.mm A24 F5 F1 F1 F6 D1 D2 D3 D4 15

16 Extensometers Fork system of extensometers to measure the lateral displacement profiles of the tunnels walls with respect to the invert slab Diagonal extensometers to check the diagonal distortions along the tunnel longitudinal axis 16

17 Experimental procedure Consolidation stabilization circles (1g, 4g, 1g ) CPT test (dry tests) Shakes (EQ1 EQ4) DAS acquisition system (sampling frequency 12.8 khz) Tunnel ~ 37 cm 22 cm CPT 13 cm 17

18 Input motions Real record from the 1994 Northridge EQ scaled up to.1g,.2g,.3g a (g) g t (sec) Fourier amplitude f o,soil f (Hz) + sine wave (.3g, f = 2.125Hz) Input type Nominal amplitude (g) Model scale Prototype scale Nominal Duration (s) Model scale Prototype scale EQ EQ2 Northridge record EQ EQ4 Pseudo Harmonic (85Hz)

19 Testing Program 7 tests x 4 earthquakes : more than 12 records of the dynamic response Test case # Test name Structure flexibility Soil Dr (%) Soil saturation Culvert surface Test month 1 Dresbus2 1 1 Flexible Dry Rough April Dresbus2 2 1 Flexible Dry Smooth May Dresbus2 3 1 Rigid Dry Rough July 212 4* 5** Dresbus2 4 1 Dresbus2 4 2 Rigid Rigid 7 Saturated Saturated Rough Rough July 212 December Dresbus2 5 1 Rigid Dry Smooth August Dresbus2 6 1 Rigid Saturated Smooth October Dresbus2 7 1 Rigid Saturated Rough October 212 * Failed ** Repetition of Drebus

20 Experimental data processing Acceleration time histories Band pass filtering (2 4 Hz) Displacement time histories (double integration) Transfer functions (frequency domain analysis) Stress strain loops soil shear modulus (Zeghal and Elgamal, 1994, Brennan et al., 25) Tunnels deformation time histories Band pass filtering (2 4 Hz) Low pass filtering (4 Hz) Pore pressures time histories Low pass filtering (4 Hz) 2

21 Representative experimental data Acceleration time histories Flexible smooth tunnel in dry sand (Dresbus2 2 1 EQ1) A/4g A/4g A/4g A/4g A/4g A1 Input A A A A25 A A A A A A A A A A A A A A A A A A A A A

22 Maximum horizontal acceleration Flexible smooth tunnel in dry sand (Dresbus2 2 1 EQ1) Array 5 A/4g Array 4 A/4g Array 3 A/4g Array 2 A/4g Depth(m) Array 5 Array 4 Array 3 Array 2 Array 1.36 A11 A5 A15 A1 A8 A14 A7 A9 A6 A13 A19 A18 A17 A4 A12 A16 A1 A2 A3 A2 22

23 Maximum horizontal acceleration Flexible smooth tunnel in dry sand (Dresbus2 2 1 EQ1) tunnel depth Depth(m) Array 1 Array 2 Array 3 Array 4 Array 5 Array 5 Array 4 Array 3 Array 2 Array 1 A11 A5 A15 A1 A8 A14 A7 A9 A6 A13 A19 A18 A17 A4 A12 A16 A1 A2 A3 A2 23

24 Stress strain loops Flexible rough tunnel in dry sand (Dresbus2 1 1 EQ1 EQ4) 2 A12 A13 2 A13 A14 2 A14 A15 2 A6 A7 stress (kpa) A7 A A9 A A1 A strain (%) stress (kpa) Northridge,.1g strain (%) strain (%) strain (%) 6 A12 A13 6 A13 A14 6 A14 A15 6 A6 A7 stress (kpa) A7 A A9 A A1 A strain (%) stress (kpa) Sine wave,.3g strain (%) strain (%) strain (%) 24

25 Soil Vs Dry sand, flexible smooth tunnel (Dresbus2 2 1) Vs(m/s) EQ Vs(m/s) EQ2 Depth(m).2.25 Depth(m) Array 2 Array 4 Array 5 Hardin & Drenvich, Array 2 Array 4 Array 5 Hardin & Drenvich, 1972 Vs(m/s) Vs(m/s) EQ3.5 EQ Depth(m).2.25 Depth(m) Array 2 Array 4 Array 5 Hardin & Drenvich, Array 2 Array 4 Array 5 Hardin & Drenvich,

26 D(mm) Walls deformations Flexible rough tunnel in dry sand (Dresbus2 1 1 EQ1) F Invert slab F F F F1 F F2 F7 One signal reversed D(mm) F F F3 F8 F5 F4 F1 F9 D(mm) F3 F2 F1 F8 F7 F6 D(mm) F F F4 F9 Low pass filtered data D(mm) F5 Roof slab F F5 F

27 Walls deformations Rigid rough tunnel in dry sand (Dresbus2 3 1 EQ4) D(mm) F1 Invert slab F F1 F One signal reversed.3 F2.3 F7.3 F2 F7 D(mm) F5 F1.3 F3.3 F8.3 F3 F8 F4 F9 D(mm) F3 F2 F1 F8 F7 F6 D(mm) F F F4 F9 band pass filtered data D(mm) Roof slab F F F5 F

28 Maximum walls deformations Flexible rough tunnel in dry sand (Dresbus2 1 1) Deformation (mm) Deformation (mm) Depth(mm) 19 Depth(mm) EQ EQ2 Band pass filtered data 38 Left side wall Right side wall 38 Left side wall Right side wall Deformation (mm) Deformation (mm) Depth(mm) 19 Depth(mm) EQ EQ4 Left side wall Right side wall Left side wall Right side wall

29 Maximum walls deformations Rigid rough tunnel in dry sand (Dresbus2 3 1) Deformation (mm) Deformation (mm) Depth(mm) 19 Depth(mm) EQ EQ2 Band pass filtered data 38 Deformation (mm) Left side wall Right side wall Deformation (mm) Left side wall Right side wall Depth(mm) 19 Depth(mm) EQ EQ4 38 Left side wall Right side wall 38 Left side wall Right side wall 29

30 Diagonal deformations Flexible smooth tunnel in dry sand (Dresbus2 2 1, EQ4).15 D1.15 D2.15 D3.15 D D(mm) Comparisons D(mm).75 D1 D2 D3 D In phase response D4 D3 D2 D1 3

31 Soil surface settlements Rigid rough tunnel in dry sand (Dresbus2 3 1) Settlement(mm) Stabilization consolidation circles Northridge.1g to.3g Sine wavelet 2 S1 1 S2 S Sampling point S1 S2 S3 31

32 Preliminary interpretation of data Horizontal soil free field A/4g EQ EQ1 (.1g) A/4g EQ EQ2 (.2g) Dry tests Depth(m) Depth(m) DRESBUS DRESBUS DRESBUS DRESBUS Saturated tests Depth(m) A/4g EQ EQ1 (.1g) Depth(m) A/4g EQ EQ2 (.2g) DRESBUS DRESBUS DRESBUS

33 Maximum walls deformations input motion amplitude tunnel stiffness D(mm) Flexible rough tunnel in dry sand (max deformation:.12mm) Depth(mm) lsw rsw EQ1 EQ2 EQ3 EQ4.1g.2g.3g.3g D(mm) Rigid rough tunnel in dry sand (max deformation:.2mm) Depth(mm) lsw rsw EQ1 EQ2 EQ3 EQ4 33

34 Tunnel rugosity effect (dry tests) EQ2 D(mm) Depth(mm) Flexible tunnel in dry sand EQ3 D(mm) EQ4 D(mm) Depth(mm) lsw rsw Rough Smooth 34

35 Tunnel rugosity effect (saturated tests) EQ2 D(mm) Depth(mm) Rigid tunnel in saturated sand EQ3 D(mm) EQ4 D(mm) Depth(mm) lsw rsw Rough Smooth 35

36 Sand saturation effect EQ2 D(mm) Depth(mm) Rigid rough tunnel EQ4 D(mm) Depth(mm) lsw rsw Dry Saturated 36

37 Preliminary numerical analysis Full dynamic time history analyses of the coupled soil tunnel systems Analyses in prototype scale using ABAQUS No slip (solid connection) vs. Full slip conditions for the soil tunnel interface 37

38 The soil mechanical properties are adopted according to the strain levels introduced by the each earthquake Gmax estimation and appropriate G γ D curves? Vs(m/s) γ (%) Depth(m) G/Go D (%) Hardin and Drenvich, γ (%) 38

39 Acceleration time histories EQL Full slip analysis Soil surface Tunnel roof slab Tunnel invert slab A (g) Soil base t (s) 39

Tunnel response EQL No slip analysis Displacement (mm) 1.5 1.5 -.5-1 -1.

40 Tunnel response EQL No slip analysis Displacement (mm) F4 Displacement (mm) Diagonal extension Displacement (mm) F2 4

41 TA Project: TUNNELSEIS 41

Project partners and research team TA User team Kyriazis Pitilakis (Professor, AUTH) Lead user Grigoris Tsinidis (Civil Engineer MSc, PhD candidate AUTH) Anastasios Anastasiadis (Assistant Professor,

42 Project partners and research team TA User team Kyriazis Pitilakis (Professor, AUTH) Lead user Grigoris Tsinidis (Civil Engineer MSc, PhD candidate AUTH) Anastasios Anastasiadis (Assistant Professor, AUTH) Dimitris Pitilakis (Assistant Professor, AUTH) Roberto Paolucci (Professor, POLITECNICO DI MILANO) Access Provider: Schofield Centre, UCAM, UK Gopal Madabhushi (Professor, UCAM) Charles Heron (PhD candidate, UCAM) Mark Stringer (Dr Civil Engineer, UCAM) 42

43 Dynamic centrifuge tests Dynamic centrifuge tests on square tunnels embedded in dry sand, under centrifuge acceleration of 5g Larger models than DRESBUS II Investigation of tunnel flexibility at extreme ends 43

44 Centrifuge facility Turner beam centrifuge Schofield Centre UCAM SAM actuator (fixed amplitude and frequency inputs or sine sweeps) Large Equivalent Shear Box (ESB) container 44

Materials Sand Hostun HN31 sand, of relative density of

section 663A aluminum alloy 1 x 1 x 22 (mm) walls

wrapped to form the section 1 x 1 x 21 (mm) walls

45 Materials Sand Hostun HN31 sand, of relative density of about 5% and 9% Tunnel models Rigid tunnel Extruded section 663A aluminum alloy 1 x 1 x 22 (mm) walls thickness: 2 mm Flexible tunnel 33 swg soft alumimum foil wrapped to form the section 1 x 1 x 21 (mm) walls thickness:.5 mm Flexibility ratios >>1 (flexible tunnels compared to the soil) weld 45

46 Models preparation Automatic pluvation device During the construction, the tunnel and all the embedded transducers positioned in the model Trial poors for calibration 46

47 Tunnel boundaries Avoid sand entrance inside the model without affecting the tunnel plane strain behavior PVC plates 11 x 11 x 1 (mm) 47

48 Models layout instrumentation scheme Accelerometers Pressures cells Position sensors (POTs) LVDTs Strain gauges Air hammer g AH4 AH3 AH2 AH1 Air hammer LVDT1 LVDT2 POT1 POT2 AH5 ACC1 ACC8 ACC15 ACC14 ACC16 ACC7 PC2 ACC13 PC1 ACC12 ACC11 ACC9 1mm ACC6 ACC5 ACC4 (Dimensions in mm) Accelerometer Pressure cell LVDT POT Strain gauge Stain gauges set ups Rigid tunnel ACC3 SG A4 ACC3 SG B3 SG B4 ACC2 ACC2 ACC1 SG A1 CC1 SG B1 SG A2 Flexible tunnel SG A1 SG B2 SG A3 SG A3 SG B2 SG A2 SG B1 Test # Tunnel Soil Dr (%) Soiltunnel interface Number of flights 1 Rigid 5 Smooth 2 2 Flexible 5 Rough* 2 3 Rigid 9 Rough* 2 * Stuck sand 48

calibration factors (b) (c) supporting frame fixity fixity fixity fixity q supporting frame fixity q box with sand (d)

49 Strain gauges calibration (a) Calibration factors are derived for simple static loading patterns ABAQUS static analysis to estimate internal forces at each strain gauge position and to establish Internal force Voltage calibration curves calibration factors (b) (c) supporting frame fixity fixity fixity fixity q supporting frame fixity q box with sand (d) Voltage (V) SG B1 LC1a LC1b Weigh (kg) (e) 3 Voltage (V) 2 1 SG B1 Gauge Factor K= M (Nmm/mm)

50 Experimental procedure Spin up in steps (1g 5g) Air hammer testing during swing up and before each shake Shakes pseudo sine or sine sweep motions Acquisition systems Swing up: CDAQS (sampling frequency: 4 Hz) Dynamic tests: CDAQS (sampling frequency: 4 khz) Air hammer testing: DasyLab (sampling frequency: 5 khz) 5

51 Input motions Test ID Tunnel Depth (mm) D r (%) Test 1 Rigid smooth external face 6 51 Test 2 Flexible rough external face 6 5 Test 3 Rigid rough external face 1 89 EQ ID Flight Input type* Frequency (Hz) Amplitude (g) Nominal Duration (s) EQ1 1 PH 6 (1.2) 1.5 (.21).4 (2) EQ2 1 PH 6 (1.2) 12.9 (.26).4 (2) EQ3 1 PH 6 (1.2) 15.7 (.31).4 (2) EQ4 1 PH 6 (1.2) (.37).4 (2) EQ1 1 PH 3 (.6) 1.29 (.26).4 (2) EQ2 1 PH 45 (.9) 4. (.8).4 (2) EQ3 2 PH 45 (.9) 4. (.8).4 (2) EQ1 1 PH 3 (.6) 1. (.2).4 (2) EQ2 1 PH 45 (.9) 4. (.8).4 (2) EQ3 1 PH 5 (1) 6.5 (.13).4 (2) EQ4 1 PH 5 (1) 12. (.24).4 (2) EQ5 1 SS 6 (1.2) 12. (.24) 3. (15) EQ6 2 PH 5 (1) 5.8 (.116).4 (2) EQ7 2 PH 5 (1) 6. (.12).6 (3) EQ8 2 PH 5 (1) 11. (.22).5 (25) *PH: pseudo harmonic, SS: sine sweep 15 EQ5 EQ6 EQ7 EQ8 7.5 A(g)

52 Experimental data processing Acceleration time histories Band pass filtering (2 4 Hz) Displacement time histories (double integration) Racking distortions (from displacement time histories) Transfer functions (frequency domain analysis) Stress strain loops soil shear modulus (Zeghal and Elgamal, 1994, Brennan et al., 25) Earth pressures, displacements, internal forces time histories Low pass filtering (4 Hz) 52

53 Representative experimental data Air hammer testing Vs profiles Test 3, second flight 1 AH1 Time histories t1 Comparisons with an empirical formulation (Hardin and Drenvich, 1972) 1 AH2 t2 Vs(m/s) Record (V) 1 AH3 t AH4 t4 Depth(m).2.25 Post EQ1 Post EQ2 1.3 Post EQ3 5g AH5 t5.35 Hardin and Drenvich,

54 Swing Up (Test 3) Increase of self weight increase of pressures and internal forces Displacement (mm) Moment (Nmm/mm) (c) (a) SG B1 SG B2 SG B4 LVDT1 LVDT t(min) Pressure (kpa) Axial force (N/mm) (d) PC1 PC2 SG A1 SG A2 SG A3 SG A4 (b) t(min) 54

55 Acceleration time histories (Test 1, EQ4).6 ACC1 Input.6 ACC2.6 ACC3.6 ACC A/5g ACC5.6 ACC6.6 ACC7.6 ACC A/5g ACC9.6 ACC1.6 ACC11.6 ACC A/5g ACC13.6 ACC14.6 ACC15.6 ACC A/5g

56 Vertical acceleration on tunnels roof slabs Tests 2 & 3: out of phase records; rocking response? Effect of shear stresses on the walls Test2 EQ2 (.8g*) Test3 EQ4(.24g*) A/5g τxy = + τyx τyx ACC15 ACC16 τxy 56

57 Soil surface displacements (Test 1) 2 Dynamic Settlements (e) D(mm) 4 6 LVDT1 LVDT LVDT1 LVDT2 57

58 Earth pressures on the tunnel side wall (Test 3) Residual values after shaking (soil densification, soil yielding) Similar response reported by Cilingir and Madabhushi (211) 75 EQ1 75 EQ2 75 EQ3 75 EQ4 Pressure(kPa) 75 Pressure(kPa) 75 Pressure(kPa) 75 Pressure(kPa) EQ EQ EQ EQ8 75 PC2 PC1 Pressure(kPa) 75 Pressure(kPa) 75 Pressure(kPa) 75 Pressure(kPa) PC1 PC2 58

59 Tunnel bending moments (Tests 2 & 3) Residual values after shaking (soil densification, soil yielding) Similar results from centrifuge tests on circular tunnels (Lanzano et al., 212) Transient stage M(Nmm/mm) Test2 EQ2 (.8g*) Flexible tunnel Steady state stage Test3 EQ2 (.8g*) Rigid tunnel Residual stage M 59

60 Axial forces bending moments (Test 3, EQ3) Small Residual values after shaking (soil densification, soil yielding, slippage) Out of phase response for the walls: Rocking response for the tunnel Axial force (N/mm) Axial force (N/mm) SG A SG A2 SG A SG A1 vs. SG A3 SG A1 SG A SG A A1 A3 6

61 Flexible tunnel collapse The flexible tunnel collapsed during an earthquake Model excavation tunnel deformed shape 61

62 Soil tunnel deformed shape (settlements up to 2m!) (b) (Dimensions in mm) (e) Tunnel Deformed shape from PIV analysis

63 Collapse mechanism: Swing up of the centrifuge (increase of the gravity loads): buckling of the roof slab right wall corner Larger compressive loads on the left side wall Buckling of the wall during the subsequent final earthquake P delta effects also affected the behavior D(mm) N(N/mm) M(Nmm/mm) Swing Up 4 Corner buckling 8 12 (a) LVDT1 LVDT SG A1 1 SG A2 15 (b) SG A SG B1 SG B2 2 (c) t(min) D(mm) N(N/mm) M(Nmm/mm) EQ (g) (f) Tunnel collapse 1 (h)

64 Preliminary numerical analysis Full dynamic time history analyses of the coupled soil tunnel systems Test 3 Analyses in prototype scale using ABAQUS Interface (Coulomb friction, μ =.84) 64

65 Soil non linear behavior Visco elastic material (Equivalent linear approximation) Combined equivalent linear elastoplastic approximation (Mohr Coulomb) Vs(m/s) A/5g Depth(m).2 G/Go D (%) Depth(m) Hardin and Drenvich,1972 Air hammer test strain(%).3.4 Experimental data EERA analysis 65

66 Accelerations.4 ACC1 Input.4 ACC2.4 ACC3.4 ACC A/5g ACC5.4 ACC6.4 ACC7.4 ACC A/5g Experimental data Numerical prediction ACC9.4 ACC1.4 ACC11.4 ACC A/5g ACC13.4 ACC14.4 ACC15.4 ACC A/5g

67 Vertical acceleration on roof slab Out of phase response reproduced by the numerical analyses (Visco elastic analysis).2 Experimental data.2 Numerical predictions.1.1 A/5g.1 ACC15 ACC ACC15 ACC16 67

68 Tunnel internal forces Differences due to the difference between the assumed and the actual in test mechanical properties of the soil, the tunnel and their interface 4 SG A1 4 SG A2 4 SG A3 4 SG A N(N/mm) SG B SG B SG B M(Nmm/mm) Experimental data Experimental data Numerical prediction Numerical prediction

69 Conclusions 69

70 Conclusions DRESBUS II Maximum soil horizontal accelerations were slightly amplified within the soil deposit, for the dry tests, while for the saturated tests the amplification effects were less important due to the probable higher variation of the soil stiffness The side walls horizontal deformations developed in a symmetrical manner The diagonal extensometers denoted the plane strain behavior of the model sections Rigid tunnels were understandably less deformed during shaking compared to the flexible sections The effects of the face rugosity and saturation are still under investigation 7

71 Conclusions TUNNELSEIS The horizontal acceleration was generally amplified towards the surface, while the presence of the tunnel affected this amplification Vertical acceleration time histories recorded on the sides of the roof slab indicated a rocking mode of vibration for the tunnels Residual values were reported after each shake for the earth pressures on the side walls and the dynamic bending moments due to soil yielding and/or densification Smaller residuals were observed for the dynamic axial forces due to the soil densification, soil yielding and a small amount of sliding at the interface 71

72 Acknoledgements The research leading to the presented results has received funding from the European Community s Seventh Framework Programme [FP7/27 213] for access to the Turner Beam Centrifuge, Cambridge, UK, and the IFSTTAR Centrifuge, Nantes, FR under grant agreement n o [SERIES] The technical support received by the Technicians of both the facilities is gratefully acknowledged DRESBUS II: TUNNELSEIS: 72

73 Publications (Submitted or near submission) Tsinidis G., Heron C., Pitilakis K., Madabhushi G. (213) Physical Modeling for the Evaluation of the Seismic Behavior of Square Tunnels. A. Ilki and M.N. Fardis (eds.), Seismic Evaluation and Rehabilitation of Structures, Geotechnical, Geological and Earthquake Engineering 26 (in press) Tsinidis G., Pitilakis K., Heron C., Madabhushi G. (213) Experimental and Numerical Investigation of the Seismic Behavior of Rectangular Tunnels in Soft Soils. Proceedings of the 4 th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 213), June 213, Kos Island, Greece Tsinidis G., Rovithis E., Pitilakis K., Chazelas J. L.(213) Centrifuge Modeling of the Dynamic Response of Shallow Rectangular Culverts in Sand. SERIES concluding Workshop, Ispra, May 28 3 (near submission) Tsinidis G., Heron C., Pitilakis K., Madabhushi G. (213) Centrifuge Modeling of the Dynamic Behavior of Square Tunnels in Sand. SERIES concluding Workshop, Ispra, May 28 3 (near submission) Tsinidis G., Heron C., Pitilakis K., Madabhushi G. (213) Experimental Investigation of the Seismic Behavior of Square Tunnels in Sand. (Journal paper near submission) Tsinidis G., Rovithis E., Pitilakis K., Chazelas J. L. (213) Seismic Behavior of Swallow Rectangular Culverts Embedded in Sand (Journal paper near submission) 73

74 Thank you 74

SEISMIC RESPONSE AND DESIGN OF RECTANGULAR TUNNELS

SECED 5 Conference: Earthquake Risk and Engineering towards a Resilient World 9- July 5, Cambridge UK SEISMIC RESPONSE AND DESIGN OF RECTANGULAR TUNNELS Grigorios TSINIDIS, Kyriazis PITILAKIS, Christos