Influence of mineralogy on granite decay induced by temperature increase: Experimental observations and stress simulation

Engineering Geology 189 (2015) 58–67

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Influence of mineralogy on granite decay induced by temperature increase: Experimental observations and stress simulation Patricia Vázquez a,b,⁎, Victoria Shushakova c,d, Miguel Gómez-Heras e a

EA3795 GEGENAA, Université Reims-Champagne-Ardenne, CREA, 2 esplanade Roland Garros, 51100 Reims, France Facultad de Geología, Universidad de Oviedo, Jesus Arias de Velasco s/n 33005 Oviedo, Spain Geowissenschaftliches Zentrum, Georg-August-Universität, Goldschmidtstr. 3, 37077 Göttingen, Germany d Bereich Forschung und Entwicklung, DBE TECHNOLOGY GmbH, Eschenstr. 55, 31224 Peine, Germany e CEI Campus Moncloa, UPM-UCM, CSIC: ETS Arquitectura, Universidad Politécnica de Madrid and Instituto de Geociencias (CSIC, UCM), Madrid, Spain b c

a r t i c l e

i n f o

Article history: Received 2 June 2014 Received in revised form 31 January 2015 Accepted 31 January 2015 Available online 11 February 2015 Keywords: High temperature Granite Stone decay Finite-element modeling Microcracking Maximum principal stress

a b s t r a c t Rocks can be subjected to high temperatures in several instances as for example in geothermal processes or if affected by fires. Temperature variations lead to a complex stress distribution in crystalline rocks due to mineral thermal expansion. In polymineralic such as granites, these stresses depend on fabric parameters such as mineral proportion, grain size and their related thermal properties. Eight granitic rocks were heated to less than 400 °C and their decay patterns were observed and quantified by means of scanning electron microscopy. Heating was also modeled by finite-element simulations (OOF software) with polymineralic microstructures. Quartz, feldspar and biotite contents were used as a variable in the model in order to elucidate the influence of mineralogy on the thermal-elastic response of granites. Real and modeled heating showed similar trends of microcracking in microstructures and of thermal expansion coefficients. Microscopic observations of real samples revealed mainly intragranular microcracks in quartz, opening of cleavage plains and deformation in mica. Simulations confirmed that in spite of the high thermal and anisotropic expansion of quartz, the microstructure of rocks with large amounts of quartz does not necessarily experience large stresses. Biotite produces a concentration of stresses along their grain boundaries. As a result, OOF models with 10% biotite showed higher stresses than monomineral ones. Thermal expansion coefficients of real granites fitted within the limits of the simulated ones proving once more the success of using finite element modeling applied to polymineralic rocks. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The study of thermal behavior of rocks at high temperatures is of great importance, as heating and cooling processes are relevant to their performance in geotechnical and engineering applications, such as radioactive waste storage (Liu et al., 2009; Yamamoto et al., 2013) and geothermal energy (Bartier et al., 2008; Marques et al., 2010). The effect of high temperatures is also essential when considering fire damage, both in forest fires or in the context of building stone. Fire is a prominent decay agent as it causes irreversible damage decay of rocks, with long-lasting effects, in a very short period of time (Gómez-Heras et al., 2009) leaving a stress legacy that may be exploited by other, less extreme decay processes for many years (McCabe et al., 2007, 2010; Ozguven and Ozcelik, 2013). As opposed to matrix-rich granular rocks, which are usually more prone to chemical changes, low-porosity crystalline rocks present ⁎ Corresponding author at: EA3795 GEGENAA, Université Reims-Champagne-Ardenne, CREA, 2 Esplanade Roland Garros, 51100 Reims, France. E-mail address: [email protected] (P. Vázquez).

http://dx.doi.org/10.1016/j.enggeo.2015.01.026 0013-7952/© 2015 Elsevier B.V. All rights reserved.

after being affected by high temperatures a noticeable mechanical decay consisting mainly of the generation or growth of cracks due to the thermal stresses (Gómez-Heras et al., 2006a; Homand-Etienne and Troalen, 1984; Menéndez et al., 1999) being the most compact rocks the ones showing the highest rates of porosity change (Gómez-Heras et al., 2006a). In monomineralic rocks, intergranular thermal stresses during a uniform temperature change depend greatly on crystal anisotropy and heterogeneity. This is typically the case of marble, in which thermal decay is deeply dependent on the fabric and orientation of the very anisotropic calcite crystals (Ruedrich et al., 2002; Ruedrich, 2003; Siegesmund et al., 2000; Ozguven and Ozcelik, 2014). However, in polymineral aggregates thermal cracking is a more complex problem, due to thermal expansion mismatch between very different mineral crystals (Homand-Etienne and Troalen, 1984). Some studies have revealed an increasing in microcracking with temperature (Inserra et al., 2013). In this case, rock's thermal behavior depends not only on mineralogy, but also on the proportion of each mineral in the rock, size, texture, orientation, and elastic properties as well as the anisotropy in thermal expansion of each mineral (Vázquez et al., 2011).

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Therefore, thermal deterioration and the way microcracks generate and grow are related to thermal diffusion, thermal expansion, mineralogy, maximum temperature attained and how quickly this is reached, as well as on, porosity, grain size and other textural factors (Calleja and Ruiz de Argandoña, 1985; Castro de Lima and Paraguassú, 2004; Shao et al., 1999; Vázquez et al., 2010). The effects of high temperatures on granite have been described and the overall changes in porosity and mechanical properties have been quantified with several techniques, such as mechanical tests, acoustic emission, ultrasound velocity propagation and mercury intrusion porosimetry (Brotóns et al., 2013; Chaki et al., 2008; Dwivedi et al., 2008; Inserra et al., 2013; Kompaníková et al., 2014; Nasseri et al., 2007; Shao et al., 1999). Microcracking patterns and the distribution of intergranular and intragranular microcracks on granites have been studied before (Kudo et al., 1992; Nasseri et al., 2005; Takemura et al., 2003; Vázquez et al., 2010) and after they were affected by fires (Gómez-Heras et al., 2006b; Nasseri et al., 2007). Mineralogy is known to play an important role in granite thermal degradation. For instance, α to β quartz transition at 573 °C, β quartz to α cristobalite at 870 °C and the possible paramorphism of α quartz after cooling have been noticed as a factor generating crystalline deformation in rocks affected by fires (Gómez-Heras et al., 2010). This is coupled with micro-deformation of crystals. Quartz content will influence deterioration even at temperatures below α to β transition, due to its high and anisotropic thermal expansion. In addition to studying experimentally the effects of temperature increase on rocks in the laboratory, computer models have been developed to understand cracking dynamics, mainly in building stone. This is the case of marble, whose thermoelastic behavior in marbles has been widely studied and modeled (Bellopede et al., 2006; Chau and Shao, 2006; Ferrero et al., 2009). Marble is one of the rocks used most extensively for modeling thermal cracking at high temperatures because it is a monomineralic compact rock. Specifically, finite-element modeling has been applied to verify the thermal stresses related to microcraking in different microstructures with various fabric parameters (Shushakova et al., 2011, 2012, 2013; Weiss et al., 2002, 2003, 2004). However, there are few references to the use of computer models of thermal cracking of granite with differences of temperature (Shao et al., 1999; Vázquez, 2010); one of the reasons is because of the difficulties associated to its variability and its polymineral character. Under the light of these considerations, the present paper aims in the first place, to model a thermal elastic behavior upon temperature change for polymineralic rocks, particularly for granites. To perform such modeling, microstructure-based finite-element simulations have been used in order to simulate the thermal stresses of polymineralic rocks upon heating up to 400 °C, which is a temperature high enough to observe damage but not to produce quartz phase change. This model focuses on mineralogy as key-variable to assess the thermal elastic response of materials. The objective of the study is also to compare the results from computer simulations to real decay patterns observed in investigated granites with similar microstructure to the simulated one and validate them from thermal expansion measurements. The variations in the rock surface were probed by microscopical observations. Microcracking and the decay of each mineral at high temperatures were recognized with Environmental Scanning Electron Microscopy. 2. Methodology 2.1. Experimental Eight granitoids used internationally as dimension stones were selected for this research. Their commercial names are Albero (“A”), Gris Alba (“GA”), Gris Mondariz (“GM”), Negro Galicia (“NG”), Rosa Porriño (“RP”), and Silvestre Moreno (“SM”) all from Spain; Golden Sky (“GS”) from Portugal, and Red Multicolor (“RM”) from India. Granites were oriented in the quarry, with (x) and (y) directions parallel to the

59

foliation plane, and (z) normal to it. All granite types were selected to cover a wide range of mineralogical composition. Quartz and feldspar have equiaxed crystal shape and biotite exhibits the elongated one. Content of equiaxed and elongated crystals in microstructure used in simulations represents microstructure of investigated granites. Mineral proportion, grain size and microcracking were studied using optical polarization microscopy. Open porosity was obtained following the standard EN 1936. Linear thermal expansion coefficients (α) were determined using a dilatometer (Koch and Siegesmund, 2004; Strohmeyer, 2003) with ΔT = 70 °C. High temperature tests were carried out up to 400 °C. This temperature was chosen as it was the lowest one to show visible damage under the microscope. Temperatures lower than 400 °C hardly generate any visible damage in granites and temperatures higher than 400 °C generate obvious cracking (Homand-Etienne and Troalen, 1984). A maximum temperature of 400 °C was selected as a usual temperature for fires in buildings (Sanjurjo-Sanchez et al., 2013) and to avoid α to β quartz transitions. In addition, both in natural and built environments, being fed by coniferous wood combustible rarely exceeds temperatures of 500 °C (Gómez-Heras et al., 2009). The specimens were dried at 60 °C to constant weight and left to cool down until reaching room temperature. After, the specimens were heated in a furnace with a heating ramp of 6 °C/min. This heating rate was chosen according to Ruiz de Argandoña et al. (1985, 1986) as enough to generate a thermal shock and irreversible damage in the rocks. The specimens were kept at the target temperature for 3 h to allow the core of the samples to reach the same temperature than the surface, as suggested by Ruiz de Argandoña et al. (1985, 1986). Afterwards, the samples were cooled unforcedly in the furnace to room temperature (approximately 24 h from the beginning of the test). Open porosity of sound rocks and after heating to 200 °C and 400 °C was compared (EN 1936, 2006). Polarizing microscope was used to assess the variations in microcracks. Thin sections of the eight granitoids before and after heating were studied. Observations were focused on differences in mineral alterations and microcraking. In addition to this, thin sections of samples of a fine-grained leucogranite obtained from a historical building affected by fires were studied with a Scanning Electron Microscope (Jeol JSM 6400). 2.2. Modeling Microstructure-based finite-element simulations have provided so far an excellent insight of the influences of rock fabric on the thermal degradation phenomena of marble (Shushakova, 2014), and the results from simulations were in good agreement with experimental findings. Therefore, this type of simulation was performed in the present study for modeling thermal-elastic response of crystalline polymineralic rocks such as granites. Shushakova et al. (2012) identified microcracks corresponded to regions with maximum principal stress in the microstructure induced by thermal expansion during temperature change. The temperature differential used here for granites was + 400 °C (i.e., heating). The two-dimensional, microstructure-based finite-element approach used here is based on the Object-Oriented Finite Element program OOF developed at the National Institute of Standards and Technology (Langer et al., 2001). The OOF software is in the public domain. Executables and manuals are available at the website: http://www.ctcms.nist.gov/oof/. The OOF1 software was used for present simulations. There are four main rock-forming minerals in granitoids: quartz, alkali feldspar, plagioclase and mica. The influence of the mineralogy on the thermal elastic response of materials was assessed by the variation of quartz percentage and its combination with alkali feldspar/ plagioclase and mica. These simulations have been validated by real experiments of thermal expansion of investigated granites. To assess the effect of mineral proportion on thermal degradation of granites it has been

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P. Vázquez et al. / Engineering Geology 189 (2015) 58–67

Fig. 1. Microstructures used in simulations: (a) equiaxed microstructure used in the simulations of pure quartz rock and pure feldspar rock, the number of crystals is 382; (b) mixed microstructure used in the simulations of mixed content of three minerals: quartz, feldspar and biotite, number of crystals is 347 crystals.

a varied percentage of quartz and microcline/oligoclase in microstructures from 0% to 90%, considering a fixed content of biotite of 10%. Additionally, thermal behavior of pure quartz rock (100% of quartz) and pure feldspar (100% of microcline and 100% of oligoclase) rock was examined. Quartz and feldspar have polygonal equigranular crystals, thereby finite-element simulations of 100% of quartz rock and 100% of feldspar rock upon heating have been performed using equiaxed microstructure (Fig. 1a). Biotite shows mainly elongated crystals; thus, to model thermal behavior upon heating of microstructures with content of three minerals: quartz, feldspar (microcline or oligoclase) and biotite mixed microstructure is used (Fig. 1b). The microstructural images have a resolution of 1000 × 1000 pixels. The number of crystals in the equiaxed and mixed microstructures, respectively, is 382 crystals and 347 crystals. Accordingly, the average crystal size increases with shape fabric from 2617.8 pixels per crystal for the equiaxed microstructure to 2881.8 pixels per crystal for the mixed microstructure. The coordinate system shown in Fig. 1 is used to describe the results: the y direction is parallel to the shape preferred orientation (SPO); the x direction is perpendicular to the SPO and in the plane of the microstructure. The finite-element meshing procedure is described in detail elsewhere (Chawla et al., 2003; Langer et al., 2001; Saylor et al., 2007; Wanner et al., 2010; Weiss et al., 2002). A uniform 200 × 200 mesh of

80 000 right triangular elements was generated in the equiaxed and mixed microstructures. Then an adaptive meshing algorithm was used to align the nodes of inhomogeneous elements (i.e., those which overlapped two or more crystals) with the crystal boundaries. After the finite-element mesh was created, crystallographic orientations and thermophysical properties of minerals were assigned to the elements. Orientation distribution functions (ODFs) with crystal texture were generated via March Dollase fiber-texture distribution (for details see Blendell et al., 2004; Dollase, 1986; Shushakova et al., 2011, 2012). The crystallographic orientations (represented by three Euler angles) of each crystal were selected from the appropriate ODF. Crystallographic orientations of random texture (multiple of a random distribution (MRD = 1)) were assigned to quartz and feldspar crystals and orientations of strong texture (MRD = 20) with c-axis aligned perpendicular to shape preferred orientation and in the plane of microstructure were assigned to biotite crystals (Fig. 2). Texture with MRD = 1 exhibits a uniform distribution of c-axes and texture with MRD = 20 shows preferred orientation of c-axes. Material properties in OOF are given in three-dimensional form and after assigning them to microstructure they are reduced to two-dimensional form by specifying plane strain or plane stress (Reid et al., 2009). OOF computes strains, stresses and thermal distortions upon temperature change. Thereby, elastic stiffness coefficients and thermal expansion coefficient of each mineral had to be assigned to each crystal in the microstructure. The single-crystal elastic values and the crystalline coefficients of thermal expansion are given in Tables 1–4 for quartz, microcline, oligoclase and biotite, respectively. Upon heating in microstructures thermal expansion anisotropy between coefficients of three minerals and the misorientation between adjacent crystals result in thermal misfit strains. These strains give rise to internal residual stresses, which are computed by the finite element method. The temperature change used here was a temperature increase of +400 °C. All of the finite-element simulations used two-dimensional elasticity with a plane-stress assumption, thereby simulating a free surface. The thermal expansion coefficients were computed for a given total temperature change, i.e., for ΔT = 400 °C by measuring the relative dimensional changes of the simulation microstructure and dividing by the temperature differential. The computed coefficient were then compared to those obtained by measuring real specimens.

Fig. 2. Representative pole figures showing individual poles of the crystallographic c-axis for each crystal in the microstructure. a. The orientations chosen from a random ODF (denoted MRD = 1). b. The orientations chosen from a March Dollase ODF with fiber texture that is 20 times random along the North and South pole (denoted MRD = 20). The contour lines correspond to multiple random distribution (MRD) from the March Dollase distribution function of 16 (nearest to NS pole), 4, 1, and 1/2 (nearest to the equator).

P. Vázquez et al. / Engineering Geology 189 (2015) 58–67

3. Results

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Table 2 The single-crystal elastic constants, Cij, in GPa (Babuska and Cara, 1991) and the crystalline coefficients of thermal expansion, αij, in 10−6 K−1 for microcline (quasi orthorhombic symmetry) (Hall et al., 2008).

3.1. Materials The eight investigated granitoids are shown in Fig. 3. All the characteristics are listed in Table 5 and their classification of QAP is shown in Fig. 4. Albero (“A”) (Fig. 3a) is a homogeneous fine-medium grained (≈ 5 mm) granodiorite. Granite “A” has elongated xenomorphic minerals, which are oriented following the foliation and have most of their boundaries interpenetrated. The mica proportion (biotite and muscovite) is very high (≈25%) and with similar proportion of both mica types. Alkali feldspar's content is one of the lowest among the studied granites. “A” shows a notable initial weathering and contains abundant phyllosilicates, which give the rock a yellow color. This rock is characterized also by open transgranular cracks, and consequently it has the highest porosity among the studied granites. Gris Alba (“GA”) (Fig. 3b) is a homogeneous fine grained (≈4 mm) monzogranite. “GA” has subhedral to anhedral minerals with irregular boundaries in quartz. Muscovite:biotite proportion is approximately of 2:1 and they exhibit mineral shape orientation. Cracks are mainly intergranular taking advantage of mica boundaries. Golden Sky (“GS”) (Fig. 3c) is a homogeneous fine grained (≈4 mm) monzogranite. “GS” exhibits evident mica orientation (biotite and muscovite), higher content in quartz than feldspars and similar proportions of alkali and plagioclase feldspars. Quartz and feldspars are subhedral, while muscovite ehuedral and larger than both the rest of the minerals in this rock and the muscovite contained in the rest of granites. Plagioclase is much smaller in this rock. “GS” is characterized also by an initial weathering with the presence of clays and intragranular crack mainly in plagioclase and open transgranular cracks which gives to this granite the second highest porosity. Gris Mondariz (“GM”) (Fig. 3d) is a heterogeneous coarse-grained (≈ 14 mm) monzogranite. Alkali feldspars show a tabular habit and higher dimensions than the rest of minerals. In general all the minerals have euhedral to subhedral shapes. Alkali feldspars have pink-brownish color, which gives the rock a heterogeneous appearance. Cracks are mainly intergranular following mica boundaries. Negro Galicia (“NG”) (Fig. 3e) is a homogeneous fine grained (≈3 mm) tonalite. “NG” has hypidiomorphic to allotriomorphic minerals with irregular boundaries in quartz and about 20% of amphibole and pyroxene. With the naked eye, dark minerals look oriented. Cracks are mainly intergranular following mica boundaries. Red Multicolor (“RM”) (Fig. 3f) is a very fine grained (b 1 mm) orthogneiss. The composition is alkali-feldspar quartz-syenitic. This rock has the smallest grain size among the studied granites, although containing isolated alkali feldspar phenocrystals of millimetric size. “RM” shows irregular grain interlocking due to metamorphic processes. The texture gives the aspect of folded centimetric red and black bands. Rosa Porriño (“RP”) (Fig. 3g) is a heterogeneous (≈ 12 mm) syenogranite. “RP” has a higher proportion of alkali feldspar than plagioclase and with a high quartz content. Feldspars are idiomorphic with straight grain boundaries while the quartz shows straight and interlobate grain boundaries. Feldspars show red color which gives a red aspect to the entire rock. The fundamental crack system of “RP” can be observed in the quartz crystals with two crack orientations, one that corresponds to the foliation plane and another one that is normal to it. Table 1 The single-crystal elastic constants, Cij, in GPa (Heyliger et al., 2003) and the crystalline coefficients of thermal expansion, αij, in 10−6 K−1 for quartz (trigonal symmetry) (Ruedrich, 2003).

Mineral

C11

C12

C13

C22

C23

C33

C44

C55

C66

α11

α33

Microcline

62.5

48.0

3.8

172

24.1

124

14.3

22.3

37.4

4.5

4.5

Silvestre Moreno (“SM”) (Fig. 3h) is a homogeneous fine sized (≈ 5 mm) monzogranite. Mineral shape is subidiomorfic in general and they all show shape preferred orientation. Quartz content is one of the highest among the studied granites. Granite "SM", together with "A" and "GS", form a group of yellow weathered granites displaying wide intra, inter and transgranular cracks, even before being heated. "SM" is, nevertheless, the less weathered granite in this group. Most of the rocks have low open porosity, with values between 0.5 and 1%. All of them are ‘quarry-fresh’ and the most common initial weathering patterns are microcracks in quartz and sericitization in plagioclase. Albero (“A”), Golden Sky (“GS”) and Silvestre Moreno (“SM”) show a notable initial weathering with the presence of clays and open transgranular cracks, and consequently the highest porosity among the studied granites (N 2%). Except for “RM”, thermal expansion coefficients are between 7.5–10 · 10−6/°C. The most porous granites (“A” and “GS”), show the highest average thermal expansion (Table 5), while “GA”, “RP” and “RM” show the lowest.

3.2. Microcraking from laboratory test Open porosity is very low in all samples with values below 6%. Those granite types which display a higher degree of weathering even before the heating tests (“A”, “GS”, “SM” and “GM”) show an initial decrease of porosity from 0 to 200 °C due to crack closure until approximately 130 °C and slight cracking if temperature continues to increase. Conversely, less weathered granite types with lower porosity show an increase of porosity, albeit small, from 0 to 200 °C. From 200 to 400 °C porosity increases in most granite types, indicating crack opening. Some types, such as “GS”, do not show any open porosity increase, but it must be noted that intragranular cracks may not be connected and therefore open porosity methods do not detect them. Thin sections of the granites were compared before and after the test. The study by optical microscopy revealed signs of heating decay. In Fig. 5a and a′, mica sheets opened due to the expansion and contraction along the c-axis, which results in basal cleavage being more noticeable in the heated sample than in the fresh samples. Fig. 5b and b′ shows quartz crystals of granite “A” before and after heating at 400 °C. Transgranular and intergranular cracks may have formed during heating or may be the result of the growth of preexisting cracks. Anyhow, in all granites tested, new intragranular cracks have formed within some of the quartz crystals. Deformed mica was also observed in heated samples (Fig. 5c). This was never the case in fresh samples. This deformation is the result of the stress produced between mica and adjacent minerals during thermal expansion. Granites with lower porosity and less mica tend to display longer and more open transgranular cracks than more porous granites once they are heated. This may have to do with the rock having more space to accommodate deformation and agrees with observations in other Table 3 The single-crystal elastic constants, Cij, in GPa (Babuska and Cara, 1991) and the crystalline coefficients of thermal expansion, αij, in 10−6 K−1 for oligoclase (quasi orthorhombic symmetry) (Hall et al., 2008).

Mineral

C11

C12

C13

C14

C15

C44

C66

α11

α33

Mineral

C11

C12

C13

C22

C23

C33

C44

C55

C66

α11

α33

Quartz

87.26

6.57

11.95

217.18

0

57.15

33.5

14.0

9.0

Oligoclase

81.8

39.3

40.7

145

34.1

133

17.7

31.2

33.3

4.5

4.5

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P. Vázquez et al. / Engineering Geology 189 (2015) 58–67

Table 4 The single-crystal elastic constants, Cij, in GPa (Nishizawa and Kanagawa, 2010) and the crystalline coefficients of thermal expansion, αij, in 10−6 K−1 for biotite (hexagonal symmetry) (Hall et al., 2008). Mineral

C11

C12

C13

C33

C44

α11

α33

Biotite

186.0

32.4

11.6

54.0

5.8

16.5

12

types of rocks in which less porous rocks tend to increase their porosity more than more porous rocks (Gómez-Heras et al., 2006a) (Fig. 5d).

3.3. Microcraking after real fire In addition to observing the above-mentioned granites, samples of a fine-grained leucogranite from historic buildings damaged in fires were observed to compare cracking patterns obtained in the models to granites damaged in real fires. Microscopic observations of granites affected by real fires showed two systems of cracks: one parallel and one perpendicular to the burnt surface (Fig. 6a). Cracks are confined to the first 2 cm of rock, where feldspars and quartz appear widely cracked. Quartz shows mainly irregular cracking patterns. Cracks develop through sericitized areas, inclusions and cleavage planes in feldspars. Biotite does not show open cracking but displays more defined basal cleavage planes (Fig. 6b), which is also observed in slabs heated in the laboratory. Outer areas (first 0.5 cm) show intergranular, intragranular and transgranular cracking. Transgranular cracks disappear below 0.5 cm from the burnt surface and intragranular cracks below 1 cm. Three cracking mechanisms are present: widening of preexisting discontinuities (such as crystal borders or cleavage planes), propagation of preexisting cracks and nucleation of new cracks from inclusions or cleavage planes. Intergranular cracks are more frequent in quartz–feldspar (both alkaline and plagioclases) borders than in quartz–mica or feldspar–mica. Nevertheless, mica's cleavage planes are a very effective seed for new cracks being formed in adjacent minerals (see Fig. 6a–b). Feldspar–feldspar unions are the ones showing the least cracking.

Table 5 Characteristics of the studied granites. Porosity (n) was calculated following UNE-EN 1936 for fresh samples (20 °C) and heated samples (200° and 400 °C).

A GS GA GM NGa RM RP SM

α (10−6 K−1)

Mineralogy (%)

Grain size (mm)

Q

FK

P

M

Q

FK

P

M

Av.

20 °C

200 °C

400 °C

Av.

Sd

35 47 23 23 18 10 29 45

10 20 37 38

30 20 23 28 37

25 13 17 11 24 50 9 15

5 4 5 14 5 b1 10 4

5 4 5 22 5 b1 17 5

6 4 4 10 5 b1 7 7

4 2 2 4 2 b1 3 4

5 4 4 14 5 b1 12 5

5.25 3.68 1.16 0.66 0.53 0.65 1.08 2.42

3.27 2.50 1.61 0.57 0.82 0.81 1.13 1.54

4.24 2.79 1.43 0.71 0.69 1.22 1.22 1.73

9.91 9.70 7.76 8.44 8.53 7.30 7.59 8.98

0.77 0.43 0.30 0.86 0.10 0.84 0.72 0.12

40 49 20

13 20

n (%)

Q: quartz; KF: alkali feldspar; P: plagioclase; M: mica. n: open porosity, Ws: water content in saturation, C: capillary coefficient, Vp: p-wave velocity; and linear thermal expansion (α). Av.: average. Sd: standard deviation. a NG has amphiboles and pyroxenes completing the percentage with 2.5 cm of average size.

3.4. Finite-element simulations Elastic strain energy density and maximum principal stress that result from the thermal expansion anisotropy of the granite crystals and their spatial distribution in the microstructure are the main precursors of microcracking. The elastic strain energy density is a key indicator of potential microcracking sites in a microstructure, since it provides the surface energy necessary to create the fracture surfaces of the microstructural cracks. Regions in the microstructure with the high values of these two precursors correspond to regions with a propensity for microcracking (Shushakova et al., 2012).

3.4.1. Thermal-elastic response of pure quartz rocks and pure feldspar rocks Fig. 7 shows the equiaxed microstructure (Fig. 7a) used for modeling the maximum principal stress distribution upon heating at 400 °C for two extreme cases: the first one in which quartz thermo-physical properties were assigned to all crystals (Fig. 7b) and the second one in which

Fig. 3. Selected granitoids. (a) Albero,(b) Gris Alba, (c) Golden Sky, (d) Gris Mondariz, (e) Negro Galicia, (f) Red Multicolor, (g) Rosa Porriño, (h) Silvestre Moreno.

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quartz crystals will be more prone to microcracking than the one with feldspar crystals only.

Fig. 4. QAP representation of the eight granitoids.

microcline thermo-physical properties were assigned to all crystals (Fig. 7c). Such spatial variation of maximum principal stress in each of the models forms the so-called networks. These networks of high maximum principal stress concentrate along crystal boundaries evidencing the Shape Principal Orientation (SPO) of the models. This spatial dependence may influence microcrack formation. The stress values are shown with a scale ranging from black (0 MPa) to white (≥600 MPa), being red-orange the intermediate color. Quartz thermal expansion is anisotropic (see Table 1) while feldspar exhibits a low and isotropic linear thermal expansion (see Tables 2 and 3). Quartz shows a maximum principal stress of 27.5 MPa while feldspar values are around 7 · 10−10 MPa. Fig. 7 shows both models with the same scale, highlighting how the stress field generated in a 100% feldspar model is negligible in comparison to a 100% quartz model. The influence of the mineralogy on the elastic strain energy density is also evident, as values in a 100% quartz microstructure are 15.4 KJ/m3 while values in a 100% feldspar microstructure are 10 · 10−21 KJ/m3. Thus, an equigranular microstructure only formed by randomly oriented

3.4.2. Influence of granite composition on thermal-elastic response Percentage of biotite content in investigated granitoids is around 10%. Thermal–physical properties and modeled orientations of biotite were assigned to elongated crystals in the mixed microstructure (see Fig. 1b) and the percentage of their content in microstructure was fixed at 10%. Maximum principal stress and strain energy density were calculated for microstructures with combinations of three minerals (quartz + microcline + biotite and quartz + oligoclase + biotite) with variation of quartz content from 0% to 90% in microstructures with 10% of biotite. Results are presented in Fig. 8. Values of 0% of quartz content correspond to values of microstructure with 10% biotite and 90% feldspar (microcline or oligoclase) and values of 90% of quartz correspond to 90% quartz, 10% biotite and 0% feldspar. Feldspars are significantly affected by biotite. Maximum principal stress of 7 · 10−10 MPa for 100% feldspar microstructure increased to 45–49 MPa maximum principal stress for microstructure of 90% feldspar (microcline and oligoclase, respectively) + 10% biotite composition. The high expansion of biotite and large anisotropy of thermal expansion coefficients between biotite and feldspar produced maximal stresses in feldspars, around the biotite–feldspar contacts. Maximum principal stress of 90% feldspar + 10% biotite model (noted as 0% Q in Fig. 8) is even higher than for the 90% quartz + 10% biotite composition. Biotite increases stress in the microstructure if combined with quartz: 27.5 MPa for a 100% quartz microstructure and 32 MPa for a 10% biotite + 90% quartz microstructure. When composition of microstructure consists of three minerals, i. e. of quartz, feldspar and biotite due to different amounts of thermal expansion of each mineral, stress increases. Fig. 9a shows the microstructure with randomly distributed equigranular quartz and/or microcline grains and with 35 elongated planar oriented biotite crystals used for modeling. The stress distributions for microstructures with different contents of minerals are shown in Fig. 9b, c and d. Spatial variations of the maximum principal stress upon heating of 400 °C are shown in Fig. 9b for 90% feldspar (microcline) + 10% biotite, in Fig. 9c for 45% feldspar (microcline) + 45% quartz + 10% biotite, and in Fig. 9d for 90% quartz + 10% biotite microstructures, respectively. The highest maximum principal stress is observed in the microstructure of 45%

Fig. 5. Microscopic images of granite affected by laboratory heating: (a) “GS” sound; (a′) “GS” heated.(b) “A” sound quartz; (b′) “A” heated quartz. (c) Deformed mica in “RP” heated; (d) Transgranular cracks in “SM” heated.

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Fig. 6. SEM images of granite affected by real fire: (a) parallel and perpendicular cracks perpendicular to the burnt surface; (b) cracks from biotite with noticeable cleavage planes.

quartz + 45% feldspar + 10% biotite content with value of 65.4 MPa for microcline (Fig. 9b) and 70 MPa for oligoclase. When the evaluated model only contains microcline and biotite (Fig. 9b), maximal stresses are located in biotite–microcline contacts. Stress concentrated at the microcline edges is noticeably larger than in the mass of the crystals. When the model includes an even proportion of microcline and quartz (45% each) plus 10% biotite (Fig. 9c), maximal stresses are evenly distributed in the whole mass of both quartz and microcline crystals. When the model is formed only by quartz and biotite (Fig. 9d), stresses are lower than the microcline's model and distributed uniformly throughout the quartz. Elongated biotite crystals do not experiment noticeable stresses in neither of the three models. Elastic strain energy density results show the same behavior as maximum principal stresses, with small variation from values of 15.4 KJ/m3 in microstructure with 100% of quartz to 21 KJ/m3 in microstructure with 10% biotite and 90% of quartz. However, feldspars increase from almost zero values in 100% feldspar structure to around 80 KJ/m3, a bit higher in oligoclase than in microcline. 3.4.3. Thermal expansion in relation to quartz content Linear thermal expansion coefficients were calculated for experimental and simulated data. Thermal expansion measurements were carried out in the temperature range 20 °C to 90 °C using a pushrod dilatometer (for details see Koch and Siegesmund, 2004; Strohmeyer, 2003). The experimental thermal expansion coefficient (αexpt) is determined from the first heating cycle by the following equation: αexpt ¼ Δl= ðl  ΔTÞ where Δl is the sample length change during the first heating cycle, l is the original sample length, and ΔT is the temperature differential. The

thermal expansion coefficient from simulations in the x direction, αx_OOF, is calculated as the relative displacement change of the right and left sides of microstructure divided by temperature differential. The thermal expansion coefficient in the y direction, αy_OOF, is computed from the relative displacement change of the top and bottom of microstructure and divided by temperature differential. A temperature change of 400 °C was used. Linear thermal expansion is higher in quartz than in feldspar. The modeled thermal expansion coefficient has a linear behavior with increasing quartz content. To validate the results from finite-element simulations, thermal expansion coefficients of the eight investigated granites were compared with modeled ones. Results from finiteelement simulations are in good agreement with experimental observations (Fig. 10). Thermal expansion coefficients were calculated in x and y directions for both modeled and real granites. Solid lines in Fig. 10 correspond to x and y simulations, while squares and rhombs correspond to x and y real expansion coefficients. Coefficients measured experimentally of real granites fit between the lines corresponding to the modeled ones. 4. Discussion As many authors already discussed mineral thermal expansion produces stresses that are confined until reaching a certain microcracking threshold, which Calleja and Ruiz de Argandoña (1985) established at around 130 °C. While heating under this threshold may lead to crack closure and a decrease in permeability (Dwivedi et al., 2008), microcracks develop above this temperature (Homand-Etienne and Troalen, 1984), which results in an increase in porosity or a decrease in Vp (Geraud et al., 1998; Gómez-Heras et al., 2006a,b; Menéndez et al., 1999). Although microcracking may develop below 400 °C, this

Fig. 7. Microstructural maps showing the spatial distribution of the maximum principal stress for the equiaxed microstructure (a): for pure quartz rock (b), for pure microcline rock (c).

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Fig. 8. Simulation results of maximum principal stress and strain energy density for granite microstructures, with the content of quartz, feldspar and mica (black dots) and of quartz, plagioclase and mica (gray dots) versus the quartz percentage in the microstructure with the fixed content of biotite of 10%.

temperature would be the lowest to produce visible damage under the microscope. Some authors revealed this threshold of damage such as Homand-Etienne and Troalen (1984) that turned out that when granites are heated to 400 °C most of the crystal boundaries are cracked, and consequently the intact boundaries decrease. In the present paper's case, microscopic observations revealed that microcracking occurred mainly as intergranular cracking related to the opening of crystal boundaries. This mechanism is the first to take place and occurs preferably at triple junctions of crystals as it needs a lower stress energy to be produced according to Gómez-Heras et al. (2006b), Homand-Etienne and Troalen (1984), Menéndez et al. (1999) and Nasseri et al. (2007). Although most quartz crystals seem almost intact, they may exhibit in some cases intragranular microcracks not connected with crystal boundaries (Fig. 5b′). Mica cleavage planes open with heating, which induces a stress in adjacent crystals (Figs. 5a′ and 6b). When polycrystalline materials with crystalline thermal expansion anisotropy or with more than one phase are heated, producing internal thermal strains and internal residual stresses develop within the microstructure, which affect properties. In polycrystals these stresses can develop a network structure, which has a length-scale including many crystals. According to thermal crack distribution, cracks in

Fig. 9. Microstructural maps showing the spatial distribution of the maximum principal stress for the mixed microstructure (a). Elongated crystals belong to biotite. The distribution of quartz and feldspar was randomly: (b) of 90% feldspar (microcline) + 10% biotite, (c) of 45% feldspar (microcline) + 45% quartz + 10% biotite, (d) of 90% quartz + 10% biotite composition, respectively.

the studied granites did not show any preferred orientation in rock scale (Menéndez et al., 1999), but follow cleavage planes or macles at mineral scale (Homand-Etienne and Troalen, 1984). OOF model indicates that stresses that lead to microcraking significantly depend on mineralogy. If monomineralic rocks were considered, 100% quartz rock differed strongly from 100% feldspar. Stresses in quartz alone or in combination with other minerals are noticeable. In both model and experimental findings, stresses are confined in quartz crystal, giving as results of intragranular cracking. Feldspars have low and isotropic thermal expansion that do not affect the structure when acting alone. Nevertheless, OOF model exhibits a spectacular increase in maximum principal stress during heating when mica is introduced in the structure. Inserra et al. (2013) found out that in some cases the amount of cracks in feldspars is higher compared to quartz. Simulations also reveal that the highest maximum principal stress and therefore the highest probability of microcracking correspond to the structure containing 10% biotite and same amount (45%) of quartz and feldspar (45%). Mica crystal boundaries concentrate all the stresses produced by mineral expansion. The stresses do not affect the mica itself but the surrounding minerals. Microscopic observations confirm these stresses since cracks propagate mainly from mica boundaries towards other minerals. Also mica deformation was observed (Fig. 5c) that means high stress concentration. Linear thermal expansion coefficients were calculated for the modeled microstructure from finite element simulations. As mentioned elsewhere, the modeled microstructure consists of a randomly distributed equigranular quartz and/or microcline with 10% of oriented planar biotite crystals. Therefore, linear thermal expansion coefficients were calculated for the whole range of mineralogy considered in the models, i.e. 10% biotite and quartz content ranging from 0 to 90% (and

Fig. 10. Linear thermal expansion coefficients: solid lines are the modeled coefficients calculated in x (gray) and y (black) directions, squares (x-direction) and rhombs (y-direction) are experimental values of investigated granites.

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consequently microcline ranging from 90 to 0%). Because of the orientation of biotite crystals included in the microstructure, linear thermal expansion coefficients were calculated for both x and y directions. These calculated coefficients are plotted in Fig. 10 together with the linear thermal expansion coefficients in x and y directions of the eight real granitoids analyzed in this paper to check the fit between real and calculated coefficients. As Fig. 10 shows, there is an excellent fit between the data from real granites and the OOF models from the microstructure proposed. Both cases exemplify how quartz content is the main parameter conditioning the linear thermal expansion of granitic rocks. 5. Conclusions The thermoelastic behavior of granites was modeled and compared to the results of samples heated experimentally and observations of samples heated in real fires. Finite-element modeling (OOF) was proved to provide a good insight of the influence of mineralogy on the thermal behavior and microcraking patterns of granitoids in a similar way it had been before for marbles. OOF simulation of thermal stress distribution was confirmed by microscopic observation of experimental heating test as well as real fired granites. Thermal expansion obtained by OOF also fits with experimental data of the eight granitoids with similar microstructure to the selected ones. This can be therefore extrapolated to granites with similar SPO. This paper shows the role of mineralogy in granite's thermal decay. Mineral composition affects to stress distribution and microcracking far more than individual mineral thermal expansion. Hence, thermal expansion mismatch is a much more relevant factor than bulk thermal expansion. The combinations of microscopic observations as well as the results of modeled granitoids show that biotite produces a concentration of stresses along their crystal boundaries, which affects the surrounding minerals. In the model, the highest stress in granites with 10% mica appeared when the proportion of quartz and feldspars is equal (i.e. 45% of both). Higher or lower quartz proportion leads to less stresses and consequently less microcracking. These results are most fit for studying building stone decay, as the volume of rock to be heated is relatively small. The accordance between model, laboratory tests and real samples needs to be understood in a context of small samples in which heat can penetrate throughout the entire sample. The low thermal conductivity of granitoids means that for large volumes of rock (as for radioactive waste storage and geothermal energy) OOF models and their subsequent interpretation would need to take into account of this factor. This, together with crystal boundary crack distribution, triple point formation and mineral–mineral stresses will be the subject of future work. Acknowledgments The authors gratefully acknowledge David M. Saylor for generating the artificial microstructures used in this study with the Microstructure Builder program, which he was developing in collaboration with Carnegie Mellon University and Alcoa Technical Center. Prof. Dr. Edwin Fuller and Prof. Dr. Siegesmund are gratefully acknowledged for their helpful suggestions. Part of this research was funded by MICINN (Spain) project IB-09-080 and Geomateriales 2S2013/MIT-2914 (Madrid). Financial support for Victoria Shushakova was provided by University of Reims Champagne-Ardenne (France) through the project MEFETRO and is gratefully acknowledged. Research by Miguel Gómez-Heras was supported by a PICATA postdoctoral fellowship of the Moncloa Campus of International Excellence (UCM-UPM, CSIC). References Babuska, V., Cara, M., 1991. Seismic Anisotropy in the Earth vol. 10. Springer.

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