- Email: [email protected]
Interpretation and back-analysis of the damage observed in a deep tunnel after the 2016 Norcia earthquake in Italy
Tunnelling and Underground Space Technology 89 (2019) 238–248
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Interpretation and back-analysis of the damage observed in a deep tunnel after the 2016 Norcia earthquake in Italy
T
⁎
Luigi Callisto , Cecilia Ricci Sapienza University of Rome, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Deep tunnel Seismic damage Soil-structure interaction
This paper deals with the interpretation of the damage originated by the 2016 Norcia earthquake, Italy, in a deep tunnel excavated in a calcareous rock mass. A careful investigation of the damage pattern, together with the availability of seismic signals recorded in the vicinity of the tunnel during the earthquake, prompted a backanalysis of the observed phenomenon. The study hinged on a combination of site response analyses, simulation of the tunnel construction, and computation of the effect of the earthquake on the tunnel lining. Specifically, the damage caused by the earthquake in the tunnel lining was evaluated both with a decoupled procedure, based on equivalent static loading, and with a fully coupled dynamic analysis of the soil-structure interaction. The results obtained from the back-analysis were in a good agreement with the observations, and contributed to evidence the main causes of the damage, related to the specific geometry and to the dynamic response of the lining. The approach used in the paper, validated for the present case study through the comparison with the observed tunnel damage, may be useful to assess the seismic vulnerability of existing tunnels and for the seismic design of new underground structures.
1. Introduction Several documented cases are available in which earthquakes of medium-high magnitude produced a significant damage to underground structures for which seismic forces had not been considered in the original design. For instance, Hashash et al. (2001) presented a compendium of cases in which underground structures were damaged by earthquakes; Wang et al. (2001) described the damage caused by the Chi-Chi earthquake to deep tunnels in Taiwan; and Yashiro et al. (2007) discussed the damage produced by four historical earthquakes on deep tunnels in Japan. More recently, Zhang et al. (2018) described the case study of the Tawarayama tunnel in Japan, that suffered extensive damage after the 2016 Kunamoto Earthquake. The technical literature provides several calculation approaches to evaluate the internal forces produced in a tunnel lining by earthquake loading, ranging from simplified solutions for basic geometries (e.g. Wang, 1993) to a combination of one-dimensional site response analyses and static numerical calculations (e.g. Argyroudis and Pitilakis, 2012), to non-linear dynamic analyses of the soil-structure interaction (e.g. Amorosi and Boldini, 2009, Argyroudis et al., 2017, Tsinidis and Pitilakis, 2018). A collection of available numerical approaches to this problem may be found in Bilotta et al. (2014), reporting the results of a benchmark test to reproduce the results of centrifuge tests involving the ⁎
dynamic loading of a circular tunnel, while Argyroudis and Kaynia (2014) reviewed available methods for the seismic fragility analysis and damage modes of transport infrastructure, including tunnels. Given the availability of such a wide range of available calculation tools, it is surprising that, in the presence of an actual disruption observed in existing tunnels, only a few studies produced a quantitative interpretation of the observed damage (e.g. Kontoe et al., 2008): in most situations the observed damage was explained on a semi-qualitative basis, invoking the possible presence of poor geological conditions or potential faults (Wang et al., 2001; Yashiro et al., 2007; Zhang et al., 2018). The objective of this paper is to describe the damage caused by a recent earthquake to a roadway tunnel in Italy, and to combine the damage observation with the available records of the seismic motion in order to produce a quantitative interpretation of the observed phenomenon. The interpretative approach is based on the investigation of the mechanical behaviour of the rock mass interacting with the tunnel and on a site-specific ground response analysis. Despite the inevitable simplifications and uncertainties of the methodology employed in this paper, which are duly evidenced in the following sections, it is believed that the strategy developed in this study is worthy of note because it provides validation and guidance for both the seismic design of new tunnels and the assessment of existing ones.
Corresponding author at: Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy. E-mail address: [email protected] (L. Callisto).
https://doi.org/10.1016/j.tust.2019.04.012 Received 27 September 2018; Received in revised form 7 February 2019; Accepted 14 April 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
km Umbria-Marche Appennine
m
T1214 damage
NORCIA
1500 1300 1200 1100
tunnel
1000 800
CALCARE MASSICCIO 0
CORNIOLA
500 920 m
San Benedetto tunnel
T1213
CAPODACQUA damaged section
1400
900
CAPODACQUA
0
1600
265 m
11 .5
k 10
12.0 km
NORCIA
elevation (m a.s.l.)
EPICENTRE
N
1000
1500
4000
distance (m)
4400 m
2 km
(a)
(b) Fig. 1. Plan view (a) and vertical profile (b) of the San Benedetto road tunnel.
2. Damage to the San Benedetto tunnel during the Norcia earthquake
pattern: large vertical cracks isolate a damaged portion of the side wall, while the remaining cracks show a combination of bending (excessive compression) and shear failure in the transverse section. Fig. 4b depicts the results of a detailed survey carried out after the event, showing the deformation of the cross-section with respect to the original one. In the most damaged section, the tunnel width shortened by about 0.15 m. The observed damage can be classified as “extensive” to “complete” according to the HAZUS-MH methodology (FEMA-NIBS, 2003). After the event, the road owner, Anas S.p.A, carried out an extensive investigation of the damage, including geometrical inspection, mechanical in-situ testing of the lining, execution of inclined boreholes from the tunnel lining, and seismic refraction tests along the damaged portion of the tunnel. The main results of these investigations were reported by Marzi et al. (2017). The borings through the tunnel lining revealed, quite unexpectedly, that in the portion of the tunnel under investigation the actual section of the lining differed from the original design, in that the more damaged Southern sidewall appeared thinner than the design thickness of 1 m, while the Northern sidewall was somewhat thicker. This flaw was probably caused by a misalignment of the tunnel excavation with respect to the road axis, which went undetected during construction. A comparison between the notional section of the lining and that resulting from the post-seismic investigation is presented in Fig. 2.
Fig. 1 shows a plan view and a vertical profile of the San Benedetto road tunnel. It has a total length of 4400 m, connecting the Italian provinces of Perugia (town of Norcia) to the West and Ascoli Piceno (town of Capodacqua) to the East. The tunnel is located in the Italian Appennines, at an elevation of about 1000 m above the sea level, with a maximum tunnel cover of about 600 m. The structure was constructed in the 1980s, excavating a small-diameter pilot tunnel with a boring machine, and enlarging the excavation with rock-blasting. A light temporary support was used, including radial bolts connected by a wire mesh and spritz-beton, followed by the cast-in-place of the final lining. Fig. 2a shows the design transverse section of the final lining: it is made of unreinforced concrete, with a constant thickness of 1 m, and is not provided with an invert. A horizontal roof, made with a 0.15 m-thick r.c. slab, and a vertical r.c. wall were constructed below the tunnel crown to obtain two ventilation chambers, as depicted in Fig. 2a. The tunnel was excavated through the geological formations of “Calcare Massiccio” and “Corniola”, as shown in Fig. 1b. After the MW = 6.5 Norcia Earthquake of 30 October 2016 a portion of the tunnel lining was damaged at about 920 m from the Western entrance, as indicated in Fig. 1b. The damaged portion of the tunnel is located in the “Corniola” formation, approximately 200 m east of the contact between the “Corniola” and the “Calcare Massiccio”. The “Corniola” formation is a grey-brown limestone containing varying fractions of flint, intensely fractured without a clear fracture orientation. In this section of the tunnel, both hydrogeologic considerations and direct measurement indicated the absence of water pressure in the rock fractures. The photographs of Fig. 3 show portions of the damaged lining. Concrete cracks and spalling were mostly located along the Southern sidewall, extending in some cases up to the crown. Fig. 4a shows a profile of the Southern sidewall with an indication of the main crack
3. Recorded seismic motion
R= 5
.1 m
The Norcia event was originated at a depth of about 9 km by a normal fault mechanism with no surface expression. Several stations in the area recorded the Norcia seismic event. The location of the two recording stations closest to the tunnel location is shown in Fig. 1a. These two stations, denoted as T1213 and T1214, are located on a stiff outcrop at an epicentral distance very similar to that of the damaged portion of the tunnel, but at different elevations: the station T1213 is
(a)
1.5 m
1.0 m SW
NE
NE
9.6
0.5 SW
(b)
Fig. 2. Notional transverse section of the tunnel lining (a), compared with the results of the post-seismic investigation (b). 239
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
Fig. 3. Damage observed in the lining after the Norcia Earthquake.
earthquake on the tunnel, as depicted schematically in Fig. 6. The following three computation phases are common to both approaches:
located at an elevation of 860 m a.s.l., lower than the tunnel axis, while the station T1214 is located at the elevation of 1490 m a.s.l., higher than the ground elevation at the tunnel site (1265 m a.s.l.). In a first stage, the horizontal components of the seismic motion recorded at these stations were projected onto the transverse and longitudinal directions of the tunnel. Fig. 5 shows a comparison between the transverse components of the accelerograms recorded at these two stations, in terms of acceleration time histories and of 5%damped elastic response spectra. Table 1 reports the properties of the transverse component of the recorded signals, where amax is the maximum acceleration, IA is the Arias intensity, T5-95 is the significant duration, and Tm is the mean quadratic period. From Fig. 5 and considering the values reported in Table 1, it is evident that the seismic motion recorded at station T1213 is significantly more severe than that recorded at station T1214. Since the epicentral distance of the two stations is about the same, assuming that the seismic waves propagated in the same stiff rock material, the difference between the two records could be ascribed to the different elevation of the recording stations, that may have produced a different dynamic response. This hypothesis is consistent with the frequency content of the records, quantified by the mean quadratic period Tm, showing that the station T1214, located at a higher elevation, recorded a motion characterised by lower frequencies.
A. the recorded seismic motion was deconvoluted to a depth corresponding to a fictitious bedrock, which was determined as described in Section 4.3.1; B. a one-dimensional propagation model was developed, extending from the fictitious bedrock to the actual elevation of the ground surface at the tunnel site (1265 m a.s.l.); C. a two-dimensional numerical sub-model of the transverse section of the tunnel was developed, and used to simulate the excavation of the tunnel. The decoupled approach (C1) consisted in carrying out one-dimensional site response analysis with the model in (B), evaluating the free-field maximum shear strain γ at the elevation of the tunnel, and applying this strain to deform uniformly the boundaries of the numerical sub-model in (C), obtaining the variation of the internal forces produced by the earthquake in the tunnel lining. In the coupled approach, the free-field site response analysis in (B) was used to derive the acceleration time-histories at the elevation corresponding to the bottom of the numerical sub-model (C). These accelerograms were used to perform a full dynamic analysis of the soilstructure interaction, to evaluate directly the dynamic response of the tunnel and the damage in its lining. A detailed description of the procedures adopted in these uncoupled and coupled approaches are provided in the following sections.
4. Modelling the effect of the earthquake on the tunnel 4.1. Outline of the modelling strategy
4.2. Mechanical model of the subsoil
A plane strain assumption was made, assuming that the damage in the tunnel lining was caused by vertically propagating SH waves, producing bending in a plane transversal to the tunnel axis. It was also assumed that only the horizontal component of the seismic motion, associated with the vertical propagation of shear waves, had an influence on the observed damage, neglecting the vertical motion component. Both a decoupled and a coupled approach were adopted to provide a quantitative interpretation of the damage induced by the Norcia
For the purpose of the present analyses, the rock mass was modelled as a uniform equivalent continuum. Compression tests carried out on intact samples provided an average uniaxial compressive strength of the rock σci = 40 MPa. The small-strain stiffness of the rock mass was evaluated from the results of seismic refraction tests carried along two 100 m-long stretches within the tunnel. At a distance of about 10 m from the sidewalls, the shear wave velocity measured in these tests is original transverse section damaged transverse section
crack pattern on South sidewall
NE (a)
SW (b)
Fig. 4. (a) Longitudinal profile of the Southern side wall with indication of cracks in the lining; (b) original and damaged transverse section. 240
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
0.8
T1213
a (g)
0.4 0
Sa (g)
-0.4 -0.8 0.8
T1214
T1213 T1214
3
0.4
a (g)
4
2
0 -0.4
(a)
(b)
1
-0.8 0 0
10
20
30
0
0.4
0.8
t (s)
1.2
1.6
T (s)
Fig. 5. Time-histories (a) and 5%-damped elastic response spectra (b) of signals recorded at stations T1213 and T1214, projected onto the transverse direction of the tunnel.
mass, because it was assumed that the simulation of the excavation phases and the seismic loading with the sub-model (C) can directly account for the disturbance caused by the tunnel construction in the vicinity of the tunnel lining. Fig. 7 shows the Hoek-Brown failure criterion, obtained with the computed Hoek-Brown parameters (mb = 1.12, s = 0.0022, a = 0.51). Starting from this curve, an equivalent Mohr-Coulomb strength criterion for the rock mass was evaluated for the stress interval of interest. Using the linearization technique proposed for tunnels by Hoek et al. (2002), the equivalent values of cohesion and angle on shearing resistance are c = 0.8 MPa, and φ = 36°, respectively. The equivalent Mohr-Coulomb failure criterion obtained with this procedure is superimposed to the Hoek-Brown criterion in Fig. 7. This figure shows also the in situ stress state at the tunnel depth before the excavation, that was assumed spherical (earth pressure coefficient at rest K0 = 1). The figure also depicts an ideal unloading stress path followed by a rock element in the vicinity of the tunnel during the excavation, showing that the equivalent Mohr-Coulomb criterion is reached in a stress interval well within the range for which this criterion is equivalent to the Hoek-Brown curve.
about uniform, with a representative value VS = 2700 m/s. The corresponding p-wave velocity measured in the refraction tests is VP = 5500 m/s. At closer distances, the velocity of s- and p-waves becomes somewhat smaller, reaching about 40% of the above values in the vicinity of the lining. This finding is consistent with the results of dilatometer tests, carried out in boreholes drilled from the tunnel lining, that showed a systematic decrease of the equivalent Young's modulus in the portion of the rock mass closer to the tunnel lining. This effect can be ascribed to the stress release associated to the excavation of the tunnel, and possibly to the earthquake loading: values of the Geological Strength Index GSI (Marinos and Hoek, 2000) equal to 45 and 30 were evaluated for the undisturbed and disturbed portion of the rock mass, respectively. The Young's modulus obtained from the dilatometer tests in the undisturbed portion of the rock mass varied between 18 and 28 GPa, corresponding to about 35–50% of the small-strain Young's modulus obtained from a combination of the VS and VP values mentioned above, considering that laboratory testing on samples extracted from the boreholes provided an average mass density ρ = 2.75 Mg/m3. An estimation of the equivalent Young's modulus for the rock mass was obtained using the relationship proposed by Hoek and Diederichs (2006), based on the σci and GSI values, providing Eeq = 4.5 GPa for the undisturbed rock mass, and Eeq = 1.6 GPa for the disturbed portion encountered in the vicinity of the tunnel lining. The strength properties of the rock mass were evaluated using the Hoek-Brown strength criterion (Hoek and Brown, 1980) in the version provided by Hoek et al. (2002):
4.3. Evaluation of the seismic action 4.3.1. Deconvolution The horizontal components of the original seismic signal recorded at stations T1213 and T1214 were projected along the transverse axis of the tunnel, low-pass filtered at 20 Hz and base-line corrected. Subsequently, a linear deconvolution of the resulting signals was performed, to transfer the accelerograms down to a fictitious bedrock. The position of this bedrock was found iteratively, searching the bedrock elevation for which the deconvolution of the two records, obtained at different elevations, provided a similar bedrock signal. The deconvolution was carried out using the constant shear wave velocity Vs = 2700 m/s measured in the refraction tests, and a constant damping
a
σ σ1 = σ3 + σci ⎛mb 3 + s⎞ ⎝ σci ⎠ ⎜
⎟
(1)
where σ1 and σ3 are the maximum and minimum principal stress, respectively, and mb, s and a are the Hoek-Brown parameters, related to GSI. The strength criterion was evaluated only for the undisturbed rock
Table 1 Motion parameters of the transverse components of the records, before and after the deconvolution. Record
T1213 T1214
Elevation (m a.s.l.)
860 1490
Recorded signals
Deconvoluted signals
amax (g)
IA (m/s)
T5-95 (s)
Tm (s)
amax (g)
IA (m/s)
T5-95 (s)
Tm (s)
0.90 0.50
6.14 2.62
6.45 6.46
0.23 0.32
0.44 0.45
2.44 1.66
7.06 6.72
0.23 0.25
241
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
A
B
deconvolution
one-D domain
a
1490 m a.s.l.
C
T1214
t
545 m a.s.l.
deconvolution
315
t
a
a t
equivalent bedrock
shear strains
γ
C1
1000 m a.s.l.
720
deconvolution
860 m a.s.l. T1213
265
630
1265 m a.s.l.
a
two-D domain
site response analysis t
C2 a t
accelerations
Fig. 6. Modelling strategy for the seismic back-analysis of the San Benedetto tunnel.
two deconvoluted signals, that is plotted in the same scale as Fig. 5b for comparison. The corresponding properties of the accelerograms are reported in Table 1. It can be seen that the deconvoluted signals are very similar to each other, and particularly that the differences in the maximum acceleration and the Arias intensity of the original records were strongly reduced by the deconvolution. The mean quadratic period Tm of the T1214 record becomes, after the deconvolution, quite similar to that of the T1213 signal.
16
σ1 (MPa)
12
8
4.3.2. Site response analysis The two deconvoluted accelerograms were propagated through a one-dimensional rock column, extending from the bedrock to the elevation of the ground surface at the tunnel site (1265 m a.s.l.), assuming a stiff bedrock. The site response analyses were performed with both an equivalent linear method, using the code MARTA developed by the first Author, (https://sites.google.com/a/uniroma1.it/luigicallisto/attivita1), and with a non-linear calculation in the time domain carried out with the finite-difference software FLAC2D v.7.0 (Itasca, 2011). In the equivalent linear analysis, the modulus reduction and damping ratio curves proposed by Bardet et al. (2000) for soft rocks were adopted, whereas in the FLAC analysis the hysteretic damping model was used to reproduce the same modulus decay curve, using the sig3 expression (Itasca, 2011) of the secant modulus with the model parameters reported in Table 2. Fig. 9 shows a comparison between the modulus decay and damping ratio curves used for the linear equivalent analyses and those resulting from the calibration of the hysteretic damping model. The results of the site response analysis showed that the seismic input engages a modest non-linearity in the rock mass, with shear strains well within the interval in which the linear-equivalent and the hysteretic damping models provide a similar response. Specifically, Fig. 10 shows the results of the site response analyses, depicting for each signal the profile of the maximum acceleration (Fig. 10a), the elastic response spectrum computed at the tunnel elevation (Fig. 10b), and the time history of the shear strain at the tunnel elevation (Fig. 10c). Fig. 10a shows that the two calculation techniques give very similar results. The maximum shear strain γmax at the tunnel elevation, equal to about 0.02%, was provided by the T1213 record (Fig. 10c). Comparing Fig. 10b with Fig. 8b it can be seen that the propagation through a soil column at the tunnel location provides some amplification at low periods (T = 0.1–1 s) but a very large amplification at longer periods (T = 1–1.4 s), which roughly correspond to the fundamental period of the rock layer resulting from the site response analysis.
unloading stress path in situ stress state
4
Hoek - Brown Mohr - Coulomb 0 0
4
8
12
σ3 (MPa) Fig. 7. Hoek-Brown and Mohr-Coulomb failure criteria assumed for the rock mass.
ratio ξ selected in the range from 1 to 5%. For each tentative bedrock elevation, a normalised error E was evaluated on the basis of the 5%damped elastic response spectra calculated from the two signals resulting from the deconvolution: E was defined as the integral of the difference between the spectral ordinates, in the period interval of 0.02–10 s, divided by the average area of the response spectra. Fig. 8a depicts the variation of the error E as a function of the elevation of the fictitious bedrock, for three different values of the damping ratio ξ, evidencing that the optimum elevation of the bedrock is not very sensitive to the value assumed for the damping ratio. The lowest error, equal to about 0.35, was obtained for a fictitious bedrock placed at an elevation of 545 m a.s.l. The resulting fundamental period of the rock column at the tunnel location (Fig. 6) is then equal to 1.07 s. Fig. 8b shows a comparison of the bedrock response spectra obtained for the 242
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
ξ=5%
0.4
1% 2%
3
Sa (g)
0.6
545 m a.s.l.
error E
0.8
0.2
0 400
500
T1213 T1214
2 1
(a) 600
(b) 0
700
0
0.4
elevation (m a.s.l.)
0.8
1.2
1.6
T (s)
Fig. 8. (a) Variation of the error E computed in the deconvolution procedure, as a function of the elevation of the fictitious bedrock; (b) elastic response spectra of the deconvoluted signals.
A first stage of the calculation consisted of the generation of the in situ stress state, assuming an earth coefficient at rest K0 = 1. Subsequently, the tunnel excavation was simulated using the force reduction method (Panet & Guenot, 1982): the rock zones internal to the tunnel perimeter were deactivated, removing gradually a percentage λ of the corresponding nodal forces; in a subsequent stage, the tunnel lining was activated and the remaining nodal forces were reduced to zero. Afterwards, additional beam elements were activated simulating the horizontal roof and the vertical wall to create the ventilation chambers. Since a very flexible primary lining was used during the tunnel excavation, a stress release factor λ equal to 90% was used. The appropriateness of this factor was confirmed by a reasonable agreement between the flat-jack tests carried out in the undamaged portion of the tunnel lining and the axial stress of about 2 MPa computed in the lining after the simulation of the tunnel construction.
Table 2 Parameters of the FLAC sig3 model to used to describe the variation of secant stiffness with strain level (Itasca, 2011). a (–)
b (–)
x0 (–)
1
−1
−0.085
10
G/G0
0.8 0.6 0.4
8 6
Bardet et al. (2000) FLAC hysteretic damping
4
0.2 0 0.0001
2
damping ratio ξ (%)
1
4.5. Decoupled approach
0 0.001
0.01
0.1
In the decoupled approach, the effect of the earthquake was represented by the shear strains computed in the free-field site response analysis. In the numerical plane-strain model of the tunnel excavation, these free-field shear strains were applied carrying out a static analysis in which a linearly variable distribution of horizontal displacements was assigned to the lateral boundaries of the model, as depicted in Fig. 11b. The displacement umax in the figure corresponds to a shear strain γ = umax/H, H = 200 m being the height of the numerical model. During this calculation phase, the rock mass was assigned the same constitutive model used for the free-field site response analyses carried out with FLAC: a non-linear elastic, perfectly plastic behaviour, with an evolution of the secant shear stiffness consistent with the modulus decay curve selected for the rock mass. In the analysis, the lateral displacements were increased progressively, monitoring the resulting internal forces in the thinner side of the tunnel lining. A check of the uniformity of the shear strain distribution was carried out (Lu and Hwang, 2017) indicating that the distance of the lateral boundaries from the tunnel was large enough to ensure a uniform strain pattern in a substantial portion of the mesh, making the internal forces computed in the tunnel lining independent of the grid size. Fig. 12a shows the distributions of the internal forces in the lining (axial force N, bending moment M, shear force S) computed after the simulation of the tunnel construction. Fig. 12b depicts the relationship between the axial force N and the bending moment M in the thinner section of the tunnel lining (point P of Fig. 12a), computed in the decoupled analysis for values of γ ranging from zero to 0.03%. The figure also shows the M-N resistance domains for the original (1 m-thick) and the actual (0.5 m-thick) unreinforced concrete sections, computed on
1
shear strain amplitude γ (%) Fig. 9. Comparison of the modulus decay and damping ratio curves used for the linear equivalent analyses (Bardet et al., 2000) and those resulting from the calibration of the FLAC hysteretic damping model.
4.4. Analysis of the tunnel excavation A numerical sub-model of the tunnel excavation was developed in plane strain with the FLAC finite difference code, as illustrated in Fig. 11.a. It consists of a 200 m × 200 m domain surrounding the tunnel, subjected to the vertical geostatic stress σv0 = 4.44 MPa exerted by the rock mass overlying the top boundary, and to the boundary conditions depicted in the figure. For the analysis of the excavation, the rock mass was regarded as an elastic-perfectly plastic material, with the Mohr-Coulomb failure criterion (c = 0.8 MPa, φ′ = 36°) derived from the Hoek-Brown equivalency as explained in Section 4.2, and the Hoek and Diederichs (2006) Young's modulus E = 4.5 GPa, with a Poisson's ratio ν = 0.3. In the numerical model, the tunnel lining was modelled with linear beam elements, with a Young's modulus of 20 GPa and characterised by a piece-wise variable axial and bending stiffness that reproduced the non-symmetric tunnel lining of Fig. 2b. No interfaces were used between the lining and the rock mass, imagining a very rough contact as obtained by rock-blasting. Relative displacements at this contact could occur as an effect of rock yielding. The model did not include pore water pressures, in accordance with the available measurements. 243
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
0.4
0.8
T1213
amax (g) 1.2 0
0.4
0.8
Sa (g)
amax (g) 0
1.2
T1213 T1214
4 3
T1214
1200 2
(b)
1000
0 0
0.4
0.8
1.2
1.6
T (s)
0.02 800
γ (%)
elevation (m a.s.l.)
1
600
0
(c)
-0.02
(a)
0
10
20
30
t (s)
equivalent linear FLAC hysteretic damping
Fig. 10. Results of the site response analyses for the two deconvoluted signals: (a) profile of the maximum acceleration obtained from the equivalent linear (MARTA) and non-linear (FLAC) analyses; (b) comparison of the elastic response spectra obtained from the non-linear analyses at the tunnel elevation; (c) time histories of the shear strain computed in the non-linear analyses at the tunnel elevation.
checked that for a boundary shear strain γ = 0.02% the internal forces on the North-Est sidewall are compatible with the resistance of the lining section. Overall, the results of the decoupled analysis indicate that the observed damage in the tunnel can be directly related to the shear strain computed in the free-field. From the results of this analysis, shear failure in the lining seems to precede a bending failure, occurring for a free-field shear strain equal to about 0.012%.
the basis of the compressive and tensile strength of the concrete measured in the post-damage investigation, as reported in Table 3. Fig. 12b shows that, starting from the end of the excavation, the internal forces increase progressively with the shear strains assigned to the lateral boundaries, and that the resistance domain of the actual section is encountered for a shear strain about equal to 0.02%, equal to the maximum value computed in the free-field site response analysis at the tunnel elevation, as shown in Fig. 10c. On the other hand, it was seen that the shear resistance of the unreinforced concrete section, equal to about 250 kN/m, is reached for a shear strain applied to the lateral boundaries equal to about 0.012%. For shear strains larger than 0.03%, the internal forces show small additional variations, because for γ ≈ 0.03% a plastic mechanism develops in the entire rock domain, causing a diffused plastic flow at nearly constant stresses. It was also
4.6. Analysis of the dynamic tunnel-rock interaction A time-domain dynamic analysis of the tunnel sub-model of Fig. 11 was carried out, with a calculation time interval of 5 × 10−5 s, by applying to the bottom boundary of the grid the acceleration time-
4.44 MPa
4.44 MPa u max
u max
200 m
γ 1
200 m
200 m
(a)
(b )
Fig. 11. Plane-strain model of the tunnel, with boundary conditions for: (a) the analysis of the excavation; (b) the decoupled seismic analysis. 244
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
(a)
P
N
0
P
10 MN / m
M
0
P
0.5 MN m / m
S
0
0.5 MN / m
(b) 1 0.8
(c)
resistance domain for original thickness
T1213 T1214
0.6 0.4 0.2
= 0.005 %
0.01
0.015
actual resistance domain 0.03 0.025 0.02
shear failure 0
initial state 0
2
4
initial state 6
8
10 0
N (MN/m)
2
4
6
8
10
N (MN/m)
Fig. 12. (a) Internal forces after the excavation; (b, c) evolution of the internal forces in the tunnel lining in the decoupled seismic analysis (a) and in the dynamic analysis (c).
lining, isolated from the surrounding rock mass, was carried out with the code SAP 2000. The modal shapes obtained int this analysis are shown in Fig. 15 for the axial and bending vibration modes: they show that the axial mode is quite stiff, and is associated to a period of about 0.04 s (frequency f = 25 Hz), which is much larger than the largest frequency contributing to the input motion. However, because the lining does not have an invert, the vibration period of the bending mode is much longer, equal to about 0.19 s (f = 5.3 Hz), which is not too different from the average quadratic period Tm of the two deconvoluted signals (see Table 1). Therefore, the bending moments and shear forces may have been amplified during the earthquake, causing the attainment of the structural capacity of the weaker part of the lining. Since the resistance of the lining was mobilised, the hypothesis of an elastic lining is not entirely appropriate: a better interpretative model of the observed damage necessitates a non-linear description of the lining behaviour. This was achieved by further dynamic analyses, in which the lining was modelled with two-dimensional finite-difference zones characterised by an elastic-perfectly plastic constitutive model. The strength of the concrete was reproduced through an equivalent Tresca plasticity criterion, with an equivalent cohesion equal to half of the uniaxial compressive strength, as reported in Table 3. Fig. 16 shows a detail of the two-dimensional representation of the lining, where it can be seen that the tunnel roof and the vertical intermediate wall were still modelled with linear beam elements. Fig. 17a shows the distribution of the plastic zones around the nonlinear tunnel lining during the earthquake, computed in the dynamic analysis using the more severe T1213 record. During strong motion, the strength of the rock mass surrounding the tunnel was attained up to a distance from the tunnel axis varying from 1.5 to 2 tunnel diameters. As expected, the thinner part of the tunnel lining attains its strength too, in a location corresponding to the position of the observed damage. Fig. 17b shows the deformation pattern of the calculation grid, magnified by a factor of about 15, at the end of the T1213 event. The final relative displacements between the two side walls computed in the dynamic analysis is equal to about 0.015 m, which is in fact smaller
Table 3 Properties of the concrete forming the tunnel lining: σc is the compressive strength, σt is the tensile strength, c is the equivalent cohesion in a Tresca failure criterion, EC is the Young's modulus. σc (MPa)
σt (MPa)
c (MPa)
EC (GPa)
22.5
2.5
11.2
20
histories computed in the free-field site response analysis at the corresponding elevation. This domain reduction technique is depicted in Fig. 13, and is similar to that adopted by Callisto et al. (2013) for the numerical analysis of a soil-structure interaction problem. In the dynamic analysis, viscous boundaries of the Lysmer and Kuhlemeyer (1969) type were applied to the lateral and top grid boundaries in order to avoid spurious reflections of motion waves. In the dynamic analysis, the soil behaviour was regarded as non-linearly elastic-perfectly plastic, with the FLAC hysteretic unloading-reloading model denoted as “hysteretic damping”, using the same modulus decay curves adopted for the free-field site response analysis and for the non-linear static decoupled approach. Additional details about usage of this model can be found in Callisto & Soccodato (2010). Fig. 14 shows the time histories of the internal forces computed in the thinner side of the lining during the propagation of the most severe T1213 seismic signal. These plots are compared with the evolution of the internal forces with the shear strain γ evaluated in the decoupled approach. As a general result, the bending moment and the shear force computed dynamically are larger than those evaluated in the static approach, while the axial forces computed with the two methods are in a good agreement. This is also visible from the diagram of Fig. 12b, that shows the N-M paths followed during the dynamic computation: the maximum axial force is similar to that computed in the decoupled analysis (Fig. 12a), while the bending moments are much larger. These results indicate that the dynamic response of the tunnel lining may have played a significant role in the seismic performance of the lining. To gain some insight into this phenomenon, a modal analysis of the tunnel 245
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
4.44 MPa 1265 m a.s.l.
365
165
viscous boundaries
720
viscous boundaries
a
t 200
a t Fig. 13. Schematic representation for the dynamic analysis of the tunnel.
5. Discussion and conclusions
than the displacement of 0.12 m measured in the post-seismic survey. This may be due to the inadequacy of the elastic-perfectly plastic model to capture the post-peak softening of the damaged reinforced concrete. However, considering that the computed damage in the tunnel lining is the final result of a quite complex series of calculations, including deconvolution of the seismic records, site response analysis, domain reduction, and characterization of the rock mass, it appears that the approach followed in this study was capable to reproduce with reasonable accuracy the onset of the damage in the tunnel lining, while the evaluation of the actual residual displacement would require a more sophisticated post-rupture model of the concrete section.
0
0.02 0.04
(%)
0.02 0.04
0
shear force S (MN/m)
8
4
bending moment M (MNm/m)
1
12
axial force N (MN/m)
– signal analysis for the deconvolution and the evaluation of an equivalent bedrock depth; – site-specific ground response analysis to evaluate the maximum
(%)
(%) 0
A careful observation of the damage pattern of the San Benedetto tunnel produced by the Norcia earthquake prompted a quantitative back-analysis, aimed at evaluating the ability of the currently available calculation tools to predict of the seismic performance of the tunnel. In order to carry out the back-analysis of the observed phenomenon, it was necessary to combine several analysis tools as follows:
0.8 0.6 0.4 0.2
(a )
0 0
10
20
t (s) decopuled ( axis)
(b)
0 30
0
10
20
t (s)
30
0.02 0.04
1 0.8 0.6 0.4 0.2
(c)
0 0
10
20
30
t (s)
dynamic -T1213 (t axis)
Fig. 14. Comparison between the time-histories of the internal forces in the lining computed with the T1213 record and the development of internal forces with the shear strain evaluated from the decoupled analysis. 246
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
generally in a good agreement with the observed damage, evidencing the following results:
axial vibration mode T = 0.04 s
– the seismic actions recorded in the vicinity of the damaged section of the tunnel during the Norcia earthquake at two different elevations showed differences compatible with the expected dynamic response of the respective sites; – the seismic actions were strong enough to damage the tunnel; the analyses showed that shear failure may have preceded a bending failure; – the damage of the tunnel in the presence of the actual seismic forces was principally caused by a non-uniform thickness of the unreinforced lining, probably due to a misalignment of the road and the excavation axes; – while static equivalent actions appeared capable to bring the tunnel lining close to rupture, the dynamic response of the particular lining adopted, associated to the absence of an invert, may have contributed substantially to the observed damage.
bending vibration mode T = 0.19 s
Fig. 15. Normalised modal shapes of the tunnel lining.
As a more general result, it would appear that simplified methods for the analysis of tunnels subjected to earthquake loading, which are based on equivalent static actions, may be reasonably adequate, provided that the static actions are evaluated considering a careful analysis of the ground response and that the excavation of the tunnel is adequately modelled. However, it may be worth considering the dynamic response of the lining, to see if particular vibration periods, like the one associated to bending in the case analysed in this paper, may interact with the frequency content of the ground motion, producing an amplification of the internal force in the lining: this amplification phenomenon could be evaluated only through the use of dynamic analysis tools.
beam elements
non-linear finite-difference zones
Declaration of interest
Fig. 16. Detail of the two-dimensional model of the tunnel lining.
None. shear strain to use in a decoupled approach; – numerical methods to simulate the construction of the tunnel; – -decoupled approach to evaluate the loads induced by the earthquake through an equivalent static analysis; – domain reduction techniques for the coupled study of the soilstructure interaction by means of a dynamic numerical analysis.
Acknowledgements The Authors wish to express their gratitude to Mr. A. Micheli and Mr. L. Cedrone of Anas S.p.A.for providing the data on the seismic damage of the San Benedetto tunnel. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
The results obtained in the decoupled and coupled analyses were
(a)
(b)
0.015 m
Fig. 17. (a) Plastic zones around the 2D tunnel lining, as an effect of record T1213; (b) deformed grid (factor of amplification = 35). 247
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
References
tunnel response. Can. Geotech. J. 45, 1743–1764. Lu, C.C., Hwang, J.H., 2017. Implementation of the modified cross-section racking deformation method using explicit FDM program: a critical assessment. Tunnel. Undergr. Space Technol. 68, 58–73. Lysmer, J., Kuhlemeyer, R.L., 1969. Finite dynamic model for infinite media. J. Eng. Mech. 95 (EM4), 859–877. Marinos, P., Hoek, E., 2000. GSI: a geologically-friendly tool for rock mass strength estimation. In: Proceedings of the GeoEng2000 at the International Conference on Geotechnical and Geological Engineering, Melbourne, Technomic Publishers, Lancaster. p. 1422–1446. Marzi, V., Micheli, A., Cedrone, L., Martino, M., 2017. Damaging of the San Benedetto tunnel caused by the earthquake of October 30, 2016 – Provision of provisional safety and functional investigation for the definitive tunnel restoration. Gallerie e grandi opere sotterranee, No. 123, pp. 25–35 (in Italian). FEMA-NIBS (Federal Emergency Management Agency and National Institute of Building Sciences), 2003. Multi-hazard Loss Estimation Methodology, HAZUS-MH MR4 Technical Manual, Prepared for the Federal Emergency Management Agency, Washington DC, United States, 712 pp. Panet, M., Guenot, A., 1982. Analysis of convergence behind the face of a tunnel. In: Jones, M.J. (Ed.), Tunnelling’82: Third International Symposium. The Institution of Mining and Metallurgy, Brighton. London, pp. 197–204. Tsinidis, G., Pitilakis, K.D., 2018. Improved R-F relations for the transversal analysis of rectangular tunnels. Soil Dyn. Earthq. Eng. 107, 48–65. Wang, J.N., 1993. Seismic Design of Tunnels: A State-of-the-Art Approach. Monograph 7. Quade & Diuglas Inc., New York, Parsons, Brinckerhoff. Wang, W.L., Wang, T.T., Su, J.J., Lin, C.H., Seng, C.R., Huang, T.H., 2001. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake. Tunnel. Undergr. Space Technol. 16, 133–150. Yashiro, K., Kojima, Y., Shimuzu, M., 2007. Historical earthquake damage to tunnels in Japan and case studies of railway tunnels in the 2004 Niigataken-Chuetsu earthquake. Quart. Rep. Railway Tech. Res. Inst. 48 (3), 136–141. Zhang, X., Jiangb, Y., Sugimoto, S., 2018. Seismic damage assessment of mountain tunnel: a case study on the Tawarayama tunnel due to the 2016 Kumamoto Earthquake. Tunnel. Undergr. Space Technol. 71 (2018), 138–148.
Amorosi, A., Boldini, D., 2009. Numerical modelling of the transverse dynamic behaviour of circular tunnels in clayey soils. Soil Dyn. Earthq. Eng. 29, 1059–1072. Argyroudis, S.A., Pitilakis, K.D., 2012. Seismic fragility curves in alluvial deposits. Soil Dyn. Earthq. Eng. 35 (1), 12. Argyroudis, S., Tsinidis, G., Gatti, F., Pitilakis, K., 2017. Effects of SSI and lining corrosion on the seismic vulnerability of shallow circular tunnels. Soil Dyn. Earthq. Eng. 98, 244–256. Argyroudis, S., Kaynia, A.M., 2014. Fragility functions of highway and railway infrastructure. In: SYNER-G: Typology Definition and Fragility Functions for Physical Elements at Seismic Risk. Springer, Dordrecht, pp. 299–326. Bardet, J. P., Ichii, K., Lin, C.H., 2000. EERA. A computer program Nonlinear Earthquake site Response Analyses of layered soil deposits, University of Southern California, Department of Civil Engineering, Los Angeles, Calif. Bilotta, E., Lanzano, G., Madabushi, S.P.G., Silvestri, F., 2014. A numerical Round Robin on tunnels seismic actions. Acta Geotech. 9, 563–579. Callisto, L., Soccodato, F.M., 2010. Seismic design of flexible cantilevered retaining walls. J. Geotech. Geoenviron. Eng. 136 (2), 344–354. Callisto, L., Rampello, S., Viggiani, G.M.B., 2013. Soil-structure interaction for the seismic design of the Messina Strait Bridge. Soil Dyn. Earthq. Eng. 52, 103–115. Hashash, Y.M.A., Hook, J.J., Schmidt, B., Yao, J.I., 2001. Seismic design and analysis of underground structures. Tunnel. Space Technol. 16, 247–293. Hoek, E., Brown, E.T., 1980. Underground Excavations in Rock. Institution of Mining and Metallurgy, London. Hoek, E., Caranza-Torres, C.T., Corcum, B., 2002. Hoek–Brown failure criterion-2002 edition. In: Bawden, H.R.W., Curran, J., Telsenicki, M. (Eds.), Proceedings of the North American Rock Mechanics Society (NARMS-TAC 2002). Mining Innovation and Technology, Toronto, pp. 267–273. Hoek, E., Diederichs, M.S., 2006. Empirical estimation of rock mass modulus. Int. J. Rock Mech. Min. Sci. 203–215. Itasca Consulting Group, 2011. FLAC 7.0: Fast Langrangian Analysis of Continua. User’s Guide. Kontoe, S., Zdravkovic, L., Potts, D.M., Menkiti, C.O., 2008. A case study on seismic
248
Contents lists available at ScienceDirect
Tunnelling and Underground Space Technology journal homepage: www.elsevier.com/locate/tust
Interpretation and back-analysis of the damage observed in a deep tunnel after the 2016 Norcia earthquake in Italy
T
⁎
Luigi Callisto , Cecilia Ricci Sapienza University of Rome, Italy
A R T I C LE I N FO
A B S T R A C T
Keywords: Deep tunnel Seismic damage Soil-structure interaction
This paper deals with the interpretation of the damage originated by the 2016 Norcia earthquake, Italy, in a deep tunnel excavated in a calcareous rock mass. A careful investigation of the damage pattern, together with the availability of seismic signals recorded in the vicinity of the tunnel during the earthquake, prompted a backanalysis of the observed phenomenon. The study hinged on a combination of site response analyses, simulation of the tunnel construction, and computation of the effect of the earthquake on the tunnel lining. Specifically, the damage caused by the earthquake in the tunnel lining was evaluated both with a decoupled procedure, based on equivalent static loading, and with a fully coupled dynamic analysis of the soil-structure interaction. The results obtained from the back-analysis were in a good agreement with the observations, and contributed to evidence the main causes of the damage, related to the specific geometry and to the dynamic response of the lining. The approach used in the paper, validated for the present case study through the comparison with the observed tunnel damage, may be useful to assess the seismic vulnerability of existing tunnels and for the seismic design of new underground structures.
1. Introduction Several documented cases are available in which earthquakes of medium-high magnitude produced a significant damage to underground structures for which seismic forces had not been considered in the original design. For instance, Hashash et al. (2001) presented a compendium of cases in which underground structures were damaged by earthquakes; Wang et al. (2001) described the damage caused by the Chi-Chi earthquake to deep tunnels in Taiwan; and Yashiro et al. (2007) discussed the damage produced by four historical earthquakes on deep tunnels in Japan. More recently, Zhang et al. (2018) described the case study of the Tawarayama tunnel in Japan, that suffered extensive damage after the 2016 Kunamoto Earthquake. The technical literature provides several calculation approaches to evaluate the internal forces produced in a tunnel lining by earthquake loading, ranging from simplified solutions for basic geometries (e.g. Wang, 1993) to a combination of one-dimensional site response analyses and static numerical calculations (e.g. Argyroudis and Pitilakis, 2012), to non-linear dynamic analyses of the soil-structure interaction (e.g. Amorosi and Boldini, 2009, Argyroudis et al., 2017, Tsinidis and Pitilakis, 2018). A collection of available numerical approaches to this problem may be found in Bilotta et al. (2014), reporting the results of a benchmark test to reproduce the results of centrifuge tests involving the ⁎
dynamic loading of a circular tunnel, while Argyroudis and Kaynia (2014) reviewed available methods for the seismic fragility analysis and damage modes of transport infrastructure, including tunnels. Given the availability of such a wide range of available calculation tools, it is surprising that, in the presence of an actual disruption observed in existing tunnels, only a few studies produced a quantitative interpretation of the observed damage (e.g. Kontoe et al., 2008): in most situations the observed damage was explained on a semi-qualitative basis, invoking the possible presence of poor geological conditions or potential faults (Wang et al., 2001; Yashiro et al., 2007; Zhang et al., 2018). The objective of this paper is to describe the damage caused by a recent earthquake to a roadway tunnel in Italy, and to combine the damage observation with the available records of the seismic motion in order to produce a quantitative interpretation of the observed phenomenon. The interpretative approach is based on the investigation of the mechanical behaviour of the rock mass interacting with the tunnel and on a site-specific ground response analysis. Despite the inevitable simplifications and uncertainties of the methodology employed in this paper, which are duly evidenced in the following sections, it is believed that the strategy developed in this study is worthy of note because it provides validation and guidance for both the seismic design of new tunnels and the assessment of existing ones.
Corresponding author at: Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Via Eudossiana 18, 00184 Rome, Italy. E-mail address: [email protected] (L. Callisto).
https://doi.org/10.1016/j.tust.2019.04.012 Received 27 September 2018; Received in revised form 7 February 2019; Accepted 14 April 2019 0886-7798/ © 2019 Elsevier Ltd. All rights reserved.
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
km Umbria-Marche Appennine
m
T1214 damage
NORCIA
1500 1300 1200 1100
tunnel
1000 800
CALCARE MASSICCIO 0
CORNIOLA
500 920 m
San Benedetto tunnel
T1213
CAPODACQUA damaged section
1400
900
CAPODACQUA
0
1600
265 m
11 .5
k 10
12.0 km
NORCIA
elevation (m a.s.l.)
EPICENTRE
N
1000
1500
4000
distance (m)
4400 m
2 km
(a)
(b) Fig. 1. Plan view (a) and vertical profile (b) of the San Benedetto road tunnel.
2. Damage to the San Benedetto tunnel during the Norcia earthquake
pattern: large vertical cracks isolate a damaged portion of the side wall, while the remaining cracks show a combination of bending (excessive compression) and shear failure in the transverse section. Fig. 4b depicts the results of a detailed survey carried out after the event, showing the deformation of the cross-section with respect to the original one. In the most damaged section, the tunnel width shortened by about 0.15 m. The observed damage can be classified as “extensive” to “complete” according to the HAZUS-MH methodology (FEMA-NIBS, 2003). After the event, the road owner, Anas S.p.A, carried out an extensive investigation of the damage, including geometrical inspection, mechanical in-situ testing of the lining, execution of inclined boreholes from the tunnel lining, and seismic refraction tests along the damaged portion of the tunnel. The main results of these investigations were reported by Marzi et al. (2017). The borings through the tunnel lining revealed, quite unexpectedly, that in the portion of the tunnel under investigation the actual section of the lining differed from the original design, in that the more damaged Southern sidewall appeared thinner than the design thickness of 1 m, while the Northern sidewall was somewhat thicker. This flaw was probably caused by a misalignment of the tunnel excavation with respect to the road axis, which went undetected during construction. A comparison between the notional section of the lining and that resulting from the post-seismic investigation is presented in Fig. 2.
Fig. 1 shows a plan view and a vertical profile of the San Benedetto road tunnel. It has a total length of 4400 m, connecting the Italian provinces of Perugia (town of Norcia) to the West and Ascoli Piceno (town of Capodacqua) to the East. The tunnel is located in the Italian Appennines, at an elevation of about 1000 m above the sea level, with a maximum tunnel cover of about 600 m. The structure was constructed in the 1980s, excavating a small-diameter pilot tunnel with a boring machine, and enlarging the excavation with rock-blasting. A light temporary support was used, including radial bolts connected by a wire mesh and spritz-beton, followed by the cast-in-place of the final lining. Fig. 2a shows the design transverse section of the final lining: it is made of unreinforced concrete, with a constant thickness of 1 m, and is not provided with an invert. A horizontal roof, made with a 0.15 m-thick r.c. slab, and a vertical r.c. wall were constructed below the tunnel crown to obtain two ventilation chambers, as depicted in Fig. 2a. The tunnel was excavated through the geological formations of “Calcare Massiccio” and “Corniola”, as shown in Fig. 1b. After the MW = 6.5 Norcia Earthquake of 30 October 2016 a portion of the tunnel lining was damaged at about 920 m from the Western entrance, as indicated in Fig. 1b. The damaged portion of the tunnel is located in the “Corniola” formation, approximately 200 m east of the contact between the “Corniola” and the “Calcare Massiccio”. The “Corniola” formation is a grey-brown limestone containing varying fractions of flint, intensely fractured without a clear fracture orientation. In this section of the tunnel, both hydrogeologic considerations and direct measurement indicated the absence of water pressure in the rock fractures. The photographs of Fig. 3 show portions of the damaged lining. Concrete cracks and spalling were mostly located along the Southern sidewall, extending in some cases up to the crown. Fig. 4a shows a profile of the Southern sidewall with an indication of the main crack
3. Recorded seismic motion
R= 5
.1 m
The Norcia event was originated at a depth of about 9 km by a normal fault mechanism with no surface expression. Several stations in the area recorded the Norcia seismic event. The location of the two recording stations closest to the tunnel location is shown in Fig. 1a. These two stations, denoted as T1213 and T1214, are located on a stiff outcrop at an epicentral distance very similar to that of the damaged portion of the tunnel, but at different elevations: the station T1213 is
(a)
1.5 m
1.0 m SW
NE
NE
9.6
0.5 SW
(b)
Fig. 2. Notional transverse section of the tunnel lining (a), compared with the results of the post-seismic investigation (b). 239
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
Fig. 3. Damage observed in the lining after the Norcia Earthquake.
earthquake on the tunnel, as depicted schematically in Fig. 6. The following three computation phases are common to both approaches:
located at an elevation of 860 m a.s.l., lower than the tunnel axis, while the station T1214 is located at the elevation of 1490 m a.s.l., higher than the ground elevation at the tunnel site (1265 m a.s.l.). In a first stage, the horizontal components of the seismic motion recorded at these stations were projected onto the transverse and longitudinal directions of the tunnel. Fig. 5 shows a comparison between the transverse components of the accelerograms recorded at these two stations, in terms of acceleration time histories and of 5%damped elastic response spectra. Table 1 reports the properties of the transverse component of the recorded signals, where amax is the maximum acceleration, IA is the Arias intensity, T5-95 is the significant duration, and Tm is the mean quadratic period. From Fig. 5 and considering the values reported in Table 1, it is evident that the seismic motion recorded at station T1213 is significantly more severe than that recorded at station T1214. Since the epicentral distance of the two stations is about the same, assuming that the seismic waves propagated in the same stiff rock material, the difference between the two records could be ascribed to the different elevation of the recording stations, that may have produced a different dynamic response. This hypothesis is consistent with the frequency content of the records, quantified by the mean quadratic period Tm, showing that the station T1214, located at a higher elevation, recorded a motion characterised by lower frequencies.
A. the recorded seismic motion was deconvoluted to a depth corresponding to a fictitious bedrock, which was determined as described in Section 4.3.1; B. a one-dimensional propagation model was developed, extending from the fictitious bedrock to the actual elevation of the ground surface at the tunnel site (1265 m a.s.l.); C. a two-dimensional numerical sub-model of the transverse section of the tunnel was developed, and used to simulate the excavation of the tunnel. The decoupled approach (C1) consisted in carrying out one-dimensional site response analysis with the model in (B), evaluating the free-field maximum shear strain γ at the elevation of the tunnel, and applying this strain to deform uniformly the boundaries of the numerical sub-model in (C), obtaining the variation of the internal forces produced by the earthquake in the tunnel lining. In the coupled approach, the free-field site response analysis in (B) was used to derive the acceleration time-histories at the elevation corresponding to the bottom of the numerical sub-model (C). These accelerograms were used to perform a full dynamic analysis of the soilstructure interaction, to evaluate directly the dynamic response of the tunnel and the damage in its lining. A detailed description of the procedures adopted in these uncoupled and coupled approaches are provided in the following sections.
4. Modelling the effect of the earthquake on the tunnel 4.1. Outline of the modelling strategy
4.2. Mechanical model of the subsoil
A plane strain assumption was made, assuming that the damage in the tunnel lining was caused by vertically propagating SH waves, producing bending in a plane transversal to the tunnel axis. It was also assumed that only the horizontal component of the seismic motion, associated with the vertical propagation of shear waves, had an influence on the observed damage, neglecting the vertical motion component. Both a decoupled and a coupled approach were adopted to provide a quantitative interpretation of the damage induced by the Norcia
For the purpose of the present analyses, the rock mass was modelled as a uniform equivalent continuum. Compression tests carried out on intact samples provided an average uniaxial compressive strength of the rock σci = 40 MPa. The small-strain stiffness of the rock mass was evaluated from the results of seismic refraction tests carried along two 100 m-long stretches within the tunnel. At a distance of about 10 m from the sidewalls, the shear wave velocity measured in these tests is original transverse section damaged transverse section
crack pattern on South sidewall
NE (a)
SW (b)
Fig. 4. (a) Longitudinal profile of the Southern side wall with indication of cracks in the lining; (b) original and damaged transverse section. 240
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
0.8
T1213
a (g)
0.4 0
Sa (g)
-0.4 -0.8 0.8
T1214
T1213 T1214
3
0.4
a (g)
4
2
0 -0.4
(a)
(b)
1
-0.8 0 0
10
20
30
0
0.4
0.8
t (s)
1.2
1.6
T (s)
Fig. 5. Time-histories (a) and 5%-damped elastic response spectra (b) of signals recorded at stations T1213 and T1214, projected onto the transverse direction of the tunnel.
mass, because it was assumed that the simulation of the excavation phases and the seismic loading with the sub-model (C) can directly account for the disturbance caused by the tunnel construction in the vicinity of the tunnel lining. Fig. 7 shows the Hoek-Brown failure criterion, obtained with the computed Hoek-Brown parameters (mb = 1.12, s = 0.0022, a = 0.51). Starting from this curve, an equivalent Mohr-Coulomb strength criterion for the rock mass was evaluated for the stress interval of interest. Using the linearization technique proposed for tunnels by Hoek et al. (2002), the equivalent values of cohesion and angle on shearing resistance are c = 0.8 MPa, and φ = 36°, respectively. The equivalent Mohr-Coulomb failure criterion obtained with this procedure is superimposed to the Hoek-Brown criterion in Fig. 7. This figure shows also the in situ stress state at the tunnel depth before the excavation, that was assumed spherical (earth pressure coefficient at rest K0 = 1). The figure also depicts an ideal unloading stress path followed by a rock element in the vicinity of the tunnel during the excavation, showing that the equivalent Mohr-Coulomb criterion is reached in a stress interval well within the range for which this criterion is equivalent to the Hoek-Brown curve.
about uniform, with a representative value VS = 2700 m/s. The corresponding p-wave velocity measured in the refraction tests is VP = 5500 m/s. At closer distances, the velocity of s- and p-waves becomes somewhat smaller, reaching about 40% of the above values in the vicinity of the lining. This finding is consistent with the results of dilatometer tests, carried out in boreholes drilled from the tunnel lining, that showed a systematic decrease of the equivalent Young's modulus in the portion of the rock mass closer to the tunnel lining. This effect can be ascribed to the stress release associated to the excavation of the tunnel, and possibly to the earthquake loading: values of the Geological Strength Index GSI (Marinos and Hoek, 2000) equal to 45 and 30 were evaluated for the undisturbed and disturbed portion of the rock mass, respectively. The Young's modulus obtained from the dilatometer tests in the undisturbed portion of the rock mass varied between 18 and 28 GPa, corresponding to about 35–50% of the small-strain Young's modulus obtained from a combination of the VS and VP values mentioned above, considering that laboratory testing on samples extracted from the boreholes provided an average mass density ρ = 2.75 Mg/m3. An estimation of the equivalent Young's modulus for the rock mass was obtained using the relationship proposed by Hoek and Diederichs (2006), based on the σci and GSI values, providing Eeq = 4.5 GPa for the undisturbed rock mass, and Eeq = 1.6 GPa for the disturbed portion encountered in the vicinity of the tunnel lining. The strength properties of the rock mass were evaluated using the Hoek-Brown strength criterion (Hoek and Brown, 1980) in the version provided by Hoek et al. (2002):
4.3. Evaluation of the seismic action 4.3.1. Deconvolution The horizontal components of the original seismic signal recorded at stations T1213 and T1214 were projected along the transverse axis of the tunnel, low-pass filtered at 20 Hz and base-line corrected. Subsequently, a linear deconvolution of the resulting signals was performed, to transfer the accelerograms down to a fictitious bedrock. The position of this bedrock was found iteratively, searching the bedrock elevation for which the deconvolution of the two records, obtained at different elevations, provided a similar bedrock signal. The deconvolution was carried out using the constant shear wave velocity Vs = 2700 m/s measured in the refraction tests, and a constant damping
a
σ σ1 = σ3 + σci ⎛mb 3 + s⎞ ⎝ σci ⎠ ⎜
⎟
(1)
where σ1 and σ3 are the maximum and minimum principal stress, respectively, and mb, s and a are the Hoek-Brown parameters, related to GSI. The strength criterion was evaluated only for the undisturbed rock
Table 1 Motion parameters of the transverse components of the records, before and after the deconvolution. Record
T1213 T1214
Elevation (m a.s.l.)
860 1490
Recorded signals
Deconvoluted signals
amax (g)
IA (m/s)
T5-95 (s)
Tm (s)
amax (g)
IA (m/s)
T5-95 (s)
Tm (s)
0.90 0.50
6.14 2.62
6.45 6.46
0.23 0.32
0.44 0.45
2.44 1.66
7.06 6.72
0.23 0.25
241
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
A
B
deconvolution
one-D domain
a
1490 m a.s.l.
C
T1214
t
545 m a.s.l.
deconvolution
315
t
a
a t
equivalent bedrock
shear strains
γ
C1
1000 m a.s.l.
720
deconvolution
860 m a.s.l. T1213
265
630
1265 m a.s.l.
a
two-D domain
site response analysis t
C2 a t
accelerations
Fig. 6. Modelling strategy for the seismic back-analysis of the San Benedetto tunnel.
two deconvoluted signals, that is plotted in the same scale as Fig. 5b for comparison. The corresponding properties of the accelerograms are reported in Table 1. It can be seen that the deconvoluted signals are very similar to each other, and particularly that the differences in the maximum acceleration and the Arias intensity of the original records were strongly reduced by the deconvolution. The mean quadratic period Tm of the T1214 record becomes, after the deconvolution, quite similar to that of the T1213 signal.
16
σ1 (MPa)
12
8
4.3.2. Site response analysis The two deconvoluted accelerograms were propagated through a one-dimensional rock column, extending from the bedrock to the elevation of the ground surface at the tunnel site (1265 m a.s.l.), assuming a stiff bedrock. The site response analyses were performed with both an equivalent linear method, using the code MARTA developed by the first Author, (https://sites.google.com/a/uniroma1.it/luigicallisto/attivita1), and with a non-linear calculation in the time domain carried out with the finite-difference software FLAC2D v.7.0 (Itasca, 2011). In the equivalent linear analysis, the modulus reduction and damping ratio curves proposed by Bardet et al. (2000) for soft rocks were adopted, whereas in the FLAC analysis the hysteretic damping model was used to reproduce the same modulus decay curve, using the sig3 expression (Itasca, 2011) of the secant modulus with the model parameters reported in Table 2. Fig. 9 shows a comparison between the modulus decay and damping ratio curves used for the linear equivalent analyses and those resulting from the calibration of the hysteretic damping model. The results of the site response analysis showed that the seismic input engages a modest non-linearity in the rock mass, with shear strains well within the interval in which the linear-equivalent and the hysteretic damping models provide a similar response. Specifically, Fig. 10 shows the results of the site response analyses, depicting for each signal the profile of the maximum acceleration (Fig. 10a), the elastic response spectrum computed at the tunnel elevation (Fig. 10b), and the time history of the shear strain at the tunnel elevation (Fig. 10c). Fig. 10a shows that the two calculation techniques give very similar results. The maximum shear strain γmax at the tunnel elevation, equal to about 0.02%, was provided by the T1213 record (Fig. 10c). Comparing Fig. 10b with Fig. 8b it can be seen that the propagation through a soil column at the tunnel location provides some amplification at low periods (T = 0.1–1 s) but a very large amplification at longer periods (T = 1–1.4 s), which roughly correspond to the fundamental period of the rock layer resulting from the site response analysis.
unloading stress path in situ stress state
4
Hoek - Brown Mohr - Coulomb 0 0
4
8
12
σ3 (MPa) Fig. 7. Hoek-Brown and Mohr-Coulomb failure criteria assumed for the rock mass.
ratio ξ selected in the range from 1 to 5%. For each tentative bedrock elevation, a normalised error E was evaluated on the basis of the 5%damped elastic response spectra calculated from the two signals resulting from the deconvolution: E was defined as the integral of the difference between the spectral ordinates, in the period interval of 0.02–10 s, divided by the average area of the response spectra. Fig. 8a depicts the variation of the error E as a function of the elevation of the fictitious bedrock, for three different values of the damping ratio ξ, evidencing that the optimum elevation of the bedrock is not very sensitive to the value assumed for the damping ratio. The lowest error, equal to about 0.35, was obtained for a fictitious bedrock placed at an elevation of 545 m a.s.l. The resulting fundamental period of the rock column at the tunnel location (Fig. 6) is then equal to 1.07 s. Fig. 8b shows a comparison of the bedrock response spectra obtained for the 242
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
ξ=5%
0.4
1% 2%
3
Sa (g)
0.6
545 m a.s.l.
error E
0.8
0.2
0 400
500
T1213 T1214
2 1
(a) 600
(b) 0
700
0
0.4
elevation (m a.s.l.)
0.8
1.2
1.6
T (s)
Fig. 8. (a) Variation of the error E computed in the deconvolution procedure, as a function of the elevation of the fictitious bedrock; (b) elastic response spectra of the deconvoluted signals.
A first stage of the calculation consisted of the generation of the in situ stress state, assuming an earth coefficient at rest K0 = 1. Subsequently, the tunnel excavation was simulated using the force reduction method (Panet & Guenot, 1982): the rock zones internal to the tunnel perimeter were deactivated, removing gradually a percentage λ of the corresponding nodal forces; in a subsequent stage, the tunnel lining was activated and the remaining nodal forces were reduced to zero. Afterwards, additional beam elements were activated simulating the horizontal roof and the vertical wall to create the ventilation chambers. Since a very flexible primary lining was used during the tunnel excavation, a stress release factor λ equal to 90% was used. The appropriateness of this factor was confirmed by a reasonable agreement between the flat-jack tests carried out in the undamaged portion of the tunnel lining and the axial stress of about 2 MPa computed in the lining after the simulation of the tunnel construction.
Table 2 Parameters of the FLAC sig3 model to used to describe the variation of secant stiffness with strain level (Itasca, 2011). a (–)
b (–)
x0 (–)
1
−1
−0.085
10
G/G0
0.8 0.6 0.4
8 6
Bardet et al. (2000) FLAC hysteretic damping
4
0.2 0 0.0001
2
damping ratio ξ (%)
1
4.5. Decoupled approach
0 0.001
0.01
0.1
In the decoupled approach, the effect of the earthquake was represented by the shear strains computed in the free-field site response analysis. In the numerical plane-strain model of the tunnel excavation, these free-field shear strains were applied carrying out a static analysis in which a linearly variable distribution of horizontal displacements was assigned to the lateral boundaries of the model, as depicted in Fig. 11b. The displacement umax in the figure corresponds to a shear strain γ = umax/H, H = 200 m being the height of the numerical model. During this calculation phase, the rock mass was assigned the same constitutive model used for the free-field site response analyses carried out with FLAC: a non-linear elastic, perfectly plastic behaviour, with an evolution of the secant shear stiffness consistent with the modulus decay curve selected for the rock mass. In the analysis, the lateral displacements were increased progressively, monitoring the resulting internal forces in the thinner side of the tunnel lining. A check of the uniformity of the shear strain distribution was carried out (Lu and Hwang, 2017) indicating that the distance of the lateral boundaries from the tunnel was large enough to ensure a uniform strain pattern in a substantial portion of the mesh, making the internal forces computed in the tunnel lining independent of the grid size. Fig. 12a shows the distributions of the internal forces in the lining (axial force N, bending moment M, shear force S) computed after the simulation of the tunnel construction. Fig. 12b depicts the relationship between the axial force N and the bending moment M in the thinner section of the tunnel lining (point P of Fig. 12a), computed in the decoupled analysis for values of γ ranging from zero to 0.03%. The figure also shows the M-N resistance domains for the original (1 m-thick) and the actual (0.5 m-thick) unreinforced concrete sections, computed on
1
shear strain amplitude γ (%) Fig. 9. Comparison of the modulus decay and damping ratio curves used for the linear equivalent analyses (Bardet et al., 2000) and those resulting from the calibration of the FLAC hysteretic damping model.
4.4. Analysis of the tunnel excavation A numerical sub-model of the tunnel excavation was developed in plane strain with the FLAC finite difference code, as illustrated in Fig. 11.a. It consists of a 200 m × 200 m domain surrounding the tunnel, subjected to the vertical geostatic stress σv0 = 4.44 MPa exerted by the rock mass overlying the top boundary, and to the boundary conditions depicted in the figure. For the analysis of the excavation, the rock mass was regarded as an elastic-perfectly plastic material, with the Mohr-Coulomb failure criterion (c = 0.8 MPa, φ′ = 36°) derived from the Hoek-Brown equivalency as explained in Section 4.2, and the Hoek and Diederichs (2006) Young's modulus E = 4.5 GPa, with a Poisson's ratio ν = 0.3. In the numerical model, the tunnel lining was modelled with linear beam elements, with a Young's modulus of 20 GPa and characterised by a piece-wise variable axial and bending stiffness that reproduced the non-symmetric tunnel lining of Fig. 2b. No interfaces were used between the lining and the rock mass, imagining a very rough contact as obtained by rock-blasting. Relative displacements at this contact could occur as an effect of rock yielding. The model did not include pore water pressures, in accordance with the available measurements. 243
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
0.4
0.8
T1213
amax (g) 1.2 0
0.4
0.8
Sa (g)
amax (g) 0
1.2
T1213 T1214
4 3
T1214
1200 2
(b)
1000
0 0
0.4
0.8
1.2
1.6
T (s)
0.02 800
γ (%)
elevation (m a.s.l.)
1
600
0
(c)
-0.02
(a)
0
10
20
30
t (s)
equivalent linear FLAC hysteretic damping
Fig. 10. Results of the site response analyses for the two deconvoluted signals: (a) profile of the maximum acceleration obtained from the equivalent linear (MARTA) and non-linear (FLAC) analyses; (b) comparison of the elastic response spectra obtained from the non-linear analyses at the tunnel elevation; (c) time histories of the shear strain computed in the non-linear analyses at the tunnel elevation.
checked that for a boundary shear strain γ = 0.02% the internal forces on the North-Est sidewall are compatible with the resistance of the lining section. Overall, the results of the decoupled analysis indicate that the observed damage in the tunnel can be directly related to the shear strain computed in the free-field. From the results of this analysis, shear failure in the lining seems to precede a bending failure, occurring for a free-field shear strain equal to about 0.012%.
the basis of the compressive and tensile strength of the concrete measured in the post-damage investigation, as reported in Table 3. Fig. 12b shows that, starting from the end of the excavation, the internal forces increase progressively with the shear strains assigned to the lateral boundaries, and that the resistance domain of the actual section is encountered for a shear strain about equal to 0.02%, equal to the maximum value computed in the free-field site response analysis at the tunnel elevation, as shown in Fig. 10c. On the other hand, it was seen that the shear resistance of the unreinforced concrete section, equal to about 250 kN/m, is reached for a shear strain applied to the lateral boundaries equal to about 0.012%. For shear strains larger than 0.03%, the internal forces show small additional variations, because for γ ≈ 0.03% a plastic mechanism develops in the entire rock domain, causing a diffused plastic flow at nearly constant stresses. It was also
4.6. Analysis of the dynamic tunnel-rock interaction A time-domain dynamic analysis of the tunnel sub-model of Fig. 11 was carried out, with a calculation time interval of 5 × 10−5 s, by applying to the bottom boundary of the grid the acceleration time-
4.44 MPa
4.44 MPa u max
u max
200 m
γ 1
200 m
200 m
(a)
(b )
Fig. 11. Plane-strain model of the tunnel, with boundary conditions for: (a) the analysis of the excavation; (b) the decoupled seismic analysis. 244
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
(a)
P
N
0
P
10 MN / m
M
0
P
0.5 MN m / m
S
0
0.5 MN / m
(b) 1 0.8
(c)
resistance domain for original thickness
T1213 T1214
0.6 0.4 0.2
= 0.005 %
0.01
0.015
actual resistance domain 0.03 0.025 0.02
shear failure 0
initial state 0
2
4
initial state 6
8
10 0
N (MN/m)
2
4
6
8
10
N (MN/m)
Fig. 12. (a) Internal forces after the excavation; (b, c) evolution of the internal forces in the tunnel lining in the decoupled seismic analysis (a) and in the dynamic analysis (c).
lining, isolated from the surrounding rock mass, was carried out with the code SAP 2000. The modal shapes obtained int this analysis are shown in Fig. 15 for the axial and bending vibration modes: they show that the axial mode is quite stiff, and is associated to a period of about 0.04 s (frequency f = 25 Hz), which is much larger than the largest frequency contributing to the input motion. However, because the lining does not have an invert, the vibration period of the bending mode is much longer, equal to about 0.19 s (f = 5.3 Hz), which is not too different from the average quadratic period Tm of the two deconvoluted signals (see Table 1). Therefore, the bending moments and shear forces may have been amplified during the earthquake, causing the attainment of the structural capacity of the weaker part of the lining. Since the resistance of the lining was mobilised, the hypothesis of an elastic lining is not entirely appropriate: a better interpretative model of the observed damage necessitates a non-linear description of the lining behaviour. This was achieved by further dynamic analyses, in which the lining was modelled with two-dimensional finite-difference zones characterised by an elastic-perfectly plastic constitutive model. The strength of the concrete was reproduced through an equivalent Tresca plasticity criterion, with an equivalent cohesion equal to half of the uniaxial compressive strength, as reported in Table 3. Fig. 16 shows a detail of the two-dimensional representation of the lining, where it can be seen that the tunnel roof and the vertical intermediate wall were still modelled with linear beam elements. Fig. 17a shows the distribution of the plastic zones around the nonlinear tunnel lining during the earthquake, computed in the dynamic analysis using the more severe T1213 record. During strong motion, the strength of the rock mass surrounding the tunnel was attained up to a distance from the tunnel axis varying from 1.5 to 2 tunnel diameters. As expected, the thinner part of the tunnel lining attains its strength too, in a location corresponding to the position of the observed damage. Fig. 17b shows the deformation pattern of the calculation grid, magnified by a factor of about 15, at the end of the T1213 event. The final relative displacements between the two side walls computed in the dynamic analysis is equal to about 0.015 m, which is in fact smaller
Table 3 Properties of the concrete forming the tunnel lining: σc is the compressive strength, σt is the tensile strength, c is the equivalent cohesion in a Tresca failure criterion, EC is the Young's modulus. σc (MPa)
σt (MPa)
c (MPa)
EC (GPa)
22.5
2.5
11.2
20
histories computed in the free-field site response analysis at the corresponding elevation. This domain reduction technique is depicted in Fig. 13, and is similar to that adopted by Callisto et al. (2013) for the numerical analysis of a soil-structure interaction problem. In the dynamic analysis, viscous boundaries of the Lysmer and Kuhlemeyer (1969) type were applied to the lateral and top grid boundaries in order to avoid spurious reflections of motion waves. In the dynamic analysis, the soil behaviour was regarded as non-linearly elastic-perfectly plastic, with the FLAC hysteretic unloading-reloading model denoted as “hysteretic damping”, using the same modulus decay curves adopted for the free-field site response analysis and for the non-linear static decoupled approach. Additional details about usage of this model can be found in Callisto & Soccodato (2010). Fig. 14 shows the time histories of the internal forces computed in the thinner side of the lining during the propagation of the most severe T1213 seismic signal. These plots are compared with the evolution of the internal forces with the shear strain γ evaluated in the decoupled approach. As a general result, the bending moment and the shear force computed dynamically are larger than those evaluated in the static approach, while the axial forces computed with the two methods are in a good agreement. This is also visible from the diagram of Fig. 12b, that shows the N-M paths followed during the dynamic computation: the maximum axial force is similar to that computed in the decoupled analysis (Fig. 12a), while the bending moments are much larger. These results indicate that the dynamic response of the tunnel lining may have played a significant role in the seismic performance of the lining. To gain some insight into this phenomenon, a modal analysis of the tunnel 245
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
4.44 MPa 1265 m a.s.l.
365
165
viscous boundaries
720
viscous boundaries
a
t 200
a t Fig. 13. Schematic representation for the dynamic analysis of the tunnel.
5. Discussion and conclusions
than the displacement of 0.12 m measured in the post-seismic survey. This may be due to the inadequacy of the elastic-perfectly plastic model to capture the post-peak softening of the damaged reinforced concrete. However, considering that the computed damage in the tunnel lining is the final result of a quite complex series of calculations, including deconvolution of the seismic records, site response analysis, domain reduction, and characterization of the rock mass, it appears that the approach followed in this study was capable to reproduce with reasonable accuracy the onset of the damage in the tunnel lining, while the evaluation of the actual residual displacement would require a more sophisticated post-rupture model of the concrete section.
0
0.02 0.04
(%)
0.02 0.04
0
shear force S (MN/m)
8
4
bending moment M (MNm/m)
1
12
axial force N (MN/m)
– signal analysis for the deconvolution and the evaluation of an equivalent bedrock depth; – site-specific ground response analysis to evaluate the maximum
(%)
(%) 0
A careful observation of the damage pattern of the San Benedetto tunnel produced by the Norcia earthquake prompted a quantitative back-analysis, aimed at evaluating the ability of the currently available calculation tools to predict of the seismic performance of the tunnel. In order to carry out the back-analysis of the observed phenomenon, it was necessary to combine several analysis tools as follows:
0.8 0.6 0.4 0.2
(a )
0 0
10
20
t (s) decopuled ( axis)
(b)
0 30
0
10
20
t (s)
30
0.02 0.04
1 0.8 0.6 0.4 0.2
(c)
0 0
10
20
30
t (s)
dynamic -T1213 (t axis)
Fig. 14. Comparison between the time-histories of the internal forces in the lining computed with the T1213 record and the development of internal forces with the shear strain evaluated from the decoupled analysis. 246
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
generally in a good agreement with the observed damage, evidencing the following results:
axial vibration mode T = 0.04 s
– the seismic actions recorded in the vicinity of the damaged section of the tunnel during the Norcia earthquake at two different elevations showed differences compatible with the expected dynamic response of the respective sites; – the seismic actions were strong enough to damage the tunnel; the analyses showed that shear failure may have preceded a bending failure; – the damage of the tunnel in the presence of the actual seismic forces was principally caused by a non-uniform thickness of the unreinforced lining, probably due to a misalignment of the road and the excavation axes; – while static equivalent actions appeared capable to bring the tunnel lining close to rupture, the dynamic response of the particular lining adopted, associated to the absence of an invert, may have contributed substantially to the observed damage.
bending vibration mode T = 0.19 s
Fig. 15. Normalised modal shapes of the tunnel lining.
As a more general result, it would appear that simplified methods for the analysis of tunnels subjected to earthquake loading, which are based on equivalent static actions, may be reasonably adequate, provided that the static actions are evaluated considering a careful analysis of the ground response and that the excavation of the tunnel is adequately modelled. However, it may be worth considering the dynamic response of the lining, to see if particular vibration periods, like the one associated to bending in the case analysed in this paper, may interact with the frequency content of the ground motion, producing an amplification of the internal force in the lining: this amplification phenomenon could be evaluated only through the use of dynamic analysis tools.
beam elements
non-linear finite-difference zones
Declaration of interest
Fig. 16. Detail of the two-dimensional model of the tunnel lining.
None. shear strain to use in a decoupled approach; – numerical methods to simulate the construction of the tunnel; – -decoupled approach to evaluate the loads induced by the earthquake through an equivalent static analysis; – domain reduction techniques for the coupled study of the soilstructure interaction by means of a dynamic numerical analysis.
Acknowledgements The Authors wish to express their gratitude to Mr. A. Micheli and Mr. L. Cedrone of Anas S.p.A.for providing the data on the seismic damage of the San Benedetto tunnel. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
The results obtained in the decoupled and coupled analyses were
(a)
(b)
0.015 m
Fig. 17. (a) Plastic zones around the 2D tunnel lining, as an effect of record T1213; (b) deformed grid (factor of amplification = 35). 247
Tunnelling and Underground Space Technology 89 (2019) 238–248
L. Callisto and C. Ricci
References
tunnel response. Can. Geotech. J. 45, 1743–1764. Lu, C.C., Hwang, J.H., 2017. Implementation of the modified cross-section racking deformation method using explicit FDM program: a critical assessment. Tunnel. Undergr. Space Technol. 68, 58–73. Lysmer, J., Kuhlemeyer, R.L., 1969. Finite dynamic model for infinite media. J. Eng. Mech. 95 (EM4), 859–877. Marinos, P., Hoek, E., 2000. GSI: a geologically-friendly tool for rock mass strength estimation. In: Proceedings of the GeoEng2000 at the International Conference on Geotechnical and Geological Engineering, Melbourne, Technomic Publishers, Lancaster. p. 1422–1446. Marzi, V., Micheli, A., Cedrone, L., Martino, M., 2017. Damaging of the San Benedetto tunnel caused by the earthquake of October 30, 2016 – Provision of provisional safety and functional investigation for the definitive tunnel restoration. Gallerie e grandi opere sotterranee, No. 123, pp. 25–35 (in Italian). FEMA-NIBS (Federal Emergency Management Agency and National Institute of Building Sciences), 2003. Multi-hazard Loss Estimation Methodology, HAZUS-MH MR4 Technical Manual, Prepared for the Federal Emergency Management Agency, Washington DC, United States, 712 pp. Panet, M., Guenot, A., 1982. Analysis of convergence behind the face of a tunnel. In: Jones, M.J. (Ed.), Tunnelling’82: Third International Symposium. The Institution of Mining and Metallurgy, Brighton. London, pp. 197–204. Tsinidis, G., Pitilakis, K.D., 2018. Improved R-F relations for the transversal analysis of rectangular tunnels. Soil Dyn. Earthq. Eng. 107, 48–65. Wang, J.N., 1993. Seismic Design of Tunnels: A State-of-the-Art Approach. Monograph 7. Quade & Diuglas Inc., New York, Parsons, Brinckerhoff. Wang, W.L., Wang, T.T., Su, J.J., Lin, C.H., Seng, C.R., Huang, T.H., 2001. Assessment of damage in mountain tunnels due to the Taiwan Chi-Chi Earthquake. Tunnel. Undergr. Space Technol. 16, 133–150. Yashiro, K., Kojima, Y., Shimuzu, M., 2007. Historical earthquake damage to tunnels in Japan and case studies of railway tunnels in the 2004 Niigataken-Chuetsu earthquake. Quart. Rep. Railway Tech. Res. Inst. 48 (3), 136–141. Zhang, X., Jiangb, Y., Sugimoto, S., 2018. Seismic damage assessment of mountain tunnel: a case study on the Tawarayama tunnel due to the 2016 Kumamoto Earthquake. Tunnel. Undergr. Space Technol. 71 (2018), 138–148.
Amorosi, A., Boldini, D., 2009. Numerical modelling of the transverse dynamic behaviour of circular tunnels in clayey soils. Soil Dyn. Earthq. Eng. 29, 1059–1072. Argyroudis, S.A., Pitilakis, K.D., 2012. Seismic fragility curves in alluvial deposits. Soil Dyn. Earthq. Eng. 35 (1), 12. Argyroudis, S., Tsinidis, G., Gatti, F., Pitilakis, K., 2017. Effects of SSI and lining corrosion on the seismic vulnerability of shallow circular tunnels. Soil Dyn. Earthq. Eng. 98, 244–256. Argyroudis, S., Kaynia, A.M., 2014. Fragility functions of highway and railway infrastructure. In: SYNER-G: Typology Definition and Fragility Functions for Physical Elements at Seismic Risk. Springer, Dordrecht, pp. 299–326. Bardet, J. P., Ichii, K., Lin, C.H., 2000. EERA. A computer program Nonlinear Earthquake site Response Analyses of layered soil deposits, University of Southern California, Department of Civil Engineering, Los Angeles, Calif. Bilotta, E., Lanzano, G., Madabushi, S.P.G., Silvestri, F., 2014. A numerical Round Robin on tunnels seismic actions. Acta Geotech. 9, 563–579. Callisto, L., Soccodato, F.M., 2010. Seismic design of flexible cantilevered retaining walls. J. Geotech. Geoenviron. Eng. 136 (2), 344–354. Callisto, L., Rampello, S., Viggiani, G.M.B., 2013. Soil-structure interaction for the seismic design of the Messina Strait Bridge. Soil Dyn. Earthq. Eng. 52, 103–115. Hashash, Y.M.A., Hook, J.J., Schmidt, B., Yao, J.I., 2001. Seismic design and analysis of underground structures. Tunnel. Space Technol. 16, 247–293. Hoek, E., Brown, E.T., 1980. Underground Excavations in Rock. Institution of Mining and Metallurgy, London. Hoek, E., Caranza-Torres, C.T., Corcum, B., 2002. Hoek–Brown failure criterion-2002 edition. In: Bawden, H.R.W., Curran, J., Telsenicki, M. (Eds.), Proceedings of the North American Rock Mechanics Society (NARMS-TAC 2002). Mining Innovation and Technology, Toronto, pp. 267–273. Hoek, E., Diederichs, M.S., 2006. Empirical estimation of rock mass modulus. Int. J. Rock Mech. Min. Sci. 203–215. Itasca Consulting Group, 2011. FLAC 7.0: Fast Langrangian Analysis of Continua. User’s Guide. Kontoe, S., Zdravkovic, L., Potts, D.M., Menkiti, C.O., 2008. A case study on seismic
248