Seismic response of bridges with cellular foundations built in soft clay Juan M. Mayoral, Miguel P. Romo & Francisco A. Flores Institute of Engineering, UNAM, Mexico City, Mexico ABSTRACT A new foundation system based on structural cells has been used for supporting the columns of the elevated section of the 12 th Metro Line, in Mexico City. This study consists on a numerical simulation employing a three-dimensional finite element model developed with the program SASSI2000, of one of the critical supports located in the so-called Lake zone, known by its difficult subsoil conditions. Clays in this region present low shear strength and high compressibility. The system response was computed for a typical seismic scenario, such as that prevailing at the zone, which assumes a potential Mw=8.2 seismic event. The cellular foundation is comprised of a rigid slab structurally tied to perimeter concrete walls, also structurally connected to each other. The computed upper deck acceleration is less than a half of that obtained directly from the recommended response spectra compiled in the Mexico City building code. RESUMEN Un nuevo sistema de cimentación basado en celdas estructuradas va a ser empleado para soportar las columnas del tramo elevado de la Línea 12 del Metro de la Ciudad de México. El estudio aquí presentado, consiste en la simulación numérica, usando un modelo tridimensional de elementos finitos desarrollado con el programa SASSI2000, de uno de los apoyos más críticos localizado en la denominada zona de Lago conocida por sus difíciles condiciones del subsuelo. Las arcillas en esta región presentan una baja resistencia al esfuerzo cortante y alta compresibilidad. La respuesta del sistema fue calculada para un escenario típico, como el que prevalece en la zona, asumiendo un evento sísmico de magnitud Mw = 8.2. La celda estructurada está conformada por una losa rígida conectada estructuralmente a muros perimetrales de concreto también conectados entre sí. La acceleración máxima calculada en la parte superior del tramo elevado es menor que la mitad de la obtenida directamente del espectro de diseño propuesto por el reglamento de construcciones de la Ciudad de México. 1 INTRODUCTION A new 28.4 km long metro line is under construction in the southeast part of Mexico City, the so-called 12 th Line. In particular, 13 km of this project will be elevated, and will cross two of the most difficult subsoil conditions in the city, the lake zone and the transition zone (Figure 1). A new foundation alternative (Romo et al., 2010) based on a skirted type foundation, consisting on a mat structurally tied to peripheral walls was used to support the columns of the elevated section (Figure 2a). This work presents the seismic performance evaluation of one of the most critical supports, hereafter referred as cl-34, which is located in the typical soft clay deposits found at the city. The seismic soil-structure interaction analyses were conducted using 3-D finite element models, considering a seismic environment characterized by a major seismic event, with moment magnitude, Mw, of 8.2. The response of the structure was obtained in terms of accelerations, displacements and response spectra. Transfer functions between free field and both foundation and structure were also computed. The high stiffness of both the column and the cellular foundation reduce the maximum accelerations obtained in the upper deck. 2 SUPPORT ANALYZED Figure 2 shows support cl-34 in elevation and plan view. Figure 2c depicts a longitudinal view of the elevated section. This consists of an upper deck resting on top of 30 m long beams, which are, in turn, supported by columns. Both beams and columns are pres-stress and made of high strength concrete. The columns have a hollow transversal section, and are structurally connected to the cellular foundation. The upper part of this foundation consists of a rigid square concrete mat 6.5 x 6.5 m 2 , with 1.7 m of thickness. This slab is rigidly attached to perimeter structural concrete walls 0.60 m thick. The embedment depth of this foundation is 15 m (Figure 2a). 3 SUBSOIL CONDITIONS To characterize the geotechnical subsoil conditions found at the site, one cone penetration test, CPT, and one standard penetration test, SPT, combined with selective undisturbed sampling were conducted. The studied site is mostly comprised by a very soft to medium clay deposits interbedded with thin sand lenses. Figure 3 shows the soil profile, the variation of tip penetration resistance with depth, SPT values, and rock core recovery percentage. Based on the field investigation and laboratory testing results, it was found that the soil profile is comprised by a sandy silt layer 3 m thick. Underlying this stratum, there is a soft to medium 25 m clay layer interbedded with silty sand lenses. Within this layer, from 3 to 7 m of depth, there is a high plasticity clay layer. At 6.5 m, water content, n , is 400 %, liquid limit, L, is 450 % and plasticity index, PI, is 172 %. Below 7 m and up to 21 m, n , varies from 50 to 200 % and the undrained shear
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Seismic response of bridges with cellular
foundations built in soft clay
Juan M. Mayoral, Miguel P. Romo & Francisco A. Flores Institute of Engineering, UNAM, Mexico City, Mexico ABSTRACT A new foundation system based on structural cells has been used for supporting the columns of the elevated section of the 12
th Metro Line, in Mexico City. This study consists on a numerical simulation employing a three-dimensional finite
element model developed with the program SASSI2000, of one of the critical supports located in the so-called Lake zone, known by its difficult subsoil conditions. Clays in this region present low shear strength and high compressibility. The system response was computed for a typical seismic scenario, such as that prevailing at the zone, which assumes a potential Mw=8.2 seismic event. The cellular foundation is comprised of a rigid slab structurally tied to perimeter concrete walls, also structurally connected to each other. The computed upper deck acceleration is less than a half of that obtained directly from the recommended response spectra compiled in the Mexico City building code. RESUMEN Un nuevo sistema de cimentación basado en celdas estructuradas va a ser empleado para soportar las columnas del tramo elevado de la Línea 12 del Metro de la Ciudad de México. El estudio aquí presentado, consiste en la simulación numérica, usando un modelo tridimensional de elementos finitos desarrollado con el programa SASSI2000, de uno de los apoyos más críticos localizado en la denominada zona de Lago conocida por sus difíciles condiciones del subsuelo. Las arcillas en esta región presentan una baja resistencia al esfuerzo cortante y alta compresibilidad. La respuesta del sistema fue calculada para un escenario típico, como el que prevalece en la zona, asumiendo un evento sísmico de magnitud Mw = 8.2. La celda estructurada está conformada por una losa rígida conectada estructuralmente a muros perimetrales de concreto también conectados entre sí. La acceleración máxima calculada en la parte superior del tramo elevado es menor que la mitad de la obtenida directamente del espectro de diseño propuesto por el reglamento de construcciones de la Ciudad de México. 1 INTRODUCTION A new 28.4 km long metro line is under construction in the southeast part of Mexico City, the so-called 12
th Line.
In particular, 13 km of this project will be elevated, and will cross two of the most difficult subsoil conditions in the city, the lake zone and the transition zone (Figure 1). A new foundation alternative (Romo et al., 2010) based on a skirted type foundation, consisting on a mat structurally tied to peripheral walls was used to support the columns of the elevated section (Figure 2a). This work presents the seismic performance evaluation of one of the most critical supports, hereafter referred as cl-34, which is located in the typical soft clay deposits found at the city. The seismic soil-structure interaction analyses were conducted using 3-D finite element models, considering a seismic environment characterized by a major seismic event, with moment magnitude, Mw, of 8.2. The response of the structure was obtained in terms of accelerations, displacements and response spectra. Transfer functions between free field and both foundation and structure were also computed. The high stiffness of both the column and the cellular foundation reduce the maximum accelerations obtained in the upper deck. 2 SUPPORT ANALYZED Figure 2 shows support cl-34 in elevation and plan view. Figure 2c depicts a longitudinal view of the elevated section. This consists of an upper deck resting on top of 30 m long beams, which are, in turn, supported by
columns. Both beams and columns are pres-stress and made of high strength concrete. The columns have a hollow transversal section, and are structurally connected to the cellular foundation. The upper part of this foundation consists of a rigid square concrete mat 6.5 x 6.5 m
2, with 1.7 m of thickness. This slab is rigidly
attached to perimeter structural concrete walls 0.60 m thick. The embedment depth of this foundation is 15 m (Figure 2a). 3 SUBSOIL CONDITIONS To characterize the geotechnical subsoil conditions found at the site, one cone penetration test, CPT, and one standard penetration test, SPT, combined with selective undisturbed sampling were conducted. The studied site is mostly comprised by a very soft to medium clay deposits interbedded with thin sand lenses. Figure 3 shows the soil profile, the variation of tip penetration resistance with depth, SPT values, and rock core recovery percentage. Based on the field investigation and laboratory testing results, it was found that the soil profile is comprised by a sandy silt layer 3 m thick. Underlying this stratum, there is a soft to medium 25 m clay layer interbedded with silty sand lenses. Within this layer, from 3 to 7 m of depth, there is a high plasticity clay layer. At 6.5 m, water
content, n, is 400 %, liquid limit, L, is 450 % and plasticity index, PI, is 172 %. Below 7 m and up to 21 m,
n, varies from 50 to 200 % and the undrained shear
strength, su, goes from 21 kPa to 40 kPa. From 21 m to 28 m of depth, there is a low plasticity sandy clay layer,
exhibiting a (%) of about 30. The preconsolidation
pressure, ’p, is 10 kPa for both 6.5 m and 9.5 m of
depth, and for 14.5 m, ’p, is 196 kPa. The coefficient of volumetric compressibility, mv, ranges from 0.162 cm
2/kg
to 0.047 cm2/kg.
Zone I
Zone II
Zone IIIa
0 1 2.5 5 10 km
Scale
-99.20 -99.15 -99.10 -99.05 -99.00
19.25
19.30
19.35
19.40
19.45
LA
TIT
UD
E
LONGITUDE
INTERNATIONAL
AIRPORT
VIADUCTO
REFORMA
INS
UR
GE
NT
ES
CIRCUITOINTERIOR
PER
IFÉR
ICO
AV. TLÁHUAC
TLA
LPAN
PR
OL. D
IV. D
EL N
OR
TE
MIXCOAC
ATLALILCO
TALLERES TLÁHUAC
Subway stationTunnel
Underground box
Shallow boxElevated section
Zone IIIb
Zone IIIc
Zone IIId
This zone will be considered as II (Transition)
Norms for foundation design
This region are no sufficiently investigated,therefore the proposed zoning is only indicative
when using the complementary Technical
STUDIED SITE
MEZICALTZINGOERMITA
12 LINE METRO
CENA
CUIG
CUIP
CUMV
Seismological stations
Figure 1. Project location and geotechnical zoning in Mexico City 3.1 Shear wave velocity distribution Due to the lack of shear wave velocity, Vs, field measurements, these were estimated with empirical correlations proposed by several authors. Equation 1 recommended by Seed et al. (1981) was used to estimate Vs for sands.
60161 N = V s [1]
Where: Vs is the shear wave velocity in m/s, N1(60) is the number of blows counts corrected by energy and overburden pressure, expressed in terms of the confining
stress, ’ , in Eq. 2.
1(60) 60
10
'N N
[2]
The shear wave velocity distribution with depth for clays was estimated using the expression proposed by Ovando and Romo (1991), in terms of the tip penetration resistance, qc, measured with CPT.
γ N
q η = V
skh
cs [3]
Where: Vs is the shear wave velocity in m/s, qc is the
tip cone penetration resistance in t/m2; s is the unit
weight of the soil, in t/m3; Nkh and are parameters that
depend on the soil type. For this study, Nkh=9.9 and
=26.4 (Ovando and Romo, 1991).
Column
Beam
2.26.5
6.5
(b)
2.2
3.2 Column
1.1
30 m
Column
Rigid
slab
Structural walls
Beam
3.2 m
30 m
0.60 0.60
Structural
walls
Rigid slab
Dimensions
in meter(a)
Dep
th, z
(m)
0
5
10
15
(c)
1.2
01.7
08.7
4
10.50
2.5
012.1
0
Figure 2.Support analyzed: (a) elevation, (b) plan view and (c) longitudinal view of the elevated section
0 5 10 15 20 25
Cone tip penetration resistance,
qc (kg/cm
2)
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
0 10 20 30 40 50
Depth, z (m)
50/20
50/20
50/25
G.S.
G. S.: Ground surface
Fill: Sandy silt
50/15
Blow counts, NSPT
50/15
Dense to very dense silty sand
with gravels
Standard penetration test, SPT
Rock core recovery
Cone penetration test
Water
table
High plasticity clay with silty
sand intercalations
Soft to medium clay with interbedded
lenses of medium dense sand and
sandy silt
Low plasticity sandy clay with
lenses of dense silty sand
Very weak rock
Low plasticity sandy silt
0 20 40 60 80 100 % recovery
15 m
Figure 3. Subsurface conditions at the studied site Figure 4 presents the shear wave velocity profile estimated with expressions 1 to 3. The solid line is the representative average of Vs considered for analysis. The
shear wave velocity of clayey soils ranges from 40 to 120m/s and for granular materials goes from 230 and 430 m/s.
curves For clays: Due to the limited experimental information available, the normalized shear modulus degradation and damping curves, recommended by Vucetic and Dobry (1991), as a function of plasticity index, were used for the clays found at the site (Figure 5). These were compared against the experimental data obtained from two sets of results of resonant column and triaxial tests. Figure 5 shows these results (Romo et al., 2010), and previous experimental results gathered by Enriquez et al. (2008). Vucetic and Dobry (1991) curves seem to provide a good match to the measured response. For sands: Curves proposed by Seed and Idriss (1970) were used for
sands (Figure 6). G/Gmax and curves presented in Figures 5 and 6 have been successfully used in one-dimensional wave propagation analyses to predict the seismic response during the 1985 Michoacan earthquake (e.g. Romo y Seed, 1986; Romo, 1995; Mayoral et al., 2008).
0
0.2
0.4
0.6
0.8
1
0.001 0.01 0.1 1 10
Measured, IP = 103 (Romo et al. 2010)
Measured, IP = 204 (Enríquez et al. 2008)
PI=100, OCR=1-15 (Vucetic & Dobry, 1991)
PI=200, OCR=1-15 (Vucetic & Dobry, 1991)
Norm
aliz
ed s
hear
modulu
s, G
/Gm
ax
Shear strain, (%)
(a)
0
5
10
15
20
0.001 0.01 0.1 1 10Shear strain, (%)
(b)
Dam
pin
g r
atio (
%)
Figure 5. Comparison of (a) G/Gmax- and (b) - curves reported in technical literature with experimental results.
0
0.2
0.4
0.6
0.8
1
0
5
10
15
20
25
0.0001 0.001 0.01 0.1 1 10 100
Sand (Seed & Idriss, 1970)
Norm
aliz
ed s
hear
modulu
s,
G/G
max
Dam
pin
g
(%)
Shear strain, (%)
(a) (b)
Figure 6. Normalized shear modulus (a) and damping curves for sands (b) 3.3 Seismic environment The seismic environment was defined using the historical seismicity recorded at the site. Initially, a search of the seismological stations, located on rock or firm soils, situated near the project site was conducted. These were identified as CUIP, CUMV, CUIG and CENA (Figure 1), which are located in average at 10 km away from the analyzed support. Only the seismic events with Mw larger than 6.5, reported in the Mexican Strong Earthquake Data Base (BMSF, 1996), were considered. Response spectra of both horizontal components of these events were obtained for the four stations. Each response spectrum was normalized with respect to its peak ground
acceleration, PGA. These were, then, scaled to a PGA of 0.085 g. This acceleration corresponds to a magnitude earthquake Mw=8.2, obtained with the attenuation relationship proposed by Crouse (1991), for an event located at about 330 km of the studied site. The response
spectrum obtained from the mean, , plus one standard
deviation, , values, was used for this study. Both frequency content and amplitude of the response spectrum compiled in the Mexico City building code
(RCDF, 2004) for the hill zone, are well covered by the
+ , spectrum. The acceleration time history shown in Figure 7b was obtained from a time domain spectral matching of the design response spectrum obtained from this study, using the methodology proposed by Lilhanand and Tseng (1998) as modified by Abrahamson (1993).
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 1 2 3 4 5
SXCU8010CENA9602
CENA9607
CENA9906CUIG9510CUIG9607
CUIG9909
CUIP8509CUMV8509
CUMV850921
RCDF, 2004 (Zone 1)
Sp
ectr
al a
cce
lera
tio
n, S
a (
g)
Period, T (s)
5 % damping(a)
-0.1
-0.05
0
0.05
0.1
0 20 40 60 80 100 120 140
Acc
ele
ratio
n, (g
)
Time, t(s)
(b)
Figure 7. (a) Normalized response spectra and (b) synthetic acceleration time history
4 SOIL-STRUCTURE INTERACTION 4.1 Numerical model To study the seismic response of cellular foundations, a finite element model of support cl-34 was developed with the program SASSI 2000 (Lysmer et al., 2000), using the flexible volume method. The flexible volume method is formulated in the frequency domain, through the complex response method and finite element technique as described by Lysmer (1978). The soil-structure system was divided into the soil, the foundation and the structure. For the analyses, the structure was modeled with beam elements and lumped masses. Both the foundation and
the near field soil were simulated with three-dimensional solid finite elements (Figure 8 and Figure 9).
0.60 0.60
Structural walls
Rigid slab
1.2
01.7
012.1
0
Column
Beam
8.7
4
2.2
10.50
2.5
0
Dimensions
in meters
3-D finitte
element
Beam elements
Lumped mass
Soil within in the cellular foundation
Input motion ü
Fill
High plasticity
clay
Soft clay
Sandy silt
Silty sand
6.50 5.30 6.50
Figure 8. Schematic representation of foundation support
1.20
1.70
12.10
6.56.5
Soft clay
High plasticity
clay
Fill
3-D finite
element
Longitudinal
axis
z
xy
Sandy silt
Transverseaxis
ColumnBeam elements
Lumped mass
6.5
6.5 6.5
6.5
Dimensions
in meters
Foundation
Figure 9. Finite element model for support cl-34 The soil was considered as axis-symmetric, and comprised by series of semi-infinite visco-elastic
horizontal layers with equivalent linear properties (i.e. shear stiffness and damping) resting on top of a visco-elastic half space. The soil-foundation–structure interaction occurs at all basement nodes. Absorbing transmitting boundaries were used at the edges of the models to simulate the free field conditions. Only transversal effects were studied.
4.1.1 Soil model The soil within the cellular foundation was modeled with three-dimensional solid finite elements. The small strain
shear stiffness (i.e. less than 10-4
%) of the soil was assumed for the elements found within the cellular foundation, considering that the ground movement is restricted by the cellular structure. Thus, a damping ratio of 3 % was deemed appropriated for these soil elements. Regarding to the near and far field soil, this was modeled with equivalent linear properties, which were obtained from a site response analysis conducted with the program SHAKE. Studies carried out by several researchers (Romo and Seed, 1986; Romo, 1995; Mayoral et al., 2008) have proven that using equivalent linear properties is enough to represent the soil-nonlinearities both in high plasticity clayey and sandy silts, at least for moderate to high level of shaking (Mw ranging from 6 to 8.2). 4.1.2 Substructure model The cellular foundation was represented with three-dimensional solid finite elements (Figure 8). The structure damping was modeled using a Rayleigh type formulation. Table 1 shows the structural members properties. Table 1. Strength concrete of structural elements.
Structural element Unit weight,
m (kN/m3)
Young modulus, E (MPa)
Strength concrete f´c (kPa)
Pre-cast columns and beam
24.5 30,000 60,000
Structural walls 23.5 25,600 35,000
Reinforced rigid slab 23.5 30,000 60,000
*Poisson ratio = 0.3
Damping ratio = 3 %
4.1.3 Superstructure model The structure was simulated with lumped masses and beam elements (Figure 9). The total mass of the upper deck and beams was concentrated in three lumped masses to distribute the upper deck inertia, connected by rigid members to the beams elements that represent the columns, simulated with eleven beam elements (Figure 2). The column was made of high strength concrete with hollow transversal section. Table 1 shows the concrete properties.
4.2 Seismic response of the support analyzed The seismic response of support cl-34 was computed at five vertical axes: in the near field, A1-A5 and B1-B-5, outside of the cellular foundation, C1-C5, and the soil inside it, D3-D5 and E3-E5. The control points shown in Figure 10 indicate the depths where response spectra were computed. These points are located at 0.0, 2.9 m, 8 m and 15 m.
Dep
th,
z (
m)
Column axis
0
5
10
15
Control points
E1D1C1B1A1
5.5 1 2.15 1.1
E2D2C2B2A2
E3D3C3B3A3
E4D4C4B4A4
E5D5C5B5A5
Column
Beam
Dimensions inmeters
Figure 10. Control points location in the soil-foundation-structure system Figure 11 shows the comparison at axis A through E of response spectra computed at different depths (i.e. ground surface, at 2.9 m, 8 m and 15 m). Important differences both in spectral amplitudes and frequency contents can be seen. Figure 12 shows the variation of the response spectra along Axis E, control points from E1 to E5, with respect to the free field, calculated at the ground surface. Important amplifications were observed in shallower points. The spectral accelerations at the bottom of the column are higher than those accelerations computed at free field for a period ranging from 1 to 1.6 s, whereas for periods going from 2 to 3 s, are lower.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Free fieldA1B1C1D1E1
Spe
ctr
al acce
lera
tion
, S a
(g
)Ground surface (0 m)
(a)
(-2.9 m)Depth
(b)
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Period, T (s)
(-8.0 m)Depth
(c)
Spe
ctr
al acce
lera
tion
, S a
(g
)
0 1 2 3 4 5
Period, T (s)
(-15.0 m)Depth
(d)
Figure 11. Response spectra calculated at several depths in axis A through E
At a soil-structure interaction period, TSEI, of 2.6 s
(fSEI = 0.38 Hz) an attenuation of 10 % of the maximum spectral acceleration with respect to the free field response was observed. However, the actual response of the structure is controlled by the high stiffness of the column-foundation system, which reduces the computed acceleration to 0.162 g at the foundation (Figure 13b), and 0.166 g at the support beam (Figure 13c). These values are closed to the response obtained from the period computed for the structure, considering it on top of a rigid base (i.e 0.16 s (f = 6.25 Hz)). This fact leads to an important reduction of the accelerations generated at the upper deck, as can be noticed in the calculated acceleration times histories (Figure 13). Figure 13 also depicts the acceleration time histories obtained at free field, foundation and support beam. Figure 14 shows the corresponding displacements, overall are very similar to those computed at the upper deck. The maximum accelerations obtained at free field, cellular foundation and support beam are 0.157 g, 0.162 g y 0.166 g, respectively. From this study it is concluded that the response of the soil-foundation-structure system is controlled by the high stiffness of the foundation-column system. Both the maximum relative displacement, between the cellular foundation with respect to the support beam, and thus, the maximum distortion of the column, occurred at 83.20s. The maximum displacements computed at the free field, cellular foundation and support beam were 23.98 cm, 21.46 cm and 22.93 cm, respectively, at this time. The distortion generated
between the foundation and support beam was obtained from the subtraction of the maximum displacements between both points, divided by the length column (L= 10.59 m). The maximum distortion was 0.00139.
Figure 14 shows the rotations of both the rigid slab and support beam. The maximum rotation of the rigid slab is 0.0032 rad (0.17º).
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 1 2 3 4 5
Free field
E1
E2
E3
E4
E5
Spectr
al a
cce
lera
tion,
Sa (
g)
Period, T (s)
(0 m)
(-1.2 m)
(-2.7 m)
(-8.0 m)
(-15.0 m)
Depth
(0 m)
Figure 12. Response spectra calculated along axis E
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Free field
Acce
lera
tio
n,
(g)
Amax
= 0.157 g
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Cellular foundation
Acce
lera
tio
n,
(g)
Amax
= 0.162 g
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0 50 100 150
Support beam
Acce
lera
tio
n,
(g)
Time, t (s)
Amax
= 0.166 g
Figure 13. Acceleration time histories calculated at the (a) free field, (b) cellular foundation and (c) support beam
-30
-20
-10
0
10
20
30
0 50 100 150
Free fieldCellular foundationSupport beam
Dis
pla
cem
en
t, (
cm
)
Time, t (s) Figure 13. Displacement time histories calculated at the (a) free field, (b) cellular foundation and (c) support beam
-0.004
-0.003
-0.002
-0.001
0
0.001
0.002
0.003
0.004
50 60 70 80 90 100
Rigid slab rotations
Support beam rotations
Rota
tio
n, (
rad)
Time, t (s)
rs
sb
max
= 0.0032 rad
0.229
0.172
0.114
0.057
-0.057
-0.114
-0.172
-0.229
Ro
tatio
n,
(°)
0
Figure 14. Rigid slab and support beam rotations
The point of rotation shifts back and for during the period of time the excitation is acting on the system. At the particular time associated to the larger movement (i.e. 68.75s), it is located at 9.67 m of depth and at 2.21 m with respect to the vertical axis column, as depicted in Figure 15. The foundation moves almost as a rigid body. The horizontal displacements of the soil at the five vertical axes previously defined are also included in this figure. For the maximum rotation, the horizontal relative displacement, between the top of the slab and the bottom of the structural concrete wall, is 0.045 m. Figure 16 shows the deformed shapes of the column at different times during the seismic event. The maximum displacement of the column was about 0.05 m at 68.75 s, which is consistent with the high stiffness of the foundation-structure system, and the column supporting the upper beam. According to the numerical study, the seismic performance of the soil-structure system is satisfactory for the design earthquake (Mw=8.2).
-20 -15 -10 -5 0
Free field
A-A axis
B-B axis
C-C axis
D-D axis
E-E axis
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
De
pth
, z (
m)
Horizontal displacement, cm
2
Rotation axis
Column
axis
1.2 m
1.7 m
12.1 m Rotation center
2.21 m
9.6
7 m
Figure 15. Movements of the cellular foundation and soil at time t = 68.75 s.
x
z
0 m
10 m
-0.4 -0.2 0 0.2 0.4 0.6
0
2
4
6
8
10
12
Deformed in x direction, (cm)
Co
lum
n h
eig
ht, (
m)
21.6 s
79.0 s
101.35 s
68.75 s
57.85 s
73.7 s
83.9 s
0 s
Figure 16. Deformed shape of the column at several times
5 CONCLUSIONS A two tridimensional finite element model was developed to evaluate the seismic response of a cellular foundation, including soil-foundation-structure interaction effects. Due to the high stiffness of both the column and soil-foundation system, the seismic response was mostly at low periods. This effect reduces the maximum acceleration, and therefore seismic forces computed at the support beam (i.e. 0.17 g). This is in agreement with the small lateral displacements computed between the foundation and support beam, which are about 0.05 m. Rotations at the cellular foundation are about 0.0032 rad. The maximum acceleration computed in the support beam is lower than half of that recommended by the RCDF building code for period from 0.2 to 1.3 s. (i.e. 0.16 g). REFERENCES Abrahamson N. 1993. Non-stationary spectral matching
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