D.rivera Cathedral

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICSEarthquake Engng Struct. Dyn. 2008; 37:12491268Published online 9 May 2008 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe.808

Evaluation of the measured seismic responseof the Mexico City Cathedral

Daro Rivera1, Roberto Meli2,,, Roberto Sanchez2 and Bernardo Orozco2

1National Center of Disaster Prevention (CENAPRED), Delfn Madrigal, Coyoacan 04360, D.F., Mexico2Institute of Engineering, National University of Mexico (UNAM), Ciudad Universitaria,

Coyoacan 04510, D.F., Mexico

SUMMARY

The seismic response of the Mexico City Cathedral built of very soft soil deposits is evaluated by usingmotions recorded in various parts of the structure during several moderate earthquakes. This unique setof records provides significant insight into the seismic response of this and other similar historic stonemasonry structures.

Free-field ground motions are carefully compared in time and frequency domains with motions recordedat building basement. The dynamic characteristics of the structure are inferred from the earthquake recordsby using system identification techniques. Variation of seismic response for different seismic intensities isdiscussed. It is shown that, due to the soilstructure interaction, due to large differences between dominantfrequencies of earthquake ground motions at the site and modal frequencies of vibration of the structure,and due to a particularly high viscous damping, seismic amplifications of ground motion in this andsimilar historic buildings erected on soft soil deposits are much smaller than that induced in most modernconstructions. Nevertheless, earthquake records and analytical results show that several components of thestructure such as its central dome and the bell towers may be subjected to local vibrations that significantlyamplify ground motions. Overall, results indicate that in its present state the structure has an acceptablelevel of seismic safety. Copyright q 2008 John Wiley & Sons, Ltd.

Received 13 June 2007; Revised 6 December 2007; Accepted 11 February 2008

KEY WORDS: historic buildings; stone masonry structures; seismic response; accelerographic networks;soft soil deposits; kinematic soilstructure interaction

1. INTRODUCTION

Mexico possesses both a large wealth of extremely valuable historical buildings and a long historyof damage and destruction of them by severe earthquakes frequently affecting most of the country.On the other hand, historic buildings in Mexico City have shown a rather good performance under

Correspondence to: Roberto Meli, Institute of Engineering, National University of Mexico (UNAM), CiudadUniversitaria, Coyoacan 04510, D.F., Mexico.

E-mail: [email protected]

Copyright q 2008 John Wiley & Sons, Ltd.

1250 D. RIVERA ET AL.

the many earthquakes that have shaken the city during their existence. Specifically, in the great1985 Mexico earthquake (Ms =8.1), they performed much better than most, supposedly moreresistant, modern structures.

Sources of weakness of historic buildings, typically heavy stone masonry structures, are ratherwell known; nevertheless, procedures for evaluating their seismic safety are not well established andquantitative information about their behavior and response is scarce. Installation and maintenance ofseismic instrumentation in historic structures, together with the study of resulting seismic records,offer a unique opportunity to gain insight into how these structures respond to earthquakes.

The main objective of the research project reported herein was to provide quantitative informationto be used during the evaluation of the seismic safety of the Mexico City Cathedral through theinterpretation of a set of instrumental records of its vibration under several moderate ground motionsrecorded by its seismic network. Additionally, the research project was aimed at improving theknowledge about several key aspects of the seismic response of large historic masonry structures,especially of the hundreds of them that are built on the very soft soil in downtown Mexico City.Special emphasis was placed on the study of (a) the difference between free-field ground motionsand those recorded in the foundation of the cathedral; (b) the dynamic characteristics of thestructure inferred from earthquake records and their comparison with those previously obtainedusing linear elastic finite element models; and (c) the possibility of extrapolating the responseunder moderate earthquake in order to estimate performance under much more severe excitations.The results of the records obtained during the first phase of the project (19971999) have beenpublished in Meli et al. [1]. A more complete interpretation of these records and those obtainedin the following years is presented in this paper.

2. THE CATHEDRAL OF MEXICO CITY

The Mexico City Cathedral (Figure 1) is one of the most important colonial monuments of theAmericas. It has five longitudinal naves; the central one is covered by a barrel vault, and the lateralones are covered by spherical domes. Two rows of eight columns support the central nave and itsheavy central dome. A close array of robust masonry walls divides the extreme naves into smallchapels constituting, along with the main (south) facade, the apse and some buttresses, a very stiffsystem that provides great lateral strength in the transverse direction of the structure (Figure 2). Inthe longitudinal direction, the lateral strength and stiffness are primarily provided by the exteriorwalls along the east and the west facades of the cathedral. The building foundation consists of agrid of foundation beams and a thick masonry mat over a dense array of short timber piles.

The cathedral was built over the remains of several Aztec constructions on clay and silty claydeposits that are geologically very young and are famous for their extremely high water contentand compressibility. The lack of uniformity in the degree of consolidation of the soft clay layersunderlying different parts of its foundation generated great differential settlements. The distortionof the buildings produced by the differential settlements, which reached a maximum of 2.4 m, hasseriously undermined its structural safety. Severe cracks crossed the roofs, floors, and walls inboth the longitudinal and the transverse directions. They constantly reappeared in spite of frequentrepairs. No significant damage could be attributed to past earthquakes, besides the reopening ofrepaired cracks due to differential settlements.

A major rehabilitation project was started in 1991, aiming at reducing differential settlementsthrough soil underexcavation. The main geotechnical aspects of the rehabilitation project can be

Copyright q 2008 John Wiley & Sons, Ltd. Earthquake Engng Struct. Dyn. 2008; 37:12491268DOI: 10.1002/eqe

SEISMIC RESPONSE OF THE MEXICO CITY CATHEDRAL 1251

Figure 1. The cathedral of Mexico City.

Figure 2. Main features of the cathedral.

found in Ovando-Shelley and Santoyo [2] and the structural aspects can be found in Meli andSanchez [3]. As a part of this program, a seismic network was installed in 1996 to measure theseismic response of the structure during the frequent earthquakes that occur in Mexico.

3. STRONG MOTION INSTRUMENTATION

3.1. Instrumentation network

Only a handful of historic buildings have been instrumented worldwide; therefore, results obtainedfrom this network could be of great value not only to the study of the cathedral itself but also tothe study of other similar buildings, mainly of colonial temples in the Americas.



Figure 3. Schematic view of the initial array of accelerographs.

The network is composed of tri-directional digital 18 bits accelerographs that are simultaneouslytriggered to provide a continuous record with a common time basis. The initial array was composedof eight accelerographs. One instrument was located at ground level, about 10 m outside thefoundation of the building; three instruments were placed at the foundation level in order to measurethe motion directly induced to the building and its possible differences along the longitudinaldirection of the building; finally four instruments were located on different locations on the roofto measure the building response at various points. The array is schematically shown in Figure 3.After the first year, two of the instruments at the basements were removed and placed on thesouthwest bell tower to study its local seismic response. More recently, some of the instrumentswere moved to other buildings, and a five instrument array has remained in place.

3.2. Seismic records obtained

Twenty seismic events were recorded by the network from 1997 to 2003; only the most significantevents are discussed in this paper. In all the cases epicenters were located at least 100 km awayfrom the building site, and in most cases they corresponded to subduction earthquakes generatedin the Pacific Coast, at a distance of more than 300 km from Mexico City. Owing to the greatepicentral distances, the intensities of the ground motion and of the building response were quitelow, even if the magnitude of some of the events exceeded 7.0 in the Richter scale.

The main features of five selected events and maximum measured accelerations at differentpoints are summarized in Table I. The maximum ground acceleration corresponds to event E1, andequals 14.84 gal, whereas the maximum acceleration recorded on the building roof, for the sameevent, is 18.09 gal, corresponding to less than 2% of the gravity acceleration. Typical accelerationhistories, presented in Figure 4 for event E1, show a very long duration and an almost harmonicvibration. This figure also shows that ground motions in Mexico City from these distant earthquakesare characterized by about 50 s between the arrival of P and S waves.

All seismic records were analyzed in the frequency domain, obtaining Fourier amplitude spectraand response spectra as well as spectral ratios among motions recorded at different points. Fromthe analyses in the time domain, histories of absolute and relative displacements between differentpoints were also obtained.



Tabl

eI.

Max

imum

acce

lera

tions

reco

rded

inth

efo

ur

mai

nev

ents

.

Even

tM

ag.(

Mc)

Com

p.A

CA

NA

SAW

SCSN

SSCL

TBTA

E1N

S14

.99

14.3

117

.48

13.4

612

.64

12.4

012

.69

14.8

4

01/11

/97

7.3

V4.

743

.72

4.3

74.

893

.81

3.5

44

.08

5.7

5

EW

15.8

913

.65

15.4

318

.09

12.4

712

.15

12.5

41

4.21

E2N

S3

.67

3.45

6.0

23.

562

.78

2.7

12

.76

3.86

04/22

/97

5.9

V2.

732.

232.

051.

811.

861.

921.

912.

09

EW

5.4

14.

574.

906.

503.

693

.72

3.90

4.12

E3N

S2

.09

2.0

52

.37

1.9

91

.88

1.8

91

.91

2.0

1

07/19

/97

6.3

V0.

640.

520.

650.

720.

560

.56

0.59

1.9

1

EW

1.8

81

.68

1.8

82

.03

1.4

01

.54

1.40

1.86

E4N

S2.

872.

574.

092.

591.

77

2.

873

.71

14.2

604

/20

/98

5.4

V2

.47

1.6

81

.56

1.5

41

.48

2.04

1.6

31

.95

EW

3.10

2.32

3.70

3.45

1.48

1.68

4.61

16.2

3E5

NS

18.

29

5.9

3

8.

3511

.61

38.2

806

/21

/00

5.9

V7

.15

6

.42

10.1

65.

267.

32E

W22

.50

5

.03

7.84

7.5

42

8.44

E6N

S1

1.03

8

.91

8.6

41

1.4

18.2

208

/09

/00

7.0

V3

.62

4

.03

3.09

14.

423

.9E

W1

2.71

1

1.2

11.

363

.35

38.

8E7

NS

17.

66

13.

7

1

5.19

15.

8323

.76

01/22

/03

7.6

V3

.55

3.

66

13

.05

3.73

4.57

EW

17.6

4

15.6

8

1

6.57

18.

683

4.64

Acc

eler

atio

nsin

gal.



Figure 4. Strong motion records for event E1.

4. MAIN RESULTS

4.1. Ground motion at the free fieldFor engineering purposes, characteristics of the seismic ground motion are usually studied throughacceleration response spectra for 5% damping. A set of these spectra is shown in Figure 5 forthe two main horizontal directions at the free-field station. It can be seen that spectral shapeschange with earthquake magnitude, and the earthquakes of highest intensity show a significantamplification of response for long periods. This is attributed to the higher content of long periodwaves in large magnitude earthquakes compared with that in moderate magnitude events. Theselong period waves are amplified by the thick deposits of very soft clay underlying the cathedralsite and most of the central part of the city. In particular, the maximum spectral acceleration forevent E1 in the northsouth components is approximately five times larger than the maximumground acceleration. It is important to note that this level of amplification of spectral accelerationis approximately twice the maximum average amplification observed at rock or firm soil sites forthe same level of damping.

To better identify site effects, spectral ratios of the Fourier spectral amplitudes were obtainedbetween the cathedral site and a station located on firm ground in Mexico City, where the sameevents were recorded (CU station). These functions, shown in Figure 6 for the five most significantevents and for both horizontal directions, allow one to clearly identify the first mode of vibrationof the soil deposits at the site, at approximately 0.37 and 0.38 Hz for the NS and EW directions,



N-S

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5PERIOD (s)

ACCE

LERA

TIO

N(ga

l)E1 (Mc=7.3)E2 (Mc=5.9)E5 (Mc=5.9)E6 (Mc=7.0)E7 (Mc=7.6)

E-W

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5Period (s)

ACCE

LER

ATIO

N(ga

l)

E1 (Mc=7.3)

E2 (Mc=5.9)

E5 (Mc=5.9)

E6 (Mc=7.0)

E7 (Mc=7.6)

Figure 5. Acceleration response spectra of records at the free field (CL).

N-S

0.1

1

10

100

1010.1FREQUENCY (Hz)

RA

TIO

CL/

CU

E1 (Mc=7.3)E2 (Mc=5.9)E5 (Mc=5.9)E6 (Mc=7.0)E7 (Mc= 7.6)

E-W

0.1

1

10

100


RAT

IO C

L/CU

E1 (Mc=7.3)E2 (Mc=5.9)E5 (Mc=5.9) E6 (Mc=7.0)E7 (Mc=7.6)

Figure 6. The ratio of Fourier spectral amplitudes at the cathedral site (CL)and a station on firm ground (CU).



respectively. The second mode of vibration of the soil deposits at the site is not strongly excitedby these motions except for the 30 September 1999 earthquake in which the second mode is moreclearly visible in the northsouth component at an approximate frequency of 1.12 Hz.

Monumental structures have fundamental periods of vibration usually smaller than 0.5 s, veryfar from the dominant periods of vibrations of the soft soil of Mexico City. This is particularlybeneficial for the seismic performance of these short period buildings, which do not experiencethe great amplifications of vibration due to near-resonance response that have been the main causeof the large damage suffered by many modern buildings in the 1985, Mexico earthquake [4].Nevertheless, it must be noted that the natural period for the second mode of vibration of thesoil deposits in downtown Mexico City (approximately between 0.6 and 0.9 s) is not far from thefundamental period of many historical buildings; therefore, some response amplification can beexpected around this period.

4.2. Motion at building basement

It is important to assess whether and how the presence of the building alters the motion of theground, thus producing a shaking at the building basis that is different from what could be obtainedfrom motions recorded in open ground.

To study this issue, the spectral ratios of the ordinates of Fourier spectra corresponding toground motions recorded in the stations at the basement center, and those of the free-field spec-trum, were computed for the two horizontal directions (Figure 7). A drastic decrease in responseamplitudes at the basement can be appreciated for frequencies exceeding 1.1 Hz. Specifically,for a frequency of 2.5 Hz (corresponding to the fundamental period of the structure, that is,approximately 0.4 s, as will be demonstrated shortly), spectral ordinates of the motion at thebasement are on average 50 and 40% of those at the free field, for NS and EW directions,respectively.

The reduction in the amplitude of motion is due to soilstructure interaction; by a kinematicinteraction, seismic waves traveling in the free field are filtered, when crossing a rigid massive bodyas the cathedral basement, thus reducing their amplitude, particularly for high-frequency waveswhose length is less than the size of the building. On the other hand, an inertial interaction givesrise to attenuation in wave amplitudes when part of the energy of the ground motion is returnedto the soil due to the vibration of the building as a rigid body or, as this is the case, due to the

N-S

0.1

1

10

1010.1

FREQUENCY (Hz)1010.1

FREQUENCY (Hz)

RAT

IO

0.1

1

10

RAT

IO

SC/CLSN/CLSS/CL

E-W

SC/CLSN/CLSS/CL

Figure 7. The average ratio of spectral amplitudes for events E1, E2, and E3 at the threepoints of the basement with respect to the free field.



bending of the whole building on its vertical plan [5]. For usual buildings only inertial effects dueto the motion of the building as a rigid body are considered, but in this case the effects of theother type of interaction are more significant.

The results shown in Figure 7 demonstrate that the soilstructure interaction greatly reduces theamplification of seismic waves having frequencies close to the fundamental period of vibration ofthe cathedral, as well as of most other historical buildings located in the central area of MexicoCity on soft soil.

An additional issue of interest was to ascertain whether the modification of the ground shakingdue to the presence of the building varies with the intensity of the seismic event and also with thechanges in soil properties due to the injections of mortar performed to achieve a more uniformsettlement of the building. As can be appreciated from Figure 8, the dominant vibration period ofthe motion at the basement center is slightly longer for events of greater magnitude, whereas itdoes not show a clear difference for events occurring during and after soil modification producedby underexcavation and mortar injection.

Another aspect to be studied is the uniformity of the motion induced at the three points ofthe foundation. In Figure 9 Fourier spectra of the horizontal motion recorded at each of thethree stations of the basement are shown. As it can be appreciated, spectral amplitudes do notshow significant differences for frequencies up to 2 Hz; thereafter, differences appear probablydue to the high-frequency noise into the signals. On the other hand, the time histories of relativedisplacements computed from the records show bending of the base, mainly in the vertical direction.Maximum relative displacements between longitudinal ends of the basement and its central pointare shown in Table II for three of the recorded events. Vertical relative displacements can reachapproximately 20% of the maximum total vertical displacement at the center; for lateral andlongitudinal motions, the ratios reach 10 and 5%, respectively. The distortion of the buildingbasement is probably due to the large transverse cracking that exists both in the foundation andin the structure; nevertheless, these relative displacements do not generate significant differencesin accelerations induced in different parts of the structures. Its main effect is probably in thegeneration of additional soilstructure interaction contributing to the attenuation of amplitudes ofthe motion imposed to the building.

0

1

2

3

4

E1 (Mc=7.3) E2 (Mc=5.9) E5 (Mc=5.9) E6 (Mc=7.0) E7 (Mc=7.6)EVENT

T(s)

End of soilinjection

Figure 8. Dominant period of motion recorded at the basement for differentseismic events (NS direction).



N-S

0.01

0.1

AM

PLIT

UDE

(cm/s)

AM

PLIT

UDE

(cm/s)

1

10

100


SC-E1

SN-E1

SS-E1

E-W

0.01

0.1

1

10

100


SC-E1SN-E1SS-E1

Figure 9. Fourier spectra of the records at three points of the basement (SC, SN and SS) during event E1.

4.3. Motion at the roofAs it can be appreciated from Figure 4, ground motion histories at the roof and at the basementare very similar in shape and amplitude, showing that the building essentially follows the motionof the ground, with very little amplification, almost as a rigid body. For instance, the maximumacceleration recorded at the roof for event E1 exceeds the maximum at the basement only by 17%(Table I).

A closer view of the similarity of the acceleration time histories at the roof and at the basementis given in Figure 10, where the signals are superimposed in a 20 s time window. As it can beseen, the motion of the roof follows the cycles of vibration of the basement very closely, overwhich small amplitude vibrations corresponding to the fundamental frequency of the structure areadded.



Table II. Maximum relative displacements among the points of the basement.

Component

NS V EW

Event Stations D (mm) R (%) D (mm) R (%) D (mm) R (%)01/11/97 SCSN 0.380 1.62 0.800 14.18 2.000 7.52

SCSS 1.140 4.87 0.440 7.80 2.340 8.80SNSS 1.000 4.27 1.100 19.50 2.810 10.56

05/22/97 SCSN 0.210 4.37 0.160 21.33 0.390 8.21SCSS 0.280 5.82 0.180 24.00 0.460 9.68SNSS 0.240 4.99 0.180 24.00 0.700 14.74

07/19/97 SCSN 0.080 1.74 0.110 11.83 0.170 5.86SCSS 0.160 3.48 0.080 8.60 0.320 11.03SNSS 0.130 2.83 0.120 12.90 0.450 15.52

D is the maximum recorded relative displacement and R is its ratio to the maximum absolute displacement atthe basement center for each direction.

Figure 10. Acceleration history at the base and the roof for a segment of event E1.

For an accurate determination of the significant modal frequencies of the structure, ratios ofspectral ordinates of the horizontal motion at the four points on the roof with respect to thecorresponding points at the basement were computed and are shown in Figure 11 for the average ofthree events. The first peak of the roof response is appreciated at about 2.5 Hz, for both directions,corresponding to the fundamental mode of vibration of the building (0.35 and 0.40 s period forNS and EW, respectively). The second mode of vibration of the building is found at a frequencyof around 6 Hz. The peak at 1.1 Hz corresponds to the fundamental mode of vibration of the belltowers, as can be appreciated in Section 4.5.

Significant differences exist among the amplitudes of the motion at the four points on the roof.In general terms, they are due to the large cracks crossing almost completely the roof in thelongitudinal and transverse directions. The main difference is found in the amplification of themotion at the south end of the roof, over the facade, at a frequency of about 6 Hz, and is attributedthe vibration of the two tall and heavy bell towers, which move together with the main facade,partially separated from the rest of the building by a great transverse crack. The west side ofthe roof also shows an important amplification (EW), due to the out-of-plane vibration of the



Figure 11. The ratio of spectral amplitudes of the four points on the roof with respect to the basement.Average for events E1, E2, and E3.

0.1

1

10


AM

PLIT

UDE

AC/ANAC/ASAC/AW

Figure 12. Ratios of spectral amplitudes of vertical motion at roof center with respect to other points ofthe roof. Average for events E1, E2, and E3.

longitudinal facade, also separated from the rest of the building by a large crack crossing almostentirely the vaults and the foundation.

The ratios of spectral ordinates of the vertical motion at the center of the roof with respect tothe other three points on the roof are shown in Figure 12, as an average for three events. The peakat 6.5 Hz indicates a local vertical vibration mode due to the motion of the heavy central domesupported by the four leaning central columns.

Relative lateral displacements between the roof and the basement of the structure were verysmall, as could be expected given the rather high frequency of the fundamental mode of vibration.Figure 13 shows the time histories of lateral displacements in the NS directions at the roof center,as derived from the corresponding accelerograms for event E1. The displacement histories at thebasement center are also shown. The great similarity between the displacements at the base andthe roof gives rise to very small relative displacements corresponding to the deformation of the



-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

8070605040TIME (s)

ACSC

-3.0

-2.0

-1.0

0.0

DIS

PLAC

EMEN

T (cm

)D

ISPL

ACEM

ENT

(cm)

1.0

2.0

3.0

0 20 40 60 80 100 120 140TIME (s)

(a)

(b)

Figure 13. Time histories of horizontal displacement during event E1 (NS direction): (a) absolutedisplacements at the roof (AC) and basement (SC) and (b) relative displacement (ASSC).

structure, as shown in the same figure; this is an indication of the very low level of stresses inducedin the structure by these seismic events.

4.4. Dynamic properties of the structureFundamental periods of vibrations in the two horizontal directions determined from the records ofthe five main events are plotted against the dates of these events in Figure 14. As it can be seen,the fundamental periods in the transverse direction, EW, consistently exceed by a slight marginthose in the longitudinal direction, NS. No clear trend of variation of the vibration period can beperceived along the six years of recording, thus indicating that the large amount of mortar injectedin the clay soil layers had not produced any significant effect on the overall seismic response ofthe structure and that no significant additional structural damage has been produced by differentialsettlements or by the earthquakes occurred in the time frame of the records.

The variation of the same vibration periods with the amplitude of the vibration during a specificevent was evaluated from segments of the signal for consecutive 20 s time windows and is shownin Figure 15 along with the record in the EW direction for event E1. The fundamental periodincreases in the zone of maximum intensity from 0.39 to 0.45 s and decreases later on, returning atthe end of the record close to its initial value; these results indicate a significant nonlinear behavior



0

0.2

0.4

0.6

E1 (Mc=7.3) E2 (Mc=5.9) E5 (Mc=5.9) E6 (Mc=7.0) E7 (Mc=7.6)EVENT

T(s)

N-S

E-W

End of soilinjection

Figure 14. Fundamental periods measured in different events for the two horizontal directions.

-20-15-10

-505

101520

ACCE

LERA

TIO

N (ga

l)PE

RIO

D (s)

RAT

IO O

F DA

MPI

NG

0 20 40 60 80 100 120 140 160 180 200TIME (s)

0 20 40 60 80 100 120 140 160 180 200TIME (s)

0 20 40 60 80 100 120 140 160 180 200TIME (s)

ACSC

0.35

0.37

0.39

0.41

0.43

0.45

0.47

WINDOWSAVERAGE

0.01

0.03

0.05

0.07

0.09

WINDOWSAVERAGE

Figure 15. Variation of the period and damping ratio for different timewindows of event E1 (EW direction).



0.00

0.02

0.04RAT

IO O

F DA

MPI

NG

0.06

0.08

0.10

0.12

0.14

8765MAGNITUDE (Mc)

N-S

E-W

Figure 16. Variation of the damping coefficient with earthquake magnitude.

during the event, which is related to the profuse cracking previously existing in the masonry; theresults also indicate that no additional damage has been produced by this event.

Damping involved in the measured response of the structure was derived from the shape ofthe ratios of spectral amplitudes between the acceleration recorded at the roof and the basement,in the neighborhood of the peak at the fundamental frequency of vibration of the structure. Thewidely used procedure proposed by Rinawi and Clough [6] was followed, by which the theoreticaltransfer function of a single degree of freedom system is fitted to the experimental shape of thesame function and the identification of the damping coefficient is based on the amplitude of thefunction for the vibration mode under consideration.

Damping coefficients obtained in this manner from the recorded acceleration time historiesvaried according to the roof site and the specific event. As shown in Figure 16, damping coefficientincreased with the magnitude of the seismic event, varying from 4 to 6% for the transverse direction(EW) and from 7 to 12% for the longitudinal direction (NS). As an average, damping was50% greater for a magnitude 7.6 than for a magnitude 5.9 earthquake. Damping coefficients fordifferent time windows along the same event were also determined and are shown in Figure 15.An increase of about 100% can be observed from the initial segment of very low intensity to thesegment corresponding to the maximum amplitude.

As a conclusion, increase in the vibration period and damping coefficient with the intensity ofthe motion indicates a significant nonlinearity in the building response, related, on the one hand, toa reduction in lateral stiffness and, on the other hand, to an increase in energy dissipation. Thesechanges cannot be attributed to intrinsic nonlinearity of the material, because laboratory tests haveshown that the material behavior is similar to the linear behavior for low levels of stress; instead,they are related to the severe cracking the structure had previously suffered due to differentialsettlements; even though these cracks have been repeatedly repaired through injections of a limegrout, they constitute zones of weakness, and as the amplitude of the vibration increases, some ofthem reopen with an increasing length, leading to a decrease in lateral stiffness and, consequently,to an increase in the vibration period; additionally, sliding along increasing lengths of reopenedcracks gives rise to increasing energy dissipation and, therefore, equivalent damping.



Table III. Comparison of measured and computed frequencies (Hz).Structuralcomponent Direction

Finite elementmodel

Ambient vibrationmeasurement Seismic records

Roof EW 3.37 2.032.27 2.30NS 3.50 2.662.73 2.60

Dome V 6.33 4.174.55 6.50SW tower EW 1.52 1.25 1.15

NS 1.69 1.411.56 1.25

It must also be noted that damping coefficients derived from the response of this building arealmost three times those measured in modern concrete or steel buildings subjected to groundmotions of moderate intensity; such high coefficients can be partially attributed not only to thehigh internal damping of this kind of relatively soft masonry but also to the profuse cracking ofstructural members.

A finite element model of the entire building including its foundation was built, consideringlinear elastic isotropic behavior, with a Young modulus determined from tests on a stone masonryspecimen with similar characteristics as those of the building, and a 5% damping that is typicalfor masonry structures. Fundamental frequencies obtained with this model are shown in Table III.As it can be appreciated from the table, fundamental frequencies computed for the model exceedthose derived from the seismic record by almost 50%; the difference can be attributed mainly to thepreexisting cracking of the structure. A common way to introduce the effect of cracking in a linearmodel is by reducing Youngs modulus and/or by increasing the damping coefficient. Previouslydescribed results show that these changes should be different for different vibration amplitudes;therefore, each event would require a specific modification of the parameters. No attempt was madeto use one of the several nonlinear computer codes recently developed for masonry structures [7],mainly because of the lack of enough information on the extent and the position of the cracksoccurred in the past, which constitute the main sources of nonlinearity in this case.

Also reported in Table III are the fundamental frequencies derived from ambient vibrationrecords obtained a few years in advance of this study. Their significant differences from those ofthe seismic records could be mainly attributed to the extremely low amplitudes of the vibrations,which are in this case induced in the structure mainly by traffic.

4.5. Motion of the bell towerAcceleration time histories recorded at the basement, roof, and top levels of the southwest belltower for event E4 are shown in Figure 17. The maximum acceleration at the top level is 7.5 timesgreater than that at the basement level, while this ratio for the roof level is about 2. From the ratiosof spectral amplitudes (Figure 18), the fundamental modes of vibration of the tower are found tobe at 1.25 and 1.15 Hz for NS and EW directions, respectively. A second peak of the graphcorresponds to the first mode of vibration of the building as a whole (about 2.5 Hz), and a third peakcorresponds to the second mode of the tower (4.5 and 7.5 Hz in NS and EW, respectively). A two-degree-of-freedom spring model was analyzed in order to identify the mass and stiffness requiredto match recorded response. The properties identified in this manner approximately correspondto those of a system composed of the tower itself plus one half of the width of the main facade,suggesting that both towers vibrate with the facade as a structure almost independent from the restof the building. This assumption is consistent with the presence of a wide transverse crack crossing



Figure 17. The response of SW tower at different heights, event E4.

Figure 18. The ratio of spectral amplitudes at the top bell tower (TA) with respect to the basement (SC).

the whole span of the nave in its first nave and due to the outwards rotation of the facade. Thelarge amplification from the top to the roof levels of the tower reveals an appendix-like vibrationdue to the high flexibility of the upper part of the tower.

5. CONSIDERATIONS ON THE SEISMIC SAFETY OF THE CATHEDRAL

In order to estimate the building response to more critical seismic events, whose intensities wouldbe much greater than those recorded by the network, first the corresponding ground motion at thebasement and then the building response to this motion should be evaluated.



Reasonably accurate estimations of the ground motion at the site and the basement for greaterearthquake intensities are feasible in this particular case, because it has been demonstrated that thebehavior of the clay soil layers remains linear elastic for a very wide range of wave amplitudes.Therefore, for instance, an estimation of the motion at the cathedral during the great Mexicoearthquake of 19 September 1985 can be based on the records at a station (CU) in another partof the city where not only the same events measured by the network at the cathedral have beenrecorded but also the great 1985 earthquake.

Ground motion that should have occurred at the cathedral site in the 1985 earthquake could beestimated by multiplying the ordinates of spectra of the record at CU for this event, by the ratiosof spectral amplitudes at the two stations, for the motion recorded in the E1 event. A great numberof records obtained in different sites throughout the city show that such a spectral ratio remainsrather stable for a wide range of seismic intensities [8].

Acceleration response spectrum computed in this manner for the basement of the cathedral isshown in Figure 19, along with the response spectrum corresponding to the most severe groundmotion recorded in 1985 in the area of soft soil of Mexico City (SCT). As it can be seen, theresponse spectrum for the cathedral basement has its peak at a longer period, and in general termssmaller ordinates than that at SCT. The reduction is drastic for short periods; specifically, for a 0.4 speriod, corresponding to the fundamental mode of vibration of the cathedral, the spectral ordinateis 53 gal for the cathedral and 235 gal for SCT, where the maximum ordinate for a period of2.0 s is about 1000 gal. This large difference is partially originated by smaller wave amplificationsat the cathedral site than at the SCT site for the whole range of vibration frequencies; however,by large, the reduction for short periods is produced by the soil interaction effects discussedearlier in this paper. Again, this large reduction explains the good seismic performance of themonument.

Extrapolating the building response from records of low intensity events is much more question-able than extrapolating ground motion intensity. Because of the nonlinear effects due to cracking,on the one hand, fundamental period is expected to increase leading the structure to zones of greaterspectral ordinates; on the other hand, damping should also increase, thus significantly reducing thestructural response. It was considered that the response obtained ignoring the variation in the twodynamic properties will give conservative results; therefore, the response for the critical earthquake

0

200

400

600

ACCE

LERA

TIO

NS (g

al)

800

1000

1200

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0PERIOD (s)

SCT-1985, E-WE1, N-SCATHEDRAL-1985, N-S

Figure 19. Acceleration response spectra of ground motion at the SCT station and cathedral basement.



could be estimated by multiplying the response parameters derived from the records of event E1 bythe ratio between ordinates of the response spectra of the two events, corresponding to the period ofthe mode of vibration governing that response. For instance, the maximum horizontal displacementat the top of the columns supporting the central dome derived from the motion of the roof forevent E1 was 1.7 mm; the ratio of spectral ordinates of the 1985 and the E1 earthquakes for thefundamental period of the roof vibration (0.4 s) is 4.4; therefore, a horizontal relative displacementof 7.5 mm could be expected for the design earthquakes. Estimated responses are in all the casesrather small, and even if actual values could be significantly increased by nonlinear behavior, theyshould remain amply smaller than those the structure has suffered due to differential settlements,and should not impair the structural safety.

6. CONCLUDING REMARKS

The seismic network installed at the cathedral has been successful in terms of the number andquality of records gathered in a limited time span and of the knowledge derived from them.Regarding the seismic response and safety of this building, the following conclusions were derived.

Seismic ground motion at the site has an almost harmonic vibration with a frequency that ismuch lower than the frequency that is critical for this kind of structure, for which the spectralamplitudes are rather small. Moreover, a favorable interaction between the structure and the soilreduces to less than one half the amplitudes of the seismic waves for the range of frequenciesthat are critical to the structure. Additionally, the response of these stone masonry structures ischaracterized by a viscous damping (between 6 and 12% for the recorded events), which is aboutthree times that obtained in modern concrete or steel buildings, and therefore gives rise to muchsmaller spectral amplitudes. These three factors explain the good performance of most historicalmasonry buildings on the soft soil of Mexico City.

The building as a whole vibrates essentially as a rigid body, the roof showing only a 17%amplification of the acceleration at its basis; its lateral drifts are also very small. Nevertheless,some parts of the structure show local vibrations: front and lateral facades have significant out-of-plane vibrations: the central dome has an important vertical vibration inducing vertical forceson the drum and on the supporting arches; the upper part of the bell towers shows a significantamplification of lateral displacement.

Approximated extrapolations of the response to moderate earthquakes, ignoring softening ofthe structure due aggravated cracking, indicate that for a severe event, as the great 1985 Mexicoearthquake, displacements and stresses will still lie within the limits corresponding to an acceptableperformance, except perhaps for the response of the bell fry.

The following are some findings of a more general nature that could be applicable to otherhistoric buildings.

High-frequency seismic waves are filtered by kinematic soilstructure interaction, when crossingrigid massive foundations as those of the most historical buildings; therefore, for the criticalvibration periods of these buildings, the spectral amplitudes of the motion imposed at their basis aresignificantly smaller than those corresponding to the records obtained in the free field. This factormust be taken into account when evaluating the seismic hazard of these buildings, independentlyof the type of the soil on which they are founded.

Vibration of stone masonry buildings of this kind is characterized by rather high dampingcoefficients, even for low amplitude motions; moreover, damping increases significantly with



earthquake intensity due to early nonlinear behavior due to cracking and has a great influence onthe reduction in seismic actions.

Finally, it must be recognized that linear elastic analyses of these structures could provide onlyan overall picture of their seismic response and that because the nonlinear behavior is significantfrom early stages, these analyses have a limited validity for evaluating seismic safety.

ACKNOWLEDGEMENTS

This study was part of the rehabilitation project of the Mexico City Cathedral, performed by the NationalCouncil for Culture and Arts. The instrumental network was installed and operated in its first stage by theNational Center for Disaster Prevention (CENAPRED), under the direction of Roberto Quaas and MauricioOrtega. Presently, the network is operated by the Institute of Engineering of UNAM and coordinated byLeonardo Alcantara. Mario Ordaz and Roberto Duran performed analyses and interpretations of resultsduring the first phase of the project and provided good insight into understanding the main aspects of theproblem. Eduardo Miranda greatly contributed to the interpretation of the results and provided significantinput to the first draft of this paper.

REFERENCES

1. Meli R, Rivera D, Sanchez R, Miranda E. Instrumentacion ssmica de la Catedral Metropolitana. Resultados19972000. Ingeniera Ssmica 2001; 65:1748.

2. Ovando-Shelley E, Santoyo E. Underexcavation for leveling buildings in Mexico City: case of the metropolitancathedral and the Sagrario Church. Journal of Architectural Engineering 2001; 7(3):6170.

3. Meli R, Sanchez AR. Rehabilitation of the Mexico City Cathedral. Structural Engineering International 1997;9(2):101106.

4. Rosenblueth E, Meli R. The 1985 Mexico earthquake. Causes and effects in Mexico City. Concrete International1986; 8(5):2334.

5. Trifunac MD. Discussion to: seismic soilstructure interaction in buildings. I: analytical methods and II: empiricalfindings. Journal of Geotechnical and Geoenvironmental Engineering 2000; 126(7):668670.

6. Rinawi A, Clough R. Improved amplitude fitting for frequency and damping estimation. Proceedings of the 10thInternational Modal Analysis Conference Society for Experimental Mechanics, Bethel, CT, 1992; 893898.

7. Lourenco PB. Computations on historic masonry structures. Progress in Structural Engineering and Materials2002; 4:301319.

8. Reinoso E, Ordaz M. Spectral ratios for Mexico City from free-field records. Earthquake Spectra 1999; 15(2):273295.


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