Influence of ground water extraction in the seismic hazard of Mexico City

Transcription

1 Geo-Environment and Landcape Evolution II 457 Influence of ground water extraction in the eimic hazard of Mexico City J. Avilé 1, L. E. Pérez-Rocha 2 & H. R. Aguilar 3 1 Intituto Mexicano de Tecnología del Agua, Mexico 2 Intituto de Invetigacione Electrica, Mexico 3 Centro de Invetigación Símica, FJBS, Mexico Abtract The influence of ground water extraction in the eimic hazard of Mexico City i examined. Available information on ettlement of the land urface i ued to evaluate the ubidence effect on the predominant ground period. Microzoning map, a a function of thi relevant ite parameter, are contructed for the preent and future geotechnical condition. Baed on thee map, ite-pecific deign pectra throughout the whole city are determined by applying eimic code proviion. It i found that the regional ubidence will generally be beneficial for tructure with fundamental period longer that the current period of the ite, but detrimental if the tructure period i horter than the ite period. Keyword: deign pectra, ground water extraction, microzoning map, regional ubidence, eimic hazard. 1 Introduction Extenive ground-water exploitation ha been identified a the main caue of land ubidence in Mexico City. The phenomenon ha caued large ettlement in the pat, up to 10 m at ome area of the city. Subidence of the city wa tudied for the firt time by Carrillo [1], howing a clear dependence with the amount and rate of water extraction from arteian well. Since then, many effort have been made to undertand the phenomenon and mitigate it conequence. A review of thee effort can be found in Ovando-Shelley et al. [2]. Thee author have tudied the conolidation proce in the central part of the city uing the well-known Terzaghi conolidation theory. They howed that exploitation of the aquifer under the lacutrine clay i reflected not only on the gradual doi: /geo060451

2 458 Geo-Environment and Landcape Evolution II reduction of their thickne, but alo on the modification of their mechanical propertie. In Mexico City, ground motion amplification during earthquake i the mot important factor aociated to the uboil characteritic. The edimentary bain meaure approximately km and the thickne of compreible clay depoit may exceed 70 m. With hear wave velocitie ranging from around 50 to 100 m/, the predominant ground period can be a long a 5. In view of thee geotechnical condition, the reonant pectral acceleration for ite with dominant period around 2 may reach up to one g when intene ubduction earthquake occur a far a 300 km. Thi wa oberved during the great 1985 Michoacan earthquake. Any variation in the preent geotechnical condition, however, will reult in a change in the eimic hazard in the future. In thi work, an empirical method to predict the effect of regional ubidence on the eimic hazard in Mexico City for the coming year i preented. Uing available information regarding precie leveling of benchmark and geotechnical oil profile, Aguilar et al. [3] have found correlation of the ubidence rate and the thickne of ediment with the predominant ground period. With the ue of thee data in a year-by-year incremental procedure, the evolution of the microzoning map and the correponding deign pectra pecified by the building code, both in term of the ite period, i predicted for an expoure period of 50 year. Thi would allow the deigner to evaluate the effect of regional ubidence during the life pan of a tructure. 2 Available information The ubidence of Mexico City i tudied here by uing an empirical method baed on extrapolating available data for predicting future trend. With pectral amplification function for about 100 intrumented oft ite at Mexico City, complemented with around 500 microtremor meaurement, predominant ground period T were computed for a rectangular grid of 80x80 point covering mot part of the city, uing the interpolation technique devied by Pérez- Rocha et al [4]. Thi reulted in the microzoning map diplayed in fig. 1, which will be referred hereafter a the 2000 verion. The ioperiod curve for T = 0.5 and 1 roughly mark the eparation between both the firm and tranition zone a well a the tranition and oft zone, repectively. For about 360 ite, the thickne of ediment H i alo known. Fig. 2 lefthand ide how the correlation of thi parameter with the ite period obtained by Aguilar et al. [3]. Thi relationhip i expreed by 1 2 [ T ( ) 0.5] for T H ( m) = 31 1 (1) Note that, for a given ite, the hear wave velocity V i defined indirectly by eqn. (1) ince, according to the one-dimenional wave propagation theory, the expreion T = 4H V applie.

3 Geo-Environment and Landcape Evolution II 459 Figure 1: Curve of predominant ground period () in Mexico City. For monitoring ubidence in Mexico City, a network of more than 2200 benchmark ditributed along the city ha been intalled. Thi network wa releveled in 1983 for the lat time. By collecting elevation meaurement at land urface during the time period , Aguilar et al. [3] etimated the amount of ubidence at oft ite. Then, the mean ubidence rate wa correlated with the ite period by the expreion 1.9 [ T ( ) ] for T υ ( cm year) = 2 1 (2) Fig. 2 right-hand ide illutrate that the ubidence rate decline a the ite period horten which in turn occur when the depth of ediment hrink (ee Fig. 2 left-hand ide). Thi i conitent with the conolidation proce in the lakebed zone of the city. It hould be mentioned that the oberved ubidence include not only the effect of ground-water extraction, but alo the conolidation from the own weight of building.

4 460 Geo-Environment and Landcape Evolution II Figure 2: Left-hand ide: thickne of compreible clay depoit in Mexico City lakebed zone. Right-hand ide: ubidence rate in Mexico City lakebed zone. 3 Predicting procedure Pumping operation in Mexico City have varied over the year, making difficult the prediction of ubidence effect. Neverthele, auming the preent pumping condition will be maintained in the near future, ueful etimation may be made a to change expected in the exiting microzoning map and the correponding deign pectra. With the information that ha been preented, a year-by-year incremental procedure can be implemented for predicting the evolution of ite period, a follow: 1 For a given ite, the initial dominant period T i taken from fig. 1. By application of eqn. (1), calculate the initial thickne of ediment 1 correponding to T. Then, Calculate the ubidence rate Calculate the amount of compaction a repreent the annual ubidence. i υ by ue of eqn. (2). Calculate the change in thickne of ediment a 1 H H = υ i t, which for t = 1 year H i+1 i = H 1 1 i+ = ( H i+ H. From eqn. (1), calculate the change in ite period a T 31) Replace i by i+1 and repeat the proce for ucceive time tep until the target expoure period i reached. Let u now illutrate the application of the propoed procedure for etimating the change expected in the microzoning map of the city for the next 50 year. Fig. 3 exhibit the modified ioperiod curve by the effect of regional ubidence. The main variation are oberved at the airport, Xochimilco and 2

5 Geo-Environment and Landcape Evolution II 461 Tlahuac area, where long ite period undergo dratic reduction. In contrat, the border between the tranition and oft zone experience little modification. The evolution of ite period can be appreciated in fig. 4 for ite with current value of T = 1 to 5. Figure 3: Modified ioperiod curve by the effect of regional ubidence for a time period running from 2000 to Evolution of eimic hazard The Valley of Mexico i affected by earthquake having different caue. They have been divided in four group, namely: 1) local earthquake, 2) continental plate earthquake, 3) intermediate depth earthquake and 4) ubduction earthquake. For the contribution of all thee event, the expected Fourier amplitude pectrum at firm ground for a 125-year return period ha been etimated with the ue of a tandard probabilitic approach. Thi reult i hown in fig. 5.

6 462 Geo-Environment and Landcape Evolution II Figure 4: Evolution of ite period in Mexico City lakebed zone for a time period running from the 2000 to 2050 year. The ite effect due to local oil condition have been explicitly conidered in the Mexican Building Code [5] after the great 1985 Michoacan earthquake. The reulting ite-pecific deign pectra are defined by the following expreion: 1+ 3Te Ta S a g = c, if Te < Ta, (3) 4 S a g = c, if T T T, (4) a e b r Tb S a g = c, Te > Tb T if. (5) e where S i the pectral acceleration expreed a a fraction of gravity, r = 1 for a the lakebed zone of Mexico City, T a and T b are the lower and upper period of the flat part of the pectrum, repectively, and c i the eimic coefficient. The flat part of the pectrum i pecified by the limiting period T = max( 0.35T,0.64 ), for T >, (6) a 1 T = (7) b T while the eimic coefficient i pecified a 4T c = (8) 4 + T 2

7 Geo-Environment and Landcape Evolution II 463 Thee pectra are intended to cover not only the reonant peak repone aociated with the firt oil period, but that with the econd period a well. Figure 5: Fourier amplitude pectrum at firm ground in Mexico City for a 125- year return period, including the effect of earthquake from different origin. To illutrate the evolution of code deign pectra, a characteritic ite with current value of T = 3.5 wa elected. The hortened ite period reulting for an expoure period of 50 year i een from fig. 4. A comparion between the 2000 and 2050 deign pectra i made in fig. 6. Alo hown are the correponding repone pectra obtained by uing a input motion the Fourier amplitude pectrum of fig. 5. The tructural repone wa computed by applying the random vibration theory [6] to a implified model coniting of a one-tory tructure placed on a uniform tratum under vertically incident hear wave, corrected empirically to account for the bedrock flexibility [7]. Although the repreentation i not perfect, the deign pectrum intend to reproduce the general trend oberved in the repone pectrum, for both preent and future geotechnical condition. It i een that regional ubidence will have either favorable or unfavorable effect on the eimic afety of exiting building, depending primarily on the period ratio of tructure and ite. The peak tructural repone can be conveniently repreented by mean of pectral contour of acceleration expreed in term of the tructure and ite period. In thi way, the maximum repone of any building at any location may be readily etimated. We computed the 2000 and 2050 pectral contour, the comparion of which i hown in fig. 7. They are contructed from ite-pecific deign pectra pecified by the building code throughout the whole city. Each ite pectrum can be recovered by drawing a ection along the ite period of interet.

8 464 Geo-Environment and Landcape Evolution II Figure 6: Comparion between the 2000 (olid line) and 2050 (dahed line) pectra for a ite with preently dominant period T = 3.5 ; deign pectra (thick line) veru repone pectra (thin line). Figure 7: Comparion between the 2000 (thick line) and 2050 (thin line) pectral contour of acceleration expreed a a fraction of gravity. Looking at the current ite pectra, notice that the plateau width i an increaing function of the ite period. Thi i to cover the influence not only of the firt mode of vibration of the oil, but of the econd mode a well (ee fig. 6).

9 Geo-Environment and Landcape Evolution II 465 In fact, the peak repone aociated to the latter may be a large a that aociated to the former for long ite period, ay, T > 3.5. Alo, it i apparent that the plateau height increae with the ite period for T < 2, but decreae for T > 2. Thu, the mot vulnerable building would be thoe with roughly 20 torie, auming a fundamental period of 0.1 per tory. Neverthele, thi i true for the time being but not for the coming year. The difference between the 2000 and 2050 pectral contour reflect the effect of regional ubidence. The 2050 pectral contour tend to rotate counterclockwie and elongate with repect to thoe for the 2000 year. Note that ite with T > 2 will migrate in the future to the region in which pectral ordinate reach their peak value. Figure 8: Subidence impact on eimic bae-hear coefficient: ratio of the 2050 to 2000 pectral contour given in fig. 7. To have a whole cenario for the change expected in the eimic hazard of the city, the ratio α = Sa( 2050 ) Sa( 2000 ) wa computed. Fig. 8 how a general view of the ubidence impact on bae-hear coefficient. Both detrimental ( α > 1) and beneficial ( α < 1) effect are oberved, depending on the period ratio of tructure and ite. For any tructure and ite configuration, the ubidence impact may be aeed directly from thi figure, entering with the correponding tructure and ite period. It can be een that, in general, regional ubidence will affect the tructural eimic afety adverely for T e < T and poitively for T > T. e

10 466 Geo-Environment and Landcape Evolution II 5 Concluion In thi propective tudy, the effect of regional ubidence on the eimic hazard for Mexico City were examined. For an expoure period of 50 year, change expected in the exiting microzoning map and the correponding deign pectra pecified by the building code were aeed. In view of complexity for making an accurate prediction, only approximation were etablihed about the magnitude of ubidence effect. After ome numerical evaluation, the following main concluion can be drawn: a) Long ite period will undergo large reduction (e.g., from T = 5 to 3.25 ), wherea hort ite period will undergo mall reduction (e.g., from T = 1 to 0.95 ). b) Site with dominant period T > 2 will migrate in the future to the region in which pectral ordinate reach their peak value. c) In general, regional ubidence will affect the tructural eimic afety adverely ( α > 1) for T e < T and poitively ( α < 1) for T e > T. The aement of ubidence effect wa made in an environment of high uncertainty, where data may change rapidly from time to time due to local pumping condition. Although the reult are location pecific, the predicting procedure may be applicable to other geographic location facing imilar problem of land ubidence due to ground water extraction. Reference [1] Carrillo N., Influence of arteian well in the inking of Mexico City, Proc. 2nd Int. Conf. on Soil Mechanic and Foundation Engineering, Rotterdam, Holland, [2] Ovando-Shelley E., Romo M. P., Contrera N. and Giralt A., Effect on oil propertie of future ettlement in downtown Mexico City due to ground water extraction, Geofíica Internacional, 42, pp , [3] Aguilar H. R., Galicia M., Pérez-Rocha L. E., Avilé J., Vieitez L. and Salazar M., Effect of regional ubidence on dynamic oil propertie, Proc. 12th Panam. Conf. on Soil Mechanic and Geotechnical Engineering, Boton, USA, [4] Pérez-Rocha L. E., Ordaz M. and Sánchez-Sema F. J., Spatial interpolation of eimic data: the cae of the Valley of Mexico, Proc. 10th Panam. Conf. on Soil Mechanic and Foundation Engineering, Guadalajara, Mexico, [5] MBC, Complementary Technical Norm for Earthquake Reitant Deign, Mexico Building Code, Federal Ditrict Government, [6] Boore D. M. and Joyner W. B., A note on the ue of random vibration theory to predict peak amplitude of tranient ignal, Bulletin of the Seimological Society of America, 74, pp , [7] Avilé J. and Pérez-Rocha L. E., Site effect and oil-tructure interaction in the Valley of Mexico, Soil Dynamic and Earthquake Engineering, 17, pp , 1998.