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247

EVALUATION OF THE RISK OF INDUCED SEISMICITY AT THE I T Z A N T U N H Y D R O E L E C T R I C SITE, C H I A P A S , M E X I C O

A. URIBE-CARVAJAL and E. NYLAND Institute of Earth and Planetary Physics, Department of Physics, University of Alberta, Edmonton, Alta. T6G 2,]1 (Canada) (Received September 20, 1982; revised version accepted July 1, 1983)

ABSTRACT

Uribe-Carvajal, A. and Nyland, E., 1983. Evaluation of the risk of induced seismicity at the Itzantun hydroelectric site¢ Chiapas, Mexico. Eng. Geol., 19: 247--259. Consolidation theory and concepts of rock failure can be used to evaluate the probable risk of induced seismicity as a result of filling of reservoirs. This evaluation indicates the safest way to fill a reservoir, and depends only on the geometry of the load, the rate of filling and the geological structures in the area. The stability function is actually a measure of the risk of having failure, with time, for a particular loading history in respect to a plane of weakness. The stability function is applied to the area of the Itzantun reservoir, which will be in southern Mexico. Drawdowns can increase the risk of triggering earthquakes in this area, which is prone to thrust faulting. It is possible to estimate the stresses after a period during which the water level is maintained and a decrease in stresses with the depth of the observation point. The estimates of the probable induced seismicity are limited as the residual stress in the area prior to the impounding is unknown. With a measure of the residual tectonic stress it will be possible to determine an optimal filling rate to reduce the probability of induced seismicity. INTR ODUCTION D u r i n g t h e last t w e n t y years, it has b e e n o b s e r v e d t h a t large engineering p r o j e c t s m a y c h a n g e t h e characteristics o f t h e seismic events in t h e surr o u n d i n g region. These c h a n g e s are i n d u c e d b y c h a n g e s in stress t h a t are a result o f m a n ' s activities. A m o n g t h e activities and events t h a t cause i n d u c e d seismicity are fluid i n j e c t i o n , fluid e x t r a c t i o n , mining, u n d e r g r o u n d d e t o n a tions, f l o o d i n g , a n d reservoir i m p o u n d m e n t (Packer et al., 1 9 7 7 ) . Here we will deal o n l y with reservoir i m p o u n d m e n t . There are m a n y e x a m p l e s o f w h e r e t h e filling o f reservoirs has c h a n g e d the characteristics o f events in an area. These changes range f r o m t h e i n d u c t i o n o f large m a g n i t u d e events t o c h a n g e s in t h e m i c r o - e a r t h q u a k e activity. The filling o f large reservoirs, h o w e v e r , has n o t a l w a y s r e s u l t e d in i n d u c e d seismicity. A t t e m p t s t o relate i n d u c e d seismicity t o size o r d e p t h o f a reservoir have h a d little success. T h e changes in seismic activity d o n o t f o l l o w 0013-7952/83/$03.00

© 1983 Elsevier Science Publishers B.V.

248 a simple pattern (Gough, 1978). Excellent reviews of the observed changes have been prepared b y Simpson (1976), and Gupta and Rastogi (1976). Induced seismicity is difficult to prove. An increase in seismic activity in areas that were already active is difficult to attribute entirely due to the filling o f the reservoir. In other areas the pattern of seismic events changes radically, and there seems to be an obvious association with the filling of the reservoir. In some areas, there appears to be an increase of seismic activity during the initial filling, whereas in others, the increase occurs some years after filling. There appears t o be a correlation between the water depth and the n u m b e r of earthquakes at some reservoirs (Withers and Nyland, 1978). And there also appears to be a relation to the rate of filling (Simpson and Negmatullaev, 1981 ). The amount of data on reservoir-induced seismicity is limited. Up to 1977, there had been 55 reported cases of reservoir-induced seismicity (Packer et al., 1977). Of these, Packer et al. classify 16 as clear cases, 35 as questionable and 4 as probably n o t reservoir-related. They reach the following conclusions regarding induced seismicity due to reservoir loading. (1) The initial state of stress in the ground is of prime importance. (2) Failure o f unfractured material as a result of reservoir filling is unlikely, but failure is likely to occur along pre-existing faults in fractured material. (3) "Instantaneous" stresses generated b y rapid reservoir filling lead to shear stress along faults without increasing the effective stress. (4) Instability along faults could occur at great depths as shown by the curvature of the failure envelope. The shearing resistance of the material is reduced as the confining pressures increase. There is by no means unanimous agreement a b o u t the existence of reservoir-induced seismicity. Other authorities claim that only 3 clear cases of reservoir-induced seismicity exist. The difficulty is to provide a viable mechanism for failure caused b y reservoirs and to use a convincing stress-strain relation for crustal rock. We believe that the evidence from other reservoirs indicates convincingly that failure can be caused by relatively small external influences (i.e., Raleigh et al., 1976; P o m e r o y et al., 1976; Cook, 1976; Gough, 1978; WetmiUer, 1981). The fact that statistically rigorous observations do n o t exist for reservoirs does n o t deny that reservoirs can induce seismicity; it merely means that seismic evidence b y itself, from reservoirs alone, is n o t sufficient to resolve the matter. Adding, however, the existence of faults on which seismicity is known to occur, the fact that stimulated seismicity has been observed for other kinds of processes, and the fact that a reasonable physical mechanism for reservoirinduced seismicity can be postulated, justifies modelling studies of this problem to determine the range of risk. Any prediction o f seismicity involves assumptions a b o u t the stress--strain relations o f crustal rock and the conditions under which faults will fail. The largest stress increment due to large reservoirs is of the order of 10 bar. Under increment loads of 10 bar most crustal rocks deform elastically. Of course the incremental response of a rock confined under 103 bar at 10 km

249 depth m a y be different from that o f a rock at the surface, b u t its elastic nature remains due to the small size o f the stress increment. Therefore, the assumption o f elastic behaviour is plausible. The variation o f elastic behaviour can be deduced from seismic data. Young's modulus deduced from seismic data for depths from 0 to 25 km varies from 6 . 1 0 s to 8. l 0 s kg cm -2. This variation is small compared with its magnitude. Hence, the assumption that the elastic properties are constant is reasonable albeit n o t entirely satisfactory. Other authorities (i.e., Turcotte, 1974; Kirby 1977) have considered the upper 25 km of the lithosphere to be elastic. Obviously water pressure plays a crucial role in the dynamics near a reservoir. The simplest extension of elasticity theory that takes into account the presence of water is the Biot consolidation theory. It is normally applied to soils and is justified here only b y the fact that it is a simple tractable extension which can deal with the presence o f pore fluids in a plausible way. It m a y n o t be correct, b u t at these relatively low pressures it is a reasonable first approximation. The general conclusion from the observation of induced seismicity is that reservoir volume is not always a reliable indicator of the risk of induced seismicity. The larger the volume, the greater the probable risk, b u t there is always the potential for suprises such as were encountered at Hydro-Quebec in Canada (Leblanc and Anglin, 1978). Manicougan 3 on the Canadian Shield caused seismicity changes while the nearby Manicougan 5, twice as deep and with a considerably larger volume, has n o t induced any seismicity. Manicougan 3 has a height of 108 m and its volume is 1.04" 101° m 3. In only a few cases have the depths of these seismic events been determined accurately. Local observations and the teleseismic data all indicate that the hypocentres are shallow. Gupta et al. (1972) have determined the depths and positions from the events at K o y n a from a local array, and found that the majority of the events occurred at a depth of less than 10 km, but some occurred as deep as 30 km. Migration of seismic events has also been observed in some reservoirs. Simpson (1976), Soboleva and Mamadaliev (1976) and Simpson and Negmatullaev (1981) indicate that the events at Nurek are migrating toward the reservoir. The focal mechanisms (Bufe et al., 1976; Gough and Gough, 1976; and others) observed that different reservoirs are consistent with the types o f preexisting faults in the neighbourhood. At Kariba, Kremasta and Oroville, dip-slip faulting was observed, while at Koyna, Hsinfenkiang and Hoover, the mechanism was strike-slip faulting. At Nurek the induced seismicity is occurring along a series of thrust faults connected b y short segments that show strike-slip motion (Simpson and Negmatullaev, 1981). Simpson (1976), Bell and Nur (1978) and Withers and Nyland (1976) suggest that rapid lowering and raising of the water level m a y be an important factor in inducing seismicity in regions o f thrust faulting. The magnitudes o f the main shocks near reservoirs have been as high as

250

6.5 at K o y n a (Gupta et al., 1972), 6.3 at Kremasta (Comninakis et al., 1968), 6.1 at Hsenfengkiang (Wang et al., 1976). It is not possible to give an upper limit for the magnitude o f induced earthquakes, as the filling of reservoirs acts only as a trigger of the preexisting stress. THE I T Z A N T U N SITE

The Itzantun site is in the state of Chiapas in the southern part of Mexico, 120 km NE of the city o f Tuxtla Gutierrez (Fig.l). It is in a region with several rivers, the most important o f which are the Tlacotalpa, the San Pedro and the Huitupan. The Tlacotalpa flows in the Itzantun gorge, and at this location the flow is 2.106 m a of water per year. The geologic formations in the area are chiefly thick assemblages o f mudstones and massive limestones. The foundation o f the Itzantun dam will be sandstone, mudstone, and limestone which appears reasonably homogeneous, at least at the surface. Many fractures in the formations near the dam have been filled with calcite but some are open and show evidence of recent movement of the order of centimetres. The Itzantun fault crosses the reservoir just upstream from the dam and 19"

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251 is clearly the significant structural feature in an analysis of the risk of induced seismicity (Fig.2). The gorge itself was not developed along a fault zone. The irregular directional changes o f the river, and the fact that no fault breccia was found in a borehole slanted to go under the gorge, indicate that the river has eroded along minor fractures and joints. Nevertheless the strike o f the river is along a potential failure plane. (The k n o w n faults in the area are approximately at right angles to the strike of the river.)

M O D E L STUDIES As a firstapproximation it is possible to model the problem as consolidation of a water-logged half space. Our computer programs for two- and three~limensional analysis treat the modelling problem by considering the earth to be a uniform, isotropic half-space consisting of an elastic matrix affected by fluid under pressure. This material is characterized by a single permeability, a relative fluid matrix compressibility, a coupling factor (or hydraulic tmnsmissibility) for the bottom of the reservoir, and two elastic moduli. The reservoir load can be approximated as a "long" two

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252 Withers and Nyland (1978). They point o u t that the incremental stresses due to a reservoir are rarely large enough to cause failure by themselves. The potential for failure must exist and may be triggered by the reservoir. S T R E S S E S IN P O R O U S M E D I A

The definition of stresses in porous media meets with certain difficulties, but some heuristic theory has been developed to deal with these stresses. Terzaghi ( 1 9 5 1 ) p r o p o s e d that stresses in porous media are a "neutral stress", the stress in the fluid, and an "effective stress", the difference between the total stress prevailing in the fluid-filled media and the neutral stress. It is the effective stress that causes deformation (Scheidegger, 1974). Biot (1941) suggested that the compaction o f softs is caused by a pheno m e n o n called "soil consolidation". This means that the settlement is caused by the gradual adaptation o f the soil to a load variation. Biot made the following assumptions: (1) isotropy of the material; (2) linear stress--strain relations; (3) the strains in the media are small; (4) the water contained in the pores is incompressible b u t may contain air bubbles; and (5) the water flows through the porous skeleton according to Darcy's law. With these assumptions, Biot developed the theory for the consolidation of porous media; the basic relations that describe the p h e n o m e n o n are given by Biot in a series of papers published since 1941. Little has changed in this theory since then (Rice and Cleary, 1976). In order to approach the consolidation problem outlined earlier, we have followed the technique described b y Withers and Nyland in their series of papers (Withers and Nyland, 1976, 1978; Withers, 1977). In order to solve the consolidation equations, use is made of the displacement functions of McNamee and Gibson (1960). This implies the development of a procedure to allow us to determine the double Fourier and Laplace transforms of the water load. The Fourier transforms are done by using the Advanced Mathematical Library of the array processor (AP-190L), which allows the whole computation to be overlapped with data-access time. This permits us to deal with the two-dimensional transforms o f the load at a given time as a vector and determine the change of the stresses up to that time. Once the values o f the transforms of the stresses at the desired location corresponding to each o f the times of the known load history are determined, we have the information necessary to construct a curve for which inverse Laplace transform will give the behaviour o f one of the components of stress at any time. From these components, a failure criterion and an assumption a b o u t the orientation of a plane o f weakness, we calculate estimates of stability o f a point in the formation. The inclusion of several segments in the loading history curve is done by applying the superposition principle Thus after the inverse Fourier transform is performed in the AP for a given c o m p o n e n t of stress, the resulting values at some X, Y, Z, are the Laplace transform in discrete form of the change in time of one c o m p o n e n t of stress. The result is a function o f time, which defines the way a point in the formation moves towards, or away from, failure.

253 FAILURE CRITERIA

In the Mohr's circle representation in three dimensions, the normal and shear stress across a plane o f weakness whose normal has director cosines l, m, n, are given by Jaeger and Cook (1979,p.27). Fixing two of the direction cosines (say n and l) two equations can be obtained. Each of t h e m represents one family of Mohr's circles in two dimensions and for a fixed value of the corresponding direction cosine each represents a unique circle. Therefore, by fixing n and l, t w o circles can be drawn such t h a t their intersection will lie at a point on the surface of a three-dimensions Mohr representation, and will be a unique location for these two circles whose centres are at (ol + 02)/2 and (02 + a 3 ) / 2 and whose ratios are A C and BD, respectively, as shown in Fig.3. With the previous procedure it is possible to determine the values of o and T for every combination o f stresses. That is, the location of point P can be determined for any time. A simple failure criterion is t h a t of Coulomb (Fig.3) which suggests that failure occurs when the shear on a failure plane exceeds 7 =So + a n t a n a

where r is the shear strength of the rock, a is the angle of shear resistance; o n is the normal effective stress on the plane of fracture; So is the apparent cohesion and is the shear strength of the material under zero normal pressures. So ranges considerably from zero in a fractured material to several hundreds of bars in an intact material (Withers, 1977). In Itzantun, fractures are present and So is probably small. If a lies between 25 ° and 45 °, then the coefficient o f friction is between 0.47 and 1.0 but it is usually around 0.6 (a = 30°). As the value o f So is u n k n o w n , we set it to zero. Now the variation of the m i n i m u m distance between the failure envelope and t h e point P, defines the changing stability o f the system. By fixing the angles 0 and ~b, the plane of weakness of the material is determined. The variation with time of the distance between the corresponding

T

Fig.3. Definition of the STABILITY function as the distance between P and the failure envelope.

254 point P on the surface of the Mohr's circles and the failure envelope will result in a " S T A B I L I T Y " history for a given location of coordinates X, Y, Z. This stability history can be represented as a curve in a stability value vs time diagram and we refer to this curve as the stability function. The stability function depends only on the loading history, the known geological structures (that will determine the angles 0 and ¢ ), and the geom e t r y or the bathimetry of the lake. Stability has been defined as a function proportional to the minimum distance between the failure envelope and P. The use o f a Coulomb failure criterion implies that the rocks will behave in an elastic way and that fracture will occur in a brittle way. Although rocks behave in a more complicated way, the assumption of elastic materials is often made in geophysics; Solomon et al. (1980) and many others have suggested that the upper few tens o f kilometres of the earth's crust can be treated as elastic materials. Turcotte (1974) determined that the upper b o u n d for this pseudo-elastic behaviour is 300°C; this temperature is well above that expected at the depths we consider here. Assuming Mohr-Coulomb failure is consistent with the assumption that the incremental stresses cause elastic deformation, particularly near failure. The assumption of brittle failure may not be true for all faults, but it is a reasonable, tractable hypothesis. We acknowledge that the treatment of the earth as a porous half-space consisting of an elastic matrix saturated with water is a simplistic model. However, the stability functions are relative, and only serve as indicators of h o w the risk of inducing seismic activity is changing with respect to a reference initial value. DISCUSSION O F R E S U L T S

We a t t e m p t here to evaluate the risk of induced seismicity in a qualitative way. In order to do this we have made and justified as far as possible a number of assumptions. (1) In the upper 25 km of the earth incremental stress changes cause an elastic response and failure occurs according to a Mohr-Coulomb failure criterion. (2) The in-situ stresses are such that small increments can cause failure. (3) The effect c f water can be modelled b y the Biot consolidation theory. (4) A uniform half-space is a reasonable approximation to reality. (5) The geologic estimates of fault orientation define the location and direction of expected failure. Intact rock will not fail under reservoir-induced loads. With these assumptions the results shown in Figs.4--7 were obtained. Figs.4 and 5 represent the stability function for t w o loading histories consisting of m o n o t o n e increasing loads, to a constant load. Both have been calculated for a point beneath the deepest part of the reservoir at a depth of 1 km and show the relation o f the resulting stress to the rate of fiUing. For the curve where the complete load is reached 16 years after the beginning o f

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Fig.4. The upper graph shows a loading history consisting of a continuously increasing exponential, where the total load is reached after 2 years of loading. The b o t t o m graph shows the stability function corresponding to a point below the deepest part of the reservoir at 1 km depth. Fig.5. The upper graph shows a loading history consisting of a continuously increasing exponential, where the total load is reached after 16 years of loading. The b o t t o m graph shows the stability function corresponding to a point below the deepest part o f the reservoir at 1 k m depth.

the impoundment, the increase in stress is much smaller than when the total load is reached after 2 years. Fig.4 also illustrates that when the load is kept constant for a certain time period, the stresses begin to decrease to a limiting value. This means that the effect of the anomalous stress produces changes that lead to an equilibrium state that does not necessarily have to be the initial state o f stress in the area. This can be thought of as related to the existence of residual stresses. The non-linear dependence o f the risk function on the rate of filling is shown in Table I. This table shows the value of the stability function 20 years TABLE I Variation o f the stability function for different rates of filling o f the reservoir, the time required to attain complete filling for each o f the loading histories considered, and the m a x i m u m and final value observed for the stability curve during each o f these cases Duration of

Stability function in bars

loading (years)

Max. value Attained

Time (years)

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Value after 20 years

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256

after impounding was begun and the maximum value attained during that period. This is done for a location at 1 km beneath the deepest part of the Izantun reservoir. The loading histories used to obtain this table are as follows, where T is the time at which the lake was first completely filled, and D is the m a x i m u m depth o f the reservoir. After .25 T the reservoir had water up to .45 D. After .5 T it had .75 D. At .75 T it was .9 D full. From the time T the reservoir remains filled. It is obvious that a peak in the stability function has been reached during this 20 years interval only for the first case of Table I. With a faster rate of filling the risk of reaching failure is higher; for the first case the risk increases sharply, it reaches its maximum value 2 years from the beginning of the filling o f the reservoir and then it decreases to a value of a b o u t .9 bar and remains constant. The rate of filling o f the reservoir is not the only way in which artificial lakes could change the seismic activity of an area. Some changes have been observed after filling and draining the reservoir, like in the case of Oroville, CA, where an event o f magnitude 5.9 occurred after this kind o f loading history (Withers, 1977). In order to see the effect of draining of a reservoir on the stability function, we applied the loading history shown in Fig.6. This example shows that the stability function for unloading tends to have a second minimum, in this case after 8 years. The effect o f a fast decrease in the value of the stability function must generate sudden changes in the stresses that might trigger seismic events. Other histories involving reduction of loads show that if lowering the water level is done rapidly, the negative slope o f the stability function moves toward a horizontal position. This reduces the risk over a thrust fault but increases it for a normal fault, as the values in the latter part o f the stability curve are much bigger. Decrease in loads in the loading history result in a stability decrease that attenuates rapidly with the depth of the observation point. For a depth o f 4 km the effect is n o t observed at all (Fig.7). CONCLUSIONS

Why the filling of some reservoirs causes seismic events is poorly understood. We give no firm predictions for Itzantun. Studies indicate residual stresses, differences in permeability, and differences in physical properties of the formations under the reservoir may determine whether there is induced seismicity risk or not. None o f these factors are known with precision at Itzantun. The changes in stability in a water reservoir due to the presence o f the water can be predicted in a qualitative way by assuming: (a) a model o f a porous half-space consisting o f an elastic matrix saturated with water, (b) that brittle failure can occur in the upper 10 km o f the lithosphere if small stress changes are made, and (c) that the effect of water in rocks can be approximated with Biot's consolidation theory.

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Fig.6. The upper graph shows a loading history in which an unload takes place in the interval from the second year o f loading until the third one, after which the increase in load is continued until the fourth year when the total load is attained. The bottom graph shows the stability function corresponding to a point below the deepest part of the reservoir at 1 km depth. Fig.7. The upper graph shows the same loading history as that of Fig.6. The bottom graph shows the stability function corresponding to a point below the deepest part of the reservoir at 4 k m depth.

We suggest that to diminish the risk o f induced seismicity at Itzantun, the filling of the reservoir should be as slow as economics permits, with intervals at which the water level is held constant. ACKNOWLEDGEMENTS

We are grateful to the Instituto de Ingenieria from the Universidad Nacional A u t o n o m a de Mexico and to the Comision Federal de Electricidad of Mexico for the support given in the first stages of this work. We are particularly grateful to J. Havskov and S.K. Singh for many valuable discussions. A. Uribe-Carvajal is supported at the University of Alberta by the Consejo Nacional de Ciencia y Tecnologia (CONACYT) of Mexico. This research was supported by the Natural Sciences and Engineering Research Council (NSERC} of Canada. REFERENCES Bell, M.L. and Nur, A., 1978. Strength changes due reservoir pore pressure and stress and application to lake Oroville. J. Geophys. Res., 83: 4469--4483. Biot, M.A., 1941. General theory for three dimensional consolidation. J. Appl. Phys., 12: 578--581. Bufe, C.G., Lester, F.W., Lahr, K.M., Lahr, J.C., Seekins, L.S. and Hanks, T.C., 1976. Oroville earthquakes: Normal faulting in the Sierra Nevada foothills; Science, 192: 72--74.

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