Site response effects on an urban overpass

Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

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Technical Note

Site response effects on an urban overpass J.M. Mayoral n, J.Z. Ramı´rez Geotechnical Department, Institute of Engineering, National University of Mexico, Building No. 4, P.O. Box 04510, Mexico City, Mexico

a r t i c l e i n f o

abstract

Article history: Received 19 January 2011 Accepted 21 January 2011 Available online 20 February 2011

Strong ground motion variability due to rapid changes in subsoil conditions may lead to different site responses, which in turn yields to beneficial or detrimental soil–foundation–structure interaction. This technical note presents the results of a seismic soil–structure interaction analysis conducted using a 2D finite difference model, developed with the program FLAC, of a critical section of a 60 km long strategic urban overpass, which is under construction in Mexico City, for a Mw 8.7 earthquake. Initially, the response of the free field was calibrated comparing the values obtained with FLAC, with those gathered using the computer code QUAD4M. Good agreement was observed between the results generated with these programs. Accelerations and displacements were determined at the upper deck and foundation of the urban overpass. Important seismic soil–structure interaction was observed along the overpass at the supports analyzed. This numerical study helps to gain insight regarding the site response ground motion incoherence effects that influence the dynamic behavior of this kind of structures during extreme events. & 2011 Elsevier Ltd. All rights reserved.

1. Introduction A major transit system 60 km long, comprised of a series of interconnected urban vehicular overpasses, is currently under construction in Mexico City. The proper design of this kind of very long structures requires evaluating the ground motion variability effects along the structure (e.g. [1,2]), in order to quantify the potential relative displacements among consecutive supports, in both longitudinal and transverse directions to avoid collapse (e.g. [3,4]). Some of the most important sources of ground motion variability are site conditions (e.g. [5]), input motion (e.g. [6]), wave passage (e.g. [7]), geometry of the structure and its foundation (e.g. [8]), and local soil–structure interaction that occur in urban areas (e.g. [9]), specially when they are heavily populated, such as Mexico City. This evaluation is crucial when the seismogenic zone controlling the seismic risk of a populated urban area has the potential of producing major seismic events. Historical seismicity has proven that the subduction zone located along the Coast of Oaxaca state is able to produce events with moment magnitude, Mw ¼8.6, with potential fault rupture lengths of about 450 km [10]. Similar conditions have been found at the ColumbiaEcuador subduction zone, where a major seismic event (Mw ¼8.8) occurred in 1906 [11]. This paper presents the results of a numerical study conducted using a 2-D finite differences model, developed using the program

FLAC [12], of one of the overpasses that comprised the aforementioned transit system for a hypothetic seismic scenario characterized by a Mw 8.7 event, with seismological zone located in the Pacific Mexican subduction zone. Only longitudinal effects were studied. The numerical model involves seven of the more critical supports of the overpass from the geotechnical stand point (Fig. 1). 2. Project description The studied overpass section is located at the North-West region of Mexico City. The overpass consists of an upper deck resting on top of central and support beams, which are in turn, structurally tied to the columns, forming a frame. Beams are connected by mobile and articulated joints (Fig. 1). The columns are monolithically attached to a rectangular raft foundation 3.6  4.6 m2, connected to four 0.8 m diameter, cast-in situ, concrete piles. This massive pile cap is approximately 4.15 m thick, as shown in Fig. 2. The separation between piles is 2.30 m in the longitudinal direction, and 3.30 m in the transverse direction. All seven supports, belonging to the analyzed section of the urban overpass, have the same raft foundation geometry. However, the pile length for support S-1 is 16 m and for the rest of the pile supports is 33 m. The columns, beams and upper deck were pre-stressed and made of high strength concrete. The concrete strength at 28 days, f c0, of the columns and beams was 58,841 kPa, and of the piles was 2417 kPa. 3. Subsoil conditions

n

Corresponding author. Tel.: +52 55 5623 3600x8469; fax: + 52 510 642 7476. E-mail addresses: [email protected] (J.M. Mayoral), [email protected] (J.Z. Ramı´rez). 0267-7261/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.soildyn.2011.01.010

The urban overpass is located in a nearly flat area. To characterize the geotechnical subsoil conditions where supports S-1–S-7 are

J.M. Mayoral, J.Z. Ramı´rez / Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

ELEVATION, m

850

2260

S-1

31 m Mobile Joint CB

SPT-1

S-2 Joint

Ground surface

24 m

33 m

Joint

Joint SB Column

35 m

45 m Mobile Joint CB

SB

CB

1 2

2250

4 5

4

2240

4

SPT-4

SPT-5 1 2

4

2230

6

2220

7

TARANGO ROCK FORMATION

2210 2200

Joint

3

5 Piles

35 m SB

SPT-3 CH-3 1 2 4

SPT-2 1 2

Joint

8

NOMENCLATURE: 1: Fill 2: Soft to medium sandy clay 3: Medium clay formation 8: Tarango formation ( > 45 m of depth) CB: Central beam SB: Support beam

4: Silty sand 5: Hard sandy silt 6: Siff sandy clay 7: Tarango SPT: Standard penetration test CH: Cross hole S: Support

Fig. 1. Supports analyzed.

GROUND SURFACE

COLUMN (f 'c = 58841 kPa) PILE

RAFT FOUNDATION (f 'c = 58841 kPa)

CONCRETE FILLING (f 'c = 686 kPa) REINFORCED CONCRETE SLAB (f 'c = 24517 kPa)

COLUMN Longitudinal axis 4.60

3.30 CONCRETE FILLING (f 'c = 24517 kPa) RAFT FOUNDATION

PILES (f 'c = 24517 kPa)

Dimensions in meters Without scale

2.30 3.60

Fig. 2. Support foundation (a) elevation (b) plan view.

placed, five standard penetration tests with selective undisturbed sample recovery were conducted. The groundwater table was not detected until the maximum explored depth. Three cross holes, CH-1, CH-2, and CH-3, were performed to measure the shear wave velocity distribution with depth. Cross holes CH-1 and CH-2 reached the socalled Tarango rock formation, and were located 2 and 1.4 km away from CH-3, respectively, which was carried out nearby SPT-3 (Fig. 1). The depth to bedrock was defined throughout seven vertical electric soundings (VES). Based on this field investigation, it was established that the soil profile deposit is mainly comprised by medium to dense silty sands deposits and medium to stiff clays, randomly interbedded

by loose sand lenses, underlain by the Tarango rock formation that even outcrops at some points. Table 1 shows the properties of the soils shown in Fig. 1.

3.1. Shear wave velocity profile Empirical correlations calibrated against the cross hole measurements, were used to estimate the shear wave velocity, Vs, distribution for the silts, sands and clays found at the site, and the Tarango rock formation.

J.M. Mayoral, J.Z. Ramı´rez / Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

3.1.1. For silts and sands Eq. (1) proposed by Seed et al. [13] was used to estimate the shear wave velocity distribution with depth for silts and sands: Vs ¼ 61ðN1 Þ0:50 60 ðm=sÞ

ð1Þ

where (N1)60 is the number of blows counts corrected by energy and overburden pressure in a SPT test. 3.1.2. For clays Eq. (2) proposed by Hara et al. [14] was deemed appropriated to estimate Vs values for clays, considering that experimental evidence has proven to provide good results for Mexico City clays [15]: Gmax ¼ 15500ðNÞ0:668 ðkPaÞ 60

ð2Þ

where (N)60 is the number of blows counts corrected by energy, in a Standard Penetration Test; Gmax is the small strain shear stiffness. 3.1.3. Tarango formation To estimate Vs in the Tarango andesitic rock formation, a statistical analysis was conducted using data obtained from cross holes CH-1 and CH-2 to derive Eqs. (3) and (4). These equations 0 relates Vs with the mean effective vertical stress, sm : u Þ0:08 Vs ¼ 320ðsm u Þ1:25 Vs ¼ 9:2ðsm

for sm u r 15 t=m2

ð3Þ

for sm u 4 15 t=m2

ð4Þ

Eqs. (3) and (4) were obtained following a model of the type Vs ¼a(s0 m)b (where a and b are constants determined statistically, and s0 m is the mean effective stress), which has been extensively used and calibrated in the past for granular materials [16]. Authors recommend using this relationship for preliminary Vs estimations only, considering the limited data employed to gather a and b.

851

3.2. Seismic environment The seismic environment was established from historical records following a deterministic approach. Initially, a search of seismological stations placed on rock or firm soil sites located near the project site was conducted. Three stations were identified. These recorded the 1985 Michoaca´n earthquake, which was taken as representative of the Mexican subduction zone. Each response spectrum was normalized with respect to its corresponding peak ground acceleration, PGA. The response spectrum obtained from the mean value+one standard deviation (s) was scaled to a PGA of 0.08 g. This acceleration corresponds to the mean plus 1s value obtained with the attenuation relationship proposed by Crouse [17] for an 8.7 Mw event located at about 470 km away, in the Pacific Mexican subduction zone. After scaling, the response spectrum was multiply by 1.5 to take into account the structure ‘‘importance factor’’, as recommended in the Mexico City building code. The acceleration time history was obtained for this study using the methodology proposed by Lilhanand and Tseng [18], as modified by Abrahamson [19]. In this approach, a time domain modification of an acceleration time history is performed to make it compatible with a user specified target spectrum. In doing so, the long period nonstationary phase of the original time history is preserved.

4. Numerical modeling A 2D finite difference model was developed with the program FLAC [12] to study the overpass seismic response in the longitudinal direction. The model included both the structure comprised by a seven supports section and the free field. Prior to assess the seismic performance of the soil–foundation–structure system, the response of the free field was calibrated comparing the results obtained with FLAC with those computed with the program QUAD4M [20]. 4.1. Free field model calibration

Table 1 Soil properties. Material

Unit weight g (kN/m3)

Cohesion c (kPa)

Fill Soft to medium sandy clay Medium clay Silty sand Hard sandy silt Stiff sandy clay Tarango formation (o 45 m) Tarango formation (445 m)

16.7 17.0 18.2 17.4 17.7 18.3 18.6 19.0

29.4 41.2 78.5 58.9 29.4 140.3 53.0 0.0

S-2

18 6 10 21 33 15 33 42

S-3

The 2-D finite difference model of the free field was calibrated against the results obtained with a 2-D finite element model developed using the program QUAD4M, which, in turn, has been extensively calibrated against theoretical and experimental data [20,21]. In the finite difference model, a grid of 850 quadrilateral plane zones was used. In QUAD4M the same number of elements was considered. The grid shown in Fig. 3 represents the idealized soil profile shown in Fig. 1. The mesh is 230 m wide and has a variable high that follows the actual ground geometry that goes from 59.7 to 59.1 m. An elasto-plastic Mohr–Coulomb model was used to represent the stress–strain relationship for soils.

S-4

S-5

S-6

S-7

59.1 m

59.7 m

S-1

Friction angle f (deg)

230 m Control points where the seismic response was computed Fig. 3. Free field model.

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852

Absorbing transmitting boundaries were used at the base of the meshes, whereas free field boundaries were placed at the lateral edges. A central frequency of 2.8 Hz was used in FLAC, to set the equivalent linear damping of the soil. This frequency corresponds to the fundamental frequency of the entire finite element model

representing the free field. Normalized shear modulus degradation and damping curves proposed by Vucetic and Dobry [22], and Seed and Idriss [23] were used to represent the dependency of dynamic soil properties with shear strain amplitude for clays and sands, respectively. The acceleration-time history obtained in the

Fig. 4. (a) Acceleration time histories and (b) response spectra at ground motion corresponding to supports S-3–S-5 location using QUAD4M and FLAC.

S-1

Mobile joint

S-2

S-3

Joint

S-4

Joint

FRAME 1

S-1 2.75 m

S-2

31 m

2.75 m

Mobile joint

Joint

FRAME 2

S-3

24 m

S-5

Joint

S-4

33 m

2.75 m

5.50 m

S-7

FRAME 3

S-5

35 m

S-6

S-6 5.50 m

45 m

5.50 m

S-7

35 m

Fig. 5. (a) Schematic representation of the superstructure and (b) finite difference model used in coupled seismic soil–structure interaction analyses.

4.50 m

J.M. Mayoral, J.Z. Ramı´rez / Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

last section was deconvolved from rock outcrop to the Tarango formation at the base of the finite difference model, and integrated once to gather a velocity time history, which was, in turn, converted to a stress history [12]. Thereafter, this stress history was applied at the base of the FLAC model through a quiet base boundary. For the finite element model developed with the program QUAD4M, the motion was applied directly as an outcrop, and internally the program deconvolved it to the base of the model, using a transmitting base boundary. In the FLAC model, a Morh–Coulomb stress–strain relationship was used. The corresponding elastic properties and damping were derived from the equivalent linear properties (i.e. shear stiffness, G, and damping ratio, l) obtained from the finite element free field analysis conducted with QUAD4M, for all the geomaterials found at the project site as a function of shear strain. The finite element formulation implemented in QUAD4M solves the equation of motion in time domain, and uses an equivalent linear approach to account approximately for soil nonlinearities. Thus, in the fully coupled approach described in the next section, each support end up excited by the ground motion affected by site effects. 4.1.1. Computed response Fig. 4 shows the acceleration time histories with its corresponding 5% damping response spectrum obtained at the ground surface with FLAC and QUAD4M at the supports S-3, S-4, and S-5 which correspond to the deepest soil deposits. It may be seen a good agreement between both models. The spectral amplitude ratio of the computed earthquake motion at ground surface with respect to the base motion was calculated to examine local site effects. The maximum amplification factor of about 7.5 occurs at support S-5. This value is consistent with the subsoil conditions found at this support (i.e. the deepest alluvial soil deposit). In this support, the PGA is equal to 0.25 g, whereas the maximum

S-5

S-4 Joint Two nodes

Support beam

853

spectral acceleration is about 1.2 g at a predominant period of 0.39 s. 4.2. Fully coupled soil–structure interaction 4.2.1. Substructure model The raft foundation and concrete filling were modeled with 42 four node quadrilateral zones for all supports, and the piles were modeled with 114 two-dimensional beam elements with an equivalent radio to account for collapsing the pile group into a row of piles. The beam elements are connected directly to the soil elements nodes. 4.2.2. Superstructure model A total of 82 two-dimensional beam elements were used to represent the beams and columns of the overpass. Fig. 5a shows a schematic representation of the superstructure. Fig. 5b illustrates the finite differences model used for the coupled seismic soil– structure interaction analyses. Fig. 6 shows a schematic representation of three of the seven aforementioned critical supports, including the substructure, superstructure, and free field. For these structural members, it was considered a Young modulus of 31,820 MPa, a Poisson ratio of 0.3, a unit weight of 24.5 kN/m3, and a damping ratio of 3%. The structure damping was modeled with a Rayleigh type formulation. A central frequency of 1.5 Hz was used in FLAC which corresponds to the fundamental period of the structure considering a rigid base. 4.2.3. Computed response Fig. 7 shows the response spectra calculated at the free field, foundation, and upper deck, at all supports. It may be noticed that the motions computed at the upper deck and foundations are

Mobile joint Two nodes

Central beam

S-6 Joint Two nodes

Nodes

Column

Beam Elements

Quadrilateral Beam element zone

Column

Connection beam

Beam Elements Pile

Fig. 6. Schematic representation of the finite difference model.

Column

Beam Elements

J.M. Mayoral, J.Z. Ramı´rez / Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

Spectral acceleration, Sa(g) Spectral acceleration, Sa(g) Spectral acceleration, Sa(g)

quite different from those computed at the free field, except in supports S-1 and S-7, where the response spectrum at the foundation is similar to that obtained in the free field, both in

amplitude and frequency content. This can be explained considering that the resistant soil layer where the piles are embedded is relatively shallow at those supports, which leads to a small soil

2 S-1 FLAC (Free Field) S-1 FLAC (Foundation) S-1 FLAC (Upper deck)

1.6 1.2

5% damping

0.8 0.4 0

2 S-3 FLAC (Free field) S-3 FLAC (Foundation) S-3 FLAC (Upper deck)

1.6 1.2

5% damping

0.8 0.4 0 2 S-5 FLAC (Free field) S-5 FLAC (Foundation) S-5 FLAC (Upper deck)

1.6 1.2

5% damping

0.8 0.4 0 0.01

0.1

1

3

Spectral acceleration, Sa(g) Spectral acceleration, Sa(g) Spectral acceleration, Sa(g)

854

2 S-2 FLAC (Free field) S-2 FLAC (Foundation) S-2 FLAC (upper deck)

1.6 1.2

5% damping

0.8 0.4 0

2 S-4 FLAC (Free field) S-4 FLAC (Foundation) S-4 FLAC (Upper deck)

1.6

5% damping

1.2 0.8 0.4 0 2

S-6 FLAC (Free field) S-6 FLAC (Foundattion) S-6 FLAC (Upper deck)

1.6

5% damping

1.2 0.8 0.4 0

0.01

0.1

Spectral acceleration, Sa(g)

1

3

Period, T (s)

Period, T (s) 2 S-7 FLAC (Free field) S-7 FLAC (Foundation) S-7 FLAC (Upper deck)

1.6 1.2

5% damping

0.8 0.4 0 0.01

0.1 Period, T(s)

1

3

20

20

15

15

10 5 0 -5 -10

Support S-1 Frame 1

-15 -20

Displacement, cm

Displacement, cm

Fig. 7. Response spectra at free field, foundations and upper deck using FLAC.

10 5 0 -5 -10

Frame 2 Frame 3

-15 -20

0

20

40

60

80 100 Time, s

120

140

160

0

20

Fig. 8. Displacements time histories at the joints.

40

60

80 100 Time, s

120

140

160

J.M. Mayoral, J.Z. Ramı´rez / Soil Dynamics and Earthquake Engineering 31 (2011) 849–855

movement amplification. In this case, the soil–foundation–structure interaction can be neglected. However, other supports show either detrimental or beneficial soil–structure interaction at the foundation level. For instance, for supports S-2, S-3, and S-7 the maximum accelerations at the top of the foundation are about 5–20% higher than those obtained in the free field. For the other supports (S-1, S-4, S-5, and S-6), the maximum accelerations are about 10–20% lower than those of the free field. The maximum spectral acceleration of the foundation and upper deck occurs at a period, T of 0.81 s in frames 1, 2, and 3. This value is reasonable considering that the fundamental period of the structure on a rigid base is about 0.7 s, and the soil foundation flexibility that tends to slightly enlarge the combined soil– structure period. The interaction effects are significant, increasing the maximum spectral acceleration of the upper deck from 1.7 to 2.8 with respect to those computed at the foundation at supports S-2 and S-7, respectively (at T¼0.81 s), and almost by a factor of 3–4 with respect to the free field. In particular the maximum spectral acceleration value of about 1.8 g occurs at frame 3. This is in good agreement with the geotechnical subsoil conditions found between supports 5 and 6. Thus, a proper soil–foundation– structure interaction evaluation is crucial to avoid underestimate or overestimate the structural response. The maximum longitudinal relative seismic displacements are 3.5 and 2.0 cm between support S-1 and frame 1, which moves essentially as frame 2, and between frames 2 and 3, respectively (Fig. 8).

5. Conclusions Both detrimental (an increase in both the foundation and upper deck response) and beneficial (a decrease in the foundation and upper deck response) seismic soil–structure interaction was observed along the supports of the urban overpass, depending on the fundamental period of a given support (i.e. mass and stiffness), pile length, relative stiffness of the foundation with respect to the surrounding soil, fundamental period and soil nonlinearities of the free field. Thus, maximum accelerations computed at the foundation top in supports S-2, S-3, and S-7 are around 5–20% higher than those obtained in the free field. On the other hand, for supports S-1, S-4, S-5, and S-6 are about 10–20% lower than those of the free field. For the case presented herein, the articulated joints help reducing relative movements between consecutive supports along the longitudinal direction to 3.5 cm approximately. However, these joints must be designed to sustain the important shear forces generated during the seismic event at the upper deck, in which for the case presented herein, leads to amplification factors with respect to the foundation of about 1.7–2.8 in supports S-2 and S-7, respectively, and almost of 3–4 with respect to the free field in all supports for the fundamental period of the foundation–structure system. Thus, the overall overpass response should be taken into account during the design process to avoid catastrophic failures. This numerical study, and future instrumentation, will help to gain insight into the

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