Control of pore fluid pressure on depth of emplacement of magmatic sills: An experimental approach

Tectonophysics 489 (2010) 1–13

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Control of pore fluid pressure on depth of emplacement of magmatic sills: An experimental approach Jean-Baptiste Gressier a,⁎, Regis Mourgues a, Ludovic Bodet a, Jean-Yves Matthieu a, Olivier Galland b, Peter Cobbold c a b c

UMR CNRS 6112, Université du Mans, Le Mans, France PGP, University of Oslo, Oslo, Norway UMR CNRS 6118, Université Rennes 1, Rennes, France

a r t i c l e

i n f o

Article history: Received 2 December 2009 Received in revised form 10 March 2010 Accepted 15 March 2010 Available online 24 March 2010 Keywords: Sill emplacement Hydraulic fracturing Pore fluid pressure Physical modelling

a b s t r a c t In sedimentary basins, the emplacement of magmatic sills tends to occur within rock of low mechanical competence and permeability, such as shale. This often contains pore fluids at abnormally high pressure. We first theoretically show that, in anisotropic media, the higher the pore fluid pressure, the deeper the sill emplacement. Then we introduce a new technique for analogue modelling of such intrusive bodies under conditions of fluid overpressure (greater than hydrostatic), which corroborate the theoretical analysis. As an analogue of brittle sediment, we use a diatomite powder. This material is a dry, fine-grained, frictional, cohesive and permeable material. As an analogue for magma, we take a silicone putty (RTV silicone), which is at first Newtonian, but then solidifies at room temperature. We use compressed air as a pore fluid. Under these experimental conditions, we investigate the intrusion of magma into the host powder under various fluid overpressures. In homogeneous diatomite powder, having uniform cohesion, intrusive bodies are segmented dykes. These become feeders to sills, if the fluid overpressure exceeds the weight of overburden. Where the sedimentary column has a horizontal discontinuity in strength, the transition from dyke to sill occurs at a smaller overpressure (hydrostatic b λex b 1). As a possible illustration of these results, we consider sills within source rocks of the Neuquén Basin and of the Parana Basin, both in South America, where overpressure may have resulted from maturation of organic material. © 2010 Elsevier B.V. All rights reserved.

1. Introduction If a magmatic sill intrudes a sedimentary basin, it may enhance geothermal activity (Wohletz and Heiken, 1986) and its thermal effects may improve petroleum prospectivity (Malthe-Sorenssen et al., 2004). Such economic applications have led to an increasing interest in the mechanisms of sill emplacement. In some areas, the intrusive bodies are sub-vertical dykes at depth, yet become sills nearer the surface. The transition from dyke to sill can be quite sharp. The depth at which it occurs may depend on the mechanical behaviours of magma and host rock. For magma, the viscosity, density and driving pressure may contribute to the transition (Anderson, 1951; Bradley, 1965; Francis, 1982; Lister, 1990; Rivalta et al., 2005). For host rock, the governing parameters may overburden thickness (Mudge, 1968), pre-existing fractures or faults (Leaman, 1975; Liss et al., 2002), regional tectonic context (Hubbert and Willis, 1957; Roberts, 1970; Gudmundsson, 1990; Sibson, 2003; Galland et al., 2006), contrasts in elastic rigidity

⁎ Corresponding author. E-mail address: [email protected] (J.-B. Gressier). 0040-1951/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2010.03.004

(Pollard, 1973; Kavanagh et al., 2006; Valentine and Krogh, 2006), variations in petro-physical properties (Gretener, 1969; Price and Cosgrove, 1990; Gudmundsson, 2002, 2004), or mechanical discontinuities (Mudge, 1968; Gretener, 1969). Magma in planar intrusive bodies (dykes and sills) is generally assumed to propagate through sediments by hydraulic fracturing without percolating the medium (Hubbert and Willis, 1957; Jaeger, 1972; Spence and Turcotte, 1990; Lister and Kerr, 1991; Rubin, 1995; Valentine and Krogh, 2006). ‘External’ designates such a mechanism of fracturing (Mandl and Harkness, 1987), during which magma comes from outside the brittle medium. Mandl and Harkness (1987) also described a hydraulic fracturing induced by pore fluids such as diagenetic fluids, water or hydrocarbons and referred to this as an ‘internal mechanism of hydrofracturing’, because the fluids percolate through the interconnected pore space. According to some field observations (Mudge, 1968; Antonellini and Cambray, 1992), sills preferentially intrude weak layers, for example shale, mudstone or hyaloclastite. In sedimentary basins, such rocks tend to be of low permeability and form seals for migrating fluids (Neuzil, 1994). Consequently, such rocks often contain pore fluids at abnormal pressures (Magara, 1978; Chapman, 1980; Hunt, 1990; Luo and Vasseur, 1992).

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According to Osborne and Swarbrick (1997), there are three main mechanisms for generating fluid overpressures in sedimentary basins: disequilibrium compaction, diagenetic reactions (e.g. the smectite/illite transition) and hydrocarbon generation. These mechanisms explain why most sedimentary basins exhibit fluid overpressures at depth (Fertl, 1976; McPherson and Garven, 1999; Madon, 2007). By reducing effective stresses (Terzaghi, 1923; Rice and Cleary, 1976), fluid overpressures favour deformation and hydraulic fracturing (Hubbert and Rubey, 1959). As magmatic sills seem to propagate by hydraulic fracturing, the influence of preexisting fluid overpressures on the mechanics of sill emplacement is an important subject. To gain a better understanding of the subject, various authors have resorted to physical modelling. In the experiments of Kavanagh et al. (2006) or Rivalta et al. (2005), water represented an intruding fluid and solid gelatin represented an elastic host rock. In contrast, Mathieu et al. (2008) used honey or golden syrup, and Galland et al. (2006) used vegetable oil. These viscous fluids intruded a granular material, which represented a host rock that yields according to a Coulomb criterion. In this article, we first provide a theoretical analysis of the effect of pore fluid on the depth of sill emplacement, based on the model of Price and Cosgrove (1990). We follow this up with the results of an experimental investigation. We simultaneously used two kinds of fluids, a silicone paste (representing magma) and compressed air (representing a pore fluid as (Mourgues and Cobbold, 2003, 2006a,b). The host material was granular, yet cohesive. In the experiments, fluid overpressures strongly controlled the depth of the dyke-to-sill transition. We compare the experimental results with natural examples, where magmatic rocks have intruded sedimentary basins. 2. Theoretical background 2.1. Emplacement of magmatic sills and dykes Magma propagates through sediment by hydraulic fracturing without percolating the medium (Hubbert and Willis, 1957; Jaeger, 1972; Lister and Kerr, 1991; Spence and Turcotte, 1990; Rubin, 1995; Valentine and Krogh, 2006). The condition necessary for the formation of a planar magmatic intrusive body in an isotropic medium is (Jaeger, 1972): Pm N σ3 + T

ð2:1Þ

Here Pm is the magmatic pressure and T is the tensile strength of the host rock. The least principal stress, σ3, controls the orientation of the intrusive body. If σ3 is horizontal, the body is a vertical dyke, whereas if σ3 is vertical, the body is a sill. If the host rock is anisotropic, because of foliation, schistosity or bedding, the tensile strength across the bedding (or folliation,…) (T⊥) may be different from the strength along the bedding (T||) (Fig. 1: anisotropic medium I). Therefore the condition for the emplacement of dykes is: Pm N σh + T jj

ð2:2Þ

Here σh is the horizontal stress. Similarly, the condition for the emplacement of sills is: Pm N σv + T⊥

ð2:3Þ

Here σv is the vertical stress. Thus, according to Price and Cosgrove (1990), the condition for a dyke turning into a sill is simple: σh + T jj N σv + T⊥

Fig. 1. Tensile strengths of isotropic and anisotropic media. Here T⊥ and T|| are tensile strengths in directions perpendicular and parallel to the bedding plane. In ‘anisotropic medium I’, anisotropy can be due to foliation, schistosity or bedding, while in ‘anisotropic medium II’, anisotropy is due to rheological contrasts (Gudmundsson, 1995, 2004, 2009; Gudmundsson and Philipp, 2006). The main difference between these two types of anisotropic medium (I or II) is that in the second one (type II) mechanical properties (such as stiffness and toughness) of formations on either side of the contact, or properties on the contact itself have to be take into account. Therefore an ‘anisotropic medium II’ with rheological contrasts very low or nil can be considered as an ‘anisotropic medium I’.

or σv −σh bT jj −T⊥

ð2:4Þ

In reality, the conditions may be more complex, if a sill intrudes along a discontinuity, between layers of different rheological properties (Fig. 1: anisotropic medium II) (Gudmundsson, 1995, 2004, in press; Gudmundsson and Philipp, 2006). Nevertheless, Eq. (2.4) provides a good approximation for conditions of sill emplacement within a rheologically uniform host rock (Fig. 1: anisotropic medium I). Rocks with a pronounced directional feature such as schistosity, foliation or lamination (e.g.: shales) are anisotropic in terms of tensile strength. Available empirical data (e.g.: Chenevert and Gatlin, 1965; Chen et al., 1998; Kwasniewski, 2009; Table 1) show that T⊥ is usually smaller than T|| (Fig. 1: anisotropic medium I). In a sedimentary sequence, the difference between T|| and T⊥ generally does not exceed about 10 MPa (e.g.: Chenevert and Gatlin, 1965). Therefore, according to Eq. (2.4) sills become emplaced only

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Table 1 Anisotropic tensile strengths data in MPa (after Chenevert and Gatlin, 1965; Kwasniewski, 2009). Shales

T|| (MPa) T⊥ (MPa) T|| − T⊥ (MPa)

Sandstone

Green river shale

Permian shale

Arkansas sandstone

Lyons laminated sandstone

Loveland sandstone I

Loveland sandstone II

21.65 13.58 8.07

17.24 11.45 5.79

11.72 9.58 2.14

7.90 1.80 6.10

1.72 1.44 0.28

0.70 0.76 − 0.06

when the difference in magnitude of the vertical and horizontal stresses (σv − σh) is very small. This condition is easily satisfied at depth in a compressive context, especially if σh N σv. However, in a sedimentary basin that is not subject to tectonic forces and suffers no horizontal strain, σh depends on σv. Thus, sill emplacement is mainly controlled by the thickness of the overburden (that mainly constrains σv), and by the difference in strengths along and across the bedding (once again, excluding mechanical interfaces (Fig. 1: anisotropic medium II)). 2.2. Effect of pore fluid pressure on magmatic intrusion In many sedimentary basins, the rocks contain aqueous pore fluids or hydrocarbons that exhibit high values of pressure, especially at depth of several kilometres. If the pore pressure (Pp) is greater than the weight of an equivalent column of water (hydrostatic pressure Ph), we follow other authors in defining the overpressure as the difference between the two (Fertl, 1976; Magara, 1978; Roberts and Nunn, 1995; Osborne and Swarbrick, 1997; McPherson and Garven, 1999; Madon, 2007). Amongst the possible causes of overpressure in sedimentary basins, the most popular is vertical compaction beneath the Fluid Retention Depth (Osborne and Swarbrick, 1997) (Fig. 3). Other mechanisms, such as mineralogical reactions (smectite to illite) or hydrocarbon maturation, may also contribute (Barker, 1990; Osborne and Swarbrick, 1997). According to the principle of Von Terzaghi (1923) and the general law of effective stresses (Hubbert and Rubey, 1959; Nur and Byerlee, 1971), pore pressure reduces the effective stress tensor, σ ′, in the solid framework, so that: σ ′ = σ−Pp ·I

Here ρb is the bulk density of the sediments. λ is a pore fluid ratio (Hubbert and Rubey, 1959; Dahlen, 1990):   λ = Pp −ρw gH = ðρb gzÞ

ð2:9Þ

ρw is the water density and H is the water depth (Fig. 3). For a typical density of 1 for water, λ = 0.4 for hydrostatic pore fluid (no fluid overpressure) and λ = 1 for pore fluid overpressure reaching lithostatic values. According to Eq. (2.6), the horizontal stresses are equal in all directions and are proportional to σ v′: σ ′h = kð1−λÞρb gz

ð2:10Þ

Thus, the differential stress depends on the magnitude of the pore fluid overpressure (λ N 0.4): σ v′ −σ h′ = σv −σh = ð1−λÞð1−kÞρb gz

ð2:11Þ

Pressure measurements in boreholes have demonstrated such a coupling between pore pressure Pp and differential stress (Engelder and Fischer, 1994; Hillis, 2001, 2003) (Fig. 2). Hillis (2003) deduced values of stress ratios k ranging between 0.2 and 0.4 for the Canadian Scotian Shelf, the North Sea and the Australian North West Shelf. In laboratory experiments on consolidation, the value of k depends on the type of sediment. The larger values of k are for fine and clay-rich

ð2:5Þ

In many sedimentary basins, pressure measurements in wells demonstrate that total minimum horizontal stress increases, on going from shallow, normally pressured sediments, to deeper sequences, where pore fluids are overpressured (Engelder and Fischer, 1994; Hillis, 2001, 2003) (Figs. 2 and 3). For these conditions, Hillis (2003) defined the effective stress ratio k (Hillis, 2003):     k = σh −Pp = σv −Pp = σ h′ = σ v′

ð2:6Þ

where σh and σv are horizontal and vertical total stresses and σ h′ and σ v′ are equivalent effective stresses. Assuming a uniaxial elastic strain and no horizontal extension (Engelder and Fischer, 1994) the value of k is: k = ν = ð1−νÞ

ð2:7Þ

where ν is Poisson's ratio. In a sedimentary basin that is not subject to tectonic stress and that suffers no horizontal strain, the maximum principal stress is vertical, as is in most basins on passive margin. The effective vertical stress as a function of depth becomes: σ v′ = ρb gz− Pp = ð1−λÞρb gz

ð2:8Þ

Fig. 2. Pressure measurements in wells (after Hillis, 2003). Total minimum horizontal stress increases with depth, as pore pressure also increases, from hydrostatic values in shallow sediment, to overpressured values in deeper sequences.

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Fig. 3. Conditions of emplacement of dykes or sills. For details, see text.

sediment. For sand, k is typically lower than 0.4 but it can reach 0.7 for mud and clay (Lambe and Whitman, 1979). In a Mohr space (Fig. 4), as fluid overpressure increases, the Mohr circle for effective stresses shifts to the left and decreases in size, following the rheological envelope defined by the stress ratio k (Hillis, 2003, Mourgues and Cobbold, 2003, Cobbold and Rodrigues, 2007). In terms of total stresses, σv remains constant while σh increases. Hydrofracturing limits the pore pressure sustainable in the sediment. Eq. (2.1) is applicable to pore fluid pressure as well as magmatic pressure (Jaeger, 1972; Mandl and Harkness, 1987):

horizontal hydrofractures limit the pore pressure to lower values, equal to the lithostatic stress (λ ≈ 1) (Eqs. (2.9) and (2.12)). When magma intrudes such a sedimentary sequence, having different values of T|| and T⊥, the differential stress prevailing in the basin controls the emplacement of sills (Eq. (2.4)). According to Eq. (2.11), formations containing high pore fluid overpressures exhibit such low differential stresses and thus they could provide favourable conditions for sill emplacement. Combining Eqs. (2.4) and (2.11), we show that the depth at which a magmatic sill is emplaced depends on pore fluid pressure λ:

Pp N σ3 + T

  Zsill b T jj −T⊥ = ðð1 − kÞð1 −λÞρb gÞ

ð2:12Þ

According to Eqs. (2.9) and (2.12), in an isotropic medium with sufficient tensile strengths (T|| = T⊥ N 0), hydrofractures may open only for a pore fluid pressure exceeding the weight of overburden and the tensile strength of the host rock (Eq. (2.13)). For such supralithostatic pore pressure, the effective stresses become tensile and the least principal stress becomes vertical (Fig. 3). Under these conditions, hydrofractures open horizontally and limit the pore pressure to the following value (Rodrigues et al., 2009): λmax = 1 + T = ðρb gzÞ

ð2:13Þ

It follows that in an isotropic sediment, having a uniform value of T and subject to no tectonic stress, sills form if the pore pressure is formation (if no tectonic stress) only requires supra-lithostatic (λ N 1) because stress tensor rotates and it does not depend on depth (Eqs. (2.4) and (2.11), Fig. 4). If we now consider an anisotropic sedimentary formation with a sufficiently high value of T|| (T|| N 0) and a very weak T⊥ (T⊥ ≈ 0),

ð2:14Þ

Assuming that T⊥ = 0, Eq. (2.14) becomes: Zsill bT jj = ðð1 − kÞð1−λÞρb gÞ

ð2:15Þ

Therefore, in anisotropic sediment, where T|| and T⊥ are different, sill form (if there is no tectonic stress) at greater depths as the overpressure increases, unlike in isotropic media (Eq. (2.14), Fig. 5). If k ≈ 0.4 (ν ≈ 0.3), ρb = 2100 kg m− 3, and T|| does not exceed 5 MPa, sills cannot form at depths greater than 600–700 m if the aqueous pore pressure is hydrostatic (λ = 0.4). In sediment under pore fluid overpressure, magmatic sills may form at depths of over 4– 5 km (λ = 0.9), or even more, depending on the values of the fluid overpressure and the stress ratio k (Fig. 5). Hence, overpressured sediment, such as undercompacted shale or source rock (Mudge, 1968), may provide favourable conditions for ascending dykes to change into sills. In isotropic sediment, having a single value of T,

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5

Fig. 4. Hydrofracturing in isotropic or anisotropic media. Mohr diagrams show shear stress in solid framework, as function of normal stress. In isotropic medium (top), increasing magmatic pressure in crack reduces normal stresses, but not differencial stresses (σd). Mohr circle for stress therefore shifts to left. If circle touches failure envelope, failure occurs. If pore pressure increases, Mohr circle decreases in size (Hillis, 2003; Mourgues and Cobbold, 2003; Cobbold and Rodrigues, 2007). For Pp = σv, the Mohr circle reduces to point at origin of Mohr diagram and fracturing of medium is prevented by rock cohesion (Eq. (2.4)). For very high overpressure, weight of overburden (λ N 1), principal compressive stresses rotate (stresses become tensile and σ h′ is the greater principal stress (σ h′ N σ v′)). Under such conditions hydraulic fractures are horizontal (Cobbold and Rodrigues, 2007). In anisotropic medium (bottom), sill formation depends on σd and (T|| − T⊥). When σd b (T|| − T⊥), σv reaches tensile part of failure envelope in first, so fracture is horizontal. Here T⊥ is null, a greater one will be shifted to the left.

sill formation (if there is no tectonic stress) requires supra-lithostatic pore pressure (λ N 1) because the stress tensor rotates and does not depend on depth (Eqs. (2.4) and (2.11), Fig. 4).

3. Experimental methods 3.1. Scaling In order to compare laboratory and natural models, a scaled model has to be geometrically, kinematically and dynamically similar to its natural prototype (Hubbert, 1937; Mandel, 1962; Ramberg, 1967). Geometrical similarity requires a fixed length ratio, z⁎, between model and nature. For kinematical similarity, a time ratio, t⁎, is necessary. Finally, dynamic similarity requires the experimenter to set ratios for forces and stresses, such as σ⁎ and η⁎, which are respectively the tectonic stress ratio and the magma viscosity ratio. Use of proper scaled materials allows similarities. For our experiments we needed to determine the mechanical behaviour of three materials, representing a brittle rock, pore fluid and magma. 3.1.1. Stress scale for the brittle crust In a slowly moving tectonic system, inertial forces are negligible. The main forces to consider are body forces (due to gravity), Fg, and surface forces (stresses), Fs (Ramberg, 1967). The Ramberg number, Ra, sets the ratio between body forces and surface forces: Ra = Fg = Fs

ð3:1Þ

In a scaled experiment, Ra should be identical in model and nature, so that: σ* = ρe*g*z*

Fig. 5. Conditions for dyke-to-sill transition. Plot is for pore pressure versus depth in anisotropic elastic medium (k = ν/(1 − ν)). Dashed lines represent dyke-to-sill transition for various values of T|| − T⊥: 0.1 MPa, 1 MPa, 5 MPa and 10 MPa.

ð3:2Þ

Here σ⁎ is the stress ratio, ρ⁎e is the density ratio, g⁎ is the gravity ratio and z⁎ is the depth ratio between model and nature. From these relations we can establish values for stress ratios in order to choose adequate model materials (Table 2). For experiments

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Table 2 Scaling ratios.

Nature Experiment Ratio

g

ρ

z

σ

V

η

9.81 9.81 1

2.00–2.70 0.30–1.50 0.10–0.75

102–103 102 10− 5–10− 4

2.0 × 107–2.7 × 108 3.0 × 102–1.5 × 103 10− 6–7.5 × 10− 5

10− 2–1 10− 2 10− 2–1

10–108 10− 10–75 10− 11–7.5 × 10− 7

in the Earth's field of gravity, the gravity ratio is unity (g⁎ = 1). The bulk density of sedimentary rocks ranges between 2000 and 2700 kg m− 3 and the bulk density of common granular model materials ranges between 300 and 1500 kg m− 3. Thus the density ratio is between 0.1 and 0.75. We need to reproduce geological structures at depths of several km in a model a few centimetres thick, so that the depth ratio z⁎ is between 10− 5 (1 cm represents 1000 m) and 10− 4 (1 cm represents 100 m). This implies that the stress ratio σt ranges between 10− 6 and 7.5 × 10− 5. We assume that brittle sedimentary rocks fail according to a linear Mohr–Coulomb criterion (Byerlee, 1978). The cohesion, C, has the dimension of stress. In sedimentary basins, the cohesion ranges from about 108 Pa for competent rocks, such as marble (Byerlee, 1978; Schellart, 2000; and references therein), to about 106 Pa for most of incompetent rocks, such as clay (Hoek et al., 1998). Thus the cohesion of the model material should be between 0 and 7.5 × 103 Pa. For a sedimentary rock, the angle of internal friction, which is dimensionless, ranges between 26° and 45° (Byerlee, 1978; Schellart, 2000 and references therein). Thus the angle of internal friction of model materials should also range between 26° and 45°. 3.1.2. Viscosity scale for magma Viscous stresses within magma tend to be much smaller than tectonic stresses. For magma with Newtonian behaviour σd = 2ėη

ð3:3Þ

Here, σd is the deviator stresses; η is the viscosity of the fluid and ė is the rate of shear. Thus, if Ra is to be identical in model and nature: σ* = ė*η*

ð3:4Þ

Here ė* is the strain rate ratio, η⁎ is the viscosity ratio and σ⁎ is the stress ratio. The strain rate ratio can be expressed in terms of the velocity ratio, V⁎, and the length ratio, l⁎: η* = σ*l* = V*

ð3:5Þ

We have already chosen the length and stress ratios in the previous section. Then we may now calculate the viscosity and velocity ratios. According to field observations and theoretical studies, the propagation velocity of dykes ranges from 10− 2 m s− 1 for the most viscous rhyolitic or granitic magmas (Clemens and Mawer, 1992; Petford et al., 1993), to about 0.1 to 1 m s− 1 for the less viscous basaltic composition (Spence and Turcotte, 1985; Roman et al., 2004). In a model, a practical rate of injection is a few ml per min, or about 10− 8 m3 s− 1. According to the length ratio, the diameter of the injection pipe has to be about 1 mm (1 mm represents 10–100 m). Thus the average liquid velocity is about 10− 2 m s− 1, and the resulting velocity ratio, V, ranges between 10− 2 and 1. In nature, magma viscosity depends on chemical composition, water content, temperature, and volume fraction of crystals. It can therefore vary widely, from 10 Pa s for basaltic melts, to 1018 Pa s for partially crystallized granitic magma (Spera, 1980; Merle and Vendeville, 1992; Petford et al., 1993). In this paper, we consider magma of low viscosity, ranging from 10 Pa s (basaltic melt with high

water content) to about 108 Pa s (more siliceous and volatile-poor magma) (Petford et al., 1993). Such a viscosity is more likely to induce a transition from dyke to sill. According to Eq. (3.5), the viscosity ratio ranges between 10− 11 and 7.5 × 10− 7. Thus, a range of viscosity for the model magma is between 10− 8 Pa s and 75 Pa s. 3.1.3. Scaling of fluid overpressure In order to introduce the effect of pore fluid overpressure in our models, we followed the method of Cobbold and Castro (1999) and Mourgues and Cobbold (2003, 2006a,b), which involves injecting compressed air into the granular material. These authors showed that the flow of air in the material had the same mechanical effect as an overpressure in sediment. Mourgues and Cobbold (2006b) discussed the scaling in detail. They showed that it was not difficult to scale the pore pressure in the same ratio as other stresses, but that is was hard to achieve a proper scaling of transitory phenomena such as a build up (or decrease) of fluid pressure in response to model deformation or a change in permeability during faulting. 3.2. Experimental setup 3.2.1. Chosen materials To simulate the brittle host rock, the challenge was to find a cohesive material sufficiently permeable to allow pervasive fluid migration through pore space. Considering these conditions and the ones given in Section 3.1.1, we could not use gelatin as did Hubbert and Willis (1957), Kavanagh et al. (2006) or Rivalta et al. (2005). Indeed, such a material is not permeable to fluids and is too strong at the scale of sedimentary basin. Also we could not use silica powder as did Galland et al. (2006), because it is not permeable enough; nor sand because of its insufficient cohesion. So, we used a diatomite powder to simulate a brittle and porous host rock, as did Rodrigues et al. (2009). Diatomite is a naturally occurring sedimentary rock, consisting mainly of fossil diatoms (86% silica). The powder is fine-grained, frictional, and cohesive. Using an apparatus similar to that of Cobbold and Castro (1999), we found that the density and cohesion of the diatomite increase with its degree of compaction. For compacted diatomite, having a density of 400 kg m− 3, we determined an extrapolated cohesion of C = 300 Pa, over a range of normal stresses between 50 and 300 Pa. In contrary to other cohesive granular material, such as silica powder or flour, the permeability of diatomite is about 1( darcy (Rodrigues et al., 2009, table 3) - high enough to allow Darcy flow of air within the model. Thus, it facilitates the control of pressure gradient in pore fluids. This makes it a good analogue for geological systems involving fluid overpressure (Rodrigues et al., 2009). To represent magma, correct scaling required a fluid of low viscosity that would not percolate through the powder. Galland et al. (2006) developed a technique based on vegetable oil (and silica powder) to model magmatic intrusion. Percolation occurred over no more than a few millimetres and was therefore negligible. In our experiments, vegetable oil would have created an oil-filled halo in the highly permeable diatomite around each intrusive body. This could have caused unwelcome deviations in pore fluid pressure. We needed a more viscous fluid that would not percolate at all through diatomite powder, to avoid the development of a halo. A suitable is material is RTV silicone. When freshly exposed to air, the silicone is Newtonian

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and has a viscosity of 25 Pa s, but after five hours it solidifies, becoming a flexible rubber (elastomer), resistant to tearing. Thus we could keep the intrusive bodies and investigate their final shapes. However, because the elastomer vulcanizes (solidifies) at room temperature, it remains Newtonian for no longer than about 50 min. This time limit and the rate of injection set by scaling allowed us to inject an average volume of 150 ml of silicone per experiment. In consequence we stopped almost all experiments before there was any extrusion or propagation as far as the edges of the model. 3.2.2. Preparation of experiments The experimental apparatus was a square hardboard box, 40 cm wide, 40 cm large and 50 cm high, having a central injection point, 10 cm from its base. The box rested on a pressure chamber, which acted as a reservoir for compressed air. Its purpose was to provide a uniform fluid pressure at the base of the model. A basal sieve of 125 μm mesh prevented the diatomite powder from falling into the chamber, while allowing air to flow into the model (Fig. 6). For experiments involving air, overpressure remained constant before and during silicone injection. Flowmeters controlled the rate of inflow, in such a way as to maintain constant pressure in the chamber during each experiment (Fig. 6). A triaxial vibrating table helped to pack a load of diatomite into the experimental tank, in order to compact the diatomite as uniformly as possible. We were able to measure the density with a mean error of ±0.75%. The experimental density value, ρex, combined with the thickness of diatomite above the injection point, zex, allowed us to calculate the experimental overburden pressure, σvex σvex = ρex gzex

ð3:6Þ

7

We measured the experimental pore fluid overpressure (air pressure), Ppex, in the pressure chamber and near the silicone injector. In our experiments, the pore fluid factor λex (Eq. (2.9)) expresses fluid overpressure as a function of experimental lithostatic stress: λex = Ppex = ðρex gzex Þ

ð3:7Þ

The fluid in our experiments was air. Without air injection (fluid overpressure), models remained under hydrostatic state, with λex = 0. For pore fluid overpressure reaching lithostatic values, λex = 1. We blended a catalyst into the RTV silicone before each experiment, to initiate its vulcanization. Then, we put the RTV into a piston and allowed it to inject the diatomite, under constant pressure of the piston (Fig. 6). After the five-hour solidification process, we removed intrusive bodies from the diatomite, for futher investigation. 4. Experimental results We did two series of experiments. In the first series, silicone intruded into homogeneous diatomite, which was uniform and isotropic in terms of cohesion. In other words, anywhere in the model T|| equalled T⊥. In the second series, we injected the fluid (RTV silicone) into a three-layer model (diatomite–sand–diatomite), to investigate the effects of a mechanical discontinuity. At the sand– diatomite interface, T⊥ was negligible. For both series, he driving pressure of the silicone was steady and intrusion resulted in planar bodies, which propagated by hydraulic fracturing. Crack propagation was radial, but the experimental apparatus did not allow us to observe the kinematics of emplacement. Consequently, we studied only the final shapes of the intrusive bodies. For experimental data, see Fig. 10 and Table 3. 4.1. Homogeneous medium (series 1) These experiments were designed to investigate if sills (horizontal cracks) could form in a material that was isotropic (in terms of cohesion) and subject to pore fluid overpressure. For each experiment, we laid down a single layer of diatomite, between 15 and 34 cm thick, and applied an arbitrary value of λex between 0 and 1.1. 4.1.1. Series 1A (λex = 0 = hydrostatic state) In Series 1A (six experiments), we investigated fracture propagation in a medium which was not subject to pore fluid overpressure, (λex = 0) (Fig. 7A, Table 3). In experiment 1A1, diatomite density was 460 kg m− 3. The intrusive body was a vertical dyke. The silicone propagated radially

Table 3 Results; where Z is the injector (or discontinuity) depth, Vinj is the injected RTV volume and Nseg is the number of segments. ⁎In experiment 1C1, the vertical part of the model (dyke) has 5 segments and the horizontal one (sill) has 6 segments.

Fig. 6. Apparatus. RTV silicone (representing magma) intrudes diatomite powder or layered diatomite–sand (representing sedimentary basin). Compressed air acts as overpressured pore fluid.

Exp. Type

σvex

ρex

Z

λex

Nseg

Comments

1A1 1A2 1A3 1A4 1A5 1B1 1B2 1B3 1C1 1C2 2A 2B1 2B2 2C1 2C2

1285 1565 370 370 225 1030 1430 980 990 1550 880 320 840 280 865

460 420 1050 380 450 420 440 400 420 465 360 360 335 310 360

28.5 38 29 10 5 25 33 25 24 34 24 8 24.5 8 24

0 0 0 0 0 0.95 0.90 0.80 1.05 1.15 0 0.15 0.65 0.80 0.85

4 5 3 2 5 8 6 6 5 + 6(*) / / / / / /

Poorly segmented dyke

Moderately to highly segmented dyke Flattened conical sill Sill Bulged dyke Bulged dyke (bottom) and inclined sheets (top) Bulged dyke (bottom) and sill (top)

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Fig. 7. Photographs of intrusive bodies from four experiments of Series 1 (isotropic medium in terms of tensile strength). Dashed line indicates depth of injection point. Stress ellipsoids are from Eqs. (2.8)–(2.11). Depending on pore pressure, body is poorly segmented dyke (1A, no overpressure, λex = 0), more segmented dyke (1B, ovepressure, 0 b λ⁎ex b1), or sill (1C, high overpressure, λex N 1). Notice different stress ellipsoids.

in the plane of fracture, above and below the injection point. The difference in density between the diatomite and the RTV silicone (ρex = 1.2) may partly explain the downward propagation of the dyke. The final shape was a vertical disc, circular, sharp and slightly segmented (b5 lobes). The ‘en-echelon’ segmentation may be due, either to heterogeneities in the diatomite, or to a mixed mode of fracture (types I and III), which commonly results from a combination of tension and out of plane shear (Pollard et al., 1982; Olson and Pollard, 1991; Rubin, 1995). This happens when a mode I dyke propagates into a material in which stresses rotate (around an axis parallel to the propagation direction). Resulting segments exhibit the typical “hooked” pattern as two en-echelon cracks grow and overlap (Olson and Pollard, 1989). In experiment 1A3, the diatomite density was lower than before (ρex = 370 kg m− 3). The resulting dyke was planar and comparable to that of Model 1A1, but it was thicker and had a rougher knobbly surface (Fig. 8A). Chang (2004) suggested that fracture thickness increases with increasing fluid viscosity and increasing applied load, and decreasing void ratio. In our experiments, because fluid viscosity and applied load were almost invariant, a change in density seems to have been the factor controlling variations in shape of the intrusive bodies.

In experiments 1A4, 1A5 and 1A6, the injection points were shallow (at depths of 10 cm, 5 cm and 5 cm respectively). Diatomite densities were 460 kg m− 3. The results were similar to those of Experiment 1A1, except that (1) in experiments 1A5 and 1A6, intrusive bodies attained the surface, (2) segmentation was more intense close to the surface, and (3) 5 cm from the surface intrusive bodies were no longer vertical but steeply inclined. We assume that the latter two features were due to interactions between the intrusive body and the surface, but this is beyond the subject of our paper (see Galland et al., 2009). 4.1.2. Series 1B (hydrostatic state b λex b lithostatic stress) The aim of Series 1B (three experiments) was to investigate crack propagation under moderate to high overpressure (0 b λex b 1) (Figs. 7B and 9). The resulting intrusive bodies were dykes. They had the same shapes as in Series 1A, but were slightly inclined and more segmented (N 5 lobes). In general, the segments had constant orientations, as in most natural examples (Gudmundsson, 1995). However, some segments had slightly different attitudes. The segments were similar in shape to those of natural examples (Fig. 9). 4.1.3. Series 1C (λex N lithostatic stress) In series 1C (two experiments), we investigated intrusion emplacement into a medium subject to pore fluid overpressures that exceeded lithostatic stress (λex N 1) (Figs. 7C and 9A). Crack propagation differed from that the two previous series. In experiment 1C1, the intrusive body had a conical shape near the injection point but flattened toward the periphery, forming a sill-like body close to horizontal. A likely explanation is stress rotation due to overpressure. Segmentation was strong in the steep lower part of the intrusive body (N8 lobes), but is less intense in the more horizontal upper part. In experiment 1C2, a slightly segmented sill formed from the injection point. The lack of a dyke is probably due to optimal conditions for sill emplacement at the time of injection. Indeed, λex in 1C2 was closer to λmax (Eq. (2.13)) than to λex in 1C1. 4.2. Heterogeneous medium (Series 2)

Fig. 8. Photographs of intrusive bodies from two experiments of Series2 (anisotropic medium in terms of tensile strength. Lowermost line (long dashes) indicates depth of injection point Upper two lines (short dashes) indicate boundaries of sand layer.Stress ellipsoids are from Eqs. (2.8)–(2.11).

This series of experiments was designed to investigate the effect of a horizontal layers or foliation under conditions of pore fluid overpressure. However, we had difficulty in finding a granular anisotropic material that was cohesive and permeable. We therefore introduced a very thin horizontal layer of sand, having low cohesion

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Fig. 9. Close-up photographs of intrusive bodies. View is downward onto sill from Series 1C (A), downward or oblique onto sills from Series 2C (B and C), sideways onto segmented dykes from Series 1B (D and E).

(C b 20 Pa), into a thick layer of diatomite. The sand layer was thinner than 3 mm and this was just enough to decrease T. The sand layer was 25 mm above the top of the injector and had its permeability (15 darcy) was similar to that of diatomite, so that the models were homogeneous in terms of permeability. The sand layer and the injection point of the RTV silicone were both below the expected depth of the dyke-to-sill transition under hydrostatic conditions (point A on Fig. 10). Such a setup avoided any sill emplacement due to insufficient weight of overburden (Eqs. (2.15) and (3.6)). Diatomite densities in experiments of Series 2 were lower than those in set 1. This enabled us to compact the models without disrupting layer of sand. The sand layer had no effect on the mechanics of propagation, except that there was little or no segmentation. Indeed, as in experiment 1A3, the dyke was thicker and had a

rougher surface. The only factor that varied, from one experiment to another in Series 2 was the pore fluid overpressure λex. 4.2.1. Series 2A (λex = hydrostatic state) In series 2A, the models were not subject to overpressure (λex = 0) (Fig. 8A, Table 3). The diatomite density was about 350 kg m− 3. The resulting intrusive bodies were vertical dykes. Their shapes were similar to those of Series 1A. The silicone propagated radially within the plane of fracture, both above and below the injection point. The silicone also crossed the sand strata layer, which did not induce horizontal crack propagation. 4.2.2. Series 2B (low λex) In series 2B (two experiments), pore fluid overpressure was moderate (0 b λex b0.75) (Fig. 8B, Table 3). Under the sand layer, the intrusive bodies were very similar to those of Series 2A. The silicone also crossed the sand layer; the pore fluid pressure was insufficient to induce horizontal crack propagation. As far up as the sand layer, intrusive bodies were steeply inclined and more like cone sheets than true dykes. 4.2.3. Series 2C (high λex) In series 2C (two experiments), models were subject to high pore overpressure conditions (0.75 b λex b1) (Fig. 9). The intrusive bodies were steep under the sand layer but a sill formed at the sand– diatomite interface. We infer that the deviatoric stresses, reduced by pore fluid overpressure, were probably low enough to induce experimental sill propagation and emplacement. 5. Discussion 5.1. Sill formation

Fig. 10. Plot of lithostatic stress versus pore pressure, showing conditions for dyke-tosill transition in elastic media (k = ν/(1 − ν)), which are either isotropic (red dahsed line) or anisotropic (blue dashed line) Numbers in blue boxes refer to experiments of Series 2 (anisotropic), red numbers refer to Series 1 (isotropic). Asterisks indicate experiments resulting in sills. Large black star indicates dyke-to-sill transition in anisotropic medium under no pore pressure, according to Price and Cosgrove (1990).

In our experiments, all intrusive bodies, whether vertical or horizontal, had circular or elliptical tip-lines, due to radial propagation. We infer that the driving mechanism was magmatic pressure gradient and not a difference in density (Rubin, 1995; Menand and Tait, 2002). However, the shapes of the bodies may also reflect some experimental limitations. Thus the RTV silicone remained liquid for a limited time period. This fact and the rate of injection set by scaling made us stop the experiments before the intrusive bodies reached the edges of the models. However, the bodies were similar in shape to those of the first stage (stage 1) of sill formation as observed and defined by Kavanagh et al. (2006). Only in some of our experiments, when the intruding material was voluminous or the overburden

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was thin, did the intrusive bodies reach the edges of the models (stage 2 of Kavanagh et al. (2006)) or the upper surface resulting in extrusion. According to our theory (Section 2.1, Eq. (2.4), Fig. 10), and experiments (Series 1), when materials are homogeneous in terms of tensile strength, magmatic sills are unlikely to form, if the pore pressure is hydrostatic (λex = 0) and the sedimentary basin is not subject to tectonic stress. Under such conditions the greatest principal stress remains vertical (σv N σh) and only vertical fractures may propagate (Eq. (2.4) and Kavanagh et al. (2006)) ones. In our experiments, dykes propagated in segments. When he pore pressure was greater than hydrostatic, but smaller than lithostatic, he dykes were steep and the segments were numerous. A common explanation for such “en-echelon” segments that they result from concentrations of tensile stress ahead of a propagating dyke (Delaney et al., 1986; Fig. 8). High overpressure (Terzaghi, 1923; Eq. (2.5)) may enhance such local stress and so increase the number of segments. When the pore pressure exceeds lithostatic values, an interface is not necessary for dyke to sill transition. Instead, under such condition (λex N 1), sills form, even in a homogenous material (isotropic in terms of cohesion), no matter what is the thickness of overburden (Figs. 10, 7 and 9A). This result fits the theory (Eq. (2.13), Fig. 10). The vertical stress becomes tensile, in response of seepage forces (Cobbold and Rodrigues, 2007). In nature, such extreme supra-lithostatic conditions of pore fluid overpressure may not persist, if hydrofracturing limits the sustainable pore pressure in the sediment. Nevertheless, Cobbold and Rodrigues (2007) recently argued that bedding-parallel fibrous veins (“beef”) are common to a number of sedimentary basins containing black shale, probably as a result of high values of overpressure. For the experiments of Series 2, containing a thin layer of sand, the results (Fig. 10) are comparable with the theoretical predictions for a homogeneous anisotropic model (Eq. (2.14)). In each experiment of Series 2A, for which pore pressure was hydrostatic, a dyke crossed the fine sand layer and no sill formed, because the overburden was thick and the rheological contrasts were small. In contrast, for each experiment of series 2B and 2C (Fig. 10), in which the model was overpressured, a steep dyke propagated upward, as far as the thin layer of sand, there becoming a sill. The transition occurred for a pore pressure lower than lithostatic, as in the theory (Fig. 10 and Section 2.2, Eq. (2.14)). Nevertheless, we wonder if the thin layer of sand (3 mm thick) behaved like an anisotropic medium of types I or II (Fig. 1) as in the theoretical models, or as a layer having its own distinct rheological properties. The thickness of the sand was not arbitrary, but a result of experimental limitations. We sprinkled the sand, so as not to disturb the underlying diatomite (i.e.: density). We were not able to make the thickness of sand regular, if it was any less than 2 mm. In contrast, a layer thicker than 5 mm would be as thick, or thicker, than the intrusive sill. A proper analysis would then require consideration of contrasting mechanical properties, on either side of the interface (Gudmundsson, 1995, 2004, in press; Gudmundsson and Philipp, 2006). The 3 mm thick sand layer in our experimental setup can be considered as a formation with a contrasting rheology (Fig. 1: anisotropic medium II), in which the contrasting rheological properties are insufficient to induce the turn of a dyke into a sill (exp. 2A1 in Fig. 10, Fig. 8A and Table 3). In this instance, the sand layer could almost be considered as a directional feature (such as schistosity, foliation or lamination), which induced an anisotropy in tensile strength representative of a type I anisotropy (Fig. 1: anisotropic medium I). In such a layered medium, T|| − T⊥ increases; because the small thickness of the sand has probably a small effect on T||, while T⊥, on sand–diatomite contact, decreases. Whatever the anisotropic medium type (I or II), pore fluid pressure should be regard as an additional factor controlling deflection of a dyke along the contact between two different layers, in addition to

mechanical properties (Gudmundsson, 1995, 2004, in press; Gudmundsson and Philipp, 2006). 5.2. Geological examples From our theoretical analysis and experiments, we infer that pore fluid overpressure favours and increases the depth of the dyke to sill transition. Hence, overpressured strata might provide preferential sites of sill emplacement. Now, let us consider possible examples of such phenomenon in the magmatic intrusive bodies in the Neuquén Basin of Argentina during Andean compression and in the Parana Basin of Brazil during the breakup of the Gondwana super continent. The Neuquén Basin is a polygenetic basin, which produces large amounts of oil and gas (Hogg, 1993; Uliana and Legarreta, 1993; Urien and Zambrano, 1994). It lies in northern Patagonia, in the foreland and foothills of the Andes. It developed in a rift setting (Turic et al., 1987) during the early Mesozoic (Triassic to early Cretaceous). It consists mainly of marine sediment (Vergani et al., 1995; Legarreta and Uliana, 1999), beneath Cenozoic continental strata. Since Aptian time, it has undergone compressional deformation, because of Andean compression (Cobbold and Rossello, 2003). Thus a fold and thrust belt developed on the western margin of the basin, especially during Late Cretaceous and Neogene times. The Vaca Muerta Fm (Weaver, 1931) consists of Tithonian black shale, overlying Kimmeridgian continental sandstone of the Tordillo Fm. Because of its high content in organic matter, the Vaca Muerta Fm is probably the main source rock for oil in the Neuquén Basin (Urien and Zambrano, 1994; Cruz et al., 1996). According to previous studies (Cobbold et al., 1999; Legarreta et al., 2005; Rodrigues et al., 2009), organic matter of the Vaca Muerta Fm started to generate hydrocarbons in the Early Cretaceous (Fig. 11). Volcanic activity has been rife in the area, as a result of Andean subduction. In the western Neuquén Basin, the numerous Pleistocene and Holocene back-arc volcanoes (such as Cerro Nevado, Payún Matru, Chachahuén, Tromen, and Auca Mahuida) lay above the Mesozoic sediment of the Neuquén Basin. Auca Mahuida (Holmberg, 1964) is near the NE edge of the basin. Sills are common in or near source rocks of the Vaca Muerta Fm and have resulted in doming of the overlying strata. Since almost all lavas on Auca Mahuida are Quaternary (Holmberg, 1964; Rossello et al., 2002), a Pleistocene age for the sills is likely (Rossello et al., 2002). Assuming this age, when sills intruded the central part of the current dome, the Vaca Muerta Fm lay between 3200 m (top of the formation) and 4300 m (bottom of the formation) below the palaeo-surface. Classical approaches (neutral buoyancy, local stress reorientation, or rigidity contrasts) seem to be insufficient to explain such deep intrusive bodies. Pore fluid overpressure may provide a better explanation. From our theoretical model (Eq. (2.14), Fig. 5), we infer that a λ N 0.75 would make it possible (assuming that (T|| − T⊥) = 10 MPa, k ≈ 0.4 (ν ≈ 0.3) and ρb = 2100 kg m− 3). Although hydrocarbon generation is perhaps not the most popular mechanism for generating overpressures, it has found acceptance in specific cases. An overpressure in the source rock, due to ongoing maturation since the Cretaceous, may explain the emplacement of sills in the Vaca Muerta Fm. Indeed, Rodrigues et al. (2009), recently argued that the formation of bedding-parallel veins of fibrous calcite (“beef”) in the Vaca Muerta formation, before sill emplacement, was probably due to supra-lithostatic (λ N 1) pore fluid pressure. Therefore pore fluid pressure conditions may have been sufficient (λ N 0.75) to induce sill emplacement. Recently Rodriguez Monreal et al. (2009) have described igneous activity in the Payún plateau, a few hundred kilometres to the north of Auca Mahuida. In this area, Vaca Muerta source rock was immature (vitrinite reflectance of 0.4–0.6%) when intrusive bodies were emplaced at shallow depths (1300 m to 2400 m less than under the Auca Mahuida). We infer that, in this northern part of the Neuquén

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Fig. 11. Sills under Auca Mahuida Volcano, northeastern Neuquén Basin, Argentina. Cross section (A-B, bottom), shows magmatic sills (black) within source rock of Vaca Muerta Fm (grey), according to Rossello et al. (2002). Current values of Transformation Ratio (% TR) of organic matter, on map (top centre) and section (top right), are from Legarreta et al. (2005).

Basin, sills and laccoliths could not form deeper because of insufficient pore fluid overpressure (or hydrostatic conditions). We therefore think that the Vaca Muerta Fm in the central part of the Neuquén Basin (Auca Mahuida area) is probably a good natural example of an overpressured sedimentary rock that has been a preferential site for sill emplacement. A second example is the Parana Basin which is a large intracratonic basin in the South-American Platform, lying mostly in southern Brazil and containing more than 7000 m of sediment. It developed from Ordovician to Cretaceous times, on the southwestern edge of Gondwana (Cordani et al., 1984; Zalán et al., 1990). Sediment accumulated during the late Ordovician, in response to successive episodes of subsidence and uplift (Milani and Ramos, 1998), and from the Early Cretaceous, in response to the breakup of Gondwana. The Parana Basin contains five major depositional sequences. The PermoCarboniferous sequence contains Upper Permian black shale (Assistência Member of the Irati Fm), which is the source rock for an atypical petroleum system, over about two thirds of the basin (Araujo et al., 2000). The black shale (Assistência Member) and overlying limestone of the Irati Fm (Kazanian age) are covered by a diagenetic seal (shale of the Teresina Fm.). During continental breakup, numerous dykes and sills intruded the sedimentary sequence (Melfi et al., 1988), first between 138 and 137 Ma, in the central part of the basin (Turner et al., 1994; Stewart et al., 1996) and then between 134 and 130 Ma in the southeastern part. These intrusive bodies fed basalt flows (Serra Geral Fm) that covered the palaeo-surface. Although the tectonic context was one extension (which should not by itself favour sill emplacement), numerous sills were emplaced in the central part of the Parana Basin at more than 2000 m below the

palaeo-surface, within black shale of the Assistência Member. Araujo et al. (2000) have shown that the diagenetic seal (Teresina Fm) maintains pore fluid overpressure in the underlying rocks (down to several thousand metres). The origin of this geopressuring would appear to be hydrocarbon maturation, due to the Cretaceous emplacement of igneous bodies. Since the top-seal was in place since the Triassic, we infer that the top-sealed Irati Fm may have sustained pore fluid overpressure before the Serra Geral magmatic event, favouring sill emplacement. In conclusion, we think that the Irati Fm, in the central part of the Parana Basin, may be another natural example of an overpressured sedimentary rock that has been a preferential site for sill emplacement. 6. Conclusions We have developed an experimental method for modelling the intrusion of magma into a deforming brittle host rock, in the presence of pore fluid pressure. More precisely, have investigated the controls of pore fluid overpressure on the mechanics of sill emplacement. Our theoretical analysis shows that fluid overpressure induces a deep emplacement of sills and that sediment may provide favourable conditions for ascending dykes to turn into sills. In isotropic media, supra-lithostatic overpressure is necessary for the formation of sills at any depth, whereas in anisotropic media, it is enough for pore pressure to exceed hydrostatic values, so as to enhance sill emplacement (the greater the overpressure, the deeper the sills). To verify the theory, we did two series of experiments involving pore fluid overpressure. We used permeable and cohesive diatomite

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powder, to model a brittle sedimentary host rock, RTV silicone as an analogue for magma, and compressed air to represent pore fluid pressure. In the first series of experiments, the silicone intruded a single uniform layer of diatomite. Under hydrostatic pore pressure, hydraulic fractures were vertical; whereas under supra-lithostatic pore overpressure they became sills. We also observed an increasing segmentation of intrusive bodies with increasing pore pressure. In the second series of experiments, the diatomite contained a thin layer of sand, which had no tensile strength. Although the mechanisms of emplacement and propagation were as in the first series, sill emplacement was dominant and occurred under lower pore pressure. We have described probable geological examples of such phenomenon, in the Neuquén Basin and the Parana Basin, both in South America. We conclude that pore fluid pressure, because it increases the depth of sill emplacement, is an additional factor controlling the mechanics of the dyke-to-sill transition. Hence, overpressured sediment may be an important host for sill emplacement. Acknowledgment J.B. Gressier would like to acknowledge a PhD salary from the Region Pays de la Loire, France. References Anderson, E.M., 1951. The Dynamics of Faulting and Dyke Formation with Applications to Britain, Second Edition. Oliver and Boyd Ltd., Edinburgh. Antonellini, M.A., Cambray, F.W., 1992. Relations between sill intrusions and beddingparallel extensional shear zones in the mid-continent rift system of Lake Superior Region. Tectonophysics 202, 331–349. Araujo, L.M., Triguis, J.A., Cerqueira, J.R., Freitas, L.C.da.S., 2000. The atypical Permian Petroleum System of the Parana´ Basin, Brazil. In: Mello, M.R., Katz, B.J. (Eds.), Petroleum Systems of South Atlantic margins: American Association of Petroleum Geologists Memoir, vol. 73, pp. 377–402. Barker, C., 1990. Calculated volume and pressure changes during the thermal cracking of oil to gas in reservoirs. American Association of Petroleum Geologists Bull. 74, 1254–1261. Bradley, J., 1965. Intrusion of major dolerite sills. Trans. R. Soc. N.Z. 3, 27–55. Byerlee, J., 1978. Friction of rocks. Pure Appl. Geophys. 116, 615–626. Chang, H., 2004. Hydraulic Fracturing in Particulate Materials. Georgia Institute of Technology. Chapman, R.E., 1980. Mechanical versus thermal cause of abnormal high pore pressure in shale. A.A.P.G. Bull. 64, 2179–2183. Chen, C.S., Pan, E., Amadei, B., 1998. Determination of deformability and tensile strength of anisotropic rock using Brazilian tests. Int. J. Rock Mech. Min. Sci. 35, 43–61. Chenevert, M.E., Gatlin, C., 1965. Mechanical anisotropies of laminated sedimentary rocks. Society of Petroleum Engineers Journal 5, 67–77. Clemens, J.D., Mawer, C.K., 1992. Granitic magma transport by fracture propagation. Tectonophysics 204, 339–360. Cobbold, P.R., Castro, L., 1999. Fluid pressure and effective stress in sandbox models. Tectonophysics 301, 1–19. Cobbold, P.R., Rodrigues, N., 2007. Seepage forces, important factors in the formation of horizontal hydraulic fractures and bedding-parallel fibrous veins (“beef” and “cone-in-cone”). Geofluids 1–10. Cobbold, P.R., Rossello, E.A., 2003. Aptian to recent compressional deformation, foothills of the Neuquén Basin, Argentina. Marine and Petroleum Geology 20, 429–443. Cobbold, P.R., Diraison, M., Rossello, E.A., 1999. Bitumen veins and Eocene transpression, Neuquén Basin, Argentina. Tectonophysics 314, 423–442. Cordani, U.G., Neves, B.B.N., Fuck, R.A., Porto, R., Thomaz Filho, A., Cunha, F.M.B., 1984. Estudo preliminar de integração do Pré- Cambriano com os eventos tectônicos das bacias sedimentares brasileiras. Bol. Cienc., Tecnica Petrol. 15 70 pp. Cruz, C.E., Villar, H.J., Munoz, N.G., 1996. Los sistemas petroleros del Grupo Mendoza en la Fosa de Chos Malal, Cuenca Neuquina, Argentina. XIII Cong. Geol. Arg. y III Cong. Expl. Hidroc. 1, pp. 45–60. Dahlen, F.A., 1990. Critical taper model of fold-and-thrust belts and accretionary wedges. Annual Review of Earth and Planetary Sciences 18, 55–99. Delaney, P.T., Pollard, D.D., Ziony, J.I., McKee, E.H., 1986. Field relations between dikes and joints: Emplacement processes and paleostress analysis. Journal of Geophysical Research 91, 4920–4938. Engelder, T., Fischer, M.P., 1994. Influence of poroelastic behavior on the magnitude of minimum horizontal stress, Sh, in overpressured parts of sedimentary basins. Geology 22, 949–952. Fertl, W.H., 1976. Abnormal Formation Pressures, Developments in Petroleum Sciences, 2. Elsevier, Amsterdam. Francis, E.H., 1982. Magma and sediment—I. Emplacement mechanism of Late carboniferous tholeiite sills in northern Britain. J. Geol. Soc. Lond. 139, 1–20.

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Glossary σ: Total stress tensor, Pa σ′: Effective stress tensor, Pa σ3: Less principal stress, Pa σv: Vertical stress, Pa σh: Horizontal stress, Pa σd: Differential stress, Pa σ v′: Effective vertical stress, Pa σ h′ : Effectiive horizontal stress, Pa σ*: Stress ratio τ: Shear stress, Pa T: Tensile strength, Pa Tll: Tensile strength tested parallel to the bedding, Pa T : tensile strength tested Perpendicular to the bedding, Pa Pp: Pore fluid pressure, Pa Pm: Magmatic fluid pressure, Pa Ph: Hydrostatic pressure, Pa λ: Pore fluid overpressure factor λmax: Maximum pore fluid overpressure factor λex: Experimental pore fluid overpressure factor Ρb: Bulk density, kg m− 3 Ρw: Fluid density, kg m− 3 ϕ: Porosity κ: Ratio between horizontal and vertical effective stress ν: Poisson ratio g: Gravitional acceleration, m s− 2 z: Depth, m Zsill: Transition depth, m C: Cohesion, Pa η: Viscosity, Pa.s é: Strain rate ρ⁎: Density ratio g⁎: Gravity ratio l⁎: Depth (length) ratio V⁎: Velocity ratio é⁎: Strain rate ratio η⁎: Viscosity ratio I: Identity matrix