The mine collapse at Lo Tacón (Murcia, Spain), possible cause of the Torre Pacheco earthquake (2nd May 1998, SE Spain)

Engineering Failure Analysis 28 (2013) 115–133

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The mine collapse at Lo Tacón (Murcia, Spain), possible cause of the Torre Pacheco earthquake (2nd May 1998, SE Spain) Isabel N. Alvarez-Garcia a, Francisco L. Ramos-Lopez b, Celestino Gonzalez-Nicieza c,⇑, M.Inmaculada Alvarez-Fernandez c, Arturo E. Alvarez-Vigil d a

Research Group of Ground Engineering, Mining Engineering School, University of Oviedo, Independencia 13, 33004 Oviedo, Spain Department of Physics, Polytechnical Engineering School of Gijon, Campus de Viesques, 33201 Asturias, Spain c Department of Exploitation and Prospecting Mines, Mining Engineering School, University of Oviedo, Independencia 13, 33004 Asturias, Spain d Department of Mathematics, Mining Engineering School, University of Oviedo, Independencia 13, 33004 Asturias, Spain b

a r t i c l e

i n f o

Article history: Received 9 May 2012 Received in revised form 10 September 2012 Accepted 12 September 2012 Available online 17 October 2012 Keywords: Seismicity Rock failure Earthquakes Underground mining Damage to underground and surface structures

a b s t r a c t On 2nd May 1998, a sudden and rapid collapse occurred in an area of abandoned metal ore mines in La Unión (SE Spain). Due to this event, surface subsidence occurred at ‘‘Lo Tacón’’ industrial park resulting in extensive damage to buildings in the affected area. This mine collapse coincided with an earthquake of magnitude 2.4 Mw recorded by seismic stations near the National Geographic Institute of Spain (Spanish acronym, IGN) that situate the epicentre in the town of Torre Pacheco, about 20 km northeast of the city of La Union, at a depth of 2.6 km. The lack of coverage of seismic stations east of Torre Pacheco created uncertainty regarding the precise location of the epicentre which we believe to be reasonable. In this paper, we consider the hypothesis that it was the failure in the mine that triggered the collapse and induced a seismic energy of Mw magnitude equal to the earthquake at Torre Pacheco. The seismic energy of the earthquake came from a percentage of the strain energy stored within the rock (massive grey dolomite) that was released by rupture of a rock volume due to the increase in the roof span when a pillar failed, thus triggering cascading pillar failure (CPF). The results of the study prove that the energy recorded at the Spanish National Geographic Institute (IGN) seismic stations is consistent with the calculated released seismic energy for the mining collapse at Lo Tacón. Ó 2012 Elsevier Ltd. All rights reserved.

1. Background Historically, earthquakes have caused damage to underground structures such as natural caves, tunnels and underground mines. The data available indicate that these effects are significant only when earthquakes have a magnitude greater than 5.5 Mw and certain levels of acceleration of ground vibration are also exceeded Ref. [1]. However, underground civil engineering structures (tunnels, hydroelectric stations, etc.) are generally resistant to earthquakes, although they can be damaged if the ground motion becomes permanent (Refs. [2,3]). 1.1. Seismic moment magnitude Aydan and Kawamoto [1] provided information of their own and that of other authors in which it is proven that the earthquakes which cause damage to underground structures are those with a magnitude greater than 6 Mw. One such example is ⇑ Corresponding author. Tel.: +34 985 10 42 66; fax: +34 985 10 42 67. E-mail address: [email protected] (C. Gonzalez-Nicieza). 1350-6307/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.engfailanal.2012.09.009

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that of the Miyagi-Hokubu earthquake, of magnitude 6.1 Mw, which occurred on 26th July 2003 near the city of Yamamoto (Japan) causing damage to abandoned lignite mines just above the hypocentre. The authors from Ref. [1] compiled a historical list of earthquakes that have caused damage to underground structures. Based on this list, a database was developed for three different damage categories: failure-induced damage (18 cases), shock-induced damage (98 cases) and induced slope failure (47 cases).The diagram in Fig. 1 shows an empirical relationship between the Mw magnitude of the earthquake and the limiting distance of damage in a number of cases. The diagram shows that for distances under 50 km from the hypocentre, only earthquakes of a moment of magnitude between 6 and 7.5 Mw cause structural damage. Lenhardt [4] also provided his own information and that of other authors indicating that earthquakes of magnitude greater than 5.5 Mw are those that cause damage to shallow underground structures. Tamura et al. [5] demonstrated that the ground motion observed at depths of 67 m is about half that measured on the surface during earthquakes in the range of magnitude between 5.5 and 7.5 Mw, with focal depths of between 10 and 80 km and distances from the hypocentre to the underground structure of between 50 and 250 km. Berardi et al. [6] confirmed this observation following the 1976 earthquake in Friuli, Italy. 1.2. Peak velocity and acceleration of ground vibration Dowding and Rozen [2] showed that the damage caused by earthquakes only becomes significant once certain levels of acceleration are exceeded. Kanai and Tanaka [7] likewise measured the acceleration of ground motion in underground caverns and on the surface during earthquakes. The data recorded by these authors indicate that surface acceleration is at least twice that measured deep underground. In this regard, Smit [8] proposed the following Eqs. (1) and (2), which allow the peak ground velocity (PGV) in m/s and peak ground acceleration (PGA) in m/s2 on the surface above the underground structure to be calculated:

Log10 ðPGVÞ ¼ M  1:66 Log10 ðRÞ  5:3

ð1Þ

Log10 ðPGAÞ ¼ 0:868M  Log10 ðRÞ  0:00159 R  3:77

ð2Þ

where ‘‘M’’ is the seismic magnitude and R the hypocentral distance in km. These formulas take into account the damping of ground motion with increasing distance due to dispersion and attenuation, as observed in the Alps (see Fig. 2). It is confirmed that peak acceleration on the surface lower than 1.77 m/s2 does not produce damage in underground structures. In the case of the Torre Pacheco earthquake, the peak velocity and acceleration values (PGV, PGA) in the ground of the underground mines at Lo Tacón are found to be minimal using the formulas proposed by Ref. [8] (Mw = 2.4, R = 20 km). 2. Justification of the research study On 2nd May 1998, seismic stations belonging to the National Geographic Institute of Spain (Spanish acronym, IGN) registered a 2.4 Mw earthquake on the scale of Ref. [9]. The epicentre was situated in the town of Torre Pacheco in the province of Murcia, SE Spain, at a depth of 2.6 km (Fig 3). The IGN associated the origin of the earthquake with a fault slippage. Coinciding in the time with this earthquake, a sudden and rapid collapse occurred in the area of abandoned zinc and lead ore mines worked by the room-and-pillar method located in the vicinity of the town of La Union (Fig. 3), causing surface subsidence with substantial damage to buildings in the affected area. This area of mines is nowadays an industrial estate named Lo Tacón, situated about 20 km northeast of the town of Torre Pacheco. The IGN stated in Ref. [10] that the mining collapse at Lo Tacón was induced by the Torre Pacheco earthquake, having its origin in a fault slippage. They said that it was impossible to think that the seismic records registered could be from mine collapse, because the wave shape due to mine collapses or blasting are completely different from those of seismic events.

Fig. 1. Plot of hypocentral distance (km) versus Mw magnitude.Compilation of earthquakes according to Ref. [1].

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Fig. 2. Plot: peak ground acceleration (PGA, m/s2) on the surface versus hypocentral distance (km) of earthquakes in the Austrian Alps according to Ref. [8].

Fig. 3. Location of the study area.

However, there are some questions that must be taken into account. The Torre Pacheco earthquake was only registered by seismic stations located far away from the epicentre. This, in adition to the lack of coverage of seismic stations east of Torre Pacheco led to uncertainty regarding the location of the earthquake’s epicentre. The seismic stations had only one channel, so it may be difficult to distinguish between P and S waves. If we compare the seismic record from this ‘‘earthquake’’ with other occurred in the same zone, near in time and with similar intensity (Mula earthquake, situated in the West of Murcia City, occurred the 9th of April 1999), we can see that are some differences that led to believe that the Torre Pacheco event can´t be classified as a typical earthquake. Fig. 4 shows the location map of the stations, in which the lack of coverage of stations east of Torre Pacheco can be observed and Fig. 5 shows the records registered by the seismic stations for both events. We therefore decided to conduct a research study on the relationship between the Torre Pacheco earthquake and the Lo Tacón mine collapse. The study begins with a brief review of articles on earthquakes related to mine collapses. We then collect geologic, geotechnical and subsidence information on the documented mine workings and on undocumented mine workings provided by personnel from the different mines. The hypothesis that we consider most plausible for the Lo Tacón collapse is that of a cascading pillar failure (CPF) event which released seismic energy equivalent to the energy released in the Torre Pacheco earthquake. We believe that the seismic energy of the earthquake originated from a percentage of the strain energy stored within the rock (massive grey dolomite) released by rupture of a rock volume due to the increase in roof span when a pillar failed progressively. The equation from Ref. [11] is used to calculate the elastic strain energy of deformation of the roof rock that is released by rupture of a single rock volume due to progressive failure of a pillar. We use the criterion from Ref. [12] regarding the percentage

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Fig. 4. IGN seismic stations in SE Spain.

Torre Pacheco

Mula

EALH seismic station

EALH seismic station

EVIA seismic station

EVIA seismic station

Fig. 5. Records for Torre Pachecho and Mula earthquakes registered by IGN seismic stations.

of released energy that is converted into seismic vibration energy. We also use the equation from Ref. [9] that relates the magnitude of the seismic moment, Mw, to the amount of energy associated with a seismic event.

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Table 1 shows the data on the Torre Pacheco earthquake of 2nd May 1998. The mean values of magnitude 2.2 mb [13,14] and 2.9 mbLg [15] with an error of 0.2 correspond to the Pg and Lg phases of the recording of the full wave field. The Modified Mercalli scale classified the earthquake as intensity I (detected only by seismographs).The distances to the hypocentre of the six nearby IGN seismic stations vary between 33 and 141 km. In light of these data, we conclude that the earthquake parameters are far removed from the standards that cause proven damage to underground structures. 3. Description of the study area 3.1. Mining history Zinc and lead ore deposits mainly associated with mantle and seam structures have been mined since Roman times in the former mining area of the city of La Unión, nowadays Lo Tacón industrial estate (Fig. 6). Intensive mining activities were carried out throughout the second half of the 19th century up until the early 20th century. The extraction method varied over time, from opencast mining to underground mining, later returning to opencast mining in the 20th century (Ref. [16]). In underground mining, the mineral structures were worked by the room-and-pillar method (see Ref. [17]). As a result of this history of mining, a high concentration of abandoned underground mining galleries is to be found in this mining area around the city of La Unión. Some mines were exploited irrationally and, before being abandoned, the system of retreat workings consisted in removing or minimizing the cross-section of the pillars. This strategy meant that the reduction in the safety factors of pillars favouring the cascading pillar failure (Ref. [18]) that triggered the phenomenon of subsidence affecting nearby buildings. Once these mines had been closed, Lo Tacón industrial estate was built on the area despite the unfavourable recommendation given by the Spanish Institute of Geology and Mining (IGME) [19]. 3.2. Collapse of 2nd May 1998 On 2nd May 1998, a rapid and sudden collapse of several underground mining cavities occurred in the industrial area of Lo Tacón. The problem began with the appearance of cracks in buildings and in the surface of the ground, coinciding in time with the seismic event of Torre Pacheco, which triggered considerable public alarm. Given these events, a topographic levelling network was set up in June 1998 which was used to measure the maximum settlement within the subsidence basin. These data were used to monitor the phenomenon of subsidence, which has continued up to the present day (see Refs. [20,21]). Fig. 7 shows the settlement isolines of the subsidence area. As can be seen, the maximum settlement of 50 cm (July 1999) is located just above the La Cierva mining concession. The estimated area of the subsidence basin is 295 m  323 m, this area being where severe damage to buildings occurred. 3.3. Geology of the study area 3.3.1. Structural geology At a regional level, the study area is characterised as comprising a series of stacked thrust sheets affected by an upward decreasing metamorphic grade. After a phase of significant erosion, this mantle structure was covered by a late-Orogenic Neogen series, after which came a phase of significant faulting followed by volcanic phenomena and the uplifting of the Sierra de Cartagena.

Table 1 Data from IGN bulletin No. 2 (May, 1998). LOC: NW TORREPACHECO, MU (NEAR) Date Time

Latitude

Longitude

Az

Depth

Gap

1998/05/02 Magnitude mb mbLg Station EALH EALH ACU ACU EVIA EVIA ECHE ESLA ETOR ETOR

37.8338 Nsta 6 5 Phase Pg Lg Pg Lg Pn Sn Pn Lg Pg Lg

1.0457 Author bull-2 bull-2 Ampl 23.9 29.1 3.6 11.2 11.6 13.2 2.6 1.0 1.4 1.1

151

2.6

233

Per 0.24 0.24 0.24 0.36 0.24 0.24 0.32 0.20 0.48 0.32

Magnitude mb mbLg mb mbLg mb mbLg mb mbLg mb mbLg

2.5 2.4 2.6 2.3 3.7 2.8 3.2 1.8 3.0 1.6

18:19:28.08 Err 2.9 0.2 2.2 0.2 Dist (°)–(km) 0.30°–33 0.84°–93 1.40°–130 1.76°–195 2.93°–325 3.08–341

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Fig. 6. Aerial view. City of La Union (right) and Lo Tacón Industrial Estate (left).

Fig. 7. Subsidence map.

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At a more local level, the underground mining area subject of this study is located on a fallen block of the Sierra de Cartagena mountain range (Ref. [19]) in the Internal Zones of the Baetic Cordillera, related to the main ‘‘Cartagena-La Unión’’ fault (60°N/70°E) (see Fig. 8). This fault constitutes the northern boundary of the mountain range and defines a clear stratigraphic and geomorphological differentiation between the blocks on both sides of these mountains. The fault is in turn displaced by other faults (130°N/140°E), among which the so-called ‘‘Las Lajas’’ or ‘‘La Cierva’’ fault stands out, as it stretches through the eastern boundary of the affected area and may potentially influence the subsidence phenomenon. South of the Cartagena-La Unión fault, the materials belong to the Paleozoic base, as the covering stratigraphic series has disappeared due to erosion, with the exception of more recent deposits. Among these, Miocene outcroppings, located in the southern part of the ‘‘La Cierva’’ mine, reach a thickness of 30 m. These materials, composed of polygenic conglomerates, are well mineralised in relation to intense 130°N fracturing. In fact, the area includes significant mined areas with cavities of up to 80 m2 in cross-section. The presence of mines in these outcroppings suggests that mined areas of a certain importance may exist north of the ‘‘Cartagena-La Unión’’ fault at moderate depths (below 100 m) regarding which no information is available. 3.3.2. Stratigraphic information In order to obtain reliable stratigraphic information on the site, three boreholes were drilled (Fig. 9) between late 1975 and early 1976 in the area between the ‘‘La Cierva’’ and ‘‘Cabeza Rajao’’ mining concessions: borehole EE, of 261 m in length, above the ‘‘Artesanía’’ mine; borehole EA, of 191 m, above the ‘‘Asunción’’ mining concession; and borehole EI, of 209 m, above the ‘‘Asunción’’ mining concession. The cores evidence the major lead and zinc mineralisations found in the Miocene conglomerate base, at a depth of between 70 and 80 m, and the Triassic dolostone in the carbonated area, at a depth of between 81 and 133 m. These mineralisations indicate that there must probably be mined areas in this area, although they have not been perforated by the borehole below a depth of 70 m. In addition, borehole A-1 was drilled in the ‘‘La Cierva’’ mine to a depth of 133 m to complete the stratigraphic characterisation survey. A limestone mine cavity with mineralised filling was detected at the end of the borehole between 131 and 133 m. This leads us to believe that there is a second level of mineralisation with significant mining workings that have not been represented on available maps, possibly down to a depth of 300 m. Core recovery was 100%, indicating very dense rock. All the information collected from the boreholes, along with the data from borehole A-1, have enabled us to draw up the geological section shown in Fig. 9, giving the position of the mineralisation which may include mining operations.

Fig. 8. Location of the study area and geological scheme of the city of La Union with superimposed subsidence isolines for the period 1998–1999 following the May 1998 collapse (based on [18,23]).

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Fig. 9. Geological cross-section.

The cores from the A-1 borehole, which went down to a depth of 200 m in the ‘‘La Cierva’’ mining concession near to the ‘‘Lo Veremos’’ mining concession in the area of subsidence (see Fig 9) shows massive grey dolomite mineralisation with 100% recovery, the absence of moisture and few fractures. According to these parameters, the index of intact rock quality (RQD) is 72 (Ref. [22]). Table 2 shows a summary of the parameters considered in the calculation of the RMR index of the rock (Ref. [23]) of the ‘‘La Cierva’’ and ‘‘Lo Veremos’’ mines. The RMR index of 72 ranks the rock mass as good and sets a time of stability for a 15 m roof span of 20 years. Note that closure of the mines was completed in the late1970s and the collapse at Lo Tacón occurred on 2nd May 1998, which represents a time span of around 20 years. Furthermore, the room width of the workings is 15 m. 3.4. Underground mining cavities in the area of Lo Tacón Some studies have revealed that the percentage of mined underground volume versus total underground volume has an average value of 67% (Ref. [24]). The collapsed volume is estimated at around 20,810 m3, which represents 7.5% of the Table 2 Parameters for calculating the RMR [22]. Parameter

Condition

Assessment

RMR

Uniaxial compressive strength (UCS) RQD Distance between joints Condition of the joints Moisture

80 MPa 100% 0.6–2 m Slightly rough separation <1 mm slightly weathered walls Dry

7 10 15 25 15

72

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mapped underground cavities that exist in the study area. These cavities are situated at depths of between 80 and 254 m. Fig. 10 shows the situation of known mining concessions. The mines situated directly below the area of subsidence are: La Cierva, Trinidad, Lo Veremos, La Ocasión and San Lorenzo. Table 3 shows the depths of the mining levels. 4. Analysis of the cascading pillar failure in the La Cierva and lo veremos mines (Lo Tacón – SE Spain, 2nd may 1998) We next carry out a study of the collapse of the underground metal ore mines La Cierva and Lo Veremos located in the former mining area worked by the room-and-pillar method. This study focuses on the analysis of the pillars in the areas adjacent to these mines, as these are the mining concessions which are just below the area of maximum subsidence. There is extensive documentation related to the behaviour of pillars, such as rock mass quality, pillar conditions, dimensions of excavation and intact rock strength. There are also several documented cases of room-and-pillar collapses in metal ore and non-metal ore mines Refs. [25–28]. All this information was used to study the collapse that occurred at Lo Tacón, as no comprehensive information is available on the state of the pillars at the time of collapse in the aforementioned mines. 4.1. Pillar stability analysis 4.1.1. Pillar strength The strength of a pillar can be defined as its maximum resistance to uniaxial compression. In a deposit with horizontal stratification, the compression of a pillar is caused by the weight of the rock mass overlying the pillar. Empirical evidence suggests that the strength of a pillar is related to its volume and shape. Numerous empirical equations have thus been developed to estimate pillar strength in hard rock mines (Refs. [29–32]). These equations are generally only applicable under similar conditions to those under which they were developed. Eq. (3) (Ref. [30]) is an example of a potential equation used in the design of hard rock pillars:

Sp ¼ k

w0:5 h

ð3Þ

0:75

where k is the strength of a unit cube of the rock material forming the pillar, w is the width of the pillar and h is its height. Lunder and Pakalnis [32] developed a new empirical formula (4) for pillar strength called the ‘‘Confinement Formula’’, which has been successfully tested in the estimation of pillar strength of any solid rock material:

SP ¼ ðK  UCSÞ ðC 1 þ C 2 kÞ

ð4Þ

Fig. 10. Map of mining concessions.

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Table 3 Mines in the Lo Tacón subsidence area. Pits and depth of the mining levels. Mine

La Cierva

Trinidad

Lo Veremos

La Ocasión

San Lorenzo

Pit

San José

San Sebastián

No. 1

No. 2

Carmelo

San Manuel

Level no.

Depth (m)

Depth (m)

Depth (m)

Depth (m)

Depth (m)

Depth (m)

1–2 3–4 5–6 7–8

80–95 149–227 256–

157–201 230–260 285–310 –

82–120 148–164 164–199 214–260

197–221 244–276 298–321 –

129–157 177–190 210–225 247–272

147–179 209–225 248–284 304–314

where k (kappa) is a pillar friction/confinement term, and C1 and C2 are constants whose value has been empirically determined as 0.68 and 0.52, respectively. K is the rock mass strength factor (size effect), whose value is 0.44. The value of k (kappa) is determined as Eq. (5) shows:

   1  C pav k ¼ tan cos1 1 þ C pav

ð5Þ

where Cpav is the average pillar confinement, which can be calculated by means of the following expression (Eq. (6)): 1:4 h w iw=h þ 0:75 Cpav ¼ 0:46 log h

ð6Þ

where w is the width of the pillar and h its height. The ‘‘Confinement Formula’’ (Ref. [32]) is derived from the analysis of a series of data recorded by Westmin Resources Ltd., which operates a metal ore mine located at the southern end of Butle Lake, Vancouver Island (Canada). The ore deposits are mass polymetallic sulphides associated with volcanic rock. In his PhD research work, Lunder expanded the database he used, the ‘‘Westmin database’’, with pillar strength data from the studies by Refs. [29,30,33–36]. Taking the combined data from the aforementioned sources, Lunder represented his ‘‘Confinement Formula’’ and other preceding expressions by means of a frequency histogram of successful predictions of pillar stability, instability and failure. He showed by means of statistical analysis that his formula predicts pillar strength more successfully than preceding formulas (Fig. 11). 4.1.2. Pillar strength in the La Cierva and Lo Veremos mines (SE Spain) Pillar dimension data from the La Cierva and Lo Veremos mines (see Table 4) were used to calculate pillar strength values from Formula (3) in Ref. [30], and strength values from Formula (4) in Ref. [32]. The pillar strength was normalised to the uniaxial compressive strength value of intact rock (Pb- and Zn-mineralised massive grey dolomite, UCS = 80 MPa). For purposes of comparison, a k value of 0.7 UCS was used in Formula (3) by Ref. [30], which is the value used by Ref. [32] in Formula (4). Fig. 12 represents normalised uniaxial compressive strength values versus the pillar width-to-height ratio. It is observed that the normalised pillar strength values of the La Cierva and Lo Veremos mines are very similar to each other for a widthto-height ratio above 0.7 and clearly diverge for a width-to-height ratio below 0.6. It is also observed that according to Lunder’s Confinement Formula (4), the normalised compressive strength remains constant for a width-to-height ratio below 0.4.

Fig. 11. Statistics on successfully predicting pillar strength for newly developed formulas for all the data in the combined database (Ref. [32]).

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Table 4 Data on the pillars in the La Cierva and Lo Veremos mines: pillar width (w) of 10 m, uniaxial compressive strength (UCS) of intact rock of 80 MPa, pillar stress calculated by means of the tributary area method, pillar strength calculated using the ‘‘Confinement Formula’’ from [27]. Depth (m)

Normalised pillar stress, rso/ UCS

Width-to-height ratio

Pillar height, (h) (m)

Normalised pillar strength, Sp/ UCS

Safety factor, FS

Assessment

80 100 120 140 160 180 200 220 240 260 280 300

0.17 0.21 0.25 0.30 0.34 0.38 0.42 0.46 0.51 0.55 0.59 0.63

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

33 25 20 17 14 13 11 10 9 8 8 7

0.3 0.3 0.3 0.3 0.3 0.4 0.4 0.4 0.4 0.5 0.5 0.5

1.8 1.4 1.2 1.1 1.0 1.0 0.9 0.9 0.9 0.9 0.8 0.8

Stable Unstable

Failure

These calculations employed a pillar width of 10 m and a pillar height that varied between 7 and 33 m. It can be concluded that Formulas (3) and (4) estimate significantly different strength values for slender pillars. Thus, on the basis of this wide range of strength values, it is not unlikely that one or other of the slender pillars in the areas adjacent to the La Cierva and Lo Veremos mines may have failed, thus initiating a cascading pillar failure process. 4.1.3. Comparative analysis To compare these results with similar cases worldwide, we provide a review of published data of general characteristics of rock pillar failure. Ref. [37] published the results of pillar failures collected in a measurement survey carried out in a number of underground mines in the United States conducted by the National Institute for Occupational Safety and Health (NIOSH), Pittsburgh, PA (USA). Fig. 13 shows a summary of the empirical results of the survey for good to very good quality rock (RMR 60-85). The cases of pillar failure are represented by pillar strength values normalised to uniaxial compressive strength (UCS) values versus the pillar width-to-height ratio. Lower and upper limits are established for pillars, defining areas that show the greatest or least likelihood of pillar failure depending on their strength and shape. It should be noted that none of the failed pillars represented in Fig. 13 and listed by the NIOSH was affected by major structures (faults), meaning that pillar failure is a reflection of the behaviour of the rock mass. Pillar strength is calculated using formulas from Ref. [29–32]. Pillar load is estimated by the ‘‘tributary area’’ method. The following observations regarding the analysis of the represented statistical data are worth highlighting: (a) The strength of pillars with a width-to-height ratio below 1 is highly variable. This variability increases as the widthto-height ratio decreases. (b) The variability in the strength of failed pillars may be caused by several factors, such as uncertainty regarding the actual rock strength, uncertainty regarding the actual rock stress, variations in the degree and severity of joints, variation in the stratification characteristics and the presence of weak stratified veins in the pillars. The results of failed pillars listed by the NIOSH provide us with an initial approximation of the characteristics of the failed pillars in the area adjacent to the La Cierva and Lo Veremos mines, where the Lo Tacón collapse was felt more intensely. The

Fig. 12. Normalised stress in the pillar versus the pillar width (w) to height (h) ratio. The La Cierva and Lo Veremos Mines.

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Fig. 13. Cases of hard rock pillars that failed (Esterhuizen, NIOSH, Pittsburgh, PA).

1–10 geological section of the study area (Fig. 9) shows that the pillars of the La Cierva and Lo Veremos metal ore mines in areas adjacent to the 2nd and 3rd mining levels are not affected by major faults at a depth of 200 m. The normalised strength of slender pillars, calculated using the formula from Ref. [32], was observed to tend towards the constant value of 0.3 as the width-to-height ratio of the pillar decreases (see Fig. 12). It can be seen that these normalised slender pillar strength values calculated for the pillars in Lo Tacón shown in Fig. 13 are situated above the line of the highest probability of failure. 4.1.4. Pillar stress and safety factor To complete the analysis of the characteristics of the pillars most likely to fail in the area adjacent to the La Cierva and Lo Veremos mines, the safety factor (FS) is calculated at different depths. Table 4 shows normalised strength values from Ref. [32] (Sp/UCS) and normalised pillar stress values (rso/UCS) versus depth and pillar width-to-height values. We consider a pillar width of 10 m. The chosen pillar height ranges between 7 and 33 m following the order of increasing pillar depth so as to obtain safety factors below 1. The depth of the pillars with the highest probability of failure is thus determined. The calculated safety factor values are accompanied by an assessment of stability following the criteria used in Ref. [32] to assess pillar stability in Westmin Ltd.’s WH Mine, as shown in Table 5. The pillar stress, rso, is calculated by the ‘‘tributary area’’ method (Eq. (7), Ref. [38]), a method commonly used in regular pillar layouts:



rso ¼ cH 1 þ

2 B w

ð7Þ

where c is the unit weight of the rock load supported by the pillar, B the width of the tributary area of the pillar, w the pillar width and H the depth of the pillar from the surface. The calculation uses a unit weight of rock c = 27 kN/m3 and a pillar width w of 15 m. The safety factor (FS) is calculated by dividing the strength of the pillar (Sp) by the stress (rso) (see Eq. (8)):

FS ¼

SP

ð8Þ

rso Table 5 Pillar stability classification ([32] – Westmin Ltd.’s WH Mine). Observed pillar conditions

Safety factor

Combined data

No sign of stress-induced fractures Failure only in the upper corners Fractures in pillar walls Fractures of length < 1/2 pillar height Fracture openings < 5 mm Fractures of length > 1/2 pillar height Fracture openings > 5 mm Disintegration of the pillar Detached blocks Fracture openings > 10 mm Fractures through the core of the pillar

FS > 1.4 1.2 < FS < 1.4 1.1 < FS < 1.2

Stable Unstable

1.0 < FS < 1.1 FS < 1

Failure

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We end this analysis of pillar stability using the pillar stability classification method developed in Ref. [32] for use in Westmin Ltd.’s H–W Mine. This graphical method introduces average normalised stress values and pillar width-to-height ratio values (see Fig. 14). Different symbols are used to represent failed, unstable and stable pillars. The graph was built for use with the ‘‘Confinement Formula’’ from Ref. [32]. The empirical data shown in Fig. 14 show that the pillars exhibit visible characteristics of failure with a safety factor in the range of 1.0–1.4, assuming that pillar failure occurs at a safety factor equal to or less than 1.0. In accordance with the graph in Fig. 14 and Table 5, the stability of the pillars in the area adjacent to the La Cierva and Lo Veremos mines may be classified as follows: 1. 2. 3. 4. 5. 6.

Stable pillars exist up to a depth of 100 m. Pillars with a height above 10 m may fail at depths greater than 160 m. Pillars at depths of between 100 and 180 m become unstable. Pillars at depths of between 180 and 300 m present a high probability of failure. Pillars at depths of between 180 and 220 m with a width-to-height ratio greater than 1 may fail. Pillars at depths of between 160 and 220 m, a width-to-height ratio between 0.7 and 1 and a Safety Factor (FS) of less than 1 (FS  1) will eventually disintegrate. The process of disintegration is as follows: detachment of blocks, development of fractures with an opening greater than 10 mm and development of fractures through the core of the pillar. 7. Pillars with a width-to-height ratio between 0.7 and 1 and safety factor greater than 1 (FS  1) will eventually disintegrate. The process of disintegration is as follows: development of fractures of length greater than 1/2 height of the pillar and fracture openings of less than 5 mm. 8. Pillars at depths of between 160 and 220 m, a width-to-height ratio between 0.7 and 1, a safety factor FS  1 and a normalised stress between 0.34 and 0.46 will eventually fail. 4.2. Pillar failure modes 4.2.1. Progressive pillar failure From observations of actual cases, progressive stress-induced failure of a pillar is known to lead to the cracking of plates of rock, which become separated from the surface of the pillar. This process continues towards the core of the intact rock. This progressive failure mode is also called ‘‘hourglass formation’’ due to the outer shape the pillar assumes. Fig. 15 shows a case of an hourglass-shaped pillar found in a limestone mine in northern Tennessee (USA) at a depth of 140 m (Ref. [37]). Almost vertical joints can be observed with a mean spacing of 50 cm, a rough joint surface and less than 3 m of continuity. Poorly developed stratification joints were also observed that do not seem to affect the stability of the pillar. The calculated mean normalised stress for the pillar is 0.10 times the UCS, which is the lowest limit value of cases of progressive cracking observed in solid rock mines in the USA (Ref. [37]. In other rock mines in the United States, it is found that in pillars with a width-height ratio equal to 1, the crack is initiated at a normalised stress of 0.11–0.12. This phenomenon is usually seen in pillars with an intermediate width-to-height ratio of 1=4 –1 (Ref. [39–44]). 4.2.2. Violent pillar failure During the process of progressive pillar failure, the reduction in pillar size causes a redistribution of the confining stress in the intact rock pillar. If the process progresses, the average stress in the core of the pillar can exceed its strength limit, resulting in violent failure. Fig. 16 shows a case of a completely failed pillar that occurred in a rock mine in the United States (Ref. [37]). It is believed that the existence of weak strata in the pillar and moisture conditions contributed to the total failure. The width-to-height ratio was 0.82 and the average stress nearly 0.11 times the UCS.

Fig. 14. Stability graph for the Confinement Formula (Ref. [32]).

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Violent pillar failure is generally found to occur when the following two conditions are met (Refs. [41,44]: condition (1), the stress in the pillar must exceed the strength of the pillar, and condition (2), the local rigidity of the mine around the column must be less than the rigidity of the pillar. According to the work of Ref. [43], the first condition is usually restricted to a pillar whose resistance exceeds the uniaxial compressive strength of intact rock (UCS) by 1/3. Empirically, it is found that brittle hard rock pillars with a low width-to-height ratio are more prone to violent failure than wider pillars. 4.2.3. Cascading pillar failure Numerous researches (Refs. [41–45]) have shown experimentally that pillars that fail violently probably initiate a progressive pillar failure mechanism, also called ‘massive pillar collapse’, ‘domino-type failure’ and ‘cascading pillar failure’ or CPF (Ref. [47]). The mechanism that initiates CPF consists in the rapid transfer of the load supported by one of the pillars that has failed violently to adjacent pillars, causing the weaker pillars to fail. This failure mechanism may lead to the rapid collapse of extensive areas of the mine in a very short time, in the order of seconds, and the number of affected pillars may range from a few dozen to hundreds and even thousands in extreme cases (Refs. [46,48,49]). Table 6 shows data calculated from the pillar in which the violent failure via the CPF mechanism was most probably initiated in the area adjacent to the La Cierva and Lo Veremos mines which occurred on 2nd May 1998. We believe that the pillar which started the CPF was located at the depth of between 160 m and 180 m. Via a process of continued deterioration of the pillar over time (cracking), for a period of at least 20 years after the mine closure in 1979 up until the collapse in 1998, the core had reached the critical size to satisfy the two conditions for the violent explosion of the pillar (Refs. [41,44]) (see Tables 2 and 4). The pillar stress is 0.34 UCS and its normalised strength, 0.30 UCS. The material of the pillar is strong and very rigid (uniaxial compressive strength, UCS = 80 MPa, rigidity modulus, G = 14.7 MPa).The rigidity of the room where the pillar is located is lower (material composed of a dolomitic conglomerate). Table 7 shows the characteristics of the CPF collapse of 2nd May 1998 at Lo Tacón. The size of the collapse is estimated considering the area of acknowledged surface subsidence of 293  323 m (Ref. [24]). Considering a regular distribution of square pillars in the affected area, by means of simple calculations we roughly estimate 140 affected pillars. The percentage of extraction is estimated at around 84%. Table 8 presents data on CPF collapses occurred in underground metal ore mines in the USA (Ref. [44]). It can be seen that the collapse of 2nd May 1998 at Lo Tacón exhibits the same characteristics as the collapses in Table 8. These common features are: (1) the percentage of extraction is usually greater than 60%, (2) the pillar width-to-height ratio is much less than 1, and (3) the collapse area is at least 15,000 m2, with a minimum dimension of 100 m . 5. CPF collapse of 2nd may 1998, Lo Tacón – SE Spain. Seismic energy released In the third part of this paper, we estimate the amount of seismic energy released by the 2nd May 1998 collapse at Lo Tacón. A review of the available literature and published information allows us to obtain results that we validate by means of the method of comparison. 5.1. Strain energy accumulated in the roof strata during mining When weak pillars fail and roof supports are removed, a strong roof becomes highly strained. If the span of the unsupported roof increases, it becomes more highly strained and finally collapses (Ref. [50]). When CPF occurs, the span becomes

Fig. 15. Partially benched pillar failing under the high stress on the edge of the mining bench. Typical hourglass shape indicating an overloaded pillar.

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Fig. 16. Total collapse of a pillar. Width-to-height ratio of 0.82. Average pillar stress around 0.11 times the UCS.

Table 6 Data on the pillar most probably the source of the violent CPF collapse of 2nd May 1998 at Lo Tacón (SE Spain). The Lo Veremos and La Cierva Mines. Depth (m)

Width (m)

Height (m)

Stress (MPa)

Strength (MPa) ([32])

160–180

10

>13

27.2–30.4

24–32

Table 7 Theoretically estimated data on the CPF which occurred on 2nd May 1998 in the area of the La Cierva and Lo Veremos underground metal ore mines (Lo Tacón, SE Spain). Mine

Depth (m)

Pillar size (m)

w/h ratio

Extraction (%)

Collapsed size (m)

Pb–Zn

160–180

10  10

0.3–0.5

84

293  323

increasingly larger and in a very brief period, in the order of seconds, the immediate very rigid mass rock of the roof rapidly exceeds the strength of the overlying strata. The roof rock fractures and/or sliding occurs along pre-existing fractures leading to collapse. This CPF phenomenon involves a large volume of rock: pillar rock, roof and floor fractures giving rise to excessive convergence of the mine cavities and sometimes surface subsidence. If the collapse is very rapid, a blast of air is forced out of the collapsed area. In any case, the involved volume of rock is de-stressed, thus releasing accumulated strain energy. A significant amount of energy is released as seismic energy and the seismic event that follows the collapse may be registered at local and regional seismic stations. The strain energy stored per unit volume of collapsed rock can be estimated by means of Eq. (9) (Ref. [11]):

W 0 ¼ ð1=2EÞðr21 þ r22 þ r23 Þ  ðl=EÞðr1 r2 þ r2 r3 þ r1 r3 Þ

ð9Þ

where W0 is the strain energy per unit volume; E, the modulus of elasticity; l, the Poisson’s coefficient; r1, r2 and r3 are the principal stresses. The principal stresses, r1, r2 and r3, may be approximated using the stress field measured in situ. Ortlepp [12] estimated that as little as 5% of the total amount of energy released by rock failure takes the form of seismic vibrations. Much higher percentages may be achieved if the rock fails in rupture. Therefore, the range of seismic efficiency for mine-induced events could be between 5% and 100% of the total energy released. If the released strain energy is sufficient, it can cause a seismic disturbance that may be registered at local stations and, in some cases, also at regional seismic stations.

Table 8 CPF data in underground metal ore mines (USA). State

Mine

Depth (m)

Pillar size (m)

w:h ratio

Extraction (%)

Collapsed size (m)

IL MT

Pb–Zinc Cu–Ag

75 300

11  11 9  90

0.4 0.5

90 60–65

90  360 90  120

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Introducing in Formula (9) from Ref. [11] data on the elasticity of the rock from the collapse area adjacent to the La Cierva and Lo Veremos mines (elastic modulus (E) = 38.67 GPa and Poisson’s coefficient (l) = 0.32) and data on regional stress in the study area (vertical stress m1 = 28.8 MPa, maximum horizontal stress m2 = 22.7 MPa, and minimum horizontal stress m3 = 16.7 MPa) yields a strain energy per unit volume of collapsed rock W0 = 5960 J/m3. The amount of total energy released is 5.02  109 joules. The considered volume is 293  323  10 m, where 293  323 correspond to the area of surface subsidence measured at the commencement of subsidence (Ref. [24]), and we consider a height of roof failure of around 10 m. The Mw magnitude of the seismic event following the collapse on the Ref. [10] scale is calculated as Eq. (10) shows:

Log10 ðESÞ ¼ 1:5M w þ 4:8

ð10Þ

where Es is the Elastic energy radiated in ground vibration in joules and Mw is the magnitude of the seismic event on the Kanamori scale (1977). Fig. 17 shows the trend of Mw magnitude using the equation of Ref. [10] as the percentage of the accumulated strain energy released from the Lo Tacón CPF collapse of 2nd May 1998 transferred to seismic energy according with the criteria of Ref. [12]. The magnitude Mw tends to a value of around 3.2. This value is consistent with the mbLg magnitude values of the Torre Pacheco earthquake of 2nd May 1998, recorded by the IGN seismic stations (see Table 1). We convert the range of magnitude 2.4–2.8 mbLg, Torre Pacheco earthquake 02/05/1998 (see Table 1), to the range of magnitude 2.2–2.5 Mw using Formula (11) from [51] adjusted to the Iberian Peninsula. Fig. 17 shows that the range of magnitude 2.2–2.0 Mw is associated with a seismic efficiency of between 5% and 10% of the total energy released as seismic energy in the Lo Tacón collapse of 2nd May 1998. 2

Mw ¼ 0:311 þ 0:637mbLg þ 0:061mbLg

ð11Þ

For the sake of comparison, we include the following facts on five potash mine collapses selected for review by Ref. [49]: (1) The major Retsof Salt mine collapse, New York, occurred at the 2YS panel on 12th March 1994, produced a seismic event of magnitude 3.6 as a 150 by 150 m section of roof collapse under 300 m of overburden. (2) The Solikamsk potash mine collapse, Verkhnekamsky deposit, in the Upper Kama district of western Ural, Russia, resulted in a 4.7 magnitude seismic event on 5th January 1994, and 4.5 m surface subsidence. A massive falling of the mine roof was noted over an area of 600 m by 600 m. The mine used a panel system of rooms and pillars under 200–400 m of overburden. Rooms were 13–16 m wide and pillars 11–14 m wide by 200 m long. An investigation throughout the Upper Kama district found that surface subsidence reached 50% of the excavation height 4–5 month after excavation. This event occurred 7 years after the mine was completed. (3) The Teutschental potash mine collapse, Germany, on 11th September 1996, involved failure of 700 long pillars over an area of 2 km2 and under 620–770 m of overburden in approximately 2 s. The collapse produces a 4.8 magnitude seismic event and 0.5 m of surface subsidence. (4) The roughly 1 by 2 km section of the Solvay Trona collapse, Wyoming (USA), on 3rd February 1995, produced a 5.1 magnitude seismic event. Seismic first-motion observation showed dilation (collapse) at all seismic stations. The failure occurred over a multiple yield panel section, 13 panels collapsing completely. The panel was mined under 450– 520 m of overburden. Surface subsidence of 0.75–0.9 m was noted over the collapse area. A number of mechanisms including a chain reaction pillar collapse have been proposed. Pechmann et al. [52] successfully fitted the seismic event to a crack closure (implosion) mechanism, the crack being the mined Trona seam. The seismic energy release was about 10% of the potential energy lost by the observed subsidence of the overburden. Miners describe the event as lasting 5–6 s. (5) The 13th March 1989 collapse of the Merkers mine, 750–900 m beneath the town of Volkershausen, Germany, involved an area of 6.5 km2, produced a 5.6 magnitude seismic event and caused catastrophic damage to the town. Failure of 3200 pillars occurred within a time span of 2–3 s, resulting in up to 1 m of surface subsidence. Descriptions of the seismic event vary. Bennet and McLaughlin [53] described the seismic event as having a seismic magnitude of

Fig. 17. Relationship between seismic magnitude (Mw) (Kanamori, 1977) and % strain energy of the roof strata transformed into seismic vibration energy in the collapse at Lo Tacón (SE Spain), 2nd May 1998.

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Fig. 18. Seismic magnitude, a logarithmic measure, plotted against the relative change in potential energy of the subsidence block.

5.4, representing 0.5% of the potential energy lost through subsidence. They also found the seismic characteristics of this event to be quite similar to that produced by the 1995 Solvay event. A strong correlation between these dynamic collapse events and the presence of strong brittle strata bridging above the bed being mined is the most relevant observation of this review. Two collapse mechanisms have been evoked: (1) cascading pillar failure, and (2) sudden shared failure of strong brittle overburden strata. Sudden strong strata failure was found to occur on near-vertical shears and generally associated with sudden subsidence events. The seismic event created by sudden collapse carries information on the source mechanism of the event. A comprehensive seismic analysis conducted for the Solvay case includes two important findings: (1) The first motion of the ground registered by the seismographs is downward, indicating a collapse or implosion often described as a horizontal crack closure motion. (2) The potential energy released through subsidence is sufficient to produce the observed seismic event. Estimates of the relative change in potential energy, based on the volume and displacement of collapsing overburden were made for several large collapses and compared to reported seismic energy. The linearity of these results (Fig. 18) shows that the energy that seismic energy release scales consistently with changes in potential energy loss (Ref. [49]). Using data on the Lo Tacón collapse of 2nd May 1998:collapsed volume 20,810 m3 (Ref. [24]), depth 160 m, average subsidence 0.25 m, 2.4 Mw, yields a relative potential energy change of 080 in log scale, which is consistent with the linearity of the above results. The crack closure (implosional) character of seismic records of these events does not provide good information on whether the event was trigged by failure of a pillar or strata. The short duration and broad extent of these events suggest that strata failure occurred first as either the initiator or immediately after the initiating failure, providing a shock load that rapidly drove failure throughout the collapse area. These results compared with those of the represent study thus lead us to think that the Lo Tacón collapse of 2nd May 1998 belongs to the latter case. A chain reaction failure of mine pillars occurred and not sudden vertical shear failure of strong brittle overburden strata.

6. Conclusions This study researches the possible relationship between a seismic event of a shallow earthquake with a sudden collapse in a shallow abandoned metal ore mine worked by means of the room-and-pillar method. It is found that, when faced with the collapse of inaccessible abandoned underground mines, a wide-ranging collection of histories of related cases supplemented by information available from the site of the collapse constitutes a good basis for initiating a study to ascertain the characteristics of the collapse. A review of cases of underground collapses recorded by local and regional seismic stations indicates that it is unlikely that a natural earthquake was the cause of a collapse of a shallow underground mine due to earthquake magnitudes below 6 Mw. The reviewed cases also reveal no structural damage when the magnitude of the earthquake is less than 6. This study provides information on the most likely causes that led to the collapse at Lo Tacón. That is, it was due to a cascading pillar failure process that probably started with the total failure of a slender pillar at a depth of 180–200 m. A good relationship of proportionality was found between the seismic energy released in the collapse and the seismic energy of the earthquake recorded at local and regional seismic stations. Comparative analysis of compiled results from other events of underground mine collapse shows a strong correlation between the potential change in energy released through subsidence and the seismic magnitude.

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Further studies of seismic records are required in order to discriminate the event of the collapse from the event of a naturally occurring earthquake.

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Glossary Earthquake: the process of generating waveforms and their subsequent propagation through the interior of the Earth. On reaching the Earth’s surface, the earthquake will be of a greater or lesser intensity depending on the amplitude of the motion (displacement, velocity and acceleration of the land) and its duration. Accelerometer: an instrument that measures the accelerations produced by ground motion. Accelerograph: an instrument that measures accelerations produced by ground motion and maximum acceleration parameters. Accelerogram: a recording made by an accelerograph. Seismograph: an instrument that records seismic waves and maximum speed and displacement parameters. Seismogram: a recording made by a seismograph. Maximum amplitude: maximum height of the peak of a seismic wave. Peak ground acceleration (PGA): the greatest absolute value of the acceleration of ground motion obtained through the components of an accelerogram. This parameter is predominant when the motions have a very small time period. Peak ground velocity (PGV): the greatest absolute value of the velocity of ground motion obtained through the components of a seismogram. Velocity is less sensitive to high frequency components in ground motion. The peak velocity is better for characterising the amplitude of motion at intermediate frequencies with greater accuracy and precision. Maximum ground displacement: the peak displacement associated with the low frequency components of an earthquake. A less commonly used parameter in measurements of seismic ground motion compared to peak acceleration and peak velocity. Interior seismic waves (body waves): elastic waves that travel through the Earth’s interior. P-waves (primary or longitudinal waves): internal waves that travel by means of displacement of particles in the direction of wave propagation. These waves give rise to processes of expansion and compression of the material they pass through, with changes in volume only and no rotation. S-waves (secondary or shear waves): interior waves that travel via the displacement of particles in the direction perpendicular to that of wave propagation. These waves give rise to shear and rotation of the material they pass through, without any changes in volume. S-waves propagate more slowly than Pwaves. Pg and Sg waves: interior waves that are recorded at a point very near the epicentre when the angle of departure is upwards from the horizontal. Pn and Sn waves: interior waves that are recorded at the farthest point from the epicentre when the angle of departure is downwards from the horizontal and which refract critically in the Mohorovicic discontinuity. Pn waves arrive before Pg waves, so they are also called head waves. Lg waves: predominantly transversal short waves (1–6 s) that travel through the earth’s crust, observed in purely continental paths. Lg waves can have large amplitudes in the three components, being visible up to 1000 km. Magnitude: a measurement of the power of an earthquake or the extraction of energy it releases determined by seismographic observation. This is a logarithmic value determined by means of the Richter scale. ML magnitude: local magnitude calculated in the vertical component of the seismogram to fit it to the standard Richter magnitude scale. Mw magnitude: moment magnitude defined by Hanks and Kanamori [12], whose expression is given as: M w ¼ ð2=3ÞlogM 0  10:7 where M0 is the scalar seismic moment in dyn cm. Seismic moment, Mo: moment of an earthquake given by: Mo ¼ lAD where l is the shear modulus of the medium, and A and D are the rupture area and amount of average displacement of the fault, respectively. mb magnitude: body wave magnitude measured in the records after applying a Butterworth filter with corner frequencies of 0.7 and 2 Hz using the Gutenberg and Richter Scale. Munuera [1] adapted the mb magnitude for the Iberian Peninsula as: mb ¼ 0:63 logðA=TÞ þ 1:207 logd þ 4:360 where A is the amplitude of the maximum surface wave train in microns, T the period in seconds and D the epicentral distance in degrees. The mb magnitude thus calculated is proportional to velocity and not to displacement. This formula is routinely used to calculate the mb magnitude in the bulletins on earthquakes near the National Geographic Institute of Spain (IGN) with the value 4.1736 for the independent term as stated by Ref. [2]. mbLg magnitude: magnitude derived from the amplitude of the Lg phase. This magnitude has been cross-referenced to Richter’s local formula, such that for a period of 1 s both scales coincide at a reference distance of 1 km. The mathematical expression of this magnitude adapted by Mezcua and Martinez Solares [3] for the Iberian Peninsula, used for earthquakes between 1962 and March 2002, is given by: mbLg ¼ logðA=TÞ þ 1:05logD þ 3:90 for D < 30 mbLg ¼ logðA=TÞ þ 1:66logD þ 3:90 for D > 30 where A is the amplitude of the maximum wave train in the Lg phase in microns, T the period in seconds and D the epicentral distance in degrees.