1684
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
5.0
s
kh
c
s
N
q
V
(1)
Where
V
s
has units of m/s,
q
c
is given in t/m
2
and
s in t/m
3
(volumetric weight of soil),
and
N
KH
are typical values for
soils from Mexico City.
4 NUMERICAL MODEL
Numerical modelling was performed using the finite difference
method, implemented in three dimensions in the analysis
platform FLAC3D (ICG, 2009). The chosen platform applies
the numerical method to geometry and arbitrary boundary
conditions defined by the user with an external preprocessor
(Romo et. al., 2005)
4.1
Characteristics of the model
The model of this site has two stations, which have 46 m
wide by 190 m long. The stations reach a maximum depth of 22
m deep at their lower point from the surface. They are limited
by two slurry trench walls in the transverse direction, which are
supported at a depth of 28 m. The tunnel is 480 m long and 10
m in diameter and its crown is at a depth of 9.4 m. The model
was conceived considering the layout plan of the section under
consideration, including changes in the alignment of the tunnel
which generate two horizontal curves, as presented in Fig.2.
Figure 2. Isometric view of the three-dimensional model.
4.2
Soil deposit model
The three-dimensional finite difference model, consisting of
630,525 nodes and 608,004 elements which form mostly 8-node
tetrahedral and the remaining correspond to 6 nodes wedges.
The model has 202 m wide and 861 m long (see Fig. 2). With
these dimensions it seeks to minimize the potential effects of
refraction of waves in the half-space, in addition to dissipating
boundaries are implemented for the same purpose.
The model consists of six layers. The first one corresponds
to soft clay, the five remaining layers underlying are more
compact, generating a significant contrast between the material
stiffness.
4.3
Detailed station and tunnel model
The stations models have a top slab corresponding to the
pedestrian circulation area, two Milan walls at sides of the
platform area where the trains are parked.
To integrate the tunnel to the stations, it has concrete walls
that connect the stations with the tunnel. The tunnel is made up
of rings of 8 segments of 40 cm thick, which have a rotation (or
phase) of 33° to each other. For modeling purposes, according
to the hypothesis behavior of the elements, this covering is
considered as a continuous stiffness properties equivalent to
those of the original reinforcement.
5 SEISMIC ENNVIROMENT
The seismic environment at the site was determined in terms of
acceleration spectra envelopes obtained from accelerations
recorded in the vicinity of the site. Finally, the surface spectrum
was scaled by the seismic coefficient specified in the Mexico
City Building Code (NTC, 2004). This meets statutory
provisions (see Fig. 3)
Figure 3. Comparative spectra.
The scaled spectrum was deconvolutioned at the model base
by means of a probabilistic analysis. To the end we generate 25
random site profiles. The analysis was made take the spectrum
corresponding to the mean plus one standard deviation in order
to cover the range of uncertainty inherent to this type of study.
The resulting spectrum is taken as the objective function to
generate a synthetic earthquake, which serves as a basis for
analyses in time domain.
Tunnel
6 EVOLUTION OF THE SEISMIC RESPONSE DUE TO
REGIONAL SUBSIDENCE
Regional subsidence in Mexico City induces changes in pore
pressure that increase effective stresses. As a result, the static
and dynamic properties of the soil are modified and therefore,
the seismic response.
6.1
Pore Pressure distribution
The variation of pore pressure distribution due to regional
subsidence was analyzed using a one-dimensional model of soil
consolidation. The model we used, considers the soil as an
elasto-viscous-plastic material in which primary and secondary
consolidation are coupled. The model was originally proposed
by Yin and Graham (1996) and implemented by Ovando and
Ossa (2004) to evaluate regional subsidence caused by water
pumping. The analysis of the variation of pore pressure
distribution due to regional subsidence considered a period of
50 years. The studied site was modeled taking into account that
compressible deposits are confined by permeable soil layers.
The initial piezometric conditions and the pore pressure
depletion rates at the permeable boundaries were estimated from
piezometric stations located near to the studied site.
Evolution of the pore pressure distribution in the studied site
is presented in Figure 4a.
6.2
CPT strength and shear wave velocity
CPT strength depends on the shear strength of the soil. On the
other hand, the relationship between vertical stress and shear
strength of normally consolidated soil (clay condition
representative of the Valley of Mexico) is constant, leading to
assume that changes in effective stress due to groundwater
