Is there a relationship between magmatic fabrics and brittle fractures in plutons?

Physics of the Earth and Planetary Interiors 157 (2006) 286–310

Is there a relationship between magmatic fabrics and brittle fractures in plutons? A view based on structural analysis, anisotropy of magnetic susceptibility and thermo-mechanical modelling of the Tanvald pluton (Bohemian Massif) ˇ ak a,b,∗ , Bohuslav Vyhn´alek a , Petr Kabele c Jiˇr´ı Z´ a

Institute of Geology and Paleontology, Charles University, Albertov 6, Prague 12843, Czech Republic b Czech Geological Survey, Kl´ arov 3, Prague 11821, Czech Republic c Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Th´akurova 7, Prague 16629, Czech Republic Received 7 October 2005; received in revised form 9 May 2006; accepted 15 May 2006

Abstract The present study focuses on the thermal and mechanical aspects of cooling of plutonic systems with respect to their internal structure. Analysis of the Tanvald pluton and the nearby Liberec granite (the Krkonoˇse-Jizera Plutonic Complex, Bohemian Massif) using the anisotropy of magnetic susceptibility (AMS) method indicates the decoupled magnetic fabrics formed by different processes in these two plutons. Two regional sets of vertical fractures cut across the plutons and their host rocks. They are interpreted as having been formed as opening mode fractures (joints) after emplacement and cooling. Our thermo-mechanical finite element modelling indicates that the thermal stresses within the Tanvald pluton were compressive and that fracture criteria were not met during pluton cooling. These results imply that the emplacement depth and confining pressure significantly affect the state of stress within a pluton during cooling and may play a crucial role in the formation of early fractures in plutons. Consequently, the formation of early fractures during pluton cooling is driven by external conditions overriding the role of internal magmatic fabrics. We argue that no genetic, geometric or temporal correlation can exist between magmatic fabrics and fractures in granitoid plutons, and thus that the original concept of Hans Cloos based on fabric/joints relationships should be reconsidered. Instead, an alternative classification of fractures in plutons should include cooling fractures, syntectonic fractures, uplift fractures and post-uplift fractures. © 2006 Elsevier B.V. All rights reserved. Keywords: Anisotropy of magnetic susceptibility (AMS); Bohemian Massif; Fracture; Magmatic fabric; Pluton; Thermomechanical modeling

1. Introduction The thermal and mechanical aspects of the evolution of magmatic systems with respect to their internal ∗

Corresponding author. Fax: +420 221951429. ˇ ak). E-mail address: [email protected] (J. Z´

0031-9201/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2006.05.001

structure are fundamental to understanding a wide range of lithospheric processes. Voluminous magmatism drives metamorphism, modifies regional stress fields, controls crustal rheology and regional deformation, and contributes to significant vertical mass and energy exchanges within the lithosphere. Therefore, the development of magmatic fabrics and fracture networks in

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and around plutonic bodies during their emplacement and thermal decay represents an important scientific issue for several reasons. First, the stress and strain fields in and around plutons may substantially control the three-dimensional geometry of inherent mechanical anisotropies (magmatic fabrics) and fracture networks on different scales (from microscopic to regional). Second, conversely, large scale fracture patterns may provide valuable constraints on the orientation of regional stress fields during and after emplacement and cooling of magmatic bodies. Third, fractures and largescale fracture zones in magmatic systems are structures through which fluids flow, and thus preserve records of fluid migration through the fractured rock mass. Finally, the genetic relationship between magmatic fabrics and brittle fractures in cooling plutons has been a widely used but controversial concept in the Earth Sciences since the pioneering works of Cloos (1925) and Balk (1937). Cloos (1925) was the first person to recognize the importance of structural analysis of magmatic bodies and his ideas represent milestones in understanding magmatic processes. He developed the concept of “granite tectonics”, establishing the relationship between magmatic fabrics and joints in plutons. Cloos (1925) interpreted magmatic foliations and lineations in the Krkonoˇse-Jizera Plutonic Complex (northeastern Bohemian Massif, Central European Variscides) to represent magma flow planes and flow lines in a magma chamber, respectively, and postulated a genetic and geometric correlation between these “primary flow fabrics” and joint patterns. He identified four classes of joints based on fabric/joint relationships: (1) “flat-lying joints (L)”, (2) “cross-joints (Q)” oriented normally, (3) “longitudinal joints” oriented parallel, and (4) “diagonal joints” oriented at 45◦ to flow lines (lineations) and flow planes (foliations), respectively (Cloos, 1925; see also Balk, 1937; Berger and Pitcher, 1970; Pollard and Aydin, 1988; Price and Cosgrove, 1990). In contrast to the close genetic relationship between magmatic fabrics and joint development in plutons proposed by Cloos (1925), many modern studies emphasize that magmatic fabrics may form during a wide range of processes commonly recording increments of regional tectonic strain superimposed on a static magma chamber, with no relationship to the magma flow, emplacement, or shape of the pluton (Paterson et al., 1989, 1998, 2003). Similarly, formation of joints in plutons is typically a result of multiple processes that operate during the protracted history of a pluton from its initial cooling through tectonic deformation to uplift and erosion (e.g., Segall and Pollard, 1983; Pollard and Aydin, 1988; Segall et al., 1990; Bahat et al., 2001a,b, 2003; Bankwitz

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and Bankwitz, 2004a,b; Bankwitz et al., 2000, 2004). This contrast in views on the nature of the relationship between plutonism and joint development leads to the need for reinterpretation of fabrics and joints in the Krkonoˇse-Jizera Plutonic Complex. In the present paper, we focus on fabrics and fractures in the Tanvald pluton along the southwestern margin of the Krkonoˇse-Jizera Plutonic Complex, a composite plutonic body that was originally explored by Cloos in the 1920s. We used the anisotropy of magnetic susceptibility (AMS) method to investigate the internal magnetic fabric of the pluton, and we correlated the fabric data with the fracture orientation in the outcropto map-scale. Furthermore, we employed finite-element thermal-mechanical modelling to analyze cooling of the pluton and to ascertain whether thermal stresses resulting from cooling could cause fracturing of the pluton. Based on the integrated structural data, AMS measurements, and thermal-mechanical modelling, we interpret the history of the formation of magmatic fabrics and the relationship between fabrics and fractures in the pluton. Finally, we challenge the concept of close genetic relationship between magmatic fabrics and joints and discuss more general implications of our study for the joint development in plutons. 2. Geologic setting The ∼1000 km2 Carboniferous Krkonoˇse-Jizera Plutonic Complex has been a classic area of granite geology since the pioneering work of Cloos (1925). It crops out in the north-eastern part of the Bohemian Massif (the area is referred to as the West Sudetes) in the Central European Variscides (Fig. 1a and b). The West Sudetes consist of several distinct units interpreted as tectonostratigraphic terranes separated by major faults and shear zones (for reviews see Aleksandrowski and Mazur, 2002; Aleksandrowski et al., 1997; Cymerman et al., 1997; Hladil et al., 2003; and Winchester et al., 2003). In the map-view, the plutonic complex has a “double lobed” shape with the narrowest central part and its longest dimension (∼70 km) elongated ∼E–W. The plutonic complex intruded several lithotectonic units, each exhibiting polyphase deformational structures and contrasting metamorphic histories (see Winchester et al., 2003 and references therein for a detailed overview of regional geology). To the north and northwest, the Jizera Metamorphic Complex consists of heterogeneously deformed Early Paleozoic (Cambrian to Lower Ordovician) metagranitoids and orthogneisses (Borkowska et al., 1980; Kr¨oner et al., 2001; Oberc-Dziedzic et al., 2005) affected by Variscan regional metamorphism. To

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Fig. 1. (a) Geological sketch map of the Bohemian Massif and its position in the European Variscides (inset). The Krkonoˇse-Jizera Plutonic Complex crops out in the north-eastern part of the Bohemian Massif (referred to as the Sudetes). (b) Geological map of the north-eastern part of the Bohemian Massif around the Krkonoˇse-Jizera Plutonic Complex. AM - Armorican Massif, BM - Bohemian Massif, JCU - Jeˇstˇed Crystalline Unit, JMC - Jizera Metamorphic Complex, KJPC - Krkonoˇse-Jizera Plutonic Complex, MC - Massif Central, SKMC - South Krkonoˇse Metamorphic Complex.

the south and southeast of the plutonic complex, the South and East Krkonoˇse Metamorphic Complexes are composed of medium- to low-grade phyllites, micaschists and gneisses of predominantly Ordovician to Devonian age. The peak HP-LT blueschist facies metamorphism dated at 360 Ma was here followed here by a greenschist metamorphic overprint at around 340 Ma (Maluski and Patoˇcka, 1997). To the southwest, Neoproterozoic to Paleozoic rocks of the Jeˇstˇed range Unit (Kachl´ık and Patoˇcka, 2001; Kachl´ık et al., 2002; Marheine et al., 1999) are juxtaposed against the granitoids of the Krkonoˇse-Jizera Plutonic Complex along a major NW-SE trending fault zone. The plutonic complex is a composite body which comprises several intrusive units (Figs. 1 and 2; Klom´ınsk´y, 1969; Slaby et al., 2002; Slaby and G¨otze,

2004). Its southwestern margin is made up of two-mica granite (the Tanvald granite; Fig. 3a) whereas much of the remainder of the plutonic complex is made up of two distinct types of coarse-grained porphyritic biotite granodiorite to granite (the Jizera and Liberec granite; Fig. 3b). Their internal contact is delineated in places by smaller intrusions of more mafic, amphibole-biotite granodiorite (the Fojtka granodiorite). Medium-grained biotite granite (the Harrachov granite) crops out in two isolated bodies in the eastern half of the plutonic complex. The uppermost exposed part of the plutonic complex is made up of fine- to medium-grained equigranular biotite granite (the Krkonoˇse or Crestal granite). In this study, we examined in detail the Tanvald pluton along the south-western margin of the plutonic complex (Figs. 1 and 2). The Tanvald pluton forms a sheet-like,

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Fig. 2. Schematic geological map of the Tanvald pluton and nearby units (Liberec granite to the north and host rock phyllites to the south). An up to 1.5 km wide thermal aureole developed along the southern margin of the pluton. JCU - Jeˇstˇed Crystalline Unit, SKMC - South Krkonoˇse Metamorphic Complex.

∼E–W elongated body (Fig. 2); its longest dimension in the map view is ∼20 km and the shortest dimension is ∼2–3 km. The northern and southern outer margins of the pluton dip at steep to moderate angles to the S (Klom´ınsk´y et al., 2000). The pluton is compositionally relatively homogeneous and is predominantly made up of medium- to coarse-grained equigranular two-mica leucogranite (the Tanvald granite; Fig. 3a). The average modal composition of the Tanvald granite is: 39.9% K-feldspar, 30.7% quartz, 22.2% plagioclase, 3.5% mus-

covite and 2.5% biotite (Klom´ınsk´y et al., 2000). The geochemical characteristics of the Tanvald granite differ from those of porphyritic granites in the remainder of the plutonic complex. To the north, the pluton has a straight, sharp and discordant ∼E–W striking intrusive contact (Fig. 2) against the porphyritic Liberec granite (Fig. 3b), whereas, to the south, the pluton intrudes metasedimentary sequences (phyllites) of the South Krkonoˇse Metamorphic Complex along a sharp, moderately to steeply dipping contact discordant to the flat-laying host rock

ˇ a Studnice quarry. Hammer for scale. (b) Fig. 3. (a) Equigranular, two-mica (leuco)granite (the Tanvald granite) with microgranitoid enclave; Cern´ The porphyritic Liberec granite near contact with the Tanvald pluton. K-feldspar phenocrysts in the granite define a steep, margin-parallel magmatic foliation; abandoned quarry west of Tanvald. Hammer for scale.

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foliation. The metasedimentary host rocks of Cambrian to Devonian age are dominated by phyllites with intercalations of marbles, quartzites, and basic metavolcanics. In the thermal aureole (up to 1.5 km wide) along the southern margin of the Tanvald pluton, phyllites were metamorphosed to cordierite- and andalusite-bearing biotite hornfels (Klom´ınsk´y et al., 2004). The maximum P–T conditions in the thermal aureole thus probably did not exceed temperatures of 650–700 ◦ C and pressures of 2–3 kbar. While the field observations indicate that the Tanvald pluton is older than the porphyritic granites (Klom´ınsk´y, 1969; Klom´ınsk´y et al., 2000; this study, see Section 8), the available geochronological information is controversial and the exact intrusion ages are open to discussion. The porphyritic granites in the eastern part of the plutonic complex were dated at 328 ± 12 Ma (Pin et al., 1987) and at 329 ± 17 Ma (Duthou et al., 1991) by the Rb-Sr whole-rock method. However, Kr¨oner et al. (1994) obtained slightly younger (304 ± 14 Ma) Pb-Pb zircon evaporation age for the Liberec granite. Contrary to the field relations, the 40 Ar-39 Ar ages of the two-mica Tanvald granite (312 ± 2 Ma) are younger than those of the porphyritic granites (320 ± 2 Ma; Marheine et al., 2002), perhaps reflecting differences in the cooling histories of both intrusive units. According to Mazur (1995), Aleksandrowski et al. (1997), Werner et al. (2000) and Aleksandrowski and Mazur (2002) the Krkonoˇse-Jizera Plutonic Complex was emplaced during east-southeast directed extensional collapse and regional doming, resulting in reorientation of older structures on the flanks of the dome during the Early Carboniferous. The collapse was broadly synchronous with dextral strike-slip displacements along major ∼NW-SE faults (e.g., Intrasudetic fault, Fig. 1b) and, as suggested by Aleksandrowski et al. (1997), these faults were later reactivated during the Late Carboniferous–Early Permian with opposite (sinistral) displacement. Large-scale brittle faulting (e.g., the Lusatian thrust, where Cretaceous sediments were thrust over the Variscan basement, Fig. 1b) and reactivation of Variscan basement faults in the area of the KrkonoˇseJizera Plutonic Complex also continued intermittently until the Cenozoic and Quaternary. 3. Host rock structures along the southern margin of the Tanvald pluton Although the host rocks along the southwestern margin of the Krkonoˇse-Jizera Plutonic Complex experienced a complex polyphase tectonic history (Marheine et al., 1999), our structural mapping revealed relatively

simple structural pattern in the nearby host rock phyllites along the southern margin of the Tanvald pluton (Fig. 4). Here, pervasive metamorphic foliation typically strikes ∼ENE-WSW to WNW-ESE and dips to the ∼NNW, ∼SSW or ∼SSE at very low to moderate angles (10–40◦ ). On a stereonet, the foliation defines a simple fold-like pattern with a gently plunging axis oriented ∼WSW-ESE (Fig. 4). Thin bands or lenses of quartz produced during metamorphism commonly form boudins or pinch-and-swell structures parallel to the metamorphic foliation. The metamorphic foliation is associated with shallowly plunging mineral stretching lineations or crenulation lineations that typically trend to the ∼E and ∼WNW-ESE or to the ∼SW (Fig. 4). However, a few lineations also trend to the ∼SE or ∼S (Fig. 4). On many outcrops, gently dipping metamorphic foliations as well as lenses of metamorphic secretion quartz are affected by minor open upright folds or reverse kink bands. The folds or kink bands typically have gently plunging, ∼WSWESE trending axes parallel to stretching or crenulation lineations. 4. Anisotropy of magnetic susceptibility (AMS) The anisotropy of magnetic susceptibility measurement (AMS; Bouchez, 1997; Borradaile and Henry, 1997; see also Tarling and Hrouda, 1993 and Hrouda, 1982 for a review and the principles of the method) was carried out in the Tanvald pluton to characterize its internal (magnetic) fabric and to quantitatively constrain magnetic fabric parameters. In addition, we investigated magnetic fabric of the Liberec granite in an approximately ∼1 km wide zone adjacent to the northern margin of the Tanvald pluton. Because no evidence for pervasive subsolidus deformation of granitoids along the southeastern margin of the Krkonoˇse-Jizera Plutonic Complex has been found, the AMS method could provide valuable information on mineral preferred orientations in both granites acquired during the presence of a melt (magmatic fabrics of Paterson et al., 1989). 24 oriented samples at 9 sampling sites in the Tanvald granite and 9 oriented samples at 5 sampling sites in the Liberec granite were taken using a portable drill. The AMS was measured with a KLY-3S Kappabridge instrument (Jel´ınek and Pokorn´y, 1997). AMS data were statistically evaluated using the ANISOFT package of programs (Hrouda et al., 1990). Two AMS parameters (Jel´ınek, 1978, 1981) were used to characterize the magnetic fabric: the intensity of the preferred orientation of the magnetic minerals, indicated by the degree of anisotropy P = k1 /k3 , and the character of the magnetic fabric, indicated by the shape factor T = 2ln(k1 /k2 )ln(k2 /k3 )−1, where 0
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Fig. 4. Structural map of metamorphic foliations and stretching lineations in the host rock along the southern margin of the Tanvald pluton. Stereograms (lower hemisphere, equal area projection) show the orientation of the main structural elements (lineations and foliations as great circles).

indicates oblate and −1 < T <0 indicates prolate shapes of the magnetic susceptibility ellipsoids and k1 ≥ k2 ≥ k3 are the principal susceptibilities. Our study revealed contrasting magnetic fabrics in the Tanvald pluton and in the nearby Liberec granite. Magnetic fabric parameters and orientations differ significantly in both units (Figs. 5–7). The mean susceptibility of the analysed samples of Liberec granite ranges

from 1.26 to 775.40 × 103 (SI), whereas the mean susceptibility of the Tanvald granite samples ranges from 21.32 to 71.10 (SI) (Fig. 5). Thus, the mean susceptibility of the Liberec granite is approximately three orders of magnitude higher than that of the Tanvald granite, suggesting that predominantly ferromagnetic minerals are the main carrier of AMS in the former, whereas, in the latter, chiefly paramagnetic minerals play this role

Fig. 5. Histograms of mean susceptibilities of the Tanvald and Liberec granites. The Liberec granite has mean susceptibility that is approximately three orders of magnitude higher than that of the Tanvald granite.

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Fig. 6. PT plots for the Liberec and Tanvald granites (a, b) showing a higher degree of anisotropy of the Liberec granite. Stereograms (lower hemisphere, equal area projection) of magnetic lineations and foliations in the Tanvald pluton (d, e) and adjacent Liberec granite (c) show discordant magnetic lineations and foliations in both units.

(cf. Bouchez, 1997). The degree of anisotropy (P) in the Liberec granite ranges from 1.047 to 1.250 and in the Tanvald granite from 1.014 to 1.204 (Fig. 6). The shape parameter (T) in the Liberec granite ranges from −0.784 to 0.657, and in the Tanvald granite ranges from −0.944 to 0.964. In general, the degree of anisotropy (P) in the Liberec granite is higher and the shape parameter (T) tends to be less variable compared to the Tanvald granite (Fig. 6). The orientation of the magnetic fabric also differs significantly in the two granites (Fig. 7). Magnetic foliations in the Liberec granite along its contact with the Tanvald granite are sub-vertical (77–89◦ dip) and strike approximately ∼E–W, and thus run parallel to the ∼E–W oriented intrusive contact between the two units. This is in agreement with commonly observed margin-parallel magmatic foliations defined by the shape-preferred ori-

entations of K-feldspar phenocrysts. Similarly, magnetic lineations in the Liberec granite plunge gently to moderately to the E and are thus also contact-parallel. In contrast, magnetic foliations in the Tanvald granite have more heterogeneous orientations with variable strikes but gentle-to-moderate dips. Magnetic lineations typically plunge gently with variable trends. Foliation poles tend to cluster around the centre of the stereonet, whereas lineations tend to concentrate around its periphery. 5. Brittle fractures in and around the Tanvald pluton Most of the outcrops in the Tanvald pluton and nearby units (Liberec granite to the N and metasedimentary host rocks to the S) are characterized by the presence of two sets of regional systematic fractures, locally variable

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Fig. 7. Maps of magnetic foliations and magnetic lineations in the Tanvald pluton and adjacent Liberec granite showing discordant magnetic fabrics in both intrusive units.

non-systematic fractures and subhorizontal exfoliation joints in the granitoids. The regional systematic fractures in both granitoids and host rock phyllites share similar characteristics. They are steep to vertical (dip ∼75–90◦ ) and form two nearly perpendicular sets, one striking ∼NE-SW and the other striking ∼NW-SE, both with some minor deviations from the dominant strike (Figs. 8 and 9). In outcrops, each set typically consists of multiple individual fractures that are approximately planar and subparallel to each other (Fig. 10). Fractures in a given set predominantly do not interact with each other even at small spacings. In some cases, fractures of the ∼NE-

SW set terminate against the fractures and quartz veins of the ∼NW-SE set, suggesting that the former set is, at least locally, younger than the latter set (Fig. 10a and d). However, no regionally consistent relative timing relationships (e.g., termination of fractures of one set at fractures of the other set, curvature of one joint set towards the other) between the two sets have been observed in the study area. Where fractures of one set intersect the other, they frequently provide ambiguous timing relationships. Most commonly, in subhorizontal exposures, vertical fractures of the two sets are straight and intersect at high angles with no changes in orientation. Fractures are barren on most of the outcrops, but

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Fig. 8. Orientation diagrams (equal area projection, lower hemisphere) showing orientations of brittle fractures and quartz and calcite veins in the Liberec and Tanvald granites and host phyllites.

in some places they are coated by thin films of chlorite, epidote and hematite or quartz and calcite to form veins. The quartz and calcite veins are typically 0.5–1 cm thick, subvertical and strike ∼NW-SE (Figs. 8d and 10d). Thus veins tend to be associated with the ∼NW-SE set of fractures, while the ∼NE-SW set is barren. Perhaps due to the coarse-grained or porphyritic texture of the granitoids, fracture surfaces are variably smooth or rough and lack fractographic markings, which prevents extensive application of fractographic techniques (Bahat, 1991; Bahat et al., 2001b, 2003; Bankwitz and Bankwitz, 1995; Bankwitz et al., 2000) to fully address the fracturing mechanisms. Where not affected by surface processes and weathering, the fracture aper-

tures are small (0.1–1 mm). The true length, size and three-dimensional shape of fractures could not be precisely determined because, in most cases, they exceed the scale of individual outcrops (maximum tens of meters). Typically, the vertical fractures of both sets cross-cut microgranitoid enclaves (Fig. 10b) or aplitic dikes without offsetting them. Also at the grain scale, the fractures consistently cut across individual grains without causing the slightest off-set (Fig. 10a). This observation was also confirmed by our investigations of rocks in several underground tunnels where the two regional sets of fractures are superbly exposed. The tunnels (locality 1 in Fig. 1b) have perfectly smooth walls, allowing examination of the direction of displacement of K-feldspar phenocrysts

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Fig. 9. (a) Rose diagram showing strikes of all the measured joints in the study area. (b) Histogram of strikes (0–180◦ ) of steep to vertical fractures in the study area.

or individual grains along fractures on a millimetre scale. The majority of fractures show no shear off-set of grains parallel to fracture planes. Moreover, where fractures are healed by quartz or calcite to form veins, the displacement of fracture surfaces occurred in the direction perpendicular to the fracture wall. Only a small number of fractures in the study area bear slickenlines or slickenfibers on their surfaces, suggesting that they are minor shear fractures or reactivated pre-existing opening-mode fractures (faulted joints, Wilkins et al., 2001). It is, however, impossible to distinguish between the neoformed shear and the reactivated fractures (faulted joints) from the preserved rock record. While the two sets share the above characteristics, they differ in spacing (defined here as the perpendicular distance between two adjacent fracture planes of the same set) and thus in fracture densities (number of fractures of the same set per one meter, inversely proportional to the spacing). In order to quantitatively constrain the spacing characteristics of each set in different intrusive units, we collected spacing data along two road cuts, one ∼100 m long in the central part of the Tanvald granite and one ∼40 m long in the Liberec granite close to the northern margin of the Tanvald pluton (Fig. 2). In addition, we complemented these data with our measurements from a ∼200 m long section (scan line) in an underground tunnel in the Jizera granite (see Figs. 1b and 2 for the locations). The latter locality provides unbiased examples of typical fracture spacing distributions since the tunnel has constant orientation (azimuth 70◦ ) and its walls are very smooth. The summary diagram of all the

spacing data (Fig. 11) shows that both sets have irregular spacing ranging from several centimetres to three metres. Most of the spacing values of fractures of the NW-SE set fall in the range of 10–100 cm; spacings greater than 120 cm are much less frequent. Fractures of the NE-SW set show a large frequency of spacing values between 100 and 110 cm, but wider spacings (200–300 cm) are also common (almost twice as abundant as the other set). Our examination of average fracture densities for each set also indicates that the fracture densities of the NW-SE set (0.42 to 0.48) are as much as twice as high as those of the NE-SW set (0.22 to 0.33). The NW-SE fractures are more abundant and tend to be more closely spaced than the NE-SW fractures, supporting the orientation distribution statistics shown in the rose diagram in Fig. 9. On the map scale, the fractures of the two regional sets are preserved in all the basement lithologic units in the study area and form a relatively simple pattern (Figs. 12 and 13). Fractures of each set cut across the contact between the Liberec granite and the Tanvald pluton, and the contact between the Tanvald pluton and its host rocks, with no significant changes in orientation or refraction at the contacts. In the map view (Fig. 13), the trajectories of each set intersect at a high angle, which varies with respect to local variations of strike of the intersecting fractures and thus form an “X-type” intersection pattern (Hancock, 1985). The two regional fracture sets are homogeneously developed throughout the south-eastern margin of the Krkonoˇse-Jizera Plutonic Complex. We have not observed any mappable regional

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Fig. 10. Photos of fractures and veins, the Krkonoˇse-Jizera Plutonic Complex. (a) Two joints cutting across microgranite sheet and K-feldspar phenocrysts with no off-set of magmatic structures along joint planes, the Jizera granite; valley of the B´ıl´a Desn´a river; coin for scale. (b) Thin veins cutting across (no off-set) a microgranitoid enclave in the Jizera granite; Bedˇrchov tunnel. (c) Typical outcrop in the Tanvald granite with two intersecting sets of regional fractures, where the two sets differ in orientation and spacing; Jablonec nad Nisou. (d) The NE-SW joints terminate against the NW-SE joints and veins in the Jizera granite, valley of the B´ıl´a Desn´a river; hammer for scale.

gradients in the orientation, spatial distribution or spacing of these fractures. In addition to the regional vertical fractures described above, which are ubiquitous not only throughout the southeastern margin of the Krkonoˇse-Jizera Plutonic Complex, but also in the entire Krkonoˇse-Jizera Plutonic Complex and its host rocks (Klom´ınsk´y, 1969; Mierzejewski, 2002), other non-systematic fractures that could not be assigned to any regional set are also found on most of outcrops. These fractures comprise short crossjoints, joints between systematic vertical fractures, or geometrically irregular fractures that have variable orientations. They are smaller (tens of metres to metres)

Fig. 11. Diagram with spacing data compiled from three different localities (locations shown in Figs. 1 and 2). Fractures of the NW-SE set tend to be more closely spaced than NE-SW fractures.

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Fig. 12. Structural maps of the two regional sets of fractures (NE-SW and NW-SE) in and around the Tanvald pluton. The fractures of each set cut across all the basement units and their contacts with no change in orientation.

than the vertical fractures. They also commonly abut vertical fractures. A majority of outcrops also contain sub-horizontal joints that usually dip less than 30◦ and have highly variable strikes, which in many places seem

to be parallel to the present-day topography. Spacing of these joints varies widely, ranging from several meters to centimetres. Our reconnaissance investigations from several underground tunnels in the eastern part of the

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Fig. 13. Trajectories of vertical fractures interpreted from field measurements to show the map-scale fracture network. Local variations in fracture strikes result in variable angles at which each set intersects with the other set.

Krkonoˇse-Jizera Plutonic Complex also indicate that these sub-horizontal joints are not present at greater depths below the present-day erosion level, and thus they are probably confined to near-surface domains that die out rapidly with increasing depth. 6. Brittle faults along the south-western margin of the Krkonoˇse-Jizera Plutonic Complex Several regional faults and fault zones cut across the south-western margin of the Krkonoˇse-Jizera Plutonic Complex, including the Tanvald pluton. Based on their orientation and map-scale pattern, these faults form two sets with orientations similar to those of the regional vertical fractures, one set striking ∼NW-SE and the other ∼NE-SW. Both sets cut across all the basement lithological units in the area, including the Tanvald and Liberec granites, and are thus younger than the granitoids of the Krkonoˇse-Jizera Plutonic Complex. We examined in detail and measured about 45 fault planes at eight localities in and around the Tanvald pluton (Fig. 14). The faults of both sets have steeply dipping to vertical fault planes and bear subhorizontal to moderately plunging lineations. The lineations are represented by ridgeand-groove lineations or slickenlines, slickenfibers of syntectonically grown minerals (calcite or quartz) are

seen only rarely. Brecciation, mineralization, cataclasis, and secondary minor faults are common features associated with these major faults. Where kinematic indicators have been preserved, they indicate that the dominant sense of movement along both the ∼NW-SE and the ∼NE-SW faults was right-lateral (dextral) in most cases. Locally, fault planes also have other orientations, have moderately to steeply plunging lineations, or exhibit a left-lateral (sinistral) sense of movement. Orientations of fault planes and lineations and the sense of shear along fault planes were used to calculate the orientation of the principal stress directions for each of the two regional fault sets. Although paleostress analyses require that many assumptions be met to determine the orientations of the principal stress directions, this analysis may provide at least rough estimates of the orientation of principal stresses during the final events of brittle faulting of the Tanvald pluton and the nearby units, and will enable comparison these orientations with the orientations of brittle fractures (see Section 8). Both numerical and graphical methods have been proposed for reconstructing paleostress orientations from fault slip data (e.g., Angelier and Mechler, 1977; Etchecopar et al., 1981; Angelier, 1979, 1984, 1989); in this study, we used the TectonicsFP software (developed by Franz Reiter and Peter Acs), based on the method of Angelier and Goguel

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Fig. 14. Fault slip data from the study area. The faults form two sets, oriented NE-SW and NW-SE, and both sets are dextral strike-slip faults. Orientations of directions of principal stresses were calculated using TectonicsFP software; the arrows show the directions of compression and extension for each data set.

(1979) and Sperner et al. (1993). The results of our paleostress analysis (Fig. 14) indicate that, for the ∼NW-SE faults, the calculated maximum compressive stress (σ 1 ) may have been subhorizontal and oriented NNE-SSW, intermediate stress (σ 2 ) subvertical and minimum stress (σ 3 ) subhorizontal, oriented WNW-ESE. For the ∼NESW faults, the calculated principal stress directions are: maximum compressive stress (σ 1 ) subhorizontal, oriented WNW-ESE, intermediate stress (σ 2 ) subvertical, and minimum stress (σ 3 ) subhorizontal, oriented NNESSW. 7. Thermal-mechanical modelling of fracture development 7.1. General considerations To ascertain whether the observed fractures could have been induced by cooling of the intrusion, finite element analyses of the thermal history and resulting thermal stresses were carried out using the general-purpose program ADINA v. 8.3.1 (www.adina.com).

In general, magma emplacement and its subsequent cooling and solidification involve complex, interdependent thermal and mechanical processes. The former include heat conduction, heat production due to radioactive decay, metamorphic reactions, and/or crystallization, and heat convection by flux of hydrothermal fluids (Spear, 1993). The latter consist in viscous magma flow, phase transition (crystallization), and deformation and fracturing of hardened magma and host rock, which took place under tectonic, gravitational, magmatic and thermal forces (Knapp and Norton, 1981). Mathematical models that describe these processes are defined by a set of simultaneous partial differential equations, which can be solved numerically by the finite element method for arbitrary geometries and time histories (e.g., Bergbauer and Martel, 1999; Bonneville and Capolsini, 1999). However, the most limiting factor for numerical analyses is the scarcity of information on the initial and boundary conditions and material characteristics. Hence, the analyses presented here must be considered to be a compromise between the accuracy of the model on the one hand and availability of the necessary input data on

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icant multiple magma pulsing during the formation of the pluton. The role of fluids during early fracturing of the Tanvald granite was also neglected in the modelling. The latter assumption is in line with the “dry” character of the leucogranite and overall lack of aplite dikes and veins in the Tanvald pluton. 7.2. Thermal analysis

Fig. 15. Geometry and finite element discretization of the analyzed domain. The gray area corresponds to the Tanvald granite pluton and the surrounding rock is phyllite.

the other hand. In particular, no direct measurements of the thermal and mechanical properties of the Tanvald pluton and its host rock were available during this research. For the purpose of the present analyses, these characteristics were adopted from experimental data on similar rock types available in the literature. When constructing the model, we considered that, at the time of intrusion, the host rock consisted entirely of phyllites, since the Liberec granite is presumably younger than the Tanvald pluton (Klom´ınsk´y, 1969; this study). We represented the analyzed domain geometry by a two-dimensional horizontal section at a depth of 8 km assuming that the pluton has a sheet-like shape with steep walls, and that its shape does not significantly change with depth. The Tanvald pluton was represented by a polygonal area positioned approximately at the centre of a rectangular domain with dimensions of 75 km × 60 km (Fig. 15). The domain size was chosen to minimize the effects of outer boundary conditions on the processes within and in the vicinity of the pluton. The magma emplacement was modelled as an instantaneous process of a single magma pulse as there is no field evidence (e.g., internal contacts or sheeting) for signifTable 1 Initial and boundary conditions used for the thermal analysis Case

Initial temperature Magma (◦ C)

1 2

750 800

Host rock (◦ C) 400 300

Ambient temperature assigned to the outer boundary (◦ C) 400 300

First, the thermal history of the pluton-host rock system was analyzed. Due to the “dry” character of the magma (mentioned in the previous paragraph) and following the arguments of Knapp and Norton (1981), heat transfer by convection was neglected and the cooling process was modelled as a 2D transient heat conduction problem with crystallization heat production (Rolph and Bathe, 1982). Materials were then characterized by two parameters: the heat capacity (ρc) and the thermal conductivity (k). Both these parameters are temperature dependent. This dependence was represented by the empirical relationships proposed by Touloukian et al. (1981) and Bonneville and Capolsini (1999) (Fig. 16). The relationships were calibrated using the data available ˇ for granite and phyllite in Cerm´ ak et al. (1982) and in Vosteen and Schellschmidt (2003). Crystallization heat production of 1 × 109 Jm−3 in the range between liquidus and solidus temperatures of 1100 ◦ C and 700 ◦ C, respectively, was used for the solidifying granite after Spear (1993). As initial conditions, different temperatures were assigned to the granite magma and host phyllite. The initial temperatures were uniform in the respective rock regions. As a boundary condition, a constant (in time and space) ambient temperature, the same as the initial host rock temperature, was prescribed on the outer boundary of the analyzed domain. Since the initial thermal conditions were not exactly known, two cases were analyzed (Table 1). Case 1 with a lesser difference between the magma and host rock temperatures was perhaps more consistent with the metamorphic conditions (medium grade phyllites, P = 200–400 Mpa) and leucocratic composition of the Tanvald granite, while Case 2 was considered to be an extreme thermal loading. The analyses yielded time-dependent temperature fields throughout the entire analyzed domain. Figs. 17 and 18 show that, due to crystallization heat production, the temperature of the intrusion in Case 2 initially rose to about 865 ◦ C (855 ◦ C in Case 1) roughly 10,000 years after the emplacement. Subsequently, heat conduction resulted in cooling of the pluton and heating of the surrounding host rock. The temperature in the host rock thermal aureole reached 520–620 ◦ C in Case

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Fig. 16. Temperature-dependent heat capacity and thermal conductivity.

1 and 450–570 ◦ C in Case 2, depending on the distance from the granite pluton. The former result is in a good agreement with petrological data from the pluton aureole (Klom´ınsk´y et al., 2004). This essentially validates the analytical results. From the viewpoint of the evolution of thermal stresses, which are caused by temperature gradients, Case 2 in fact does lead to more severe loading. The cooling process is judged to be complete by 600,000 years after emplacement; at this time, the temperature variation within the analyzed space was within 100 ◦ C in both Cases 1 and 2 and the temperature field lacked any abrupt changes.

7.3. Mechanical analysis The goal of the mechanical analysis was to estimate stresses in the pluton and the host rock resulting from lithostatic loading due to overburden, magma pressure, and temperature changes. These stresses were then compared with the appropriate fracture and failure criteria. As we pointed out earlier, the geometry of the analyzed problem could be reduced to the horizontal y–z plane (Fig. 15). Also, most fractures observed in the field were apparently almost vertical surfaces, which projected onto the horizontal plane as lines. In order to allow

Fig. 17. Computed temperature field (◦ C) in and around the Tanvald pluton (a) 1000 years, (b) 10,000 years, (c) 50,000 years, (d) 600,000 years after emplacement (Case 2).

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Fig. 18. Computed temperatures along line AB crossing the Tanvald pluton from the north to the south (see Fig. 15) at different times after emplacement (Case 2). The solid vertical lines correspond to the pluton boundaries.

for the presence of vertical stress due to overburden, we discretized the problem by a single layer of thin 3D brick elements. The entire outer bounding surface of the body was then exposed to lithostatic pressure corresponding to a depth of 8 km, estimated to be 205.6 MPa (neglecting any variation through the depth of the analyzed body). In addition, a vertical pressure of 150 MPa was applied to the top and bottom of the granite magma region to account for the magma pressure. Consequently, the timedependent temperature field obtained from the thermal analysis was transferred to the body. It was assumed that the initial temperature field did not induce any thermal stresses. Both granite and phyllite were modelled as elastic isotropic materials. In the case of phyllite, this simplification was justified by the fact that metamorphic foliations representing significant mechanical anisotropy of the rock were nearly horizontal and parallel to y–z plane. The mechanical properties of both materials, however, were considered to be temperature-dependent. The depen-

dences were obtained by approximating the measurements published by Heuze (1983). The Young modulus E of both rocks decreased linearly with increasing temperature, reaching 0 GPa at 1100 ◦ C. The Poisson ratio ν of the host rock (phyllite) was assumed to be independent of temperature. To indicate that, at the time of intrusion, the granite magma behaved as an incompressible fluid, its Poisson ratio was set at 0.499 at and above the intrusion temperature (750 ◦ C in Case 1 and 800 ◦ C in Case 2). In the range between the intrusion temperature and the solidus temperature of the granite (700 ◦ C), the Poisson ratio was assumed to decrease linearly with temperature. Below this temperature, ν was constant. The specific values of the material characteristics were taken from Yamaguchi et al. (2002), Lama and Vutukuri (1978), and Heuze (1983) and are listed in Table 2. As shown by Heuze (1983), the coefficient of thermal expansion α of granitic rocks increases with temperature until the temperature of the α–β transition of quartz is reached. Beyond this temperature, α drops to almost zero. It also decreases with pressure. Taking into account the data in Heuze (1983) and the actual pressure level of several hundreds of MPa, α was approximated as a linear function of temperature with α = 0 ◦ C−1 at 0 ◦ C and α = 15 × 10−6 ◦ C−1 at 700 ◦ C. At higher temperatures, the thermal expansion (α) was assumed equal to zero. The mechanical analysis was carried out incrementally. The results included time-dependent stress, strain, and displacement fields within the analyzed domain. By comparing Figs. 17 and 19, it is evident that the changing temperature field caused nonuniform stressing of the pluton and the adjacent host rock. To find out whether this process resulted in fracturing of the rocks, two fracture criteria were employed. First, we assumed that tensile fracture would occur if the maximum principal stress exceeded the uniaxial tensile strength. Second, compressive failure was assumed to take place if the stress state

Table 2 Mechanical properties of rocks used for the numerical analysis Rock type

Young modulus E GPa

Granite Phyllite

56a 76.5c

Poisson ratio ν –

Uniaxial tensile strength MPa

Uniaxial compressive strength MPa

Compressive strength at confining pressure of 1500 MPa and temperature of 300 ◦ C MPa

0.11a 0.2d

21a 22.8c

229a 126c

5185b 3527d

Except for the last column, the values correspond to room temperature. a Westerly granite, Yamaguchi et al. (2002). b Dry Westerly granite, Heuze (1983). c Michigan phyllite, Lama and Vutukuri (1978). d Assumed.

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Fig. 19. Computed contours of maximum (P1) and minimum (P3) principal stresses (MPa) in and around the Tanvald Pluton (a, b) 10,000 years, (c, d) 50,000 (Case 2).

at any point satisfied the Drucker-Prager criterion: √ aI1 + J2 − κ ≥ 0 (1) where I1 is the first invariant of the stress tensor, J2 the second invariant of the deviatoric stress tensor, and a and κ are material parameters that can be obtained, for example, from the results of uniaxial and triaxial tests. Both of the criteria were adapted to approximately reflect the effect of temperature on the rock strength (Heuze, 1983). The uniaxial tensile strength (Table 2) was assumed to

decrease linearly with increasing temperature, so that it reached 0 MPa at 1100 ◦ C. Parameters a and κ were also taken to be linear functions of temperature. They were calibrated from the uniaxial compressive strength and triaxial test data listed in Table 2 and from the assumption that, at a temperature of 1100 ◦ C, the rocks could sustain only the state of hydrostatic compression (all principal stresses equal and negative). After examining the computed stress histories, we found that neither of the two criteria were ever satisfied

Fig. 20. Computed values of maximum principal stress (a) and Drucker-Prager yield function (b) along line AB crossing the Tanvald pluton from the north to the south (see Fig. 15) at different times after emplacement (Case 2). The solid vertical lines correspond to the pluton boundaries.

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study for the fabric/fracture relationships in plutons in general. 8.1. Interpretation of fabrics and fractures in the Tanvald pluton

Fig. 21. Time histories of the Drucker-Prager yield function value in point C (see Fig. 15) computed for different initial temperature states (Case 1 and 2).

within the Tanvald pluton when the initial thermal conditions denoted as Case 1 (see Table 1) were used. With the ultimate loading (Case 2), tensile principal stresses were also not observed within the body (Figs. 19a,c and 20a). Fig. 20b shows that the stress state approached the Drucker-Prager criterion of compressive fracturing in the central part of the Tanvald pluton (in the vicinity of point C marked in Fig. 15) about 50,000 years after emplacement. However, Fig. 21 shows that in Case 2, the fracture criterion was met only very shortly and that it was not significantly exceeded, while in Case 1 it was indeed never attained. For the sake of correctness, we should mention that some tensile stresses and stresses exceeding the compressive fracture criterion were observed at certain times in isolated elements at the boundary between the pluton and the host rock. Nevertheless, we believe that this occurred due to using distorted finite elements in these locations and due to idealizations adopted in the model (the pluton shape modeled as a polygon with sharp bends, sudden change in applied vertical pressure, etc.). The implications of these findings are discussed in the next section. 8. Discussion Below, we first interpret the formation of magnetic fabrics and brittle fractures and explore fabric/fracture relationships in the granitoids and host rocks from the south-western margin of the Krkonoˇse-Jizera Plutonic Complex. We then discuss the results of our numerical modelling and compare these results with the measured field data. Finally, we challenge the ideas first hypothesized by Cloos (1925) in the light of our present investigations and discuss the broader implications of our

Our AMS study revealed that contrasting magnetic fabrics have been preserved in the Tanvald pluton and the adjacent Liberec granite (Figs. 5–7). We have shown that ∼E–W, margin-parallel vertical magnetic foliations and shallowly plunging lineations define the fabric of the Liberec granite along the sharp, discordant intrusive contact with the Tanvald pluton; the contact was presumably formed by magmatic stoping. The magnetic foliations correlate well with the steep margin-parallel magmatic foliations defined by the shape-preferred orientation of K-feldspar phenocrysts in the Liberec granite (Fig. 3b). In contrast, the fabric pattern in the Tanvald pluton is characterized by sub-horizontal to moderately dipping magnetic foliations and shallowly plunging magnetic lineations, both having variable strikes and trends, respectively. Our interpretation of these fabric patterns follows. Generally speaking, interpretation of margin-parallel magmatic fabrics in plutons is problematic since strain caused by several processes or their combination (convection, expansion of a magma chamber, emplacement of inner magma batches or magma surges, internal flow along margins or chamber walls, stress and strain refraction in a crystallizing magma chamber) may cause margin-parallel mineral alignment (Paterson et al., 1998). Based on our AMS and structural data we cannot precisely attribute the formation of the margin-parallel fabric in the Liberec granite to any of the above processes or estimate their contribution to the final fabric from the preserved rock record. Importantly, the margin-parallel magnetic foliations and lineations in the Liberec granite are discordant to both host rock deformational structures and magnetic fabrics in the Tanvald pluton in that ∼E–W margin-parallel vertical foliations are not found in the Tanvald pluton nor in the host rock as the pluton is approached. Therefore, the formation of the ∼E–W margin-parallel magnetic fabrics in the Liberec granite is clearly decoupled from regional tectonics and fabrics in the Tanvald granite and thus most likely resulted from strain during internal boundary processes along the chamber wall. In contrast, the gently to moderately dipping magnetic foliations and shallowly plunging lineations in the Tanvald pluton are both independent of the pluton geometry and are commonly discordant (at a high angle) to the pluton margins. Instead, they roughly correspond to

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widespread sub-horizontal to gently dipping metamorphic foliations in host rock phyllites, suggesting that the magnetic fabric in the Tanvald pluton may have recorded strain increments (i.e., sub-vertical shortening) after emplacement and construction of the pluton. The decoupled fabric patterns may also confirm the relative ages of both intrusive units established previously from field observations, suggesting that the Tanvald pluton is older than the Liberec granite (Klom´ınsk´y, 1969). We have shown that the two regional vertical fracture sets, along with variably oriented sub-horizontal joints, dominate most of outcrops in the study area, and we have also documented that the vertical fractures cut across the Tanvald pluton and the Liberec granite and their intrusive contact with no changes in orientation (Figs. 12 and 13). In addition, none of the regional vertical fracture sets terminate at the outer contacts of either intrusive unit; instead they continue into the host metamorphic complexes south of the Tanvald pluton. Thus they could not be related to emplacement or pluton cooling. Although the distinction between extensional, hybrid and shear fractures may be problematic in general (Hancock, 1985; Price and Cosgrove, 1990; Engelder, 1999), our data indicate that, with minor exceptions, both veins and regional vertical fractures of the two sets predominantly represent opening-mode (mode I) extension fractures (joints) consistently showing no evidence for shear displacement along the fracture walls, even at the grain scale. Our observations are thus contradictory to previous interpretations of the two regional vertical fractures in the Krkonoˇse-Jizera Plutonic Complex as conjugate sets of shear fractures formed during a ∼N–S regional tectonic compression (Mierzejewski, 2002). Even though the association of veins with the ∼NWSE regional fractures may imply that, at least locally, the ∼NW-SE set is older than the ∼NE-SW set, ambiguous butting of fractures of one set against the other points to more complex timing relationships. In addition, the ∼NW-SE and ∼NE-SW regional strike-slip faults have the same sense of shear (right-lateral) and thus most likely did not represent a conjugate fault system. All of these observations indicate multiple episodic reactivations and reorientations of regional paleostress fields over a protracted period of time. Given that the reactivation of the Variscan basement in the area of the Krkonoˇse-Jizera Plutonic Complex continued intermittently until the Cenozoic and Quaternary, we suppose that the multiple fracturing and faulting events and paleostress field reorientations may have occurred at any time after emplacement and crystallization of the KrkonoˇseJizera Plutonic Complex.

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The explanation of the sub-horizontal joints, which are ubiquitous on most of the outcrops throughout the Tanvald pluton and the Krkonoˇse-Jizera Plutonic Complex, is problematic given that the roof of the plutonic complex has been eroded off and thus the original vertical extent and three-dimensional shape of the upper part of the plutonic complex is unknown. Therefore, the relationship of flat-lying fractures to the roof of the plutonic complex cannot be firmly established and remains a matter for speculation. In most cases, however, the flat-lying fractures are parallel to the present-day topography and, as confirmed by our investigations in underground tunnels, are also confined to the presentday near-surface level, dying out rapidly with increasing depth. In this perspective, most of the flat-lying fractures in the Krkonoˇse-Jizera Plutonic Complex could be interpreted as exfoliation or sheeting joints (Bahat et al., 1999), resulting from uplift and post-uplift near-surface processes having no relationship to the original roof of the plutonic complex nor to pluton cooling. In summary, no genetic, geometric or temporal correlation has been found between the multiple magnetic (magmatic) fabrics and brittle fractures (joints) in the examined granitoids along the south-western margin of the Krkonoˇse-Jizera Plutonic Complex. Instead, we argue that the multiple magnetic fabrics, interpreted to represent magmatic fabrics, recorded finite strain during both internal magma chamber processes and regional tectonics. The fabrics thus do not represent flow lines and flow planes of flowing magma. The formation of brittle fractures took place after the emplacement and cooling of the Tanvald and Liberec granites during a polyphase tectonic history including uplift and post-uplift processes. 8.2. Implications of the numerical modelling We believe that our numerical modelling (Figs. 15–21) provides an intriguing insight into the formation of brittle fractures not only in the Tanvald pluton, but may also apply to other plutonic bodies in general. In most cases, previous numerical analyses of pluton cooling employed oversimplified pluton geometries (e.g., rectangular blocks) and temperatureindependent elastic behaviour of granitoids (i.e., the Young modulus, Poisson ratio and coefficient of thermal expansivity were assumed to remain constant during pluton cooling). In contrast, our numerical modelling was set up to involve both more realistic two-dimensional pluton shapes in horizontal section (i.e., map) and, importantly, also the variation of the thermal and mechanical parameters with temperature.

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Interestingly, our analyses show that almost no tensile stresses were generated as a result of cooling of the Tanvald pluton (Figs. 19 and 20). Instead, the computed stresses are compressive throughout the pluton, and thus no extensional fractures (as those observed in the field) are expected to form during its thermal decay. We interpret that, even though decreasing temperature causes volumetric contraction, the resulting stresses within the pluton remain compressive in consequence of large confining pressure due to lithostatic loading of the overburden at the pluton emplacement depth (at least 8 km). In addition, when the model was exposed to the ultimate thermal loading (Case 2), the resultant stresses only attained but did not significantly exceed the compressive failure criterion of the model granite in a very limited area in the central part of the pluton. It was thus concluded that the cooling of the pluton resulted in very little, if any, compressive fracturing of the model granite. Therefore, the results of our thermo-mechanical modelling fit the structural data well in the sense that we have not found any substantial field evidence for fractures related to cooling of the Tanvald pluton. More general conclusions that can be drawn from our modelling of thermal stresses and fracture development in cooling plutons are as follows. First, we emphasize that emplacement depth and vertical lithostatic stresses significantly affect the stress state within a given pluton during its cooling and thus play a crucial role in the formation of early fractures in plutons. Second, we have shown that the formation of early fractures during pluton cooling may be, at least in some cases, largely driven by external conditions (pluton shape, emplacement depth and confining pressure) and the thermal and mechanical characteristics of both the pluton and the host rocks. We suggest that the external conditions may override the role of internal magmatic fabrics (foliations and lineations) as inherent mechanical anisotropies during early thermal fracturing of a pluton. 8.3. Is there a relationship between fabrics and fractures in plutons? We believe that the above data, numerical thermomechanical analysis and theoretical considerations provide an intriguing background for re-evaluation of the model first suggested by Cloos (1925), of a genetic relationship between magmatic fabrics and fracture patterns, and fabric-to-fracture relationships in plutons in general. Cloos (1925) used an example from the eastern half of the Krkonoˇse-Jizera Plutonic Complex and interpreted magmatic foliations and lineations to represent magma flow planes and flow lines in a chamber, respectively

and, from correlation of these “primary flow fabrics” with joint patterns, defined four main classes of joints (Cloos, 1925; Balk, 1937; Berger and Pitcher, 1970; see also Price and Cosgrove, 1990 for review): (i) cross joints (Q) that are perpendicular to the foliation and lineation as a result of elongation during drag of the mobile core against the walls or roof, or as a result of continued expansion of the intrusion; (ii) longitudinal joints (S) that are parallel to the lineation and perpendicular to both the foliation and cross-joints and were interpreted to be formed during cooling (thermal contraction) of the intrusion; (iii) flat-lying joints (L) that develop near the roof as the intrusion shrinks during cooling or as a result of relaxation of vertical stress during and after emplacement; (iv) diagonal joints that form as shear fractures at 45◦ or less to the foliation as a result of shear stress during lineation-parallel stretching of the intrusion. Although the idea of a close genetic relationship between magmatic fabric and joints as suggested by Cloos (1925) and Balk (1937) has been widely employed and cited in many textbooks and papers, several lines of evidence indicate that more complex relationships may exist between fabrics and fractures in plutons than the simple relationships outlined above. For example, unlike the original model proposed by Cloos (1925) and Balk (1937) of foliations and lineations representing flow planes and flow lines in flowing magma, modern studies largely indicate that magmatic fabrics in plutons form in rheologically complex crystal-rich mushes and reflect strain during a wide variety of processes (see Paterson et al., 1998 for review). Magmatic fabrics in plutons also commonly record increments of regional tectonic strain superimposed on a static magma chamber with no relationship to the magma flow, emplacement, or shape of a pluton (Paterson et al., 1998, 2003). An exciting additional complexity to this issue is represented by multiple magmatic fabrics in a single pluton (Paterson et al., 1998; ˇ ak et al., 2005) or even by composite fabrics where a Z´ single magmatic fabric was formed by several different processes (Paterson et al., 2003). Similarly, the formation of joints in plutons is a complex, polyphase process that may involve initial thermal fracturing during cooling (Bergbauer and Martel, 1999), hydraulic fracturing due to fluid overpressure (Bahat et al., 2003), fracturing caused by external tectonic stresses (Segall and Pollard, 1983; Pollard and Aydin, 1988), and fracturing related to uplift of a pluton and post-uplift processes (Bahat and Rabinovitch, 1988; Hancock and Engelder, 1989; Bahat et al., 1999; Ehlen, 1999). Moreover, as suggested by our numerical analysis, formation of early fractures during pluton cooling is largely dependent on external conditions and the ther-

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mal and mechanical parameters discussed above. Apparently, the external conditions and thermal and mechanical characteristics of a pluton/host rock system are independent of the processes of formation of internal magmatic fabrics in plutons (outlined above; see Paterson et al., 1998 for review). Therefore, as exemplified by both the present study from the Tanvald pluton and the above considerations, we suggest that possibly no correlation exists between fabrics and fractures in granitoid plutons and, in addition, ambiguities and uncertainties commonly arise in many cases when interpreting both fabric-forming processes and the mechanisms of fracture formation. We argue that the concept suggested by Cloos (1925) and Balk (1937) of fabric/joints relationships in plutons, based solely on genetic and geometric grounds, represents an oversimplification and thus should be reconsidered. Instead, we suggest that a possible classification of fractures in granitoid plutons should take into account the inferences in fracture formation described above. In our view, four end-member classes of fractures (not only joints) can be distinguished in granitoid plutons as follows (cf. Bahat, 1991, 1999; Bahat et al., 2003, 2005, p. 355): (i) cooling fractures that form as a result of thermal contraction during pluton cooling and that terminate against pluton margins; the orientation of these fractures should be predictable by thermal-mechanical modelling; (ii) syntectonic fractures that result from regional tectonic stresses superimposed on a crystallizing or already entirely solidified pluton; these fractures cut across pluton boundaries, are preserved both in pluton and host rocks, and may form at any time after emplacement and cooling of a pluton and have arbitrary orientation with respect to the pluton shape; (iii) uplift fractures that form during uplift, (iv) post-uplift fractures that may be represented, for example, by sheeting or exfoliation joints, and are also related to near-surface processes, such as glaciation and weathering. As we mentioned in the introductory section, the relationship between fabrics and fractures in plutons is a challenging scientific issue. We believe that the results of our study discussed above may provide some background for further progress in understanding relationships between magmatic fabrics and fractures, and evaluation of the role of magmatic fabrics as inherent mechanical anisotropies and precursors for fracture propagation in granitoid plutons. In our view, one of the major challenges for future research is exploring fracture development in plutons as an interplay between fabric development, thermal, tectonic, and lithostatic stresses and fluid pressure during pluton cooling. Such future research should, at best, integrate detailed struc-

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tural mapping and field observations, micro structural studies, quantitative fabric and textural analyses, fractographic investigations of fracture surface markings, and thermal-mechanical modelling. 9. Conclusions The main conclusions of our study are: (i) The magnetic fabric in the Liberec granite is parallel to its intrusive contact with the Tanvald pluton and is unrelated to the regional tectonic deformation. We interpret this fabric as recording internal processes along a magma chamber boundary. In contrast, magnetic fabrics in the Tanvald pluton are commonly discordant (at high angle) to the pluton margins and roughly correspond to widespread subhorizontal to gently dipping metamorphic foliations in host rock phyllites. This suggests that the magnetic fabric in the Tanvald pluton may have recorded strain increments (i.e., sub-vertical shortening) after emplacement and construction of the pluton. (ii) The two regional sets of vertical fractures cut across all lithological units and are interpreted to be formed as opening mode (mode I) fractures (joints) during regional tectonic deformation after the emplacement and cooling of the Tanvald and Liberec granites. Along with the ∼NW-SE and ∼NE-SW regional strike-slip faults they probably did not represent a conjugate system of shear fractures. These observations are at variance with previous interpretations of the regional vertical fractures in the Krkonoˇse-Jizera Plutonic Complex presumed to form a conjugate set of shear fractures resulting from ∼N–S tectonic compression. Instead, the faults and fractures indicate multiple reactivations and reorientations of regional paleostress fields over a protracted period of time. Given that the reactivation of the Variscan basement in the area of the Krkonoˇse-Jizera Plutonic Complex continued intermittently until the late Mesozoic and Cenozoic, we suggest that the multiple fracturing events and stress field reorientations may have occurred at any time after emplacement and crystallization of the Krkonoˇse-Jizera Plutonic Complex and also involved uplift and post-uplift processes. (iii) Based on careful examination of internal magnetic fabrics and brittle fractures, we argue that no genetic, geometric or temporal correlation exists between the multiple fabrics and fractures (joints) in granitoids along the south-eastern margin of the KrkonoˇseJizera Plutonic Complex.

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(iv) Our thermo-mechanical analysis indicates that no tensile stresses were generated as a result of cooling of the Tanvald pluton. The modelled stresses are compressive throughout the pluton and result from the confining pressure due to lithostatic loading. No extensional fractures form during its thermal decay. In our model, the magnitudes of the thermally induced stresses do not exceed the compressive failure criterion of the model granite and are thus too small to cause significant brittle fracturing. As a general implication, we point out that the emplacement depth and vertical lithostatic stresses significantly affect the stress state within a given pluton during its cooling and play a crucial role in the formation of early fractures in plutons. The formation of early fractures during pluton cooling is largely driven by external conditions, and the thermal and mechanical characteristics of the pluton/host rock system override the role of internal magmatic fabrics (foliations and lineations) during early fracturing of a pluton. (v) No relationship between fabrics and fractures commonly exists in plutonic systems, and ambiguities may arise in many cases when interpreting both fabric-forming processes and the mechanisms of fracture formation. We propose an alternative classification of fractures in plutons including cooling fractures that form as a result of thermal contraction during pluton cooling, syntectonic fractures that result from regional tectonic stresses, uplift fractures that form during uplift, and post-uplift fractures related largely to near-surface processes and weathering. Acknowledgements We gratefully acknowledge the valuable comments and thoughtful suggestions of four anonymous reviewers, which have improved the original manuscript. In particular we also wish to thank Josef Klom´ınsk´y (Czech Geological Survey, Prague) for many discussions on the geology of and showing us around the KrkonoˇseJizera Plutonic Complex. Frantiˇsek Hrouda is gratefully acknowledged for continuous discussions on AMS and help in measuring AMS in the laboratories of AGICO Ltd. (Brno, Czech Republic). The research benefited from discussions with Jiˇr´ı Konop´asek, Marta Chlup´acˇ ov´a and V´aclav Kachl´ık, who are also gratefully acknowledged. Kryˇstof Verner is thanked for help with AMS sampling. The research was supported by Czech Geological Survey Internal Research Project No. ˇ ak), by the Radioactive Waste Reposi3238 (to Jiˇr´ı Z´ ´ tory Authority of the Czech Republic (SURAO) project

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