to

curr

uctu

ctru

lyti

ea.

lyin

w

wa

abi

ck as input motion for all 2501 virtual proles. Finally, a design response

rea

1. Introduction

Driven by the extensive damage obseMichoacan earthquake, several studies wethe seismic risk in Mexico City valley, wsoil property determination (e.g. [15]), gltions (e.g. [69]), and amplication studie

e beens morrmatioLake, tored, aefore,gn in

developed 2501 virtual soil proles. The seismic environment was

nearby rock outcrop, UHSrock. Finally, throughout 2501 probabil-

input motion, a suit of response spectra were developed for the

diedmen-

ted with four seismic stations, TXSO, TXS1, TXS2 and TXCH. A fth

Contents lists available at SciVerse ScienceDirect

elsevier.com/locate/soildyn

Soil Dynamics and Ear

Soil Dynamics and Earthquake Engineering 48 (2013) 252266including a power plant, an electric network, and a new airport,E-mail address: jmayoralv@iingen.unam.mx (J.M. Mayoral).istic site response analyses were performed using the UHSrock as

3. Available data

Data obtained from different projects developed in the area,

0267-7261/$ - see front matter & 2013 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.soildyn.2013.01.013

n Corresponding author. Tel.: 525 55 5622 35x8469; fax: 510 642 7476.characterized in terms of a uniform hazard spectrum derived for a station used in the analysis, TXRC, is located to the east, on arocky outcrop, about 18.70 km away from the studied site.thickness layer, and normalized modulus degradation and damp-ing curves were characterized in a grid of points spaced 250 m, to

Mexico, UNAM, to the polygon center that encloses the stuarea is approximately 31.70 km. The region studied is instrupresents the exploration and laboratory works, and analyticalanalyses carried out for obtaining a design response spectrum fora 150 km2 area located at the northeast Texcoco Lake region.Based on available geotechnical information and geo-statisticaltechniques (e.g. [1517]), the parameters that affect the dynamicresponse of a soil deposit, such as the shear wave velocity,

index varied from approximately 59 to 106%. Underneath thiselevation a competent layer of very dense sandy silt is found.Fig. 1 shows the location of the studied area, whose length andwidth are 15.00 km10.00 km, respectively, and has a total areaof 150.00 km2. The distance from the National University ofHowever, most of these studies havMexico City, where the damage wasidering the large amount of infoeffort, the so-called virgin Texcocoof downtown, is still limitedly explCity building code [14], Fig. 1. Thernot available for engineering desirved during the 1985re launched to reducehich included dynamicobal seismicity evalua-s (e.g. [10,2,1113,3]).focused on downtowne notorious. Even con-n gathered from thisowards the north easts stated in the Mexicoseismic parameters arethis zone. This paper

area, which, in turn, were nicely enveloped by a proposed designspectrum for the studied area.

2. Description of the studied area

The studied area is located at a side of the former TexcocoLake, commonly the soil prole at this zone presents a desiccatedcrust of clay at the top extending up to a depth of 1.0 m, which isunderlain by a soft clay layer approximately 25.0 m thick, withinterbedded lenses of sandy silts and silty sands. The plasticityindex varied from 139 to 265%. Underlying the clay there is a4.0 m thick layer of very dense sandy silt, which rests on top of astiff clay layer which goes up to a 60.0 m of depth. The plasticitySeismic microzonation for the northeas

Luis Osorio, Juan M. Mayoral n

Instituto de Ingeniera, Universidad Nacional Autonoma de Mexico, Mexico City, Mexic

a r t i c l e i n f o

Article history:

Received 22 October 2012

Received in revised form

19 January 2013

Accepted 21 January 2013Available online 8 March 2013

a b s t r a c t

The Texcoco Lake area is

building strategic infrastr

code design response spe

works, as well as the ana

northeast Texcoco Lake ar

the studied zone, and app

for site response analysis

The seismic environment

nearby rock outcrop. Prob

spectrum computed in ro

spectrum for the studied a

journal homepage: www.was proposed.

& 2013 Elsevier Ltd. All rights reserved.Texcoco lake area, Mexico

ently undergoing a rapid urbanization. This has required designing and

re. However, this zone has been poorly explored, and thus, a building

m is not available. This paper presents the exploration and laboratory

cal studies conducted for obtaining a design response spectrum for the

From geotechnical information gathered previously for other projects in

g the ordinary kriging technique, the necessary dynamic soil parameters

ere determined. A total of 2501 virtual soil proles were generated.

s characterized throughout a uniform hazard spectrum obtained in a

listic site response analyses were performed using the uniform hazardthquake Engineering

ITIONE

18.

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 25319.50

19.55

19.60

LATI

TUD

EX. -

TEX.

"CARACOL"TEXCOCO

TRANSZONLAKE

ZONE

STUDIEDAREA

TXSO

Ecombined with site specic exploration, were used as input forthe geo-estatistical analyses. A total of 28 Standard PenetrationTests, SPT, combined with selected undisturbed sampling recov-ery, and 67 Cone Penetration Tests, CPT, were available. Thelocations of the existing borings are presented in Fig. 2, andTable 1 shows their corresponding UTM and geographic coordi-nates. In addition, four piezocone tests, PZC, were carried out tocharacterize the in situ pore water pressure distribution, and fourPS suspension loggings were used to determine in situ values of

Zone I

Zone II

Zone IIIa

0 1 2.5

Scale

19.45

AUTOP.

M

Zone IIIb

Zone IIIc

Zone IIId

T

TXCH

10.000 km

REYE

S - T

EXCO

-99.10 -99.05 -99.00 -98.95 -98.19.40

TEXC

OCO L

AK

INTERNATIONALAIRPORT

Fig. 1. Location of the area of study with respect to the seis

Fig. 2. Location of explored sitHILLSZONE

TXCR15.0

0 km

70 kmshear wave velocity. The information gathered allowed identify-ing the general layering sequence and thicknesses, shear wavevelocities distribution with depth at some points, and index andmechanical soil properties. Estimations of shear wave velocitiesfor clays and silts were carried out through the application of theexpression proposed by Ovando and Romo [2] in terms of the tipcone penetration resistance, qc, whereas the relationship pro-posed by Seed et al. [18] was used for sands, based on the SPTblow counts, as described in Mayoral et al. [5]. Thus, 69 shear

5 10 15 20 km

his zone will be considered as II (transition)

Norms for foundation design

This region are no sufficiently investigatedtherefore the proposed zoning is only indicative

when using the complementary Technical

CO

90 -98.85LONGITUDE-98.80 -98.75

mic zoning proposed by the Mexico City building code.

es and virtual soil proles.

Table 1UTM and geographic coordinates of the sites with available data.

Project Boring Coordinates

UTM Geographic

X Y Longitude Latitude

ELECTRIC NETWORK LINE 400 AND 230 kV L400-T12-SPT 504,817.944 2,168,612.44 98.954053 19.6125932L400-T13-CPT 504,763.715 2,168,310.64 98.9545709 19.6098659L400-T15-CPT 503,955.022 2,168,279.92 98.9622831 19.6095901L400-T18-CPT 503,290.581 2,168,272.59 98.9686195 19.609525L400-T19-CPT 503,071.455 2,167,887.14 98.9707098 19.606042L400-T20-CPT 502,843.298 2,167,972.3 98.9728855 19.6068119L400-T22-CPT 502,665.594 2,167,495.36 98.9745808 19.602502L400-T23-SM 502,522.902 2,167,112.39 98.975942 19.5990413L400-T25-CPT 502,245.524 2,166,312.28 98.978588 19.591811L400-T27-CPT 501,923.168 2,165,560.27 98.9816626 19.5850153L400-T29-CPT 501,319.294 2,165,628.89 98.9874205 19.5856359L400-T31-CPT 501,252.734 2,165,027.63 98.9880555 19.5802023L400-T32-CPT 501,009.331 2,165,024.73 98.9903763 19.5801762L400-T35-SM 500,228.632 2,165,467.52 98.99782 19.584178L400-T39-CPT 499,064.618 2,165,375.08 99.0089188 19.5833425L400-T42-CPT 498,262.264 2,164,705.45 99.0165685 19.5772904L230-P1-CPT 498,165.272 2,164,511.52 99.0174931 19.5755377L230-T6-CPT 498,601.701 2,163,426.51 99.0133312 19.5657328L230-T14-CPT 498,652.811 2,161,415.25 99.0128425 19.5475567L230-T23-CPT 498,648.369 2,159,139.9 99.0128832 19.5269941L230-T24-CPT 498,547.46 2,159,036.87 99.013845 19.5260629L230-T33-CPT 498,533.284 2,156,741.62 99.0139783 19.5053203L230-T41-CPT 498,492.279 2,154,787.1 99.0143675 19.4876569L230-T42-CPT 498,281.089 2,154,623.46 99.0163799 19.4861779L230-T46-CPT1 497,241.512 2,154,470.35 99.026286 19.484793L230-T47-CPT 497,077.68 2,154,357.73 99.027847 19.483775L230-T51-CPT-1 496,381.013 2,154,686.35 99.0344862 19.4867436L230-P55-CPT2 495,452.172 2,155,056.73 99.0433383 19.490089L230-T60-CPT2 494,543.825 2,155,495.77 99.0519956 19.4940544

NEW AIRPORT SCE-1 500,557.705 2,157,077.57 98.9946848 19.5083568SCE-2 502,482.281 2,156,944.57 98.9763428 19.5071533SCE-3 503,976.899 2,156,878.07 98.9620985 19.5065499SCE-4 505,491.991 2,156,791.1 98.9476594 19.5057604SCE-5 500,921.106 2,158,154.38 98.9912209 19.5180879SCE-6 505,865.629 2,157,878.14 98.9440951 19.5155831SCE-7 501,310.116 2,159,254.21 98.9875124 19.5280271SCE-8 503,244.929 2,159,172.36 98.9690706 19.5272852SCE-9 504,749.784 2,159,075.17 98.9547271 19.5264038SCE-10 506,259.757 2,158,967.74 98.940335 19.5254288SCE-11 501,699.126 2,160,365.75 98.9838035 19.5380719SCE-12 503,613.465 2,160,273.67 98.9655557 19.5372372SCE-13 506,633.412 2,160,074.16 98.9367697 19.5354265SCE-14 502,072.78 2,161,414.43 98.9802406 19.5475486SCE-15 503,024.831 2,161,358.16 98.9711649 19.5470389SCE-16 503,971.764 2,161,312.12 98.9621381 19.5466212SCE-19 502,886.63 2,158,077.64 98.9724874 19.5173926SCE-22 503,505.975 2,161,327.46 98.9665784 19.5467607SCE-28 504,493.856 2,159,310.48 98.9571659 19.528531SCE-31 502,573.951 2,155,168.53 98.9754715 19.4911028SCE-32 505,635.31 2,155,650.35 98.9462969 19.4954508SCE-33 508,081.069 2,162,407.95 98.9229605 19.5565119SCE-34 505,558.515 2,162,447.76 98.9470087 19.5568803SCE-35 503,306.352 2,162,442.64 98.9684794 19.5568391SCE-36 501,985.765 2,162,427.29 98.981069 19.5567022SCE-37 505,926.603 2,154,943.45 98.9435231 19.4890616

POWER PLANT CPT-1 498,218.696 2,164,609.7 99.0169839 19.576425CPT-2 498,264.552 2,164,630.81 99.0165467 19.5766158CPT-3 498,227.526 2,164,559.99 99.0168996 19.5759758CPT-4 498,172.84 2,164,588.58 99.017421 19.5762341CPT-5 498,209.867 2,164,659.4 99.0170681 19.5768741SCE-6 498,191.354 2,164,623.98 99.0172446 19.5765541SCE-7 498,232.522 2,164,636.14 99.0168521 19.576664SCE-8 498,237.074 2,164,600.08 99.0168086 19.5763381SCE-9 498,204.87 2,164,583.25 99.0171157 19.5761859SCE-10 498,318.673 2,164,611.44 99.0160306 19.5764408

ZONATION TXSO 498,037.161 2,164,894.98 99.018715 19.579003TXS1 502,669.995 2,155,490.15 98.9745558 19.4940093TXS2 502,683.001 2,155,067.71 98.9744325 19.4901916TXCH 505,253.726 2,148,537.45 98.949953 19.431171

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266254

wave velocity proles were generated. In addition, series ofresonant column and triaxial tests were carried out in twinsamples to determine modulus degradation and damping curves,in specimens recovered at the studied site, to develop normalizedmodulus degradation and damping curves from small to largestrains. Each sample was tested with three different conningpressures, ranging from 1.5 to 2 times the in situ effective verticalstress, to reproduce, in a practical manner, the eld conditionsprevailing at the site, and other two loading scenarios.

4. Geostatistical determination of soil parameters

A mesh of 41 columns and 61 rows was built to establish thelocation of the virtual soil proles. Fig. 2 shows the location of thesites were geotechnical information is available (dots), and theinterpolation points (circles) selected for the geostatistical ana-lyses. This array leads to 2501 virtual soil proles, in addition to

and CPT tests, and is in good agreement with observations madeby other researchers (e.g. [2224]). The interpolation mesh wasalready depicted in Fig. 2. To obtain a continuous shear wavevelocity prole from the surface to a depth of 50 m, interpolationswere carried out at each meter, in each virtual soil boring. Fig. 5adepicts the shear wave velocity distribution at 1 m of depth,and Fig. 5b shows the shear wave velocity proles along soilcolumn 1221.

4.3. Modulus degradation and damping curves

4.3.1. Darendeli and Stokoe model (2001)

Modulus degradation and damping curves can be obtainedthrough out laboratory testing in undisturbed soil samples, orthroughout empirical models function of soil type and othervariables. Darendeli and Stokoe [20], developed an empiricalmodel from that proposed by Hardin and Drnevich [25], togenerate modulus degradation and damping curves, which take

0

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 255the layering sequence and thickness it was necessary to infer withthe ordinary kriging technique [19], the shear wave velocitydistribution with depth and modulus degradation (G/Gmax), and(lg) damping curves for each material, which were characterizedthroughout the Darendeli and Stokoes model [20], as a functionof the plasticity index and other soil parameters, as will bedescribed later.

4.1. Layering sequence and thickness

Based on the information regarding layering sequence, includ-ing soil type and thickness gathered at each exploration boring,and using the ordinary kriging technique implemented in theprogram GS Gama Design Software, V.9, 2008, a total of 2501virtual soil proles were constructed. The soil thicknesses wereestablished considering a linear distribution among interpolationpoints, accounting for the general geological setting of theTexcoco Lake region [21]. In particular, Fig. 3 shows the layerthickness distribution of stratum number ve, which correspondsto clay.

4.2. Virtual shear wave velocity proles

Applying again the ordinary kriging technique, 2501 virtualshear wave velocity proles were developed considering a log-normal distribution for this parameter. This assumption wascorroborated by the probability density functions computed baseon shear wave velocities, presented in Fig. 4, derived from the SPTFig. 3. Thickness distribution prediction of the fth linto account conning pressure effects, s 0, plasticity index, PI,overconsolidation ratio, OCR, the frequency of loading, f, and thenumber of loading cycles, N. This model is given by the followingrelationships:

G

Gmax 1

1 ggr a 1

gr f1f2PIOCRf3 s0f4 2

l lminbG

Gmax

0:1lmsg 3

lmsg c1lmsg,a 1:0c2lmsg,a 1:02c3lmsg,a 1:03 4

lmsg,a 1:0 100

p4ggrln ggrgr

g2

ggr

224

35 5

where a0.9190 (curvature coefcient), b0.620 (scalingcoefcient), g is the shear strain (%), gr is a reference shear strain,s0 effective conning stress (atm), lmin is damping ratio at smalldeformations, lmsg is the massing damping, and lmsg,a1.0 is thedamping for a1.0. The model coefcients are given by

c11.1143na21.8618na0.2523c20.0805na20.0710na0.0095c30.0005na20.0002na0.0003ayer (clay) using the ordinary kriging technique.

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266256f10.0352, f20.001, f30.3246, f40.3483, f60.801,f70.0129, f80.107,f90.289

For this research work the curves proposed by Darendeli andStokoe were deemed appropriated because they can be used for

Fig. 4. Probability density functions of e

Tridimensional Model

Vs at 1 m

Fig. 5. Prediction of shear wave velocity distribution using ordinary kriging technsands and clays, taking into account explicitly the most importantfactors that can inuence the dynamic soil behavior. To obtain themodulus degradation and damping curves, the over consolidationratio, OCR, was taken as one, considering that the studied zone islocated in the virgin former Texcoco lake, and that the over-consolidation of the soil for desiccation occurred only in the rst

stimated shear wave velocities, Vs.

0 200 400 600 800 10000

10

20

30

40

50

60

Shear wave velocity, Vs (m/s)

Dep

th (

m)

Bidimensional Model

ique at 1 m of depth (a) and shear wave velocity proles of column 1221 (b).

couple of meter. Thus, changes in the seismic response of the soildeposit due to this fact are expected to be negligible. In thismanner, the denition of the modulus degradation and dampingcurves results in only a function of plasticity index, PI. As anexample, Fig. 6 shows the modulus degradation and dampingcurves, for a sample of clay recovered at 51.90 m of depthand PI of 51%, retrieved from site TXS1. It can be seen that

Darendelis model follow closely the experimental G/Gmaxgcurve. The Darendeli and Stokoe [20] model used a x value ofthe reference shear strain, gr, corresponding to 50% of thedegradation of the stiffness model. Regarding the damping curvelg, although the general data trend is captured by the model,this consistently over predicts the measured response for shearstrains larger than 0.1%. Thus, spectral accelerations computed

0

0.2

0.4

0.6

0.8

1

10-6 10-5 0.0001 0.001 0.01 0.1 1 10

MeasuredDarendeli and Stokoemodel (2001)Romo model (1995)

Nor

mal

ized

she

ar m

odul

us, G

/Gm

ax

Shear strain, (%)

Site: TXS1Depth: 51.90 mPI=51 %

0

5

10

15

20

10-6 10-5 0.0001 0.001 0.01 0.1 1 10

MeasuredDarendeli and Stokoemodel (2001)Romo model (1995)

Dam

ping

ratio

,

(%)

Shear strain, (%)

Site: TXS1Depth: 51.90 mPI=51 %

Fig. 6. Comparison of the G/Gmaxg and lg curves obtained with the Darendeli and Stokoe [20] and Romo [3], with the experimental data.

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 257Fig. 7. Probability density functions of measured plasticity indexes.

Tridimensional Model Bidimensional Model

PI at 2 m

Fig. 8. Plasticity index distribution at 2 m of depth determined using the ordinary kriging interpolation technique.

0

10

20

30

40

50

60

0 200 400 600 800 1000

Suspension loggingP-55 (Measured)Virtual point PV7(Estimated)

Dep

th (m

)

Shear wave velocity, VS (m/s)

Fig. 9. Comparison of measured Vs at exporation boring P-55, and estimatedvalues at virtual prole PV7.

0

10

20

30

40

50

60

0 200 400 600 800 1000

Suspension loggingT-42 (Measured)Virtual point PV310(Estimated)

Dep

th (m

)

Shear wave velocity, VS (m/s)

Fig. 10. Comparison of measured Vs at exporation boring T-42, and estimatedvalues at virtual prole PV310.

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266258

above this strain may be slightly underpredicted. However thisfalls outside the range of shear strains computed in clays duringthe site response analyses in most cases. In this gure were alsoincluded the curves determined by Romos [3] model, which iscommonly used in Mexico City, and which lead to a similar soilbehavior.

4.3.2. Virtual proles of plasticity index

To determine the modulus degradation and damping curvesthat dene the dynamic behavior of the geomaterials found at thesite, it is necessary to obtain the plasticity index, as establishedpreviously. The plasticity index is a parameter that stronglyaffects the dynamic properties of clayey soils [3,26]. In this sense,it can be seen that the linear behavior of the soils found in thestudied zone increases when the plasticity index increases, lead-ing to small degradation of the shear modulus even for strains aslarge as 10%. From the information gathered in the laboratoryregarding plasticity indices, and geo-statistical analyses, this

parameter was estimated in the virtual soil proles. Again, theordinary kriging interpolation technique was used to infer thevalues of plasticity index in each virtual point, assuming a normalprobability distribution. This assumption agrees with the prob-ability density functions obtained from measured data, as shownin Fig. 7. The spatial distribution of the plasticity index at 2 m ofdepth is depicted in Fig. 8.

4.3.3. Assessment of geostatistical model

The geostatistical model that lead to the virtual soil proleswas validated in two stages. Initially, the appropriateness ofpredicted shear wave velocity proles was tested comparing thein situ measured response at points P-55, T-420 and SEL1, whichof course were not taken into account during the kriging inter-polation procedure, with the closest virtual shear wave proles.The comparisons are presented in Figs. 911. As can be noticedthe predicted values are in good agreement with the measureddata. To assess the validity of the rest of the parameters, anindirect approach was followed, which consisted on computingthe seismic response of the soil deposit using the uniform hazardresponse spectrum derived for a nearby rock outcrop for amoment magnitude Mw8.2, as described in the following sec-tions, at the closest virtual soil prole to seismic station TXSO,

(e.g. [2730]) are: (1) identication of all earthquake sources capable

0

10

20

30

0 200 400 600 800 1000

Suspension loggingSEL1 (Measured)Virtual point PV350(Estimated)

Dep

th (m

)

Shear wave velocity, VS (m/s)

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 25960

Fig. 11. Comparison of measured Vs at exporation boring SEL1, and estimated40

50values at virtual prole PV350.of producing damaging ground motions, (2) characterization of theearthquake recurrence model, (3) denition of the attenuationrelationship, (4) calculation of seismic risk and uniform hazardresponse spectrum, and (5) computation of deaggregation of theprobabilistic seismic risk. Fig. 13 shows schematically these steps.

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Mean measured Envelope measuredNS componentEW componentPV350 Estimated(Mw=8.2)

5 % damping

Spe

ctra

l acc

eler

atio

n, S

a (g

)

Period (s)

Fig. 12. Response spectrum computed at virtual soil prole 350 and measuredwhich recorded the ground movement during the 1985 Michoa-can earthquake, and compare both responses. As can be seen inFig. 12, the computed response agrees well, from a practicalstandpoint, to the measured response, considering that the 1985Michoacan earthquake had a moment magnitude of Mw8.1.

5. Seismic environment

The seismic environment at the studied site was characterizedthrough a probabilistic seismic hazard analysis, PSHA. In general, thesteps needed to conduct a probabilistic seismic hazard analysisresponses at TXSO station.

Returnperiod

Returnperiod

Period (TA) Period (TB) Period (TC) Period (TD) Period (TE)

Seismic hazard curves for diferent periods (T)

Sa (TA) Sa (TB) Sa (TC) Sa (TD) Sa (TE)

Spectral acceleration, Sa

Exce

edan

ce p

robab

ilit

y,

(S

a)

(TA) (TB) (TC) (TD) (TE)

Spec

tral

acc

eler

atio

n, S

a

Sa (TA)

Sa (TB)

Sa (TC)

Sa (TD)

Sa (TE)

Period (s)

Uniform hazard spectrum (UHS)for a return period given reference

Step 4

Fig. 13. Steps required for performing a probabilistic seismic hazard analysis (modied from Klugel [29]).

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266260

5.1. Identication of earthquake zones capable of producing

damaging ground motions

All seismogenic zones considered in this study were estab-lished according to the zonation that Nishenko and Singh [31]carried out for the mexican subduction zone (Fig. 14) becausethese corresponds to where the more damaging earthquakes forMexico City have been generated. Tables 2 and 3 include thecorresponding source parameters.

As described by Ordaz and Reyes [32], for each source, eachparameter was obtained from the Mexican catalog of earthquakesprepared by Zuniga and Guzman [33], in which bayesian statisticsprocedures described by Rosenblueth and Ordaz [34], and Arbo-leda and Ordaz [35] were used.

5.2. Earthquake recurrence models

The recurrence models allow for determining of the averagetime that has to pass to have an earthquake with equal char-acteristics, in a given site. Selection of an appropriate model isessential considering that the variability of the seismic periodicitycan be very signicant, reaching up to 40% in the averagerecurrence [36]. Several recurrence models of earthquakes areavailable in the technical literature, among the more used are:

o u

instead of a quit drop.

5.2.3. Characteristic earthquake models

An alternative model is the so called characteristic earthquakemodel. In this model, the maximum earthquake that is generatedin a fault, or in a fault zone, is presented with a larger frequency ofwhat is deduced from the Gutenberg and Richter model. Thisrecurrence model has been studied by a number of researchers inthe past decades (e.g. [3847]). A characteristic earthquakereleases all the seismic potential storage in the system, whichhas to be recovered during a given period of time. It is common tobe found in the technical literature studies of seismic risk thatadopt models that combine aspects of the characteristic modeland the GutenbergRichter model (e.g. [38]). For any adoptedmodel, the parameters needed to dene the seismicity in eachzone or fault, for the computation of seismic risk, are themaximum magnitude, Mu; minimum magnitude, M0; the rate ofearthquakes above the minimum magnitude l(M0), and the

Lat

itude

1S1

1

1S2

2

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 261Table 2Seismic sources parameters for small and moderate events, in all cases M04.5and Mu7.0 (after Ordaz and Reyes [32]).

Zone Exceedance rate, l0 (1/year) b

1S1 2.014 1.827

1 4.792 1.547

1S2 6.717 1.847

2 18.938 2.059

Longitude

Fig. 14. Seismogenic zones studied (a) earthquake of small to moderate intensity,and (b) characteristics earthquakes.Longitude

Lat

itude5.2.1. GutenbergRichter model

loglm abm 6Where lm, is the exceedance rate of earthquakes with larger orequal magnitude than m, a and b are constants, which areestimated using statistical analysis of the historical observationsof earthquakes and the data obtained from the geologic evidence.The value of a indicates the total rate of earthquakes in the region,and b the ratio of earthquakes of low intensity to large magnitude.Usually, expression 6 is expressed in complementary accumula-tive exponential form as

lM l0ebMM0 ,if M0rMrMu

0 ,if M4Mu

(7

where l0, is the magnitude exceedance rate for MM0, M0 is theminimum reference magnitude, b, which is a parameter control-ling the relative frequencies from large to small events, is equal tobln(10), and Mu, is the maximum possible magnitude at thesource.

5.2.2. Gutenberg-Richter modied model [37]

lM l0ebMebMuebM0ebMu , if M0rMrMu

0 , if M4Mu

(8

This model is very similar to the previous one for magnitudesclose toM , but it shows a smooth transition to l(M)0 atMM ,

Table 3Exceedance rate parameters for zones of occurrence of characteristics earthquakes

with M47.0 (after Ordaz and Reyes [32]).

Zone Name Exceedence rate,

l(7) (1/year)

1 Chiapas 0.0369

2 Tehuantepec Gap 0.03344

3 Oaxaca east 0.02793

4 Oaxaca center I 0.01898

5 Oaxaca center II 0.01339

6 Oaxaca west 0.01116

7 Ometepec 0.02899

8 San Marcos 0.01116

9 Gerrero 0.02232

10 Petatlan 0.01563

11 Michoacan 0.03356

12 Colima 0.01786

13 Brecha de Colima 0.01675

14 Jalisco 0.04566coefcient b.

the measured data, in both seismic stations. Based on theseresults, the model was considered representative of the groundmotions observed in Mexico City in rock outcrops.

5.4. Solution of the integral of seismic risk

Once established the earthquakes recurrence models, theseismogenic zones where they occur, and the attenuation law

0.4 6.7632 1.2513 0.09682 0.5 0.00727 0.442140.5 6.9039 1.2236 0.08753 0.5 0.00753 0.41710.6 6.5941 1.2748 0.06768 0.5 0.00693 0.435160.7 6.7755 1.3445 0.04662 0.5 0.0076 0.452360.8 6.5941 1.3676 0.03662 0.5 0.00705 0.44770.9 6.4534 1.347 0.0244 0.5 0.00648 0.428671 6.5638 1.3387 0.05429 0.5 0.00665 0.427751.1 6.6701 1.3186 0.05696 0.5 0.00703 0.436261.2 6.6903 1.3167 0.05225 0.5 0.00723 0.445761.3 6.6186 1.3183 0.04406 0.5 0.00723 0.457221.4 6.4825 1.3203 0.06347 0.5 0.00662 0.458861.5 6.3741 1.3742 0.08896 0.5 0.00616 0.478241.6 6.4614 1.4268 0.10542 0.5 0.00632 0.483861.7 6.3949 1.4291 0.10135 0.5 0.00604 0.501091.8 6.0912 1.4088 0.09393 0.5 0.00516 0.527121.9 5.9378 1.3967 0.07854 0.5 0.00494 0.527482 5.8698 1.3854 0.05267 0.5 0.00505 0.537092.1 5.8057 1.3938 0.03657 0.5 0.00522 0.56942.2 5.8367 1.4032 0.04392 0.5 0.00547 0.593542.3 5.8408 1.4162 0.05743 0.5 0.00561 0.592142.4 5.838 1.4032 0.07922 0.5 0.00559 0.582372.5 5.8323 1.3937 0.08121 0.5 0.0057 0.5842.6 5.858 1.3951 0.06917 0.5 0.00601 0.587562.7 5.754 1.3905 0.06887 0.5 0.00589 0.579042.8 5.6616 1.3937 0.0717 0.5 0.00583 0.579342.9 5.5518 1.4126 0.07024 0.5 0.00579 0.584073 5.4214 1.4344 0.0608 0.5 0.00568 0.591343.1 5.323 1.4555 0.06183 0.5 0.0056 0.594883.2 5.1785 1.4662 0.06368 0.5 0.00537 0.591293.3 5.0476 1.4684 0.06438 0.5 0.00519 0.585943.4 4.8327 1.4731 0.06784 0.5 0.00477 0.578143.5 4.6026 1.4899 0.06365 0.5 0.00438 0.575453.6 4.4198 1.5125 0.06782 0.5 0.00412 0.569373.7 4.2003 1.5357 0.06716 0.5 0.00377 0.56493.8 3.9923 1.5517 0.0638 0.5 0.00344 0.568633.9 3.8123 1.5584 0.06047 0.5 0.00314 0.58174 3.6367 1.5601 0.05951 0.5 0.00283 0.596614.1 3.4877 1.5489 0.0618 0.5 0.00254 0.607564.2 3.3429 1.5375 0.06438 0.5 0.00225 0.611564.3 3.2848 1.5117 0.05615 0.5 0.00219 0.62094.4 3.1955 1.4952 0.05207 0.5 0.00203 0.627764.5 3.098 1.4864 0.05698 0.5 0.00187 0.633154.6 3.0614 1.4894 0.06039 0.5 0.00196 0.635494.7 3.0962 1.5011 0.06049 0.5 0.00232 0.636834.8 3.1583 1.5143 0.0536 0.5 0.00276 0.644594.9 3.2384 1.5218 0.04547 0.5 0.00325 0.655585 3.2887 1.5282 0.03953 0.5 0.00364 0.664435.1 3.2792 1.5237 0.03394 0.5 0.00379 0.670035.2 3.213 1.5208 0.0312 0.5 0.00375 0.673155.3 3.1213 1.5266 0.03198 0.5 0.00364 0.674955.4 3.0212 1.5268 0.03054 0.5 0.0035 0.677665.5 2.9345 1.523 0.0244 0.5 0.0034 0.680025.6 2.8914 1.5329 0.01676 0.5 0.00348 0.683365.7 2.9014 1.5408 0.00898 0.5 0.00371 0.687175.8 2.9438 1.5417 0.00253 0.5 0.00403 0.694775.9 3.0208 1.5413 0.01408 0.5 0.00444 0.704596 3.0975 1.5468 0.02315 0.5 0.00484 0.71082

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266262In this research work, the recurrence law for the characteristicearthquake proposed by Ordaz and Reyes [32] was adopted, inwhich it is assumed that the behavior of the characteristic earth-quake observed by Singh et al. [48] in the Mexican subductionzone follows a Gaussian distribution, and is dened for eachsource with the following expression:

lM l7 1F MEMsM

, if M47 9

where, l(7) is the exceedance rate for M47, EM and sM are themean and standard deviation, respectively, of the magnitude, andF(U) is the normal cumulative distribution function.

5.2.4. Parameters that dene the seismicity in the seismogenic zones

For this study, as suggested by Reyes [49], the seismicity of theseismogenic zones was modeled with the modied GutenbergRichter recurrence law, to dene the exceedance rate of earthquakeswith magnitudes larger than 4.5 and lower of 7. In addition, to denethe exceedance rate of earthquakes with magnitude larger than 7, itused the recurrence law dened by the expression 9, correspondingto characteristics earthquakes. The parameters that dene the seis-micity of the seismogenic zones studied for the GutenbergRichtermodied model, are presented in Table 2. Table 3 compiles the modelparameters that dene the seismicity of the seismogenic zonesstudied for the characteristic earthquake model.

5.3. Attenuation relationship

The attenuation relationship relates the ground movement in agiven site, through a generic parameter of the motion, Y, whichusually is an acceleration or velocity, with the parameter thatestablished the size of the earthquake in the source (e.g. magni-tude, M), distance from the site to the zone of energy release (R),and a measure of the model dispersion. Some models includeother terms such as the soil type factor, the fault type thatgenerates the earthquake, or the earthquake type as a functionof its hypocentral location (e.g. [5059]). The same cited authorshave proposed several attenuation models to estimate the peakground acceleration, PGA, the spectral acceleration correspondingto a given specic frequency, Sa (T), or the maximum groundvelocity, PGV, for a given site. For this research it was used theattenuation law proposed by Reyes [49], which allows theestimation of the spectral acceleration, Sa, in rock outcrops inMexico City, and that has the following functional form:

ln YT ln SaT a1Ta2TM6a3TM62a4Tln Ra5TReT 10

where Y represents the maximum ground acceleration in one ofthe orthogonal directions, or its geometric mean, MG, in cm/s2; Mis the seismic moment magnitude; R is the minimum distancefrom the site to the rupture area, in km; ai are coefcientspresented in Table 4 for the geometric mean, and in Reyes [49]for the EW and NS components; e is the error made whenestimating the response spectrum with the attenuation law. Thisfunctional is the same as that proposed by Joyner and Boore [60].

5.3.1. Validation of the attenuation law for rock outcrops

Seeking to corroborate the appropriateness of the attenuationlaw used, the response spectrum for the 1995 September earth-quake was obtained in two sites located in rock, CU (UNAM), andTXCR. The earthquake had a moment magnitude, Mw7.3, and anepicentral distance of 280 km, with epicenter in the subductionzone. Fig. 15 depicts the response spectra estimated with Eq. (10)for the geometric mean and EW component, and those obtainedwith the records measured for sites CU (UNAM) and TXCR,

showing a good agreement overall between the predicted andTable 4Values of coefcients ai and s for the geometric mean (MG) of the spectralacceleration (Reyes [49]).

T (s) E00[a1] E00[a2] E00[a3] E00[a4] E00[a5] E00[s]

0 5.8929 1.2457 0.09757 0.5 0.00632 0.419830.1 6.0831 1.1954 0.09668 0.5 0.00643 0.433410.2 6.7942 1.0675 0.09858 0.5 0.00732 0.430050.3 6.9623 1.1303 0.10357 0.5 0.00768 0.38868for the studied site, the integral of seismic risk needs to be solved

0 1 2 3 4 5 6

EW measured

(cm

Period (s)

CR for the September 14 earthquake 1995, Mw7.3.

TXCR

TXCR

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 263according to the probabilistic approach (e.g. [61,27]). The risk isevaluated as the probability of exceeding an upper value of theparameter of the ground motion at the site, due to the activity of allseismogenic zones that surround it, and which may contribute to theexpected ground motion. The functional form of the integral ofseismic risk due to a set of N seismic sources is the following [28]:

gy XNi 1

niZ RmaxRmin

Z MmaxMmin

f MiMf Ri R PiY4y M,R dMdR 11

where the double integral has limits as the minimum and maximumof the magnitude and distances from the source. g(y) represents theannual rate of exceeding the level of motion, y, due to the occurrenceof earthquakes in the N sources, which is the sum of the annual ratesof exceedance g(y) in each of the sources (that have an annual rate ofoccurrence of ni earthquakes). The term Pi[Y4y9M,R] gives theprobability of exceedance of y, conditioned to the variables M andR. Finally, the functions fMi(M) and fRi(R) are probability densityfunctions (PDF) of the magnitude and distance, respectively. Inparticular in this research, it was adopted the particular simpliedcase of point-source, thus fRi(R)18R, is equal to one for every point.

5.5. Probabilistic seismic hazard curves for the TXCR site

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6

EW modelGeometric meanmodelEW measured

Spec

tral a

ccel

erat

ion,

Sa

(cm

/s2 )

Period (s)

5 % damping

Fig. 15. Spectral acceleration in sites CU and TXProbabilistic seismic hazard curves for the San Miguel TlaixpanTXCR site were determined for a range of seismic moment magni-tudes varying from 4.5 to 8.2. Seismogenic zones with irregularshapes were subdivided in regular constant areas (squares of3030 km), see Fig. 16, as suggested in Ordaz and Reyes [32]. Thissubdivision allowed to assume that the forms generated are pointsources with all the tributary seismicity concentrated at its geome-trical center [62], simplifying the probabilistic seismic hazard analy-sis. For each point the distance from the source to the study site wasdetermined for each seismic zone to where they belong. With theseanalyzes 61 seismic hazard curves for a range of periods from 0 to6.0 s were obtained. In particular, Fig. 17 presents the seismic hazardcurves for periods of 0, 3.0 and 6.0 s.

5.6. Uniform hazard spectrum for the TXCR site

The uniform hazard spectrum determined to characterize theseismic environment was developed at the same location as the rockstation TXCR, at about 18.70 km from the site, to be able to compareit directly with measured responses, if needed, for future earthquakes.As it is well known, the uniform hazard spectra, UHS, is a0

2

4

6

8

Spec

tral a

ccel

erat

ion,

Sa

5 % damping10

12EW modelGeometric meanmodel/s

2 )representation of the relationship between the natural vibrationperiod, T, and spectral acceleration, Sa, for a given exceedanceprobability associated with a return period. A uniform hazardspectrum for return period 125 years was obtained from the seismichazard curves (see Fig. 18). This gure also shows the uniform hazardspectrum for CU site (UNAM) for the same return period, obtained byOrdaz et al. [63]. Note that this spectrum denes the seismicenvironment of the area. Therefore it was used as input motionduring the site response analyses.

6. Site response analysis

The seismic response of each virtual soil prole was obtainedusing random vibration theory. The algorithm used to computethe probabilistic site response of horizontally stratied soil

Fig. 16. Seismogenic areas studied, earthquakes of small to moderate intensity(a) and characteristic earthquakes (b).

eler1

ce

s for periods of 0, 3.0 and 6.0 s.

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 25226626410-7

10-5

10-3

10-1

101

103

105

0.01 0.1 1 10 100

T= 0 s

Spectral Acceleration, Sa (cm/s2) Spectral Acc

10-4

10-2

100

102

104

0.01 0.1

Exce

edan

ce R

ates

,

(Sa)

(1/y

ear)

Exce

edan

ce R

ates

,

(Sa)

(1/y

ear)

Fig. 17. Seismic hazard curve

0.08

0.1

0.12

0.14

0.16

CU (Ordazet al., 2000)TXCR (Osorio, 2012)

acce

lera

tio, S

a (g

)

5 % dampingdeposits subject to two dimensional SH waves propagatingvertically is formulated in the frequency domain, assumingequivalent linear soil properties. It uses the ThompsonHaskell[64] solution. The input motion is dened in terms of a responsespectrum from which the equivalent power spectrum of theexcitation is computed. The accelerations, strains and responsespectra in different points of the system are computed from thecorresponding power spectrum and the extreme value theory.Thus, this random process is completely characterized by itspower spectra. Using the random vibration theory, the maximumresponses of a linear system excited by a stochastic process can becomputed for a given condence level. Physically this character-ization of the seismic environment is equivalent to consider aninnite number of acceleration time histories with the samemean frequency content but with randomly distributed phases.A total of 2501 site response analyses were carried out using theUHSrock as input motion. Following the recommendation ofRosenblueth et al. [65], a reduction of 40% was applied to theenveloped of the maximum response spectra computed to obtainthe suggested response spectra for the studied area. Fig. 19 showsthe response spectra obtained for all sites, as well as the proposedresponse spectrum. Given by the following equations:

Sa a0caOT

Ta; if ToTa 12

Sa c; if TarTrTb 13

0.02

0.04

0.06

0 1 2 3 4 5 6

Spe

ctra

l

Period (s)

Fig. 18. Uniform hazard spectra for a return period of 125 years for TXCR and UCsites, obtained with the parameters of the geometric mean of the attenuation

relationship proposed by Ordaz et al.ation, Sa (cm/s2) Spectral Acceleration, Sa (cm/s2)10 100 1000

10-7

10-5

0.01 0.1 1 10 100 1000

Exce

edanT=3 s

10-3

10-1

101

103T=6 s

Rat

es,

(Sa)

(1/y

ear)Sa c TbT

r; if T4Tb 14

The parameters to be used in these expressions are summar-ized in Table 5.

6.1. Comparison with measured response

Fig. 20 presents a comparison of the design response spectrumproposed, with the medium, medium plus one standard deviation,s, and enveloped of the recording measured in sites TXSOand TXCH, scaled to a Peak Ground Acceleration, PGA0.13 g.The mean, mean1s and enveloped response spectrum of mea-sured responses in the sites TXSO and TXCH, were obtained

Fig. 19. Response spectra obtained for the studied area.

Table 5Parameter values needed to compute the proposed design spectra.

c a0 Taa Tb

a r

0.37 0.13 0.40 3.0 2.2

a Period in second.

nd m

tes T

ce (k

L. Osorio, J.M. Mayoral / Soil Dynamics and Earthquake Engineering 48 (2013) 252266 265following the methodology proposed by Mayoral et al. [5], usingthe subduction earthquakes compiled in Table 6.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5

EnvelopeMean + 1MeanProposed

Spe

ctra

l acc

eler

atio

n, S

a (g

)

Period (s)

5 % damping

TXSO

Fig. 20. Mean, mean1s, and enveloped of recorded grou

Table 6Earthquakes used to obtain the mean, mean1s and the envelope measured at si

Site Event Ms Epicentral distan

TXSO 25/OCT/81 7.3 311.97

21/SEP/85 7.60 381.1

19/SEP/85 8.10 444.42

TXCH 07/JUN/82 (2) 7.0 353.74

07/JUN/82 (1) 6.9 365.94

14/MAR/79 Mb7.0 324.747. Conclusions

This paper describes the framework used to develop a designresponse spectrum for a 150 km2 area located within the Texcocolake region to be used in future updates of the Mexico Citybuilding code. This involved eld investigation, laboratory testing,and analytical studies. Geo-statistical analyses were carried out tocharacterize the main parameters that affect the seismic responseat the studied site, using a grid of 2501 virtual soil proles. Inparticular, it was observed that the spatial variation of measuredshear wave velocity exhibited a lognormal probability distribu-tion, whereas the measured plasticity index data followed anormal probability distribution. Regarding modulus degradationand damping curves, the Darendeli and Stokoes [20] modelseems to capture well the laboratory data, in particular for shearstiffness, under predicting the damping for shear strains largerthan 0.1% in the clayey materials. The geo-statistical modelgenerated to infer the virtual soil proles in the area, based onthe ordinary kriging interpolation technique was able to capturefairly well good shear wave velocity distributions measured atfour exploration borings, as well as the dynamic responserecorded at the seismic station TXSO, located within the area,during the 1985 Michoacan earthquake. Regarding the uniformhazard spectrum computed at seismic station TXCR, located atabout 18.7 km for the site in a rock outcrop, it was observed anslightly difference, specially in the frequency content, withrespect to that determined by other researchers at the CU (UNAM)station, located at about 31.7 km, supporting the fact of groundmotion modication in the different rock formations of MexicoCity, even for distances relatively small. The potential spatialvariability observed in the area was captured by a single envelopeobtained from the 2501 site response analyses, from which, inturn, the proposed response spectrum was derived.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5

EnvelopeMean + 1MeanProposed

5 % damping

Period (s)

Spe

ctra

l acc

eler

atio

n, S

a (g

)

TXCH

otions compared with the proposed response spectrum.

XSO and TXCH.

m) Soil type PGA (gal)

Soft clay NS23.793; V4.324; EW28.320Soft clay NS38.561; V0.000; EW34.748Soft clay NS103.036; V25.529; EW102.973Soft clay NS11.41; V5.47; EW12.19Soft clay NS22.17; V5.33; EW14.30Soft clay NS31.86; V12.49; EW22.43References

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[17] Maximilian Huber, Axel Moellmann, Andras Bardossy and Vermeer Pieter A.,

Seismic microzonation for the northeast Texcoco lake area, MexicoIntroductionDescription of the studied areaAvailable dataGeostatistical determination of soil parametersLayering sequence and thicknessVirtual shear wave velocity profilesModulus degradation and damping curvesDarendeli and Stokoe model (2001)Virtual profiles of plasticity indexAssessment of geostatistical model

Seismic environmentIdentification of earthquake zones capable of producing damaging ground motionsEarthquake recurrence modelsGutenberg-Richter modelGutenberg-Richter modified model [37]Characteristic earthquake modelsParameters that define the seismicity in the seismogenic zones

Attenuation relationshipValidation of the attenuation law for rock outcrops

Solution of the integral of seismic riskProbabilistic seismic hazard curves for the TXCR siteUniform hazard spectrum for the TXCR site

Site response analysisComparison with measured response

ConclusionsReferences