Largest Aftershock for Dam Design and Safety: Delay and Induced PGA Likelihood Bachir Touileb ARTELIA GROUP (ex-SOGREAH), 6, rue de Lorraine, 38130 Echirolles, France E-mail:
[email protected]
Summary Earthquake aftershocks are of particular importance, especially during the hours and days following the occurrence of a strong earthquake. Although most modern dams are designed to resist major earthquakes, there is evidence in favour of establishing a framework to understand the natural hazard posed by aftershocks: a natural hazard that could strike within hours or days after the mainshock, as indicated by field observations. A strong mainshock could induce pore-water pressures in earthdams, modify the water uplift pressures and disrupt the drainage system of concrete dams, and potentially decrease the initial factor of safety before the occurrence of the largest aftershock. For dam design and safety purposes, the Probabilistic Magnitude-Distance-Time (PMDT) model, proposed hereafter, can be used to evaluate the largest aftershock scenarios, such as time of occurrence and peak ground acceleration (PGA) at the dam site. The model is inherently bounded, meaning that not all scenarios are possible. Indeed, it is found as the probability becomes lower, the time of occurrence of the largest aftershock is earlier, and its PGA is higher.
Introduction Aftershocks resulting from large earthquakes pose a significant hazard, a fact that was highlighted by the damaging aftershocks that occurred following the 1999 M7.4 Izmit (Turkey) and M7.6 Chi Chi (Taiwan) earthquakes [30]. Recent earthquakes such as the 2011 M7.1 Canterbury (NewZealand), the 2012 M6.0 Emilia Romagna (Italy) and the 2012 M6.4 East Azerbaijan (Iran) were also very informative in terms of aftershocks. It is found that aftershocks become the central issue, and are feared as one of the most undesirable natural hazards, only once a dam has already been shaken, or damaged, by a strong earthquake.
The PMDT model (Probabilistic Magnitude-Distance-Time of the largest aftershock), presented herein, can be used to evaluate all possible scenarios of time of occurrence and peak ground acceleration (PGA) at the site.
Laws governing aftershocks Aftershocks are governed by three mathematical relations. The first is the Gutenberg-Richter relation (1954) [12] which states that larger magnitude earthquakes are less frequent than lower magnitude events. The second is the (MOL) modified Omori law [18]-[26] which states that aftershock frequency decreases by approximately the reciprocal of time after the main shock. Recent work by an international team of researchers [17], using the most recent worldwide catalogues has led to the development of the band-limited power law model (LPL), and compared it advantageously to the MOL. The third relation is Båth’s rule (1965), which states that the largest aftershock is, on average, 1.2 units of magnitude smaller than the main shock [3].
Magnitude of the largest aftershock Based on Båth’s law, the magnitude of the largest aftershock is commonly accepted, at least in comparison to the other two unknowns (location and time of occurrence of the largest aftershock). It states that the magnitude of the largest aftershock is M=1.2 lower than the mainshock magnitude. Recent research work, [13]-[22], reviewed this rule, raising a number of relevant observations regarding its field of application, but retained its validity for general purposes. For instance, it was found that for reverse faults the M of largest aftershock is on average greater than that of strike slip events, all being independent of magnitude [22].
Time of occurrence of the largest aftershock As far as dams are concerned, the time of occurrence of the
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largest aftershock is certainly the most important issue. In the particular case of embankment dams, the mainshock may have induced pore water pressures that need a certain amount of time to dissipate. Hence, the earlier the largest aftershock, the higher is the vulnerability of the dam.
Indian catalogue [6] The time of occurrence and magnitude of the largest aftershock in relation to the mainshock have been studied for the Indian subcontinent and neighbouring regions based on USGS data collected during the period 1963–1971. The largest aftershock occurs within 2 hours (0.083 day) after the mainshock in about 50% of the cases, and the frequency of occurrence n(t) of the largest aftershocks decreases hyperbolically with the interval t after the main event: n(t)=A t–h, where A and h are constants. The results of this study showed that the largest aftershock could occur very early after the mainshock. Worldwide catalogues [22]-[23] In general, the time of occurrence of the largest aftershock is found to be characterized by a large scatter. For all types of faults, the average time is found to be about 50 days. However, the median time is found to be much lower, in the region of only a few days. Indeed, a median time of 3 days is derived from these studies. The distribution of time intervals between mainshocks and their largest aftershocks is consistent with a power law but with a somewhat faster rate of decay than for aftershocks in general. This implies that the largest aftershock is more likely to occur earlier than later in a given sequence of aftershocks (i.e., median ~ 3 days). Apart from the statistical analysis of the catalogue, the time of occurrence of the largest aftershock was assessed through more specific seismological aspects such as diffusion. It was found that a time of 5 days is consistent with the deadline of occurrence of the largest aftershock, since it corresponds to the boundary between two different diffusion regimes.
Geographical location of the largest aftershock Introduction As far as dams are concerned, the geographical location of the largest aftershock is of greatest importance. Simply stated, the migration of the largest aftershock towards the dam could give raise to high PGA values. Worldwide catalogues [22] The distance to mainshock is normalized as D* = |D/L|, D being the aftershock distance to the mainshock, which is
measured as the arc length on the earth’s surface. Parameter L is the earthquake rupture length. D* is found to be in the vicinity of 0.43 in the general case corresponding to all type of faults. It was also found that the largest aftershocks of strike slip faults mainshocks are, on average, smaller than and occur at a larger distance from the mainshock than those triggered by reverse faults shocks [22]. Relevant relationships for different faults types are given in [28] and recalled in Table 1. For instance, the fault rupture length during the Landers earthquake was about 80 km. TABLE 1: RUPTURE LENGTH VERSUS EARTHQUAKE MAGNITUDE (AFTER [28]) Fault type Strike-slip Reverse Normal All
Rupture Length (m) Log (L) -3.55+0.74Mw -2.86+0.63Mw -2.01+0.50Mw -3.22+0.69Mw
Log RL 0.23 0.20 0.21 0.22
Dam performance against aftershocks Man-made dams [16] Dam performance records show that no man-made dam has collapsed due to an aftershock. However, No.2 dike, a tailings dam at the Mochikoshi gold mine near Izu Oshima in Japan could have failed as a result of the M5.7 aftershock (15 January 1978: 7.32am) following the M7.0 earthquake (14 January 1978: 12:24am). Officially, the No.2 dike is reported to have failed between 12:30pm and 1:00pm. An aerial photograph was apparently taken at 10:00am (i.e., 2.5 hours after the aftershock), proving the dike was still stable. One of the tailings dams (Dam No.1) failed during the mainshock. Although, no direct measurements on Dike No.2 were taken in order to assess its stability after the mainshock, or after the largest aftershock, it cannot be excluded that the dike failed due to the combined effects of both shocks. Landslide (natural) dams [8] Chinese historical documents recorded that on 1 June 1786, a strong M=7.75 earthquake occurred in the Kangding-Luding area, Sichuan, south-western China, resulting in a large landslide that blocked the Dadu River. A 70m high natural landslide dam formed and created a 50,106m3 reservoir. The researchers demonstrated, by means of historical documents and geomorphic evidence, that the landslide dam suddenly breached due to a major aftershock on 10 June 1786, i.e., ten days after the mainshock. Historic records reported over 100,000 deaths from the resulting flood.
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Present situation on the consideration of aftershocks for dams Aftershocks are given particular importance only after the occurrence of a large earthquake. All parties concerned are then interested to know the intensity of a possible aftershock, if it is safe to launch the post-earthquake dam inspection, and if not, to raise the question of the opportunity to evacuate downstream in case of a large aftershock. Under these circumstances, some guidance is certainly required in order to encompass the probability of occurrence of aftershocks within the framework that is already established for mainshocks. FERC guidance for the consideration of aftershocks Among available dam safety guidelines, it is worth noting that FERC (Federal Energy Regulatory commission, USA) suggests that aftershocks should be considered as one of the most relevant post-earthquake loading cases. The aftershock to be considered is to be selected based on observed earthquakes like those listed below [9]: TABLE 2: LARGEST AFTERSHOCKS [9] Earthquake Largest Main Shock Aftershock Year Location 1983 Idaho ML = 7.3 ML = 5.8 1984 Morgan H. ML = 6.2 ML = 4.5 1985 Chile Ms = 7.8/Mb = 6.9 Mb = 6.5 1987 Wittier N. ML = 5.9 ML =5.3 1988 Armenia Mb = 6.3 Mb = 5.9 1989 Loma Prieta Mw = 6.9 Mw = 5.0 1994 Northridge Mw = 6.7 Mw = 5.9 ML= Local; Ms = Surface-wave; Mb = Body-wave.
Delay 6 hours 9 days 52 minutes 3 days 5 minutes 33 hours 1 minute
Consideration of aftershocks in dam design: A case history. From the available literature, an aftershock with one order of magnitude less than the main earthquake was considered in only a single case; this was for the 85m high Mokihinui RCC dam in New-Zealand [2]. In this case, the dam was very close to the fault (1km) and the PGA associated with the 10,000-year return period was about 0.91g for the main shock in the case of an RCC dam founded on rock. The time delay between the mainshock and the largest aftershock was not available, possibly because it may not have been considered to be an important issue. Hazard mapping of probabilistic aftershocks The Reasenberg and Jones model [19]-[20] was developed by combining the Gutenberg-Richter [11] and the modified Omori laws [27]. This model describes the rate (t,M) of aftershocks of magnitude M or larger (in [30]):
(t , M ) 10 ab( MmM ).(t c) p
(1)
where: a, b, c and p are empirical parameters, Mm = mainshock magnitude, and t = time after the mainshock. The probability P of one or more earthquakes occurring in the magnitude range [M1
