Download Seismic Response of High Plasticity Clays subjected

6th International Conference on Earthquake Geotechnical Engineering
1-4 November 2015
Christchurch, New Zealand
Seismic Response of High Plasticity Clays subjected
to Extreme Seismic Events
J. M. Mayoral 1, N. Sarmiento 2 and E. Castañon 3
ABSTRACT
Current seismic design criteria of strategic infrastructure used worldwide have striven for having
larger return periods for design uniform hazard spectra, considering recent large magnitude
(M>8.5M w ) seismic events. Mexico City high plasticity clays present an almost linear behavior
for shear strains as large as 0.1%, which leads to both small shear stiffness degradation and small
damping increment, even for long duration subduction strong ground motions, such as the 8.1M w
1985 Michoacan earthquake. This paper presents the study of the seismic response of typical high
plasticity clays found in the so-called Texcoco Lake, in the surrounding of Mexico City valley, for
larger to extreme events. An instrumented soft soil site was used in the study. The shear wave
velocity profiles were established using down-hole tests, and the suspension logging, SS,
technique. The seismic hazard considered for this study was established from a set of uniform
hazard response spectra developed for a nearby rock outcrop for return periods of 125, 250, 475
and 2475 years. Time-domain spectral matching was used to develop acceleration time histories
compatible with each uniform hazard response spectrum. Frequency domain site response analysis
was carried out considering each seismic scenario. Computed ground amplification was validated
with actual measurements taken at the site during the 1985 Michoacan earthquake, using the UHS
for 125 years. Ground nonlinearities were clearly observed in the soil response, which were further
explored through nonlinear site response analyses, performed using the program FLAC3D. From
the results gathered in this study, it was concluded that even high plasticity clays deposits may
exhibit important ground motion attenuation during extreme ground shaken, which must be taken
into account to avoid site amplification overestimation and, in turn, costly seismic designs.
Introduction
Traditionally, high plasticity clays (i.e. plasticity index larger than 250%), such as those found in
the Mexico City valley, have been considered to exhibit a very small amount of soil nonlinearity
during strong ground shaking, such as that observed in the 8.1M w , Michoacan earthquake, even
for shear strains as large as 0.1%. Recently, extreme magnitude subduction earthquakes (i.e.
larger than 8.5M w ), such as the Tohoku, Japan 9.0M w , and Maule, Chilean 8.8 M w events, have
caused considerable damage in densely populated cities. Thus, current seismic design criteria of
strategic infrastructure used worldwide have striven for having larger return periods to
characterize the seismic environment when dealing with major strategic infrastructure, within a
probabilistic seismic hazard analysis framework, PSHA [Cornell (1968), McGuirre (1995),
Klügel (2008) and Baker (2008)]. Nevertheless, when performing a site response analysis, large
return periods can increase the seismic demand unrealistically when soil nolinearity is not
1
Researcher Institute of Engineering, UNAM Mexico City, [email protected]
Engineering Researcher Institute of Engineering, UNAM Mexico City, [email protected]
3
Graduate student Institute of Engineering, [email protected]
2
accounted for, missing both spectral accelerations magnitude as well as frequency content,
leading to costly and sometimes unsafe seismic designs. This is particularly important in Mexico
City, because historical seismicity has proven that the subduction zone located along the Coast of
Oaxaca state is able to produce events with moment magnitude, M w , of 8.6, with potential fault
rupture lengths of about 450km [Suarez (2009)]. This paper presents the study of the seismic
response of common high plasticity clay deposits found at Mexico City Valley subjected to large
and extreme ground shaking. The studied area is instrumented with four seismological stations.
Typical shear wave velocity profiles were characterized using down-hole tests. The seismic
hazard considered for this study was established from a set of uniform hazard response spectra,
UHS, developed for a nearby rock outcrop considering return periods of 125, 250, 475 and 2475
years. From the results gathered here in, is evident the importance of accounting for soil
nonlinearities when dealing with return periods larger than 125 years, even in high plasticity
clays, to avoid costly and, in some cases, unsafe seismic designs.
Description of the Studied Site
19.60º
TXSO
"CARACOL"
TEXCOCO
19.50
TXS2
AU
TO
P.
X.
MÉ
TXS1
X.
- TE
SITE-1
19.45
SITE-2
TXCH
STUDIED
SITES
S-
SITE-3
TE
XC
OC
O
19.55
YE
19.40
RE
LATITUDE
Typical subsoil conditions found at the former Texcoco Lake has been studied by several
researchers [Mayoral et al. (2008), Osorio and Mayoral (2013), Mayoral and Castañon (2014)
and Stephenson et al. (2006)]. Usually the soil profile at this zone presents a desiccated crust of
clay at the top extending up to a depth of about 5.0m, which is underlain by a soft clay layer
approximately 38 to 66m thick, with interbedded lenses of sandy silts and silty sands. The
plasticity index ranges from 87 to 293%. Underneath this elevation, a competent layer of very
dense sandy silt is found. The distance from the Autonomous National University of Mexico,
UNAM-CU, to the polygon center that encloses the studied area is approximately 25.90km, and
from the Mexico City International Airport is about 10.5km, as depicted in Figure 1.
ZA
19.35
-99.05
RA
G
O
ZA
-99.00
-98.95
-98.90
-98.85º
LONGITUDE
Figure 1. Studied area location
The studied area is instrumented with four seismological stations, TXSO, TXS1, TXS2 and
TXCH. In particular, TXSO recorded the devastating 8.1M w 1985 Michoacan earthquake. A
fifth station used in the analysis, TXRC, is located to the east, on a rock outcrop, about 19.20km
away from the studied site. Cone penetration, and standard penetration tests, along with selective
sampling recovery were conducted to established three representative high plasticity clay
deposits (Figure 2). The shear wave velocity distribution was measured at each site using downhole tests.
DOWN-HOLE 1
SITE-1
Vs (m/s)
0
0
200
400
600
DOWN-HOLE 2
800
0
UPPER CRUST
5
10
15
DOWN-HOLE 3
Vs (m/s)
0
200
400
600
800
0
UPPER CRUST
5
5
10
10
15
15
20
20
25
25
30
30
30
35
35
40
40
45
55
Depth (m)
35
50
SITE-3
Vs (m/s)
0
200
400
600
800
25
CLAY
γ=11.8 kN/m3
40
Depth (m)
Depth (m)
20
CLAY
γ=11.8 kN/m3
SITE-2
45
50
CLAY
γ=11.8 kN/m3
45
50
55
55
60
60
60
65
65
65
70
70
70
75
75
75
HARD LAYER
HARD LAYER
SAND
γ=13.7 kN/m3
HARD LAYER
Figure 2. Soil profile
Modulus Degradation and Damping Curves
For this research, the curves proposed by Darendeli and Stokoe (2001) were deemed appropriate
to establish the modulus degradation and damping curves for clays, because they take into
account explicitly the most important factors that can influence the dynamic soil behavior.
Furthermore, in previous research this model has provided a good estimate of the cyclic clay
behavior of Texcoco Lake clays [Mayoral et al. (2008), Osorio and Mayoral (2013) and Mayoral
and Castañon (2014)]. To obtain the modulus degradation and damping curves, the over
consolidation ratio, OCR, was taken as one, considering that the studied zone is located in the
virgin former Texcoco lake, and that the over consolidation of the soil due to desiccation
occurred only in the first couple of meters. Regarding the sand layers, the upper bound of the
curves proposed by Seed and Idriss (1970), for shear soil stiffness degradation and damping were
deemed appropriate. Although there are not site specific laboratory tests results for the cases
analyzed, Darendeli´s model has been validated in previous research (Osorio and Mayoral, 2012)
against actual data gathered from nearby sites in the Texcoco Lake, and it seems to provide a
close approximation to the measured response if the reference shear strain, γ r , is properly
derived. Figure 3 shows a comparison of the results predicted with Darendeli´s model and those
obtained from resonant column and cyclic triaxial tests performed in clay samples with plasticity
index, PI, of 194 and 229 % that were retrieved in the Texcoco Lake. The parameter γ r was taken
as the shear strain corresponding to the 50% degradation of the normalized soil shear stiffness
G/Gmax. As can be noticed, there is a very good agreement between the model and the
experimental curves.
1
25
0.8
20
Damping ratio, λ (%)
Normaized shear modulus, G/G
max
PI=194%, Depth= 4.9m
PI=229%, Depth= 25.9m
0.6
0.4
0.2
0
0.0001
PI=194%, Depth= 4.9m
PI=229%, Depth= 25.9m
Experimental result
Experimental result
0.001
0.01
15
10
5
0.1
1
10
0
0.0001
0.001
0.01
0.1
1
10
Shear strain, g (%)
Shear strain, γ (%)
Figure 3. Comparison experimental curves and Darendeli model´s
Uniform Hazard Spectrum for Analyses
Uniform hazard spectra for four return periods, T r , 125, 250, 475, 2475 years, were developed
for the nearby rock outcrop site, where the TXCR seismological station is located, conducting a
probabilistic seismic hazard assessment, PSHA, as described by Osorio and Mayoral (2013).
These UHS are presented in Figure 4a. Each of these spectra is used to derive the input motion
for site response analysis. For this research the attenuation law proposed by Reyes (1999) using
geometric mean was used to estimate the spectral acceleration, Sa, in a rock or stiff soil outcrop
located near by the project in Mexico City. This relationship has the following functional form:
ln Y (T ) = ln Sa (T ) = a1 (T ) + a 2 (T )( M − 6 ) + a3 (T )( M − 6 ) + a 4 (T ) ln R + a5 (T ) R + ε (T )
2
(1)
Where Y represents the maximum ground acceleration in one of the orthogonal directions, or its
geometric mean, MG, in cm/s2; M is the seismic moment magnitude (M w ); R is the closest
distance from the site to the rupture area, in km; a i are coefficients for the geometric mean, and
for the EW and NS components [Reyes (1999)]; ε is the error made when estimating the
response spectrum with the attenuation law. This functional is the same as that proposed by
Joyner and Boore (1988). The appropriateness of this attenuation law has been corroborated in
Osorio and Mayoral (2013), comparing its prediction with the measured response observed
during the 1995 September earthquake in two sites located in rock. This relationship was derived
using records measured in seismological stations located in the National Autonomous University
of Mexico, UNAM, which are placed on top of volcanic rock that is underlain by a layer of
cemented sandy silt or silty sands. Therefore, the spectral shape is different from the expected for
a sound rock. Other stiff soil sites stations in Mexico City also exhibit the same spectral shape,
and are also located in this compacted silty sand or sandy silt known as tobaceous formation
Synthetic Time Histories
To develop time histories which response spectra reasonably match the design response
spectrum, the selected (recorded) time histories were modified using the method proposed by
Lilhanand and Tseng (1988) as modified by Abrahamson and Somerville (1993). This approach
is based on a modification of an acceleration time history to make it compatible with a user
specified target spectrum. The adjustment of the time history can be performed with a variety of
different modification models. In doing so, the long period non-stationary phasing of the original
time history is preserved. The seed and synthetic response spectra of the modified ground
motions compared with those of the targets, are shown in Figure 4b, for each return period. The
seed ground motion is a long duration record (i.e. 200sec) typical of the subduction Pacific
Coast, with a PGA of 0.0026g. This ground motion was measured in September, 14 of 1995 at
seismological station TXRC during a 7.3M w earthquake. Station TXCR is located, as previously
stated, in a rock outcrop, about 19.20km away from the studied site [Osorio and Mayoral , 2013].
The epicenter event was in the coast of Guerrero state, about 122km from Acapulco City. It can
be seen that the response spectra calculated from the modified time histories reasonably match
the target spectrum.
0.3
0.3
Tr = 125 years
Tr = 250 years
Tr = 475 years
Tr = 2475 years
0.25
Spectral Acceleration, S (g)
0.2
a
Spectral Acceleration, Sa (g)
0.25
OBJECTIVE T = 125YEARS
OBJECTIVE T = 250YEARS
OBJECTIVE T = 475YEARS
OBJECTIVE T = 2475YEARS
SYNTHETIC T = 125YEARS
SYNTHETIC T = 250YEARS
SYNTHETIC T = 475YEARS
SYNTHETIC T = 2475YEARS
0.15
0.1
0.05
0.2
0.15
0.1
0.05
0
0
1
2
3
4
5
0
0
1
Period (s)
(a)
2
3
4
5
Period (s)
(b)
Figure 4. Objective and synthetic ground motion response spectra
Site Response Analyses
Initially, as usually considered in site response analyses carried out in Mexico City clay soil
deposits, equivalent linear properties were deemed appropriate to account for soil nonlinearities
approximately for the three sites analyzed, considering the high plasticity exhibited by the clay at
the site. Constant soil properties render poor modelling for cases in which the level of shear
strain may change significantly during the dynamic event, as can occur during strong ground
motions involving large levels of shaking [Seed et al. (1993)], such as those expected for return
periods higher than 125 years. Soil nonlinearities during shear deformation are better captured by
nonlinear hysteretic material response models. Hysteretic behaviour has been modelled with
mechanical models, empirical models and total (or effective) stress elastoplastic models.
Elastoplastic formulations are often implemented within a finite element [Taylor (2001)] or finite
differences [Itasca (2005)] framework. Therefore, to further explore soil nonlinerities a fully
non-linear site response analysis was carried out for site 2. In the study described herein, the
hysteretic non-linear site response analysis was carried out with the program FLAC3D. The threedimensional finite difference model of the free field at site 2 has a depth of about 40m, as
depicted in figure 5. This model was calibrated against the results obtained with the program
SHAKE, which, in turn, has been extensively calibrated against theoretical and experimental
data. Free field boundaries were considered at each site of the model. Due to the lack of
experimental data, the practical-oriented hysteretic model available in FLAC3D Itasca (2005) was
used to approximately deal with both modulus stiffness degradation and damping variation
during the seismic event. The shear stiffness degradation curves for the soils found at the soil
deposit were fitted with an S-shaped curve given by a cubic equation, with zero slope at both low
strain and high strain, which starting points are defined by two parameters L1 and L2. Thus, the
𝑳𝑳 −𝑳𝑳
secant modulus, Ms, is given by the expression Ms=s2(3-2s), where 𝒔𝒔 = 𝑳𝑳 𝟐𝟐−𝑳𝑳 , and L is the
𝟐𝟐
𝟏𝟏
logarithmic strain defined as L = log10 (γ). The calculation is based on the explicit finite
difference scheme, to solve the full equations of motion, using lumped grid point masses derived
from the real density of surrounding zones. Accordingly, to find the ground motions in
underlaying bed rock to be used in time domain site response analyses, time histories computed
at the rock outcrop were deconvolved to the stiffer materials found at the base of the soil profile.
Figure 5. Three-dimensional finite difference model
Model Calibration
The three-dimensional finite difference model of the free field was calibrated against the
equivalent linear results obtained with the program SHAKE, considering a linear-elastic model,
which, in turn, has been extensively validated against theoretical and experimental data. An
elastic analysis considering the equivalent linear properties determined with SHAKE was carried
out with the program FLAC3D. Figure 6 shows a comparison between the acceleration time
histories computed at the surface with both computer programs for 125 and 2475 years of return
period. As can be seen, there is a very good agreement between both results.
SITE-2, T = 2475 YEARS
SITE-2, T = 125 YEARS
r
r
0.15
0.15
SHAKE
FLAC
SHAKE
3D
0.05
0
-0.05
3D
0.05
0
-0.05
-0.1
-0.1
-0.15
FLAC
0.1
ACCELERATION, g
ACCELERATION, g
0.1
0
50
100
150
-0.15
200
0
50
100
r
r
0.5
SHAKE
SHAKE
3D
FLAC
VELOCITY, m/s
VELOCITY, m/s
3D
0.25
0.25
0
0
-0.25
-0.25
-0.5
-0.5
0
50
100
150
0
200
50
100
150
200
TIME, s
TIME, s
SITE-2, T = 2475 YEARS
SITE-2, T = 125 YEARS
r
r
0.3
0.3
SHAKE
SHAKE
FLAC
3D
FLAC
0.2
DISPLACEMENT, m
0.2
DISPLACEMENT, m
200
SITE-2, T = 2475 YEARS
SITE-2, T = 125 YEARS
0.5
FLAC
150
TIME, s
TIME, s
0.1
0
-0.1
3D
0.1
0
-0.1
-0.2
-0.2
-0.3
-0.3
0
50
100
150
200
0
50
TIME, s
100
150
200
TIME, s
Figure 6. Computed acceleration, velocity and displacement time histories with SHAKE and
FLAC3D using equivalent linear properties.
Equivalent Linear Analysis Results
The response spectra computed at ground surface in sites 1, 2 and 3, assuming equivalent linear
properties, are presented in Figure 7 for each return period (i.e. 125, 250, 475 and 2475 years).
For comparison purposes, linear response spectra computed considering a constant 5% damping
for the soil are also included in this figure. As it can be easily seen, important attenuation is
generated in the soil as a function of the predominant period, for all cases.
SITE-2
SITE-1
SITE-3
2
2
2
T = 125 years
T = 125 years
T = 125 years
T = 250 years
T = 250 years
T = 250 years
T = 475 years
T = 475 years
T = 475 years
r
1.5
r
1
0.5
r
1
0.5
0
0
0
1
2
3
4
1.5
T = 2475 years
r
1
0.5
0
0
5
r
a
T = 2475 years
a
r
Spectral Acceleration, S (g)
r
T = 2475 years
a
r
r
Spectral Acceleration, S (g)
Spectral Acceleration, S (g)
1.5
r
r
r
1
2
3
4
5
0
1
2
Period (s)
Period (s)
3
4
5
Period (s)
(a)
SITE-1
SITE-3
SITE-2
0.5
0.5
0.5
T = 125 years
T = 125 years
r
r
r
0.3
0.2
0.1
r
0.3
0.2
0.1
0
1
2
3
4
r
0.3
0.2
0
0
5
r
T = 2475 years
0.1
0
0
r
T = 475 years
a
T = 2475 years
a
T = 2475 years
0.4
T = 475 years
Spectral Acceleration, S (g)
Spectral Acceleration, S (g)
r
T = 250 years
r
0.4
T = 475 years
a
r
T = 250 years
r
Spectral Acceleration, S (g)
T = 125 years
r
T = 250 years
0.4
1
Period (s)
2
3
4
5
0
1
2
3
4
5
Period (s)
Period (s)
(b)
Figure 7. Response spectra for a) linear analysis and b) equivalent linear analysis
The uniform shear strains distribution with depth is presented in figure 8 for the site analyzed as
a function of the return period. The uniform shear strain is defined as the maximum shear strain
reduced by the equivalent linear factor, E f .
SITE-2
0
10
DEPTH, m
20
30
40
T = 125 years
r
T = 250 years
r
T = 475 years
r
T = 2475 years
50
r
0
0.5
1
1.5
Uniform shear strain, γ (%)
2
2.5
Figure 8. Maximum shear strains distribution with depth for each return period studied
Nonlinear Site Response Analysis Results
The response spectra computed from the nonlinear analysis at the surface of site 2 is presented in
figure 9, for each return period. Figure 9 includes results for both the linear analysis with
equivalent linear properties and the nonlinear hysteretic model obtained with FLAC3D. Site 2 was
selected to be analyzed with the fully nonlinear approach because it exhibits the larger spectral
accelerations in the equivalent linear analyses (Figure 7b). This is associated with the fact that
the predominant period of this soil deposit is around 2sec, close to the period where most of the
energy of the excitation is focus. It can be observed, as expected for this level of shaking, that the
equivalent linear analysis overestimates nonlinear effects in the soil deposit response, especially
for return periods larger than 125 years. This leads to a spurious migration of the inelastic soil
deposit period, T su with the return period, T r . Thus, T su calculated with the equivalent linear
stiffness varied as a function of the return period from about 1.8 sec to 2.3 sec, when T r goes
from 125 years to 2475 years. Furthermore, the damping is also over predicted, and the spectral
accelerations are underestimated. This limitation is associated with the fix value of shear strain
used to estimate the equivalent linear properties. On the other hand, the hysteretic nonlinear time
domain analysis allows for soil nolinerities modifying each time step both the stiffness and
damping as function of the current shear strain increment Itasca (2005). This leads to a better
estimation of the actual soil predominant period in particular, which is around 2sec, and the
frequency content, in general. Regarding the spectral accelerations the nonlinear analysis clearly
shows an important attenuation with respect to those computed assuming linear soil properties.
In the fully nonlinear analysis conducted herein, the soil nonlinearity affect the site response
mostly throughout the development of hysteretic damping during cyclic loading, in which the
soil stiffness goes back to its original value each loading-unloading cycle. Thus, the soil stiffness
degradation is low, due to its high plasticity index, which physically means that can undergo
cyclic loading without a significant pore water pressure increment due to soil structure damage.
This is also in agreement with the fact that no significant period enlargement is observed when
comparing the actual response spectra of three different earthquakes of medium to large
magnitude measured in TXSO station (Figure 10).
0.7
0.7
T = 125 years
T = 125 years
r
r
0.6
0.6
T = 250 years
T = 250 years
r
r
T = 475 years
T = 475 years
r
r
0.5
0.5
T = 2475 years
T = 2475 years
r
r
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
1
2
3
Period (s)
(a)
4
5
0
1
2
3
4
5
Period (s)
(b)
Figure 9. Computed response spectra for each return period for site 2 considering a) equivalent
linear properties and b) non-linear hysteretic model
COMPONENT EW
COMPONENT NS
0.6
0.6
MEASURED NS 801024, Mw=7.1
MEASURED NS 801024, Mw=7.1
MEASURED NS 790314, Mw=7.4
a
Spectral Acceleration, S (g)
a
Spectral Acceleration, S (g)
0.5
MEASURED NS 790314, Mw=7.4
0.5
MEASURED NS 850919, Mw=8.0
0.4
0.3
0.2
MEASURED NS 850919, Mw=8.0
0.4
0.3
0.2
0.1
0.1
0
0
0
1
2
Period (s)
3
4
5
0
(a)
1
2
Period (s)
3
4
5
(b)
Figure 10. Response spectra of earthquakes of several magnitudes measured at TXSO station a)
North-south component, and b) East-west component
Conclusions
Traditionally, high plasticity clays (PI larger than 250%) such as those found in the Mexico City
valley have been considered to behave in their quasilinear range, exhibiting a very reduced soil
stiffness degradation as well as damping increment during seismic loading, even for shear strain
as large as 0.1%. However, the results of this study, provide evidence that under large to extreme
ground shaking, such as that associated with return periods higher than 125 years, important soil
nonlinearities can be developed in the ground, which can lead to a reduction of about 30% of the
elastic response. This attenuation increases rapidly with the return period. This fact must be
taken into account to avoid site amplification overestimation and, in turn, costly seismic designs.
From the numerical studies and ground motion recorded at the studied site, it can be concluded
that attenuation is mostly due to hysteretic damping, and in a small amount to shear stiffness
degradation. Regarding the equivalent linear method, overall, amplitudes and predominant
periods computed during the analyses seem to be affected by the more pronounced degradation
of the soil stiffness, especially for strong shaking, associated to the fix value of the effective
shear strain. Therefore, the seismic loads can be understimated if you conduct an equivalent
linear analysis for large magnitude or extreme earthquakes, but you overestimate the response if
your analysis is linear. Thus, you need to conduct a nonlinear analysis when dealing with high
plasticity clays subjected to strong ground shaking, such as that associated to a return period of
2475 years, to properly assess the ground amplification, and frequency content.
References
Abrahamson, N. A. Somerville, P. G. 1993. Estimation of hanging wall and footwall effects on peak acceleration,
Proc. International Workshop on Strong Motion Data, Menlo Park, California, December 13-17, 1993.
Baker JW. 2008. An introduction to probabilistic seismic hazard analysis (PHSA), White paper, Version 1.3, 72p.p
Cornell, C. A., 1968. Engineering seismic risk analysis, Bulletin of the Seismological Society of America, 58: 15831606
Darendeli MB, Stokoe KH. Development of a new family of normalized modulus reduction and material damping
curves. Geotechnical Engineering Report GD01-1, University of Texas at Austin, Austin, 2001.
Itasca Consulting Group. FLAC, Fast Lagragian Analysis of Continua, User´s guide. Minneapolis Minnesota, USA,
2005
Joyner, W. B. y Boore, D. M., 1988. Measurement, characterization, and prediction of strong ground motion. Pages
43-102 of: Proceeding sof Earthquake Engineering & Soil Dynamics II. Geotechnical Division, ASCE.
Klügel, J. U., 2008. Seismic Hazard Analysis - Quo vadis?, Earth-Science Reviews, Volume 88, Issues 1-2, May,
Pages 1-32, ISSN 0012-8252.
Lilhanand K. y Tseng W. S., 1988. Development and application of realistic earthquake time histories compatible
with multiple damping response spectra. Proceedings of the 9th World Conference on Earthquake Engineering,
Tokyo, Japan, Vol. II, pp 819-824
Mayoral, J. M. y Castañon E., 2014. Internal Report, Institute of Engineering, UNAM (Spanish).
Mayoral, J. M., Romo, M. P. and Osorio, L., 2008. Seismic parameters characterization at Texcoco lake, Mexico.
Soil Dynamics and Earthquake Engineering, Volume 28, Issue 7, Pages 507-521, July.
McGuire, R. K., 1995. Probabilistic seismic hazard analysis and design earthquakes: Closing the loop, Bulletin of
the Seismological Society of America, 85: 1275-1284
Osorio, L. and Mayoral, J. M., 2013. Seismic microzonation for the northeast Texcoco lake area, Mexico. Soil
Dynamics and Earthquake Engineering, Volume 48, Issue 7, Pages 252-266, Jan.
Reyes, C. E1 estado limite de servicio en el diseño sísmico de edificios, Ph D Thesis, School of Engineering,
National Autonomous University of México (UNAM); 1999.
Seed, H. B., Dickenson, S. E., y Mok, C. M., 1993. Recent lessons regarding seismic response analysis of soft and
deep clay sites. Seminar Proc., Seismic design and retrofit of bridges, U.C. Berkeley, EERC, Caltrans, June
Seed H.B., Idriss I.M. 1970. Soil moduli and damping factors for dynamic response analyses, Technical Report
EERRC-70-10, University of California, Berkeley
Stephenson WR (Bill), Lomnitz C, Flores H. Late resonant response at Texcoco, valley of Mexico, during distant
earthquakes. Soil Dyn Earthquake Eng 2006; 26:791–8.
Suarez G, Albini P. Evidence for great Tsunamigenic earthquake (M w 8.6) along the Mexican subduction zone.
Bulletin of the seismology and society of America 2009; 99:892-6.
Taylor R. 2001. FEAP. A Finite Element Analysis Program. University of California at Berkeley.