NUMERICAL MODELS FOR SEISMIC RESPONSE OF “EL BUEY” DAM Puentes, José1 ; Rodríguez, Lucía2 and Rodríguez, Edgar3 1

Civil Engineer, Geotechnical Sp, Project Manager INGENIERÍA Y GEORIESGOS, Bogotá D.C. e-mail: [email protected] 2 Civil Engineer, MSc Geotechnical Engineering, Bogotá D.C. e-mail: [email protected] 3 Civil Engineer, MSc Geotechnical Engineering, Earthquake Engineering Sp. Manager INGENIERÍA Y GEORIESGOS, Bogotá D.C. e-mail: [email protected] ABSTRACT The “El Buey” dam is located at 45Km of Medellin in the NW of Colombia, placed in an area of high seismic activity. This dam is part of the main water supply system of the city. The “Study of seismic vulnerability of El Buey dam", was developed and included analysis of instrumentation records, local geological study, seismic hazard evaluation with EZ-FRISK v6.2 software and subsoil exploration. Static and dynamic laboratory test and numeric analysis were made for evaluation of seismic response of the dam with QUAD4M and PLAXIS V8.1. In this paper, a summary of the executed activities is presented. Keywords: earthdam, FEM, seismic hazard, seismic response, dynamic numerical analysis

1

Introduction

The embankment is part of the supply of water and energy system for Medellin city, and the Aburra valley. Regionally, the dam is located into the West Rock Mass of Antioquia. The dam is an earth structure, compacted, with 75000 m³, it has maximum height of 26m from the bottom of the cutoff trench and 23m from the channel of the river El Buey. The crest has 47m of length and 8m of width. The slopes are 3H:1V in the upstream side, while in the downstream side they are 2.5H:1V. The major transversal section is shown in Figure 1. ROCKFILL

GRANULAR SOIL

SEDIMENTS

WEATHERING WEAK ROCK FILL

WEATHERING WEAK ROCK FILL ROCA DESCOMPUESTA

HARD ROCK FILL

HETEROGENEOUS FILL

Figure 1 Major transversal section of El Buey dam The upstream slope is protected by rip rap placed on a granular bedding layer. The rip rap is situated between the levels 2053msnm and 2044msnm. The downstream slope is 2.5H:1V, too. To prevent the seepage through the foundation, in the design phase conceive a cut-off trench in the base of the dam. The earthdam was build with 6 principal types of materials: i) sandy silt or silty sand, constitute the principal volume of the dam; below crest of dam. This material extend among levels 2053msnm and 2030msnm ii) “upstream weak rock” fill that correspond to sandy silt that enclose boulders and constitute the upstream slope between the crest and the 2044msnm level ; iii) “downstream weak rock” fill similarly to previous, but it extends between the levels 2053msnm and 2038msnm in the downstream side iv) “hard rock” is a boulders and pebbles in a silty matrix situated in the base of the dam, in the downstream side, below “downstream weak rock” v) heterogeneous fill places in the downstream side at the level 2038msnm vi) foundation rock, is a fractured granitic mass.

2

Instrumentation Analysis

In the dam an instrumentation system formed by 13 pneumatic piezometers, 12 surface landmarks, and finally 9 vertical movement devices has installed. Only the first and second type of instruments is functioning. The historical records of water pressure into the dam not show relation with the variation of embankment level, because the level is controlled by open the sluice of derivation tunnel, to prevent the occurrence of flood. In spite of this, it can be establis hed a habitual operation level for the analysis: 2045msnm, although the level of water range between

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2044msnm and 2046msnm. Along with this, and trough statistical study of records of pressure, it was possible determine the position of piezometric surface. About surface landmarks, this indicates little movements in the last ten years. The horizontal displacement is less than 0.02m, and the settlement too. Only in the left abutment, the movement of the superficial weathering soil is greater than 0.10m. About to monitoring with vertical movement devices, the measurement was realized after construction of dam, between 1984 and 1986. The records show that internal deformations of dam vary between 0.12m and 0.18m among the levels 2053msnm and 2028.6m. To depth of 25m, the settlement measured was of 0.25m.

3

Subsoil Exploration And Dynamic Characterization

This stage of study included two conventionally types of exploration: i) direct exploration by execution of perforations and ii) indirect exploration or subsoil geophysical investigations that consist in refraction and downhole tests. During direct exploration, 8 mechanic drilling, and 3 test pits was realized. Figure 2 summarizes the soil profile with SPT and Vs in the S4 boring –below crest of dam-. In the sandy silt soil, the SPT varies between 20 - 40 blows/ft. The foundation rock shows rejection to penetration. Additionally, percolation tests were developed. About of indirect exploration, 4 down-hole tests and 5 seismic refraction lines tests were executed. The down hole tests measured shear wave velocity, Vs, varying among 200m/s to 400m/s in sandy silt. (Figure 2). With respect to dynamic characterization of materials, shear modulus reduction curves were developed from results of in-situ and laboratory test for each one (Figure 3). Additionally, damping ratio reduction curves also performed (Figure 4).

4

Geologic Study

The geologic environment corresponded to metamorphic and intrusive igneous rock, affected by numerous systems of geologic faults. Granodiorites with local facies of quartzmonzonite and tonalite, from Stock of El Buey outcrop in the dam site. Although, the rock mass shows high degree of fracturing due to tectonic activity or gravitational processes, there are not evidences of neotectonic activity. SPT (blows/ft) 0

Vs (m/s) 50

0

500

1000

0

5

Depth (m)

10

15

20

25

30

Figure 2 Profile of SPT and velocity Vs into dam

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25

1.0

0.9

FRACCIÓN DE AMORTIGUAMIENTO CRÍTICO D (%)

0.8

0.7

G/G max

0.6

0.5

0.4

0.3

0.2

20

15

10

5

0.1

0.0 0.0001

0.001

0.01

0.1

DEFORMACIÓN POR CORTANTE

1

10

0 0.0001

γ (%)

0.001

0.01

0.1

DEFORMACIÓN POR CORTANTE

S4 - M3 LL= 31.7 IP=14.4 30KPa (EB) S2-M1 LL=28.9 IP= 5.2 60KPa (EB)

S4 - M11 LL= 32.2 IP= 12.6 100KPa (EB)

S6 - M5 LL=36.3 IP=13.7 60KPa (EB)

S5-M4 LL=30,5 IP= 5,4 100KPa (EB)

Figure 3 Modulus reduction curves

5

1

10

γ (%)

S4 - M3 LL= 31.7 IP=14.4 30KPa (EB)

S6 - M5 LL=36.3 IP=13.7 60KPa (EB)

S2-M1 LL=28.9 IP= 5.2 60KPa (EB)

S5-M4 LL=30,5 IP= 5,4 100KPa (EB)

S4 - M11 LL= 32.2 IP= 12.6 100KPa (EB)

Figure 4 Variation of damping ratio with cyclic shear strain

Seismic Hazard Study

For obtain design acelerograms, a probalistic analysis of seismic hazard was realized with the software EZ-FRISK v6.2 (Risk Engineerign, 2004). Exceedance curves for different periods was determined: T=0.0s, 0.1s, 0.2s, 0.6s, 1s and 2s. Based on it, Romeral fault was determined like fault with greatest influence of seismic hazard (Figure 5). The subduction sources participation growths when the return period increases. For verify that accelerograms were recorded on rock, Nakamura criterion was used, and Fourier criterion for review spectral forms was utilized. Finally, four accelerograms of near source was selected: Cordoba (Colombia, 2002) - Calarca station, Quindio (Colombia, 1999) Pereira station, Chi Chi (Taiwan, 1999) Ilan Station, and Northridge (USA, 1994) Burmbank station. For subduction source, Calima (Colombia, 1995) Calarca station, and Sipi (Colombia) Cala rca station were chosen. Respective response spectrums are shown in Figure 6. ESPECTROS TR= 2500 AÑOS 1E+00 1.1 1

1E-01

Promedio Chi - Chi Taiwan Ilan N-S Quindio Bocatoma E-W

0.8

1E-02 ACELERACION (a/g)

FRECUENCIA DE EXCEDENCIA

0.9

1E-03

Córdoba Calarca N-S Sintético Northrigde Burbank 330 Sintético Calima NS_0.15

0.7 0.6

Sipí NS_0.15 0.5 Calima NS_0.20 Sipí NS_0.20

0.4

1E-04 0.3

PGA

0.2

1E-05 0.01

0.1

1

10

0.1

ACELERACION PICO DEL TERRENO (a/g) 0

Ambraseyes (1996)

Sadigh (1997)

Campbell (1997)

Abrahamson-Silva (1997)

Boore-Joyner-Fumal (1997)

Promedio

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

PERIODO (seg)

Figure 5 Exceedance curve for T=0.0s

Figure 6 Response spectrum for return period Tr=2500years

The attenuation relationships used were: Abrahamson-Silva (1997). Boore et al (1997), Sadigh (1997) and Ambraseys (1997). The analysis were made for 3 different periods of return: 200 years (DBE), 500 years (MPE), and 2500 years (MCE), and the PGA values were 0.138g, 0.188g and 0.302g, respectively (Figure 7).

6

Response Dynamic

The objective of this phase was determination of accelerations and deformation owing of seismic excitation. Two different methodologies of numerical analysis were used by granted the objective, by means two FEM commercial software (QUAD4M and PLAXIS v8.1). Two transversals sections of dam were analyzed.

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0.8

0.7

Ambraseyes (1996) Sadigh (1997) Campbell (1997)

0.6

ACELERACION (a/g)

Abrahamson-Silva (1997) Boore-Joyner-Fumal (1997)

0.5

Promedio

0.4

0.3

0.2

0.1

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

PERIODO (seg)

Figure 7 Uniform hazard response spectrum for MCE 6.1

QUAD4M One of the used meshes (major section) is shown in Figure 8. Due that the QUAD4M processing time is less of PLAXIS processing time , QUAD4M was taken as it bases to choose the significant and representative events , considering maximum accelerations generated. The average amplification factor –defined like the relation between the maximu m acceleration in the dam and the acceleration on rock- was 2.2. The maximum shear strain during the earthquake for the DBE, are smaller to 0.15%; for the MPE, minor to 0,2% and for the MCE oscillates between 0,1% and 0,5%, that values allows to conclude that after the earthquake occurrence, would not be reached plastification state. The displacements calculated from the double integration of accelerograms, saved the limitations of the methodology of Seed (1975), were used to generate the set of possible deformations of the dam (several points, earthquakes, sections, periods of return, etc). Data allowed to identify orders of magnitude, size of deformations in the dam body and relationships between the derived consequences of the different earthquakes (Figure 9): The displacements increase from the base of slopes towards the center and from the inferior levels towards the crest. For major section the displacements do not exceed 0.20m, the highest values (between 0.05 and 0.20m) are reached about the nodes located in the upstream slope, after a MCE events; although, DBE and MPE show almost null deformations. For the downstream slope, the displacements are despicable too (smaller to 0.05m). The representative events of the subduction source, in spite of being most frequent in Antioquia, display very small displacements (<0.01m) for the major section. The numerical results of displacements in which Gmax was assigned as function of Vs - down hole test, are more conservative than those of the method of the octahedral stress.

Figure 8 FEM grid used for response analisys QUAD4M 6.2 PLAXIS V8.1 With this software, a hardening soil model was utilized for simulation of stress-strain behavior. The analysis was made, below undrained conditions using FEM. The discretization of major section of analysis is shown in Figure 10. Initially, a static revision of dam behavior was developed, with order to fix geomechanics parameters to real performance of earthdam. To model the groundwater condition, in a first step, horizontal and vertical coefficients of hydraulic conductivity were fixed, using as initial values, the results of percolations test. In next stage, a seismic excitation in form of accelerogram –that was obtained of seismic hazard study- was applied in the base of the FEM models. Additionally, lateral borders of model was fitted with viscous law in order to prevent stress wave reflection.

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To model natural damping of materials, Rayleigh damping coefficients were used; owing PLAXIS v8.1 can’t simulate shear modulus degradation with cyclic shear strain. These coefficients were fixed to obtain accelerations and comparables response spectrums with QUAD4M results that are shown in Figure 11. The maximum horizontal acceleration of response occurs in downstream slope (0.67g), while in the crest is 0.60g and 0.56g in the upstream slope. 30

Desplazamiento (cm)

Tr Sismo

25

a) SBO - Sis 1 a) SBO - Sis 2 20

a) SBO - Sis 3 a) SBO - Sis 4 b) SMP - Sis 1

15

b) SMP - Sis 2 b) SMP - Sis 3 b) SMP - Sis 4

10

c) SMC - Sis 1 c) SMC - Sis 2 c) SMC - Sis 3

5

c) SMC - Sis 4

0 dh

oc

Node 811X

dh

oc

Node 773X

dh

oc

Node 712X

dh

oc

Node 638X

dh

oc

Node 489X

A. Arriba

dh

oc

Node 438X

dh

oc

Node 385X

dh

oc

Node 335X

A. Abajo Sec 1

Figure 9 Permanents displacements - QUAD4M

Figure 10 FEM grid used for response analisys PLAXIS

Horizontal Acceleration (g)

About to displacements, in the major section, the maximum displacement occurs on the downstream slope, with magnitude range between 0.08m and 0.45m. On the crest, the displacement varies among 0.05m and 0.20m. These events no implicate a loss of free board and no affect normal operation of the embankment. In the minor section, numerical analysis show displacement varying between 0.10m and 0.20m on the downstream slope while in the crest the movement is 0.03m. (Figure 12). Respect to shear strains, for an analysis period of 2500 years; these vary between 2% and 6% on the major section, and 12% in the minor section. 0.70

Crest Upstream slope

0.65

Downstream slope

0.60 0.55 0.50 0.45 0.40 MCE1

MCE2

MCE3

MCE4

Seismic event

Figure 11 Horizontal response acceleration for MCE events

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Figure 12 Deformations for an SMC event - PLAXIS

7

Conclusions

During the project, various stage was developed: an historical record of monitoring revision, geologic and tectonic study, seismic hazard evaluation, subsoil exploration what included drillings and geophysics test, static and dynamic laboratory test, geomechanical characterization, numerical analysis with QUAD4M and PLAXIS v8.1. After the seismic hazard evaluation, four Colombian and two international accelerograms was selected, holding similitary with the hazard spectrum and reproducing the earthquake sources. Based on results of both numerical analysis, the study determined that maximum deformations and accelerations would occur on downstream slope due and MCE event (Tr=2500 years). Free board would suffer a diminution less 1.0m without risk of overwhelming. Additionally, on the upstream slope take place deformations also less 1.0m. These results show that minors preventive works are necessary for granted the dam stability when the earthquakes occur.

8

Acknowlegments

We have to acknowledge to Emp resas Publicas de Medellin by permit the publication of the results of the study of seismic actualization of the El Buey Dam.

9

References

Ambraseys N., Simpson K. and Bommer J. 1996. “Prediction of horizontal response spectra in Europe”. Earthquake engineering and structural dynamics. Vol. 25, 371-400. Boore D., Joyner W. and Fumal T. 1997. “Equations for estimating horizontal response spectra and peak acceleration from western North American earthquakes: a summary of recent work”. Seismological research letters. Vol. 68, number 1. Campbell K. 1997. “Empirical near-source attenuation relationships for horizontal and vertical components of peak ground acceleration, peak ground velocity, and pseudo-absolute acceleration response spectra”. Seismological research letters. Vol. 68, number 1. Cornell, C.A. (1968), Engineering seismic risk analysis. BSSA, Vol.58, No.5, 1583-1606. HMV Ingenieros Ltda (2004). Estudio de actualización sísmica de la presa La Fe. INTEGRAL, Ingenieros Consultores (1998) Estudio de evaluación de la Presa Santa Rita. Actualización del estudio de sismología. INGEOMINAS (1999), Catalogo de Sismos de Colombia para estudios de amenaza sísmica 1566-1998. INGEOMINAS, Bogotá, 1999. INGEOMINAS (1999), Base de datos de fallas activas en Colombia. INGEOMINAS, Bogotá, 1999. INGEOMINAS (2001-2003), Catálogos de movimiento fuerte. INTEINSA – MEJIA Y VILLEGAS Evaluación de la Amenaza Sísmica de la Estación Primavera, Medellín (2004) Kanamori, H. (1977), The energy release in great earthquakes, J. Geophys. Res. 82, 2981-2987. Lay T., and Wallace T.C. (1995), Modern Global Seismology. Academic Press, San Diego, CA., 1995. Reiter L., Earthquake Hazard Analysis, Issues and Insights (1990). Columbia University Press, New York. 1990. Sadigh K., Chang C., Egan J., Makdisi F. and Youngs R. 1997. “Attenaution relationships for shallow crustal earthquakes based on California strong motion data”. Seismological research letters. Vol. 68, number 1. Wells D.L., and Coppersmith K.J. (1994). New empirical relationship amo ng magnitude, rupture length, rupture width, rupture area, and surface displacement. BSSA, Vol. 84, No. 4, pp. 974-1002.

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