SEISMIC PERFORMANCE OF CIRCULAR TUNNELS

Paper No. 1502

SECOND INTERNATIONAL CONFERENCE ON PERFORMANCE-BASED DESIGN IN EARTHQUAKE GEOTECHNICAL ENGINEERING

May 28-30, 2012 - TAORMINA (ITALY)

SEISMIC PERFORMANCE OF CIRCULAR TUNNELS: CENTRIFUGE

TESTING VERSUS NUMERICAL ANALYSIS

Grigorios TSINIDIS 1, Kyriazis PITILAKIS2

ABSTRACT

Tunnels constitute significant components of the build environment. The importance of this type of structures, for life safe and from an economic point of view, reveals the need for proper seismic design. Taking into consideration the specific conceptual features of tunnels that makes their seismic behavior

very distinct from aboveground structures and the lack of knowledge on many crucial issues, their seismic design becomes a very demanding procedure. Several methods have been proposed in the literature for the

seismic design. However their results may vary considerably, proving again the need for further improvement of the existing knowledge and design practices. To this end, dynamic centrifuge tests were

carried out in 2007, on circular tunnel models embedded in sand, within the framework of ReLUIS Project. Experimental data of one test case made available to the scientific community within a blind prediction contest, the Round Robin Tunnel Test (RRTT) organization. In this paper, we describe the numerical procedure to simulate the test, emphasizing on the success of the simulation and the good

validation of the numerical analysis with the experimental data. The numerical predictions compared with the experimental results, in terms of ground acceleration and bending moment of the tunnel lining. This first blind prediction test is successful providing better insight in the physical problem and the numerical

modeling. The ongoing further numerical modeling of the test and the further analysis of both the experimental and numerical results will contribute to the better understanding and modeling of the seismic

behavior of circular tunnels in alluvial deposits, with a final goal to develop a comprehensive methodology for the seismic design of tunnels and underground structures using in a certain extend the

PBD approach. Keywords: Tunnels, Soil-tunnel interaction, Centrifuge experiments, Numerical analysis

INTRODUCTION Tunnels constitute crucial components of the transportation network and the build environment. The last decades, tunnels were more frequently constructed to facilitate different needs (i.e. subways, underground parking stations, mountain tunnels, sewages etc.), especially in densely populated areas. Considering their significance for life safe and economy, their proper seismic design is of prior importance, especially in seismic prone areas. 1 Civil Engineer, MSc, PhD Candidate, Department of Civil Engineering, Aristotle University of Thessaloniki, Greece, e-mail: [email protected] 2 Professor, Department of Civil Engineering, Aristotle University of Thessaloniki, Greece, e-mail: [email protected]

II International Conference on Performance Based Design in Earthquake Geotechnical Engineering

May 2012, 28-30 - Taormina, Italy Seismic Performance and behavior of tunnels The available data shows that, in general, tunnels seem to be less vulnerable than aboveground structures, but not always. The collapse of the under construction (up to that date) twin Bolu tunnels, during the 1999 Kocaeli earthquake, is an indicative example of bad performance (Hashash et al., 2001, Kontoe et al. 2008) (Figure 1).

Figure 1. Collapse of Bolu tunnel during the 1999 Kocaeli earthquake (after Kontoe et al., 2008) Generally, moderate to heavy damages were observed for PGAs larger than 0.5g, whereas for PGAs smaller than 0.2g, none to slight damages were reported. The lining type and the soil-lining interface conditions are of prior importance for the seismic behavior of a tunnel. Unlined tunnels or tunnels constructed by masonry found to be more vulnerable. Tunnels have geometrical and conceptual features that make their seismic behavior very distinct from aboveground structures (i.e. Owen and Scholl, 1981 etc.). The ground deformations, introduced by the surrounding soils, are prevailing, while the inertial forces are of secondary importance. During an earthquake, tunnels can be affected by: (i) ground shaking and/or (ii) permanent displacements by ground failure (i.e. liquefaction, slope instabilities, fault displacements). During ground shaking the tunnel can be deformed in various modes, both in the longitudinal and transverse direction, i.e. longitudinal axial deformation, longitudinal bending, cross sectional compression and cross sectional ovaling (Owen and Scholl, 1981). The latter is of prior importance, as it can cause large stresses on the tunnels lining. Seismic analysis methods Several methods have been proposed in the literature for the seismic design, ranging from closed form solutions (i.e. to compute the lining internal forces) and simplified uncoupled methods, to the more accurate full dynamic time history analysis of the soil-tunnel system (i.e. Wang, 1993, Penzien, 2000, Hashash et al., 2001, ISO 23469, 2005, FWHA, 2009 etc). A comprehensive review is made by Pitilakis and Tsinidis (2012). The results of these methods may significantly vary, demonstrating the relative lack of knowledge regarding the seismic behavior and design of tunnels. The proper estimation of several crucial parameters like of the design input motion, the distribution and the magnitude of the seismic shear stresses around the tunnel and the impedance functions, adequate for circular tunnels, are among the open issues that need further research. To this end, dynamic centrifuge tests were carried out on circular tunnel-models embedded in dry sand. The tests were performed in 2007 at the geotechnical centrifuge facility of the University of Cambridge (Schofield Center), by researchers of University of Napoli Federico II, within the framework of the ReLUIS Project (2005-2009) (i.e. Bilotta et al., 2009, Lanzano et al., 2009, Lanzano et al., 2010 etc).

0.30

.4m

DetailInvertheaveup

to0.5m

Backfillfoamconcrete

Previousshotcreteshell

BuckledandshearedHEBsteelribs


May 2012, 28-30 - Taormina, Italy Experimental data of one of these tests were made available to the scientific community within a blind prediction program, the Round Robin Tunnel Test (RRTT) organization. In this paper, we describe the numerical modeling of the test, emphasizing more on the successful simulation of the tunnel and ground response. The numerical predictions are presented and compared with the experimental results, in terms of accelerations and bending moment of the tunnel lining.

DYNAMIC CENTRIFUGE TESTS Four centrifuge tests were carried out on circular aluminum models embedded in dry sand (in two different burial depths), under a centrifugal acceleration of 80g (Bilotta et al., 2009, Lanzano et al., 2009, Lanzano et al., 2010, Bilotta et al., 2011). The tests were performed, using a small laminar box (500x250x300 mm3), at the 10m-diameter Turner Beam Centrifuge of the Schofield Center at the University of Cambridge. The beam-like structure that is rotating around a central vertical axis accommodates a swinging platform with the model and the actuator on the one end, and a counterweight on the other. Earthquake input motions are applied using the Stored Angular Momentum (SAM) actuator (Madabhushi, 1996), which is designed to apply sinusoidal input motions at a maximum frequency up to 60Hz and at a maximum amplitude of 20g (in model scale). All the models were made using dry Leighton Buzzard sand (grade E) reconstituted at two different relative densities (about 50% and 80%). Special care was taken during the pooring procedure to keep the soil models as uniform as possible. The circular tunnel models were manufactured by an aluminum tube having an external diameter D=75mm and a thickness t=0.5mm. Taking into consideration the scale factor N=80, this correspond to a 6m diameter prototype tunnel with a shotcrete lining of about 6cm. To avoid interaction of the model with the laminar box, the model was shorter than the box. Two square plates were placed at each end of the model, to avoid the entrance of the sand inside the model. The plates were lubricated to reduce any friction between the plate and the model that could affect the plane strain behavior of the model. The models were instrumented using miniature piezoelectric accelerometers to measure the horizontal and the vertical accelerations at several points into the soil and on the laminar box. Moreover the tunnel-model was instrumented with strain gauges to measure the bending moments and the hoop forces at four locations along 2 transverse sections (at the mid-span of the tunnel-model and 50mm aside to check the plane strain conditions). Two linear variable differential transducers (LVDTs) were attached on two gantries above the model to measure the soil surface settlements. During the test, the model was swung up to 80g in steps of 10g. Then the earthquakes (sine waves of increasing amplitude and frequency) were fired in a row, leaving some time between each earthquake. After four earthquakes, the centrifuge was slowed to 40g and one final earthquake was fired.

(a)

(b) (c)

Figure 2. (a) Turner beam centrifuge, (b) Tunnel-model with strain gauges, (b) Tunnel-model placement in the laminar box (after Bilotta et al., 2011)


May 2012, 28-30 - Taormina, Italy The experimental data of one of the tests, namely T3, were made available to the scientific community within a blind prediction program, the Round Robin Tunnel Test (RRTT) organization that was formed as a joint venture among technical committees TC104, TC203 and TC204 of ISSMGE. The main objective of this program was to numerically model the test and predict the experimental results, having only some general information about the layout of the test (Figure 3).The experimental data were made available for comparisons and further study after the submission of the numerical predictions.

NUMERICAL SIMULATION For the numerical simulation of the test we used the general purpose FE code ABAQUS (ABAQUS, 2009). Full dynamic time history analyses of the coupled soil-tunnel system were performed, under plane strain conditions, on prototype scale models (Figure 4). Appropriate scaling laws were used to convert the computed quantities from prototype scale to model scale (i.e. Schofield, 1981). The soil was meshed with quadratic planestrain elements, while the tunnel-model was modelled with beam elements. Linear elastic behavior was assumed for the tunnel specimen (E=70GPa, v=0.33 for the aluminum alloy), while soil behavior was modelled as (i) a linear visco-elastic material or (ii) an elastoplastic MohrCoulomb material, as described in detail in the ensuing. The base boundary of the model was simulated as rigid bedrock, while for the vertical boundaries kinematic constrains were introduced, forcing the opposite vertical sides to move simultaneously preventing any rotation. The soil-tunnel interface was modelled using a Coulomb friction model, introducing a coefficient of friction between the soil and the aluminum tunnel lining, =0.4. The later was estimated using available data from the literature (i.e. Uesugi & Kishida, 1986, Kishida and Uesugi, 1987) and assuming a rather smooth surface for the lining. It is noted that this parameter might be very crucial for the tunnels behavior. Neither separation nor penetration between the soil and the model was allowed, assuming full contact in normal direction during the test. The input motion was introduced at the base boundary in terms of acceleration time histories, referring to the motion recorded at the reference accelerometer (Acc 13). The signals were filtered using a 4th order Butterworth band-pass filter embedded in SeismoSignal software (Seismosoft, 2011). In all cases, the analyses were performed in two steps. In the first step the gravity loads were introduced (i.e. geostatic step), while in the second step the earthquake input motion was applied in a dynamic step. Soil constitutive model To describe the inelastic soil behavior under seismic loading, in the case of the visco-elastic analyses, the soil shear modulus was reduced and the material damping was adequately increased according to the shear deformation level estimated for each earthquake scenario by means of 1D equivalent linear soil response analysis. The calculation was performed in the frequency domain using the code EERA (Barbet et al., 2000). The G--D curves required for the analyses were derived from available laboratory tests results (Visone, 2009). In the 2D full dynamic time history analyses, the soil shear modulus and the damping were assumed to be constant with depth (mobilized values in Table 1). In the final analysis of the test the soil was modelled with an elasto-plastic Mohr Coulomb material. The elastic stiffness was kept constant with depth and assumed to be reduced with respect to the small strain elastic stiffness corresponding to the computed (from the 1D EQL response analysis) shear strain level of the fourth earthquake (EQ4). Regarding the shear strength parameters of the soil model, the values were adopted according to the laboratory test results for the specific fraction of sand (Visone, 2009). All the mechanical properties for the sand, utilized in the analyses, are tabulated in Table 1.


May 2012, 28-30 - Taormina, Italy

1g

500mm

290m

m

110mm 110mm124mm 124mm

Acc11

ScaleFactorN=80Shakedirection

125m

m144m

m

Acc15

Acc16

Acc13

Acc8 Acc9

Acc1Acc4SW SE

NW NE

LVDT045 LVDT059

Acc5

Acc7

45mm

130m

m

Acc14Acc6

Acc10

Acc12Acc3

57.5mm

57.5mm

Tunneld=75mm

Accelerometersensingdirectiontowardsleft

LVDT

Straingauge

Referenceaccelerometerrecordinginputsignal

DryFractionEsand

Dr=75.9%

Accelerometersensingdirectionvertical

Figure 3. Layout of model T3 (modified after Bilotta et al., 2011)

Figure 4. (a) Numerical model in ABAQUS, (b) G--D curves adopted in the analyses (black solid line) vs. triaxial shear and resonant column tests results (experimental results after Visone, 2009)

Table 1 Mechanical properties in case of visco-elastic dynamic analyses of the coupled system Rayleigh damping

parameters Test case Vsm

(m/sec)

(t/m3) Gm

(MPa) v Damping

(%) a b () () c (MPa)

Equivalent linear analyses EQ1 136 28.8 3.0 0.1371 0.0039 EQ2 129 25.8 5.0 0.2218 0.0047 EQ3 126 24.5 7.0 0.4423 0.0062 EQ4 116

1.55

20.9

0.333

12.0 0.8815 0.0103

- - -

Elasto-plastic analyses All 116 1.55 20.9 0.333 10.0 0.734 0.0085 38 9 0.001

23.2m

40.0m

Displacementconstrainsa(t)

GD

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1(%)

G/Go

0

10

20

30

40

50

0.0001 0.001 0.01 0.1 1

DT(%)

FittingTSTestsRCtests

(a) (b)


May 2012, 28-30 - Taormina, Italy A crucial parameter for the numerical analyses was the determination of the small strain shear modulus. According to Brennan et al. (2005), it is better to obtain the small strain shear modulus through the actual test results rather than using empirical formulations, as the latter can lead to an overestimation of the modulus. Unfortunately, we did not have enough data to compute the small strain shear modulus from test results and so we proceeded with the estimation of the modulus using the following procedure. First, the shear modulus was computed according to Hardin and Drnevich (1972) formulation. Using the estimated shear modulus distribution with depth, in a 1D equivalent linear soil response analysis of the free field soil deposit (EERA), the G/Gmax ratios were computed, for each earthquake scenario. The reduced shear moduli (mean values) were compared with the mobilized shear moduli, evaluated from the experimental data of this specific case study (Test T3), as were reported by Lanzano et al. (2010). The comparison indicated an overestimation of the small strain shear modulus. To this end we applied a try and error procedure to evaluate the accurate small strain shear modulus, assuming gradually reduced small strain shear modulus distribution (in respect with the initial estimation) (Figure 5a). The comparisons of the computed shear moduli (from the 1D soil response analyses) with the experimentally derived shear moduli (Lanzano et al. 2010) are presented in Figure 5b, for the final iteration of the aforementioned procedure.

0.00

0.06

0.12

0.17

0.23

0.29

0 20 40 60

Gmax(MPa)

Depth(m

)

0.00

0.06

0.12

0.17

0.23

0.29

10 15 20 25 30

Shearmodulus(kPa)

Depth(m

)

Testresults EQ1 TestresultsEQ2Testresults EQ3 TestresultsEQ4EERAEQ1 EERAEQ2EERAEQ3 EERAEQ4

(a) (b) Figure 5 (a) Small strain shear modulus distribution to depth at the final iteration of the

procedure, (b) Comparisons of the mobilized shear moduli computed from the 1D equivalent linear analyses in EERA with the derived from experimental data shear moduli (after Lanzano et al.,

2010)

NUMERICAL PREDICTIONS VS EXPERIMENTAL RESULTS In this section, indicative numerical predictions are presented, compared with experimental records, and discussed, in terms of accelerations and dynamic increments of bending moments of the tunnel lining. All the comparisons are made in model scale. Accelerations As mentioned the acceleration time histories were recorded at several points in the soil deposit and on the laminar box, by miniature accelerometers forming three arrays, namely the reference array, the free field array and the tunnel array. In Figures 6-10 indicative computed acceleration time histories are presented and compared with the recorded data. It is noted that both time histories were filtered. Considering the general character of the assumptions we made for the numerical simulation, as we did not have all the experimental data, the numerical predictions are compared to the experimental results reasonably well.



Acc4

84048

0 0.5 1 1.5

t(s)

A(g)

Acc7

84048

0 0.5 1 1.5

t(s)A(g)

Acc8

84048

0 0.5 1 1.5

t(s)A(g)

Acc4

84048

0.5 0.55 0.6 0.65 0.7

t(s)

A(g)

Acc7

84048

0.5 0.55 0.6 0.65 0.7

t(s)A(g)

Acc8

84048

0.5 0.55 0.6 0.65 0.7

t(s)A(g)

Acc7Numerical prediction Experimental results

Figure 6. Indicative acceleration time histories for EQ1; Experimental records vs. equivalent linear analysis results

Acc4

84048

0 0.5 1 1.5

t(s)A(g)

Acc7

84048

0 0.5 1 1.5

t(s)A(g)

Acc8

84048

0 0.5 1 1.5

t(s)A(g)

Acc4

84048

0.5 0.55 0.6 0.65 0.7

t(s)A(g)

Acc7

84048

0.5 0.55 0.6 0.65 0.7

t(s)A(g)

Acc8

84048

0.5 0.55 0.6 0.65 0.7

t(s)A(g)


Figure 7. Indicative acceleration time histories for EQ1; Experimental records vs. Mohr-Coulomb analysis results

Acc3

84048

0 0.2 0.4 0.6 0.8 1

t(s)A(g)

Acc6

84048

0 0.2 0.4 0.6 0.8 1

t(s)A(g)

Acc9

84048

0 0.2 0.4 0.6 0.8 1

t(s)

A(g)

Acc3

84048

0.4 0.45 0.5t(s)

A(g)

Acc6

84048

0.4 0.45 0.5t(s)

A(g)

Acc9

84048

0.4 0.45 0.5t(s)

A(g)

Acc7Numerical prediction Experimental results Figure 8. Indicative acceleration time histories for EQ2; Experimental records vs. Mohr-Coulomb

analysis results



Acc5

14707

14

0 0.45 0.9

t(s)

A(g)

Acc14

14707

14

0 0.45 0.9t(s)

A(g)

Acc15

14707

14

0 0.45 0.9t(s)

A(g)

Acc5

14707

14

0.25 0.3 0.35

t(s)A(g)

Acc14

14707

14

0.25 0.3 0.35t(s)

A(g)

Acc15

14707

14

0.25 0.3 0.35t(s)

A(g)


Figure 9. Indicative acceleration time histories for EQ3; Experimental records vs. equivalent linear analysis results

Acc5

20100

1020

0 0.45 0.9t(s)

A(g)

Acc6

20100

1020

0 0.45 0.9t(s)

A(g)

Acc8

20100

1020

0 0.45 0.9t(s)A(g)

Acc5

20100

1020

0.25 0.3 0.35t(s)

A(g)

Acc6

20100

1020

0.25 0.3 0.35t(s)

A(g)

Acc8

20100

1020

0.25 0.3 0.35t(s)

A(g)


Figure 10. Indicative acceleration time histories for EQ4; Experimental records vs. Mohr Coulomb analysis results

Experimentaldata

0

0.3

0.6

0.9

1.2

0 100 200 300f(Hz)

Amplitu

de

EQLanalyses

0

0.3

0.6

0.9

1.2

0 100 200 300f(Hz)

Amplitu

de

MCanalyses

0

0.3

0.6

0.9

1.2

0 100 200 300f(Hz)

Amplitu

de

Figure 11. Fourier Spectra of Acc8 as computed from numerical and experimental results for EQ3

The relatively minor discrepancies are mainly attributed to the difference of the assumed soil stiffness and damping with the actual one. Generally, the predictions of the Mohr-Coulomb analysis were closer to the experimental results. This is again attributed to the different soil stiffness assumed in the two analyses cases. Actually, when applying the Mohr-Coulomb criterion, the small strain shear modulus was assumed to be smaller than the equivalent static analyses for the test cases EQ1, EQ2 and EQ3.



Similar results, to the time domain, are observed in the frequency domain. In Figure 11, the computed Fourier spectra are compared with the experimental results at the soil surface just above the tunnel (Acc8), for the EQ3 earthquake scenario. It can be seen, that both the numerical models are generally reproducing the frequencies recorded during the test. There are some differences around 50-120Hz that are attributed, as mentioned before, to the difference of the assumed and the actual soil stiffness. Tunnel lining internal forces Both bending moments and axial loads were measured at four locations of the lining. However, only the bending moments were made available after the blind prediction phase. During each shaking, three distinctive stages were observed for the tunnel lining bending moments, namely: a transient stage following by steady state circles and finally a post-earthquake residual stage (Figure 12). This behavior is expected in case of flexible structures (i.e. Cilingir and Madabhushi, 2010) and it is probably attributed to the soil plastic deformations that can lead to large stress redistributions in the soil around the tunnel. Numerical models did not manage to capture the exact evolution of these experimental bending moments, although similar phenomena (residual values for the elasto-plastic analysis etc.) were observed. The accuracy of the measured values, the relatively higher shear strength parameters adopted in the analyses or even the modeling of the soil-tunnel interface could possibly cause the discrepancies between the experimental and the computed values. Probably, the plastic deformations predicted by the numerical model where much lower that the actual ones.

Experimentaldata

20

2

4

6

8

0 1 2 3 4 5 6t(s)

M(N

mm/m

m) NW NE

SW SE

Figure 12. Bending moment records at four locations

In Figure 13 the experimental results are compared with the numerical predictions and the results of the closed form solutions proposed by Wang (1993) for the full slip case. As mentioned, the computed total bending moments, are not always matching the experimental results. However, the dynamic increments were in a relatively better agreement. These increments were computed as the maximum values of the semi-amplitude of cycles in the time histories, during the steady state stage. It can be also seen that the soil plastic deformations in case of the Mohr Coulomb analyses (Figure 14) are leading to important redistributions of the bending moment increments. Generally, the experimental results are closer to the Mohr Coulomb analysis results, while the predictions of the closed form solution are quite close to the numerically computed results. As we did not have any detailed information on several important issues we were forced to make general assumptions, as mentioned above, causing in a certain degree the differences between the experimental results and the numerical predictions. Having all the experimental data, we will proceed with a second phase of analyses, where the comparisons between the numerical and the experimental bending moments and strains in the tunnel lining are expected to be better and more reliable.



EQ1

0

0.01

0.02

0.03

0.04

0.05

0.06

0 60 120 180 240 300 360(deg)

|Mpk|(

Nmm/m

m)

EQ2

0

0.02

0.04

0.06

0.08

0.1

0.12

0 60 120 180 240 300 360(deg)

|Mpk|(

Nmm/m

m)

EQ3

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 60 120 180 240 300 360(deg)

|Mpk|(

Nmm/m

m)

EQ4

0

0.05

0.1

0.15

0.2

0.25

0.3

0 60 120 180 240 300 360(deg)

|Mpk|(

Nmm/m

m)

EQLanalysesExperimentaldataMCanalysesWang(1993)

2|Mpk|

Figure 13. Bending moment increments; Numerical predictions vs. experimental data

CONCLUSIONS

A first attempt to model numerically a dynamic centrifuge test of a circular tunnel embedded in dry sand is presented. The simulation was done in the framework of a blind prediction test within the Round Robin Tunnel Test (RRTT) organization. One test (T3), of a series of centrifuge tests that were performed on circular tunnels within the ReLUIS Project, at the Schofield Centre of University of Cambridge, is used as the benchmark case. The test was performed on an aluminum circular tunnel model embedded in dry sand and excited with sine wavelets of increasing amplitude and frequency, under centrifugal acceleration of 80g. Full dynamic time history analyses of the coupled soil-model system were performed using ABAQUS, under plane strain conditions. We were forced to make several assumptions regarding crucial parameters of the problem as the experimental data were not known at that time. In a first series of analyses the soil non-linear behavior was modeled as a linear visco-elastic material according to the equivalent linear approach, while in the final analysis an elastoplastic Mohr Coulomb material was adopted. The soil-tunnel interface was modelled using a Coulomb friction model.



Figure 14. Plastic deformations around the tunnel at the end of the dynamic analysis

The numerical predictions in terms of soil acceleration time histories and dynamic increments of bending moments at several locations of the tunnel lining are in good, if not excellent (i.e. accelerations) agreement, considering the absence of detailed experimental data. Having all the experimental data, further analysis will be performed, trying to better model the test and better understand the seismic behavior of this type of structures.

ACKNOWLEDGEMENTS The support we had by Prof. Emilio Bilotta and Prof. Francesco Silvestri, during the running of the Round Robin numerical test program, is kindly acknowledged. The work is partially supported by the SERIES research project.

REFERENCES ABAQUS (2009). Analysis Users Manual Volumes I - IV v6.9 [Computer Program], Dassault

Systmes, SIMULIA Inc, USA. Bardet, J. P., Ichii ,K. and Lin, C. H. (2000). EERA a Computer Program for Equivalent-linear Earthquake

site Response Analyses of Layered Soil Deposits. Univ. of Southern California, Dep. of Civil Eng. Bilotta, E., Lanzano, G., Madabhushi, S.P.G., Russo, G., Santucci de Magistris, F. and Silvestri, F. (2011)

RRTT, Round Robin numerical Test on Tunnels under seismic loading A joint venture between TC104, TC203 and TC204.

Bilotta, E., Lanzano, G., Russo, G., Silvestri, F. and Madabhushi, S.P.G. (2009). Seismic analyses of shallow tunnels by dynamic centrifuge tests and finite elements. Proc. 17th Int. Conf on Soil Mechanics and Geotechnical Engineering, Alexandra, Egypt.

Brennan, A. J., Thusyanthan, N. I. and Madabhushi, S.P.G. (2005). Evaluation of shear modulus and damping in dynamic centrifuge tests. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 131, No. 12, pp. 1488 1497.


May 2012, 28-30 - Taormina, Italy Cilingir, U., Madabhushi, S.P.G. (2010). A model study on the effects of input motion on the seismic

behavior of tunnels. Soil Dynamics and Earthquake Engineering, Vol. 31, pp.452 462. EERA, Equivalent-linear Earthquake site Response Analysis (Version 2000). [Computer Program Add-

in]. Available at: http://gees.usc.edu/GEES/Software/EERA2000/Default.htm (Accessed: March 2011). FWHA (2009). Technical manual for design and construction of road tunnels Civil elements. U.S.

Department of transportation. Federal Highway Administration. Publication No. FHWA NHI 09 010 March 2009. 629p.

Hardin, B.O. and Drnevich, V.P. (1972). Shear modulus and damping in soils: design equations and curves. Journal of the Soil Mechanics and Foundations Division 98 (SM7), pp. 667 92. ASCE.

Hashash, Y.M.A., Hook, J.J., Schmidt, B. and Yao, J.I-C. (2001). Seismic design and analysis of underground structures. Tunnel and Underground Space Technology, Vol. 16, No. 2, pp. 247 293.

ISO 23469 (2005). Bases for design of structures - Seismic actions for designing geotechnical works. ISO International Standard. ISO TC 98 / SC3 /WG10.

Kishida, H. and Uesugi, M. (1987). Tests of the interface between sand and steel in the simple shear apparatus. Geotechnique Vol. 37, No. 1, pp. 45 52.

Kontoe, S., Zdravkovic, L., Potts, D. and Mentiki, C. (2008). Case study on seismic tunnel response. Canadian Geotechnical Journal, Vol. 45, pp. 1743 1764.

Lanzano, G., Bilotta, E., Russo, G., Silvestri, F. and Madabhushi S.P.G. (2009). Experimental assessment of performance-based methods for the seismic design of circular tunnels, Performance-Based design in Earthquake Geotechnical Engineering, Kokusho, Tsukamoto & Yoshimine (eds.), Taylor & Francis Group, London.

Lanzano, G., Bilotta, E., Russo, G., Silvestri, F. and Madabhushi S.P.G. (2010). Dynamic centrifuge tests on shallow tunnel models in dry sand. VII International Conference on Physical Modelling in Geotechnics, Zurich, Springman, Laue & Seward (eds.), Taylor & Francis Group, London.

Madabhushi, S.P.G., Schofield, A.N. and Lesley, S. (1998). A new stored angular momentum (SAM) based earthquake actuator. Proceedings of centrifuge 98. Rotterdam: Balkema, pp. 111 116.

Owen, G. N. and Scholl, R.E. (1981). Earthquake engineering of large underground structures. Report No. FHWA/RD-80/195, Federal Highway Administration and National Science Foundation, 279p.

Penzien, J. (2000). Seismically induced racking of tunnel linings. Earthquake Engineering and Structural Dynamics, Vol. 29, pp. 683 691.

Pitilakis, K. and Tsinidis, G. (2012). Performance and seismic design of underground structures. Proceedings of II International Conference on Performance Based Design in Earthquake Geotechnical Engineering (State of the art lecture). May 2012, Taormina, Italy.

Schofield, A. N. (1981). Dynamic and earthquake geotechnical centrifuge modelling. Proc. of Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri-Rolla, MO, USA, 10811100.

Seismosoft, Seismosignal (Version 4.1.2). [Computer Program]. Available at: http://www.seismosoft.com (Accessed: March 2011).

Uesugi, M. and Kishida, H. (1986). Frictional resistance at yield between dry sand and mild steel. Soils and Foundations, Vol. 26, No. 4, pp. 139 149.

Visone, C. (2009). Performance based design of embedded retaining walls. Ph.D. Thesis, Universit di Napoli Federico II.

Wang, J.N. (1993). Seismic Design of Tunnels: A Simple State-of-the-Art Design Approach. New York: Parsons Brinckerhoff Inc.

SEISMIC PERFORMANCE OF CIRCULAR TUNNELS

Documents

Transcript of SEISMIC PERFORMANCE OF CIRCULAR TUNNELS