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\begin{document}

\title{Seismic~ Analysis of Underground Works and Practice: the Case of
MetroLima}



\author[1]{Marco Zucca}%
\affil[1]{Dipartimento ABC. Politecnico di Milano}%


\vspace{-1em}



  
  \date{May 19, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup








\sloppy


\section*{ABSTRACT}

{\label{650096}}

The evaluation of the seismic behaviour of underground structures
represents~ one of the most actual seismic geotechnical and structural
engineering research~ topics about the study of the complex phenomena of
soil-structural interaction.~In the last decades, different types of
simplified and numerical approaches~ have been developed for the correct
analysis of the seismic vulnerability of~ these important
infrastructures and a series of laboratory tests for the~ seismic
behaviour characterization of the soils (resonant column test, etc.)~
and of the coupled soil-structure system (centrifuge test, etc.) have
been~ conducted, especially after the recent strong earthquakes where
the underground~ structures have been subjected to significant damages.
In the same way, in the~ last few years, the International Codes are
beginning to pay attention to the~ concepts of the seismic design of
these structures.

Despite the significant development of~ knowledge, described above,
still remain open several uncertainties of the~ correct reproduction of
the underground~ structures behaviour under seismic load.~In this paper,
the evaluation of the~ seismic behaviour of Mercato Santa Anida metro
station was conducted through~ the application of two different seismic
input, considering the soil-structure~ interaction effects. The results
of the nonlinear Time History analysis are~ analysed in terms of bending
moment acting on the concrete retaining walls of~ two different
significant sections of the metro station.

\par\null

\textbf{Keywords}

Underground structures; Soil-structure~ interaction; Finite element
analysis; Earthquake; Seismic vulnerability.\textbf{~~~~~~~~~~}

\par\null

\section*{INTRODUCTION}

{\label{702980}}

Underground structures can be grouped into three broad categories
{[}1{]}, each having~ distinct design features and construction methods:
bored or mined tunnels, cut~ and cover tunnels and immersed tube tunnels
(Figure 1).

Unlike surface constructions, underground~ structures were considered,
for a long period, practically invulnerable to~ earthquakes. This
consideration about underground structures safety, however,~ has been
changed after some of them suffered serious damages caused by~
earthquakes, including the 1995 Kobe (Japan), the 1999 Chi-Chi (Taiwan)
and the~ 1999 Kocaeli (Turkey) earthquakes {[}3{]}.

Damaging effects of earthquakes on~ underground structures can be
classified into two main groups:

\begin{itemize}
\tightlist
\item
  damages caused by vibratory~ motion (shaking) of the ground;
\item
  damages due to ground failures.
\end{itemize}

This study has the purpose of determining the most important aspects of
the~ soil-structure interaction effects on underground structures
subjected to~ seismic loads, taking as case study the new Lima Metro
line 2 project.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.28\columnwidth]{figures/Schermata-2017-05-29-alle-11.29.06/Schermata-2017-05-29-alle-11.29.06}
\caption{{Cross sections of tunnels {[}8{]}.
{\label{496428}}{\label{496428}}%
}}
\end{center}
\end{figure}

\section*{CASE STUDY: LIMA METRO LINE
2}

{\label{248081}}

\subsection*{Project Description}

{\label{760836}}

The new Lima Metro line 2 is the first~ underground structure project in
Per\selectlanguage{ngerman}ù. The area where the Lima Metro line 2 is~ located extends from
Puerto del Callao (near the harbor) to Municipalidad de~ Ate. The total
length of the line is about 26.87 km and the tunnel length is~ near 21
km, where 13.60 km are excavated with tunnel boring machine (TBM) and~
the remaining with the new Austrian tunneling~ method (NATM). The
project includes 27 stations realized by Cut and Cover~ method.~The
project~ involves the realization of the first part of the Lima Metro
line 4 (Figure 2),~ totally excavated with TBM and the stations, also~
in this case, are realized by Cut and Cover method.~The~ characteristics
of the tunnel supports and the construction types of the~ stations
depend on geological and geotechnical conditions and on the possible~
presence of water.~

The construction phase will be developed in two distinct phases:

\begin{itemize}
\tightlist
\item
  Phase 1: expected to be completed within 4 years after the start of~
  construction (year 2018 in the estimated~ schedule):
\end{itemize}

\begin{quote}
\begin{quote}
\begin{enumerate}
\tightlist
\item
  ~phase 1A is expected to be operational in February 2017 as it
  requires 3~ years of construction;
\item
  ~phase 1B is expected to be completed within 4/5 years after the start
  of~ construction (year 2018 in the estimated schedule).
\end{enumerate}
\end{quote}
\end{quote}

\begin{itemize}
\tightlist
\item
  Phase 2: is expected to be completed in about 6 years after the start
  of construction (year 2020 in the estimated schedule).
\end{itemize}

\par\null

\subsection*{~Geological and Geotechnical
Framing}

{\label{641067}}

The deposits in the project area were interested by different surveys,
in particular~ in the part of the line involved in the phase 1A: 16
drilling, 7 test pits (5~ to 10 meters deep) in order to determinate the
soil's stratigraphy and 16~seismic tomographies that include seismic
refraction lines (70 to 140 m length)~and MASW in order to evaluate the
seismic waves velocity and for the~ acquisition of seismic profile, were
performed.~~~~~

The investigations have shown the sequence~ of these following
lithological units (Table A) having different geomechanical
characteristics:

\begin{itemize}
\tightlist
\item
  a backfill consisting of silty sands with gravels and~anthropically
  reworked materials;
\item
  inorganic clay of low to medium plasticity and inorganic silt~of low
  plasticity;
\item
  silty sand;
\item
  poorly graded gravel with sand, clay~and silt;
\item
  diorite, tonalite and philonian rocks.
\end{itemize}

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-11.39.28/Schermata-2017-05-29-alle-11.39.28}
\caption{{Lima Metro line 2.
{\label{515321}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-09.18.07/Schermata-2017-05-29-alle-09.18.07}

\end{center}
\end{figure}

\subsection*{Hydrogeology}

{\label{352230}}

The Gran Lima aquifer consists of Quaternary alluvial deposits of Rimac
and Chillon~ valleys. These deposits are characterized by the presence
of boulders, gravel,~ sand and clay interspersed in layers and/or mixed.
Another aspect is the~ presence of groundwater level that changes~
during the project area. In particular, the groundwater is located near
the~ harbor zone in correspondence to the first part of line 2 and to
the total of line~ 4.

\par\null

\subsection*{Tectonics and Seismicity}

{\label{334491}}

Per\selectlanguage{ngerman}ù is located on the east coast of the Pacific in so-called ``Cinturon
de~ Fuego del Pacifico'' area that due to the interaction between the
South America~ plate and Nazca plate, which generates a subduction zone
near the Perù coast,~ represents one of the most active~ earthquake
zones in the world. For this reason, a study of seismic risk of the~
project area was carried out in order to evaluate the correct seismic~
parameters. This study is based on seismic hazard determination which
is~ defined as the exceedance probability of a determinate ground motion
intensity~ value due to an earthquake in a given location and during a
defined time~ period. According to this study (with deterministic and
probabilistic methods)~ and taking into account the spatial variability
of the seismic action, the~ maximum value of the peak ground
acceleration equal to 0.40 g has been~ obtained. For the evaluation of
seismic design parameters five representative~ zones, each having
different geophysical and geological characteristics, were considered
(Table B).

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-09.18.54/Schermata-2017-05-29-alle-09.18.54}

\end{center}
\end{figure}

\section*{SEISMIC VULNERABILITY OF MERCADO SANTA ANITA METRO
STATION}

{\label{203267}}

\subsection*{Mercato Santa Anita Metro
Station}

{\label{785623}}

The first step of the evaluation of the~ seismic vulnerability of the
new Lime Metro line 2 is the study of the seismic behaviour~ of the
metro stations included in the Phase 1A, in particular of the Mercado~
Santa Anita Metro Station. In this area, as mentioned before, the
groundwater~ is not present. The investigations around this area have
shown the sequence of~ four lithological units having different
geomechanical~ characteristics (Table C).\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-09.19.45/Schermata-2017-05-29-alle-09.19.45}

\end{center}
\end{figure}

The~station is characterized by a rectangular plan (132.16 x 29.00
meters) and it~ is subdivided into 3 different zones (Figure 3). Each
zone is, further, subdivided into 3 different levels.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-09.20.42/Schermata-2017-05-29-alle-09.20.42}
\caption{{Mercato Santa Anita Metro Station.
{\label{656328}}%
}}
\end{center}
\end{figure}

The principal structural elements that characterized the metro station
are the concrete retaining walls, 1 m thick, and a series of concrete
circular columns, 1.2 m diameter, positioned in a regular grid 14.70 x
12.00 m. The foundation of the columns consists of circular concrete
piles, 1.8 m diameter and 9 m deep Figure 4. The materials mechanical
properties of the structural elements are shown in Figure 5.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-09.23.17/Schermata-2017-05-29-alle-09.23.17}
\caption{{Metro station plan.
{\label{104963}}{\label{104963}}%
}}
\end{center}
\end{figure}

\subsection*{Numerical Analysis}

{\label{133887}}

The analysis of the seismic behaviour of the metro stations is carried
out~ considering static and dynamic loads. Two finite element models
representing~ both structure and soil are implemented. The two
bi-dimensional models~ implemented by {[}6{]} software represents~ the
section 4-4 of the Zone 2 (Figure 6) and the section 2-2 representing
both~ Zone 1 and Zone 3 (Figure 7).~The~ FEMs are characterized by plane
strain elements and an example of geometry and the~ relative computation
grid are shown in Figure 8. The maximum size of~ computation mesh
elements has been fixed in order to allow the correct~ propagation of
harmonic with 15 Hz maximum frequency, which is the maximum~ frequency
of the seismic signals adopted in this study, according to {[}4{]}. The~
formulation to optimize the size of the mesh is given in {[}7{]}. For
each model, the boundary conditions are the~ following: vertical
supports in the base nodes to restrain the vertical~ displacements
and~horizontal supports in the lateral nodes of the mesh to permit
vertical soil settlements. In dynamic conditions, in order to minimize
reflection effects on vertical lateral boundaries of the grid, free
field boundary conditions available in MIDAS GTS library have been used.
The structure is represented, in the first approach, by linear elastic
beams while for the soil an elastic perfectly plastic model with
Mohr-Coulomb strength rule, characterized by the mechanical properties
shown in Table 3, was adopted. The soil hysteretic behaviour was modeled
using the shear modulus decay curves given by {[}9{]} and {[}11{]}. The
hysteretic damping is, however, computed by applying the generalized
Masing criteria implemented in the computer code mentioned before. The
contact between soil and walls was modeled by using elastic-perfectly
plastic interface elements, with a friction angle equal to 20\selectlanguage{ngerman}°.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-30-alle-07.19.24/Schermata-2017-05-30-alle-07.19.24}
\caption{{Section 4-4 and materials mechanical properties of structural elements.
{\label{650604}}%
}}
\end{center}
\end{figure}

\subsection*{Loads}

{\label{957248}}

\emph{Static Loads}

The loads considered in the analysis are~ described in the following:

\begin{itemize}
\tightlist
\item
  dead load on the on the sides~ of the station equal to 50
  kN/m\textsuperscript{2} due to the presence of existing~ buildings and
  streets;
\item
  dead load in correspondence to~ the station equal to 20
  kN/m\textsuperscript{2} due to the presence of the streets;
\item
  self-weight of the structure and the soil.
\end{itemize}

The structural condition of the metro~ station under the considered
static loads are determined by performing a~ construction stage
analysis, taking into account all the main phases involved~ in the
construction of the station and in order to reproduce the excavation
and~ the realization of the structure with cut and cover method, before
the dynamic~ stage of the analysis. The principal construction phases
are

\begin{itemize}
\tightlist
\item
  the realization of an~ excavation, characterized by a provisional
  slope 1H:5V, in order to create a~ first entrance ramp;
\item
  the realization of the~ diaphragm walls and of the wells for the
  realization of the foundation
  piles;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\item
  the realization of the top~ cover slab made from reinforced concrete
  and 1.2 m thick;
\item
  the execution of a second~ excavation;~~~~
\item
  the realization of the~ intermediate slab made from reinforced
  concrete and 0.6 (section 2-2) - 0.9 m~ (section 4-4) thick;~~~
\item
  the execution of a third excavation;
\item
  the realization of the concrete~ bottom slab 0.25 m thick;
\item
  the road surface restoration.
\end{itemize}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-10.55.55/Schermata-2017-05-29-alle-10.55.55}
\caption{{Section 4-4.
{\label{399667}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-11.02.38/Schermata-2017-05-29-alle-11.02.38}
\caption{{Section 2-2.
{\label{691977}}%
}}
\end{center}
\end{figure}

\emph{~Seismic Action~~~}

The seismic~ design approach of underground structures is generally
characterized by two~ different type of earthquake events: the maximum
design earthquake (MDE) and~ the operating design earthquake (ODE)
typically defined as:

\begin{itemize}
\tightlist
\item
  MDE: is the earthquake event that has a return period of several
  thousand years. It has a small probability of exceedance,
  approximately 5~\% or less, during the 100 years facility life. It is
  aimed at public life~safety.~~~
\item
  ODE: is the event for which recurrence interval is several
  hundred~years; the probability of exceedance of this event is
  approximately 40 \% during the facility life. It is aimed to guarantee
  full functioning of the~structure. The response of underground
  structures should, therefore, remain within the elastic range.
\end{itemize}

In this case, two different type of artificial~ seismic accelerograms
are taking into account for the evaluation of the seismic~ behavior of
Mercato Santa Anita Metro Station, according to the study of seismic
risk of the project area described in the~ previous paragraph and to the
values shown in Table D:~ one seismic event characterized by a return~
period equal to 1000 years in order to represent the ODE (Figure 9) and
another~ seismic event characterized by a return period equal to 2450
years in order to~ represent the MDE (Figure 10), according to
GB50909-2014. The recording has been corrected with a low-pass filter at
the~ cut-off frequency of 15 Hz using {[}2{]}.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-11.03.28/Schermata-2017-05-29-alle-11.03.28}
\caption{{Example of geometry and computation grid of Mercado Santa Anita Metro
Station.
{\label{154261}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-11.05.05/Schermata-2017-05-29-alle-11.05.05}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-11.09.54/Schermata-2017-05-29-alle-11.09.54}
\caption{{ODE seismic input.
{\label{219321}}%
}}
\end{center}
\end{figure}

\emph{Static~ Analysis}

Geological studies and investigations~ have led to the definition of the
geomechanical~ characteristics of the soils to be used in the numerical
analysis. In the following, a summary of~ these characteristics is
reported in Table E. The mechanical properties of the structural~
elements are shown in the previous Figure 5.~

The static analysis carried out by the~ application of all the before
mentioned vertical loads has pointed out the~ characteristic behaviour
of the retaining~ walls of the Metro Station's structure: it appears
similar to a double~ multi-span (simply supported) beams.~

The~ structural conditions of the Metro Station under the considered
static loads~ are determined by performing a construction stage
analysis, taking into account~ all the main phases historically involved
in the construction of the station.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-11.13.07/Schermata-2017-05-29-alle-11.13.07}
\caption{{MDE seismic input.
{\label{883035}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-11.14.00/Schermata-2017-05-29-alle-11.14.00}

\end{center}
\end{figure}

Section 4-4

The characteristics of the Section 4-4 FEM~ are shown in Figure 11. The
soil is characterized by 4-node plane strain~ elements and the maximum
size of computation mesh elements is determined by the~ following
relation, in order to perform correctly the next dynamic analysis:

\(h\le h_{\max}\ =\ \frac{V_s}{\left(5\ -\ 8\right)f_{\max}}=6.83\ m\)

\(\)where f\textsubscript{max}~ is the maximum frequency
of the seismic signals adopted in this study, equal to~15 Hz. The
dimensions of the model have been fixed in order to avoid the~ boundary
effects and in this case have~ been taken equal to three times the size
of the structure (in horizontal and~ vertical direction). The structure
is represented, in the first approach, by linear elastic beams while~
for the soil an elastic perfectly plastic model with Mohr-Coulomb
strength~ rule, characterized by the mechanical properties shown in
Table E, was adopted.~ The contact between soil and walls was modeled~
by using elastic-perfectly plastic interface elements, with a friction
angle~ equal to 20\selectlanguage{ngerman}° {[}10{]}. The values of the stiffness of the
interface elements are~ evaluated according to {[}6{]}:

\(K_n=\frac{E_{0ed,i}}{t_v}\)

\(K_t=\frac{G_i}{t_v}\)

where:

\(G_i=R\cdot G_{soil}\)

\(E_{0ed,i}=2G_i\frac{\left(1-\nu_i\right)}{\left(1-2\nu_i\right)}\)

and~~~ ~~~~ ~~~~~~~~~~~

\begin{itemize}
\tightlist
\item
  t\textsubscript{v} = the virtual~ thickness which depends on the
  difference in stiffness between soil and~ structure and the value
  varies from 0.01 to 0.1. In this study the value~ considered is equal
  to 0.05 for each model;
\item
  R = strength reduction factor~ taken as 1.
\end{itemize}

Known the geometry and the values of the~ static loads, the results are
obtained in terms of bending moments acting on~ the retaining walls
(Figure 12). The maximum values of the bending moment~ acting on the
retaining walls obtained in static conditions is equal to 600~ kNm.

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-22/Figure-22}
\caption{{Section 4-4 FEM.
{\label{337970}}{\label{337970}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.26.00/Schermata-2017-05-29-alle-12.26.00}
\caption{{Bending moment acting on the Section 4-4 retaining walls in static
conditions.
{\label{852569}}{\label{852569}}{\label{852569}}%
}}
\end{center}
\end{figure}

\emph{Dynamic Analysis~~~}

The dynamic analysis is performed, after~ the final step of the
construction stage described before, by using Nonlinear~ Time History
analysis, considering the seismic inputs described in previous~
paragraph. The present analysis is repeated for all the two above
described characteristic sections~ (Figures 17 and 18).

In order to minimize reflection effects on~ vertical lateral boundaries
of the grid, as mentioned before, free field~ boundary conditions
available in MIDAS GTS library have been used.

The soil~ hysteretic behaviour was modeled using the shear modulus decay
curves~ given by {[}9{]} and {[}11{]} (Figure 16).~In order to evaluate
the seismic response~ of the system (Figure 19), the amplification of
the seismic input was evaluated~ at the remarkable points A, B, C and D
represented in Figures 17 and 18.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=1.00\columnwidth]{figures/Schermata-2017-05-29-alle-12.28.36/Schermata-2017-05-29-alle-12.28.36}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-23/Figura-23}
\caption{{Section 2-2 FEM.
{\label{494850}}{\label{494850}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-24/Figura-24}
\caption{{Bending moment acting on the Section 2-2 left retaining wall.
{\label{397918}}{\label{397918}}{\label{397918}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-25/Figura-25}
\caption{{Bending moment acting on the Section 2-2 right retaining wall.
{\label{874136}}{\label{874136}}{\label{874136}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.36.10/Schermata-2017-05-29-alle-12.36.10}
\caption{{Example of~ G-gamma and D-gamma decay curves.
{\label{827622}}{\label{827622}}{\label{827622}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figura-26/Figura-26}
\caption{{~~~~~~~~~~~~~ Section 4-4 FEM (dynamic conditions).
{\label{179616}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figure-27/Figure-27}
\caption{{Section 2-2 FEM (dynamic conditions).
{\label{173399}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.46.04/Schermata-2017-05-29-alle-12.46.04}
\caption{{Amplification effect of the seismic input.
{\label{680950}}{\label{680950}}%
}}
\end{center}
\end{figure}

Figure 20 shown an example of~ \selectlanguage{greek}τ -\selectlanguage{english}gamma cycles obtained, respectively,
at a depth of 1 meter (soil type R), at 2.6 meters (soil type GP-Ss), at
8.7 meters (soil type GP-Sm) and at 22 meters (soil type GP-Sf) for the
seismic input characterized by a return period equal to 1000 years.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.47.46/Schermata-2017-05-29-alle-12.47.46}
\caption{{Example of \selectlanguage{greek}τ -\selectlanguage{english}gamma cycles obtained for the seismic input RP = 1000
years.
{\label{124817}}%
}}
\end{center}
\end{figure}

Figures 21, 22, 23 and 24 shown the results of the Section 4-4 under
seismic inputs characterized by a return period, respectively, equal to
1000 years and 2450 years.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.49.34/Schermata-2017-05-29-alle-12.49.34}
\caption{{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Maximum values of bending moment
acting on the Section~ 4-4 left retaining wall during the Nonlinear Time
History Analysis (RP = 1000~ years) - the dashed line represents the
values of yielding moment.
{\label{766481}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.50.42/Schermata-2017-05-29-alle-12.50.42}
\caption{{~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Maximum values of bending moment
acting on the Section~ 4-4 right retaining wall during the Nonlinear
Time History Analysis (RP = 1000~ years) - the dashed line represents
the values of yielding moment.
{\label{146630}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.51.39/Schermata-2017-05-29-alle-12.51.39}
\caption{{Maximum values of bending moment acting on the Section 4-4 left
retaining wall during the Nonlinear Time History Analysis (RP = 2450
years) - the dashed line represents the values of yielding moment.
{\label{209826}}%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.53.22/Schermata-2017-05-29-alle-12.53.22}
\caption{{Maximum values of bending moment acting on the Section 4-4 right
retaining wall during the Nonlinear Time History Analysis (RP = 2450
years) - the dashed line represents the values of yielding moment.
{\label{318539}}%
}}
\end{center}
\end{figure}

\par\null

The results of the Section 4-4 showed that the Metro Station remain~
within the elastic range for a seismic input characterized by a return
period~ equal to 1000 years. On the contrary, for the seismic input
characterized by a~ return period equal to 2450 years, only the section
near the intermediate slab~ shows localized plastic deformation.~For the
Section 2-2 the same~ considerations could be made.

\section*{CONCLUSION}

{\label{527381}}

Seismic~ response of Mercato Santa Anita Metro Station to two seismic
inputs~ characterized, respectively, by a return period equal to 1000
years and 2450~ years shows:

\begin{itemize}
\tightlist
\item
  an elastic behavior of the retaining walls for a seismic input
  characterized by a~ return period equal to 1000 years;
\item
  for~ the seismic input characterized by a higher return period, the
  Station shows~ localized plastic deformations only in the section near
  the intermediate slab.~ This behavior is considered acceptable for the
  Maximum Design Earthquake~ because the public life safety is
  guaranteed.
\end{itemize}

Taking as a~ reference the static case, the maximum increment of bending
moment during the~ earthquake is equal to 700 kNm for the operating
design earthquake and 1100 kNm~ for the maximum design earthquake. The~
results of the analysis indicate a complex response of the system due
to~ particular soil-structure interaction effect and local seismic
response~ phenomena because the soil response is related to the
vibration modes excited~ by the signal. It may be noted that the
signals, now taken into account, gives~ rise to possible soil resonance
with the first vibration mode, which leads to~ increasing shear strain
in the deeper soil layers, and, consequently,~ additional damping
according to the strongly nonlinear soil behaviour (Figure 25).

\par\null\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Schermata-2017-05-29-alle-12.57.16/Schermata-2017-05-29-alle-12.57.16}
\caption{{Seismic signal frequency domain and the main natural frequency of the
soil profile evaluated according to {[}5{]}.
{\label{647780}}{\label{647780}}{\label{647780}}%
}}
\end{center}
\end{figure}

\section*{REFERENCES}

{\label{430748}}

\begin{enumerate}
\tightlist
\item
  Bickel J.O. (ed.) Tunnel engineering handbook; Chapman and~ Hall, New
  York, (1996).
\item
  DEGTRA A4 Version 5.1, Instituto de Ingenieria, UNAM.
\item
  Hashash Y. M.A., Hook J., Schmidt B., Yao J. Seismic design and
  analysis~ of underground structures; Tunnelling and Underground Space
  Technology 16, pp.~ 247 -- 293, (2001).
\item
  Kuhlemeyer R. L., Lysmer J.~ Finite element method accuracy for wave
  propagation problems, Journal of Soil Mechanics \& Foundations~
  Division. ASCE, 99 (SM5), pp.~ 421 -- 427, (1973).
\item
  Maugeri M., Carrubba P., Frenna~ S.M. Frequenze e modi di vibrazione
  di terreni~ eterogenei. Associazione Geotecnica Italiana, (1988).
\item
  MIDAS GTS NX, Analysis~ Reference.
\item
  Pagliaroli A., Lanzo G., San\selectlanguage{ngerman}ò~ T. Confronto fra tre codici di calcolo
  2D della~ risposta sismica~ locale. XII Congresso Nazionale~
  ``l'Ingegneria sismica in Italia'', ANIDIS, (2007).
\item
  Power M.S., Rosidi D.,~ Kaneshiro J. Vol. III Strawman: screening,~
  evaluation, and retrofit design of tunnels. Report Draft. National
  Center for~ Earthquake Engineering Research, Buffalo, New York,
  (1996).~~~ ~~~~~~
\item
  Seed H.B., Idriss I.M. Soil moduli and damping factors for dynamic~
  analysis. Report No. EERC 70-10, University of California, Berkeley,~
  (1970).~~
\item
  Soccodato F.M., Tropeano G. The role of ground motion characters on~
  the dynamic performance of propped retaining structures, 6ICEGE,
  6\textsuperscript{th} International Conference on Earthquake~
  Geotechnical Engineering, Christchurch, New Zealand, 1--4 November,
  (2015).
\item
  Stokoe K.H., Jung M.J., Menq~ F.-Y., Liao T., Massoudi N., McHood M.
  Normalized shear modulus of compacted~ gravel, 18\textsuperscript{th}
  International~ Conference on Soil Mechanics and Geotechnical
  Engineering, Paris, France,~ (2013).
\end{enumerate}

\par\null

\selectlanguage{english}
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\end{document}

