# In situ seismic measurements in claystone at Tournemire
(France)

M. Zillmer, J.-M. Marthelot, C. Gélis, Justo Cabrera, G. Druivenga

► To cite this version:

M. Zillmer, J.-M. Marthelot, C. Gélis, Justo Cabrera, G. Druivenga. In situ seismic measurements in claystone at Tournemire (France). Geophysical Journal International, 2014, 199 (3), pp.1798-1807. 10.1093/gji/ggu363. hal-02641753

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# *In situ* seismic measurements in claystone at Tournemire (France)

M. Zillmer,<fnref n="1" /> J.-M. Marthelot,<fnref n="1" /> C. Gélis,<fnref n="2" /> J. Cabrera<fnref n="2" /> and G. Druivenga<fnref n="3" />

Accepted 2014 September 15. Received 2014 June 28; in original form 2013 December 16

## SUMMARY

Compressional and shear wave seismic measurements were performed in an old railway tunnel and in galleries excavated in a 250-m-thick Toarcian claystone formation in the Tournemire experimental station (France). Three component (3C) geophones and three orthogonal orientations of the vibroseismic force source were used. Additionally, vertical seismic profiling (VSP) measurements were recorded with a 3C borehole geophone, a hydrophone and a microphone in a 159 m deep borehole (ID180) in the tunnel. The seismic data show that Toarcian claystone has strong transverse isotropy (TI) with a vertical symmetry axis. The *qP*, *SH* and *qSV* wave propagation velocities in horizontal directions—the plane of isotropy of the TI medium—are measured as 3550, 1850 and 1290 m s⁻<fnref n="1" />, respectively. The zero-offset VSP reveals that only one shear wave propagates in the vertical (depth) direction and the *P*- and *S*-wave velocities are 3100 and 1375 m s⁻<fnref n="1" />, respectively. Four elastic moduli of the TI medium are determined from the seismic velocities and from the bulk density of 2.53 g cm⁻<fnref n="3" />: *c*₁₁ = 31.9 GPa, *c*₃₃ = 24.3 GPa, *c*₄₄ = 4.5 GPa and *c*₆₆ = 8.7 GPa. A walkaway VSP with the borehole geophone at 50 m depth in borehole ID180 and shot points in the galleries leads to oblique seismic ray paths which allow us to determine the fifth elastic modulus of the TI medium to *c*₁₃ = 16 GPa. The tube wave recorded by a hydrophone in the water filled lower part of the borehole propagates with 1350 m s⁻<fnref n="1" />, which confirms the estimate of the elastic constant *c*₆₆. The analysis of body wave and surface wave data from a seismic experiment in Galerie Est shows reflections from several fracture zones in the gallery floor. The thickness of the excavation damaged zone (EDZ) in the floor of Galerie Est is estimated to 0.7 m.

**Key words:** Body waves; Seismic anisotropy; Wave propagation.

## 1 INTRODUCTION

Claystone formations are discussed as a host rock for the underground storage of high-level nuclear waste. The French Institute for Radiological Protection and Nuclear Safety (IRSN) conducts research programs in the experimental station of Tournemire in order to improve its ability to expertise projects of radioactive waste disposal in a geological claystone formation. The Underground Research Laboratory of Tournemire is located at the southern border of the French Massif Central in the Aveyron region. An inoperative 1.9 km long railway tunnel excavated during the years 1882–1888 gives direct access to a 250 m thick subhorizontal layer, which consists of argilites and marls of Toarcian age. This claystone layer is located between limestone and dolomite layers. Galleries have been excavated perpendicular and parallel to the tunnel since 1996 and several up to 250 m deep boreholes were drilled in the underground works. The claystone formation is affected by natural fractures associated with tectonic events and by artificial fractures associated with the excavation of the tunnel and galleries (Cabrera 2002; Gélis et al. 2010a). Mechanical properties of rock samples were investigated in

laboratory experiments: Ultrasound measurements showed that the Toarcian claystone is of transversely isotropic (TI) elastic symmetry and that the anisotropy is strong (Zinszner et al. 2002). Five static elastic constants were determined from compression tests (Niandou et al. 1997; Valès et al. 2004).

From 2009 to 2013 we performed seismic measurements at frequencies around 100 Hz in the tunnel and in the galleries as well as vertical seismic profiling (VSP) experiments in the 159 m deep borehole ID180 with the goal of characterizing the seismic properties of Toarcian claystone. The traveltimes of the *qP*, *SH* and *qSV* waves enable us to determine the seismic velocities in the horizontal plane of isotropy, in symmetry axis (depth) direction and in other directions of the TI medium. As a consequence, all five dynamic elastic moduli can be calculated. This information is useful for computer simulations of seismic wave propagation and for the analysis of seismic data sets, for example the 3-D high resolution seismic reflection data acquired in 2001 on the plateau 230 m above the Tournemire tunnel (Cabrera 2003).

Discontinuities may increase the very low permeability of unfractured claystones (Boisson et al. 2001). This problem is investigated

<footnote n="1">¹Institut de Physique du Globe de Strasbourg, Université de Strasbourg/EOST, CNRS UMR-7516, 5 rue René Descartes, F-67084 Strasbourg Cedex, France. E-mail: matthias.zillmer@unistra.fr</footnote>

<footnote n="2">²Institut de Radioprotection et de Sûreté Nucléaire, BP 17, F-92262 Fontenay-aux-Roses Cedex, France</footnote>

<footnote n="3">³Geosym GmbH, Forstgrund 16, D-30629 Hannover, Germany</footnote>
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**Figure 1.** The 1.9-km-long railway tunnel at Tournemire (Tunnel de la Boutinenque) is directed 16° east of north. For simplicity we use the notation W-E and N-S in the figures. Galerie Sud (74 m length) is parallel oriented to the tunnel, Galeries Ouest (132 m) and Est (31 m) are perpendicular to the tunnel. The 159 m deep borehole ID180 is located 15 m south of the intersection between the tunnel and galleries Ouest and Est. The strike lines of faults F1 and F2 are shown. Note that Galerie Sud was previously called Nouvelle Galerie and the part with positive coordinates has been renamed to Galerie Nord.

in the Tournemire laboratory, where Galerie Ouest and horizontal boreholes intersect two tectonic faults (F1 and F2 in Fig. 1) with small vertical displacement (Cabrera 2002). A preliminary analysis of the 3-D seismic reflection data showed a subvertical tectonic fault in the limestone layer below the claystone (Cabrera 2003). Electrical resistivity tomography on the plateau has traced this fault also in the limestone layer above the claystone (Gélis et al. 2010a). Both of these methods failed to detect the fault zone in the claystone layer itself. Bretaudieu et al. (2014) investigated the fault zones F1 and F2 by traveltime inversion and full waveform inversion of *qP* wave data in the horizontal plane of isotropy. Cabrera et al. (1999) describe three types of fractures in the galleries: Pre-existing fractures of tectonic origin, vertical fractures mainly in the floor caused by the excavation, and fractures in the stratification plane of the claystone, which are related to the desaturation process (Charpentier et al. 2003; Matray et al. 2007; Lavielle et al. 2012). The excavation of underground structures leads to a fracture network around the structures which is called the ‘excavation disturbed zone’ (EdZ) or ‘excavation damaged zone’ (EDZ; Bossart et al. 2002; Blümling et al. 2007; Tsang et al. 2012). The difference in terminology refers to the reversability of the effect. Investigations of the EDZ around the tunnel and the galleries at Tournemire with different seismic methods were presented by Cabrera et al. (1999), Gélis et al. (2010b) and Leparoux et al. (2012).

We have acquired a refraction seismic profile with 71 geophones at 0.25 m spacing in Galerie Est by using a small hammer as a vertical force source (*qP*-*qSV* acquisition) and a vibroseismic source as a horizontal force (*SH* acquisition). We identify two fracture zones and estimate the thickness of the EDZ in the gallery floor.

## 2 SEISMIC EXPERIMENTS IN THE GALLERIES

The seismic measurements in the galleries and in the borehole were intended to determine the body wave velocities in different directions and the elastic moduli of the claystone.

<figure><img src="image_4.png" /></figure>

**Figure 2.** Seismic acquisition in Galerie Ouest with the ElViS vibroseismic source. View from the tunnel to the end of Galerie Ouest in the west.

In 2009, we recorded a 9C data set with three component (3C) geophones (4.5 Hz GS-11 D Oyo Geospace) and three orthogonal directions of the force source. Two electrodynamic mini-vibrator sources acted as a vertical force and as a horizontal force (Geosym ElViS P8 and S8; Fig. 2). The horizontal vibrator was oriented both in-line and cross-line. The sweep signal was of 5 s duration with a linear increase in frequency from 60 to 360 Hz, sometimes from 20 to 160 Hz. The recording system was composed of three 24 channel Daqlink III seismographs (Seismic Source Company). The sampling rate was 0.25 ms, the acquisition time 0.5 s longer than the sweep. The recorded vibroseismic data were correlated with the sweep signal to obtain a pulse compressed seismic section.

The first experiment was performed in the 132-m-long Galerie Ouest with twelve 3C geophones at profile coordinates (−10, −20, ..., −120 m) (Fig. 1). The mini-vibrator source was shifted with 1 m steps along the profile with a maximum source-receiver offset of 122 m. A second profile was recorded in a direction perpendicular to the first profile with eight 3C geophones in the 74-m-long Galerie Sud positioned at coordinates (−50, −40, ..., +20 m). The source position was changed in 2 m steps. In a third seismic experiment data were recorded in Galerie Ouest, while the source was shifted in the tunnel with 5 m steps along a 70 m long profile parallel to Galerie Sud. Two more experiments were performed with shots in Galerie Sud and receivers in Galerie Ouest and vice versa.

A part of these data are shown in Fig. 3. The data are correlated with the sweep signal, trace-normalized and sorted in common-receiver gathers. Due to the source radiation pattern and the horizontal propagation direction the *qP*-wave signals can be seen most clearly on the in-line horizontal geophone in the case that the force source is also directed in-line. The *SH* wave is recorded on the cross-line horizontal geophone when the force is also cross-line oriented. The *qSV* wave can be identified on the vertical geophone, when the force is vertically oriented.

Seismic velocities of *qP*, *SH* and *qSV* waves were determined by sorting the data of a seismic line according to source-receiver offset and plotting it with a reduced time axis for different reduction velocities. This lead to the velocities given in Table 1. Results are less precise when the source was in the tunnel probably due to a 1-m-thick ballast layer below the tunnel floor which might deteriorate the radiated signal. If we neglect the results with the larger error then the average wave propagation velocities in claystone are given
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Seismic common receiver gathers recorded by 3C geophones at 10 m spacing and with the ElViS mini-vibrator as seismic source. The displayed traveltimes are computed with velocities $v_{qP} = 3550 \text{ m s}^{-1}$, $v_{SH} = 1850 \text{ m s}^{-1}$ and $v_{qSV} = 1290 \text{ m s}^{-1}$, respectively. (a) 6 of 12 common receiver gathers in Galerie Ouest at profile coordinates $-110, -90, -70, -50, -30, -10 \text{ m}$. 131 sweeps with 1 m spacing. (b) 4 of 8 receiver gathers in Galerie Sud at coordinates $-50, -30, -10, +10 \text{ m}$. 72 sweeps with 1 m spacing. (c) 15 sweeps at 5 m spacing in the tunnel were recorded by 12 geophones in Galerie Ouest.</figcaption></figure>

by $v_{qP} = 3550 \text{ m s}^{-1}$, $v_{SH} = 1850 \text{ m s}^{-1}$ and $v_{qSV} = 1290 \text{ m s}^{-1}$ with a relative accuracy of about 2 per cent. The claystone is strongly anisotropic with two different shear wave velocities. Traveltime curves are plotted together with the data in Fig. 3. We have measured the same velocities in all five experiments with different directions

of wave propagation in the horizontal plane, which confirms that it is the plane of isotropy of the TI medium.

The *qP*-wave velocities coincide with logging velocities in symmetry axis direction of the TI medium (Zinszner *et al.* 2002; Malochet & Besson 2007). Bretaigne *et al.* (2014) performed
<table><caption>**Table 1.** Seismic *qP*, *SH* and *qSV* wave propagation velocities (m s⁻¹).</caption><thead><tr><th>Seismic ray path</th><th>qP</th><th>SH</th><th>qSV</th></tr></thead><tbody><tr><td>In Galerie Ouest</td><td>3500</td><td>1825</td><td>1280</td></tr><tr><td>In Galerie Sud</td><td>3575</td><td>1850</td><td>1290</td></tr><tr><td>From Galerie Ouest to Sud</td><td>3525</td><td>1875</td><td>1290</td></tr><tr><td>From Galerie Sud to Ouest</td><td>3575</td><td>1875</td><td>1290</td></tr><tr><td>From tunnel to Galerie Ouest</td><td>3650</td><td>1875</td><td>1300</td></tr></tbody></table>

full waveform inversion of *qP* wave data in the plane of isotropy. They obtained *qP* velocities between 3400 and 3700 m s⁻¹ where the lowest values are located in the area of the fault zones F1 and F2 (figs 18 and 19 of Bretaudieu *et al.* 2014).

Toarcian claystone has a grain density of 2.704 g cm⁻³, a porosity between 8 and 12 per cent and more than 95 per cent water saturation of the pore space (Matray *et al.* 2007; Lavielle *et al.* 2012). This gives a bulk density of 2.49–2.56 g cm⁻³ depending on porosity. If we use the value 2.53 g cm⁻³ and the seismic velocities in the galleries then we obtain the following elastic moduli: $c_{11} = 31.9$ GPa, $c_{44} = 4.2$ GPa and $c_{66} = 8.7$ GPa.

## 3 VERTICAL SEISMIC PROFILING IN BOREHOLE ID180

The 159 m deep uncased borehole ID180 is located in the tunnel 15 m south of the intersection with Galeries Ouest and Est (Fig. 1). Below 121 m depth the borehole is filled with water from a limestone aquifer beneath the claystone layer.

A zero-offset VSP measurement offers the possibility to check if only one shear wave propagates in depth direction, which should be the case in a TI medium (Fedorov 1968). A walkaway VSP with shots in galleries Ouest and Est allows us to determine the elastic modulus $c_{13}$ due to the fact that the seismic rays cover a wide range of propagation directions.

### 3.1 Zero-offset VSP

We performed zero-offset VSP measurements with a 5 kg sledge-hammer as a vertical force source and three different types of receivers. First, a 3C borehole geophone BHG-3 from Geostuff

equipped with 15 Hz OMNI-2400 Oyo Geospace sensors was used. The device has a clamping mechanism with a spring and a compass for the N-S and W-E orientation of the two horizontal geophone sensors. Our borehole geophone was a modified version with preamplifiers. In 2012 June, we recorded a VSP in the lower part of borehole ID180 and we completed the measurement in the upper part in 2012 September. The cable length restricted the measurements to a maximum depth of 145 m. The borehole geophone was shifted in 1 m steps. We observe a compressional *P* wave with a velocity of $v_P = 3100$ m s⁻¹ and a shear *S* wave with a velocity of $v_S = 1375$ m s⁻¹ (Fig. 4). The velocities were again obtained by plotting the data with a reduced time axis. The fact that only one shear wave is recorded confirms that the depth direction is the direction of the symmetry axis of the transversely isotropic Toarcian claystone. The *S*-wave velocity is slightly higher than the *qSV*-wave velocity in horizontal directions, which was measured with the experiments in the galleries. The small 5° dip of the claystone formation to the north (Cabrera 2002) is too small to explain this difference.

The *P*-wave velocity allows to determine a fourth modulus of the TI medium $c_{33}$ to 24.3 GPa. The *S*-wave velocity leads to $c_{44} = 4.8$ GPa.

Zinszner *et al.* (2002) determined *P*-wave velocities of 3100 m s⁻¹ in the first 20 m of borehole ID180 from sonic logs. Malochet & Besson (2007) performed sonic logging in another borehole in the tunnel and obtained an average *P*-wave velocity of 3000 m s⁻¹ down to the interface with the limestone at a depth of 220 m below the tunnel. These velocities coincide with our results.

In a second experiment we used a hydrophone (Oyo Geospace MP-25) in the water-filled lower part of borehole ID180 between 120 and 158 m depth. The tube wave in the air-filled upper part of the borehole hits the water level in 121 m depth and is transmitted as a tube wave in the water filled part which is then reflected at the bottom of the borehole (Fig. 5). We determined the tube wave velocity to 1350 ± 20 m s⁻¹ by plotting the data with a reduced time axis.

White & Sengbush (1953) calculated the tube wave velocity *c* for TI media in the low frequency limit to

$$ \frac{1}{\rho_f c^2} = \frac{1}{\rho_f v_f^2} + \frac{1}{c_{66}}. \qquad (1) $$

<figure><img src="image_6.png" /><figcaption>**Figure 4.** In the zero-offset VSP the 3C borehole geophone in borehole ID180 records a *P* wave and one *S* wave, which propagate in symmetry axis direction of the TI claystone with 3100 ± 25 and 1375 ± 25 m s⁻¹, respectively. There is also a tube wave (T), which propagates with the velocity of sound and a cable wave (C) with ~2000 m s⁻¹. The VSP has been recorded in two experiments from 95 to 145 m depth in 2012 June and from 1 to 100 m in 2012 September under slightly different noise conditions.</figcaption></figure>
<figure><img src="image_7.png" /><figcaption>**Figure 5.** In the zero-offset VSP the hydrophone records a tube wave in the water filled lower part of borehole ID180, which is generated in transmission by the tube wave in the air filled upper part of the borehole. The tube wave is reflected at the bottom of the borehole.</figcaption></figure>

Here $\rho_f$ and $v_f$ are bulk density and P-wave velocity in the fluid, respectively. Using this formula and a density of 2.53 g cm⁻³ we obtain $c_{66} = 9.6$ GPa with a 20 per cent error which confirms the result from the experiments with the SH waves in the galleries. The large error of $c_{66}$ is a consequence of the structure of eq. (1).

In a third experiment we used a condenser microphone (Behringer ECM 8000) in the air-filled upper part of borehole ID180 from 1 to 119 m depth. A tube wave with the velocity of sound is recorded which is reflected at the water level in 120 m depth (Fig. 6). The first arrivals are two cable waves with velocities of 2000 and 700 m s⁻¹. When the cable waves arrive at the plastic casing of the microphone they generate reflected and transmitted waves propagating with the speed of sound. This causes multiple tube wave reflections between the top of the borehole and the microphone casing and also between the microphone casing and the water below. Later we confirmed the existence of the fast cable wave in an experiment in the staircase of the IPGS institute. The cable of the borehole geophone was used with an adapter for the microphone. The fast cable wave has nearly the same velocity as the SH wave in horizontal direction. In a previous VSP experiment in the same borehole in 2010 the horizontal sensors of the borehole geophone started to oscillate when the cable wave arrived. This was erroneously interpreted as the shear wave velocity (Zillmer et al. 2011). The cable wave can still be seen in the geophone data (Fig. 4). The microphone data also show a tube wave reflected at 104 m depth, which could be caused by a variation in the borehole diameter (Fig. 6).

## 3.2 Walkaway VSP

To determine the remaining fifth modulus $c_{13}$ of the TI medium it is necessary to record wave propagation in directions other than the symmetry axis or the plane of isotropy. For this purpose we performed a walkaway VSP experiment in borehole ID180 in 2013 July. A 5 kg sledgehammer was used as a source at shot points with 5 m spacing in galleries Ouest and Est. The borehole ID180 is at a distance of 16 m perpendicular to the shot profile (Fig. 1). The seismic rays cover polar angles with the vertical symmetry axis between 18° and 67°. The qP, SH and qSV waves recorded with the geophone at a depth of 50 m are shown in Fig. 7. The SH wave appears on the N–S geophone component. Greenfield (1978) has

<figure><img src="image_8.png" /><figcaption>**Figure 6.** In the zero-offset VSP the microphone records data in the air filled upper part of borehole ID180. The first arrivals are two cable waves with 2000 m s⁻¹ (C1) and 700 m s⁻¹ (C2), respectively. The tube wave (T) propagates with sound velocity and generates a reflected tube wave (R) perhaps due to a discontinuity in the borehole diameter. All other events are generated when the unclamped plastic casing of the microphone moves then it generates new tube waves, which propagate upward and downward in the borehole.</figcaption></figure>

shown that a directed force which acts on the surface of a cylindrical cavity in an isotropic medium also generates SH waves.

The potential energy of an elastic medium in the deformed state is positive definite (Fedorov 1968). This implies for TI media that $c_{13}^2 < c_{33}(c_{11} - c_{66})$, which means for Toarcian claystone that $|c_{13}|$ is smaller than 24 GPa. The energy of a body wave propagates in direction of the seismic ray which is a straight line in homogeneous anisotropic media. The ray velocity $\xi$ for a plane wave which propagates in a medium with elastic constants $c$ and bulk density $\rho$ is given by (Fedorov 1968)

$$ \xi_i = \frac{1}{\rho v} c_{iklm} A_k A_m n_l, \quad i = 1, 2, 3. \qquad (2) $$

Phase velocity $v$ and polarization $\vec{A}$ are obtained by solving Christoffel's eigenvalue equations

$$ \frac{1}{\rho} c_{iklm} n_k n_m A_l = v^2 A_i, \quad i = 1, 2, 3, \qquad (3) $$

where $\vec{n}$ is a unit vector perpendicular to the plane of constant phase. We compute the ray velocity numerically using eqs (2) and (3). The SH-wave velocity does not depend on $c_{13}$. The qSV-wave velocity is much more sensitive to changes in $c_{13}$ than the qP-wave velocity. Cusps appear near the diagonal of the qSV ray velocity surface for $c_{13}$ smaller than 16 GPa. For $c_{13}$ larger than 21 GPa cusps appear near the symmetry axis direction and close to the plane of isotropy. There is no evidence for cusps in the recorded data and therefore we use values of $c_{13}$ between 16 and 21 GPa to compute seismic velocities and corresponding traveltimes to compare with the recorded seismic data.

Traveltimes of qP, SH and qSV waves are shown in Fig. 7 for the case of $c_{13} = 16$ GPa (solid lines) and for $c_{13} = 21$ GPa (dashed
<figure><img src="image_9.png" /><figcaption>**Figure 7.** In the walkaway VSP the 3C borehole geophone recorded data at 50 m depth in borehole ID180. A 5 kg sledgehammer was used for 31 shots with 5 m spacing along a profile in Galeries Ouest and Est. The shortest distance between the borehole and the shot line was 16 m (compare Fig. 1). Traveltimes for the case $c_{13} = 16$ GPa (solid lines) and $c_{13} = 21$ GPa (dashed lines).</figcaption></figure>

lines). The solid line fits the data of the qSV wave much better than the dashed line. Therefore, we conclude that the elastic modulus $c_{13}$ is about 16 GPa and we estimate the relative error again to 5 per cent.

## 4 THE STIFFNESS TENSOR OF TOARCIAN CLAYSTONE

Hooke's law of linear elasticity was used to derive the propagation velocities of the plane body waves (eqs 2 and 3). For a transversely isotropic medium it is given in stiffness form by

$$ \begin{pmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \\ \sigma_{23} \\ \sigma_{13} \\ \sigma_{12} \end{pmatrix} = \begin{pmatrix} c_{11} & c_{12} & c_{13} & 0 & 0 & 0 \\ c_{12} & c_{11} & c_{13} & 0 & 0 & 0 \\ c_{13} & c_{13} & c_{33} & 0 & 0 & 0 \\ 0 & 0 & 0 & c_{44} & 0 & 0 \\ 0 & 0 & 0 & 0 & c_{44} & 0 \\ 0 & 0 & 0 & 0 & 0 & c_{66} \end{pmatrix} \begin{pmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \\ 2\epsilon_{23} \\ 2\epsilon_{13} \\ 2\epsilon_{12} \end{pmatrix} \quad (4) $$

where $c_{12} = c_{11} - 2c_{66}$. Here $\sigma_{ik}$ and $\epsilon_{ik}$ are the stress and strain tensor components in cartesian coordinates, respectively, and $c_{\alpha\beta}$ is the stiffness tensor in Voigt notation.

We conclude from our seismic measurements that the stiffness tensor of Toarcian claystone at Tournemire is given in units of GPa by

$$ \mathbf{c} = \begin{pmatrix} 31.9 & 14.5 & 16 & 0 & 0 & 0 \\ 14.5 & 31.9 & 16 & 0 & 0 & 0 \\ 16 & 16 & 24.3 & 0 & 0 & 0 \\ 0 & 0 & 0 & 4.5 & 0 & 0 \\ 0 & 0 & 0 & 0 & 4.5 & 0 \\ 0 & 0 & 0 & 0 & 0 & 8.7 \end{pmatrix} \quad (5) $$

where a bulk density of 2.53 g cm⁻³ has been used. The modulus $c_{44}$ is an average of the two values obtained from seismic measurements in the galleries and the zero-offset VSP. With 2 per cent accuracy

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Group velocities and slownesses (solid lines both) for qP, SH and qSV waves which propagate in Toarcian claystone. The phase velocities (dashed lines) and Thomsen's approximation (circles) are also displayed.</figcaption></figure>

of the measured seismic velocities and 1 per cent of the density the elastic moduli are accurate to 5 per cent.

Eqs (2), (3) and (5) are used to compute cuts through the x-z plane of the group velocity, phase velocity and slowness surfaces (Fig. 8). The surfaces are rotational symmetric around the z axis and mirror symmetric to the x-y plane.

Thomsen's anisotropy parameters are non-linear functions of the elastic moduli (Thomsen 1986). They are calculated from the elastic constants (5) to $\gamma = 0.47 \pm 0.07$, $\epsilon = 0.16 \pm 0.05$ and $\delta = 0.03 \pm 0.09$. The corresponding approximations to the phase velocities are shown in Fig. 8. The approximation for $v_{SH}$ is poor near the x-axis because $\gamma$ is not small compared to 1.
Hooke's law can be written in compliance form. For TI media it takes the following form for the normal stress and strain components (Jaeger et al. 2007)

$$ \begin{pmatrix} \epsilon_{11} \\ \epsilon_{22} \\ \epsilon_{33} \end{pmatrix} = \begin{pmatrix} \frac{1}{E_p} & -\frac{\nu_p}{E_p} & -\frac{\nu_{zp}}{E_z} \\ -\frac{\nu_p}{E_p} & \frac{1}{E_p} & -\frac{\nu_{zp}}{E_z} \\ -\frac{\nu_{zp}}{E_z} & -\frac{\nu_{zp}}{E_z} & \frac{1}{E_z} \end{pmatrix} \begin{pmatrix} \sigma_{11} \\ \sigma_{22} \\ \sigma_{33} \end{pmatrix}. \quad (6) $$

Here $E_p$ and $E_z$ are the Young moduli in the plane of isotropy (p) and in symmetry axis direction (z), $\nu_p$ is the Poisson ratio in the plane of isotropy for a stress applied in the same plane, and $\nu_{zp}$ is the Poisson ratio in the plane of isotropy when the stress is applied in symmetry axis direction. From eqs (4) to (6) we obtain for Tocrian claystone the dynamic elastic constants $E_p = 20.6 \pm 1.4$ GPa, $E_z = 13.3 \pm 1.8$ GPa, $\nu_p = 0.19 \pm 0.09$ and $\nu_{zp} = 0.34 \pm 0.03$.

## 5 THE EXCAVATION DAMAGED ZONE AND TECTONIC FRACTURES IN GALERIE EST

The floor of Galerie Est gives direct access to the rock. A map of the fractures in the floor was published by Cabrera et al. (1999) and for Galerie Est coordinates between 11 and 22 m by Okay (2011). The cartography shows that there is a zone with subvertical N-S oriented tectonic fractures between coordinates 14 and 18 m and another fracture zone between 23 and 25 m. The excavation has created a network of fractures of the same N-S orientation.

The thickness of the EDZ has been investigated by different authors. Cabrera et al. (1999) performed a few refraction seismic profiles and concluded that the EDZ is 0.35–0.65 m thick below the floor of Galerie Est and 0.35 m thick in the wall. Contrucci et al. (2007) used an ultrasonic logging tool with frequencies around 100 kHz in eight 5 m deep radial boreholes in Galerie Est. They determined the EDZ thickness to about 0.7 m in the walls and the ceiling and obtained both higher (1.1 m) and smaller values in the floor depending on the borehole. Magnin et al. (2008) performed refraction seismics with a hammer and 30 accelerometers at 0.1 m spacing on two profiles parallel and perpendicular to vertical fractures in the floor of Galerie Est. The traveltimes of the qP wave differed on these profiles and consequently also the EDZ thickness with 0.4 and 0.8 m, respectively. A similar result for the EDZ thickness in Galerie Est has been obtained from a VSP with a sparker source in borehole GEM180bis which showed an increase of the P-wave velocity in depth direction in the first meter (Gélis et al. 2010b). Okay (2011) used electric resistivity and induced polarization measurements and obtained 0.5–0.8 m (resistivity) and 0.7–0.8 m (induced polarization) EDZ thickness for a profile perpendicular to the subvertical fractures on the gallery floor and 0.4–0.6 m (resistivity) and 0.4 m (induced polarization) for a parallel profile. Leparoux et al. (2012) used surface waves to investigate the EDZ in Galerie Ouest which is covered by a high velocity 0.25-m-thick layer of concrete. They obtained an isotropic S-wave velocity depth profile by inverting the dispersion curves of the fundamental mode and the first higher surface wave mode. The resulting model is a 0.55–0.75-m-thick layer with shear wave velocity 500–600 m s⁻¹, above a 1 m thick layer with an average velocity of about 1000 m s⁻¹, and a halfspace with about 1400 m s⁻¹ (interpreted from fig. 13 of Leparoux et al. 2012).

In 2012 June, we performed a seismic experiment in Galerie Est with 71 omni-directional 30 Hz geophones (ION Sensor SM-11) at 0.25 m spacing on a 17.5 m long profile between 9.85 and 27.35 m distance from the tunnel (Fig. 9). First, a small 1.7 kg hammer was

used as a source and the geophones oriented as vertical sensors (qP-qSV acquisition). Secondly, the Geosym ElViS S8 mini-vibrator applied a horizontal force perpendicular to the seismic profile in N-S direction and the same orientation was used for the geophones (SH acquisition). The sweep was 10 s long with frequencies from 30 to 240 Hz. Coupling of the vibrator base plate to the floor was suboptimal due to the rough surface of the rock. During the experiment there was a problem with triggering the recording system. Therefore we analyse only one seismic section with shot point at coordinate 27.6 m at the eastern end of the geophone line.

The first arriving qP wave is displayed in Fig. 9(a), where automatic gain control (AGC) is used with a window length of 1 ms. Fig. 9(b) shows the qSV wave and a surface wave R and Fig. 9(c) displays the SH wave and another surface wave L. The seismic data in (b) and (c) are trace normalized. Peak-to-peak amplitudes of the waves are displayed in Fig. 9(d). The amplitudes of the body waves decay with increasing distance from the source point due to geometrical spreading, while the two modes R and L have constant amplitudes for large offset ranges. The R wave has nearly constant amplitude between 14 and 21 m, and the L wave between 14 and 24 m.

The qP wave has traveltime variations between coordinates 13 and 17 m (Fig. 9a). The R mode have a sudden drop in amplitude by a factor of 10 between coordinates 13 and 14 m, and the L mode also has an amplitude decay between coordinates 12 and 14 m. We attribute it to scattering at the fracture zone. The seismograms of the L wave between 22 and 24 m are of low quality, which is related to the fact that the rock on the floor was fractured and the horizontal sensors were not well coupled.

A Rayleigh wave and an S wave were also recorded by Lüth et al. (2008) in the Piora adit of the Gotthard base tunnel. Stilke (1959) has shown theoretically that surface waves propagate at the boundary of a hollow cylinder in an isotropic elastic medium. He calculated group velocity dispersion curves which have minima when the circumference of the cylinder is about 5–10 times bigger than the wavelength. Galerie Est is 4 m wide and 3.5 m high, so that the circumference is about 25 m. The seismic data show that the Rayleigh wave R has a velocity of 1100 m s⁻¹ and a dominant frequency of 350 Hz (Fig. 9b) with a corresponding wavelength of about 3 m. Then the ratio of tunnel circumference to wavelength is 8 in agreement with Stilke’s theoretical results. The Rayleigh wave was not observed in the experiments in Galerie Ouest (Fig. 3) because the vibroseismic source frequencies were lower. Stilke (1959) also calculated that one mode has a minimum of the group velocity curve when the wavelength is twice the circumference of the cylinder. This corresponds to a frequency of 20 Hz which is lower than the frequencies emitted by our sources.

In Fig. 10 the same section as in Figs 9(a and b) is displayed. A longer time interval is used and a 5 ms AGC window. A reflected Rayleigh wave can be seen in the centre of the figure between coordinates 15.5 and 21.5 m. We conclude from the geometry of the traveltime curves that the reflection occurs at a vertical discontinuity at coordinate 6.5 m. After propagating back to the east the R wave is then reflected at the end of Galerie Est (indicated by arrows in Fig. 9) where also the EDZ ends. The discontinuity at 6.5 m has not been marked in the cartography. It may be related to the large and strong EDZ of the tunnel that creates intense fracturing in the floor of Galerie Est.

We estimate the thickness h of the EDZ from the crossover distance x' between the traveltime curves of the direct wave and the head wave for the model of an isotropic layer over an isotropic half-space. We denote by $v_1$ the velocity of the direct wave in the EDZ
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Seismic data from a refraction experiment recorded by 71 geophones at 0.25 m spacing. The shot point is at the eastern end of the geophone line at 27.6 m near the end of the gallery at 31 m. The origin of the coordinate system is located at the tunnel wall at the intersection with the gallery, which differs by 2.5 m from the coordinates in Fig. 1. (a) and (b) The source is a small hammer and the geophones are vertically oriented (qP-qSV acquisition). (c) The ElViS S8 horizontal vibrator is used as source and the geophones are horizontally oriented perpendicular to the seismic profile (SH acquisition). (a) The first arriving *qP* wave is displayed. An AGC with a 1 ms window is applied. (b) Same as (a) with focus on the *qSV* wave and the Rayleigh wave *R*. Trace normalized data. (c) *SH* wave and probably another mode *L*. The solid line shows the body wave traveltimes in the first layer (EDZ). The dashed line indicates the traveltimes for the head wave which propagate at the interface to the second layer (intact rock). (d) Peak-to-peak amplitudes of the waves on a logarithmic scale.</figcaption></figure>

and by $v_2$ the head wave velocity in the intact rock at the boundary of the EDZ. The velocities are determined by plotting the data with a velocity-reduced timescale. For the *qSV* wave we obtain $v_{qSV1} = 1000 \text{ m s}^{-1}$ and $v_{qSV2} = 1300 \text{ m s}^{-1}$, so that $x' = 3.75 \text{ m}$ gives $h = 0.7 \text{ m}$. The velocity $v_{qP1}$ is not well constrained due to interference of the *qP* wave with the *qSV* wave at very short distances from the source and the velocity $v_{qP2}$ is not well constrained due to the limited source-receiver offset and the traveltime variations caused by the fracture zone at 14–17 m. From $v_{qP1} = 1300–1400 \text{ m s}^{-1}$, $v_{qP2} = 2800–3800 \text{ m s}^{-1}$ and $x' = 2.5 \text{ m}$ we obtain $h = 0.7–0.9 \text{ m}$. This value is consistent with the one inferred from the *qSV* head wave.

# 6 DISCUSSION AND CONCLUSIONS

The combination of seismic measurements in tunnel galleries with VSP borehole measurements and the use of a shear waves source

allowed us to determine all five dynamic elastic moduli of the transversely isotropic Toarcian claystone at Tournemire from traveltimes of *qP*, *SH* and *qSV* seismic body waves. Generally, the five elastic constants of TI media are determined by ultrasonic measurements (Thomsen 1986; Johnston & Christensen 1995) and rarely by seismic measurements (Robertson & Corrigan 1983).

Zinszner et al. (2002) performed seismic measurements with a sparker source in one borehole and a hydrophone chain in another borehole. In doing so they determined Thomsen's parameters $\delta$ and $\epsilon$ from *qP* wave traveltimes for a fractured zone west of borehole ID180 (area of fault F2 in Fig. 1) and an unfractured zone east of the borehole. We note that the values for $\delta$ and $\epsilon$ of Zinszner et al. (2002) are inconsistent with the measured *qP* velocities displayed in the corresponding figure of their article. The phase velocity surfaces shown in fig. 3 of Bretaudieu et al. (2014) are incorrect because they are calculated from these erroneous Thomsen parameters.
<figure><img src="image_12.png" /><figcaption>**Figure 10.** Same data as in Figs 9(a) and (b). Seismic data are displayed by AGC with window length 5 ms. The Rayleigh wave is reflected between a structure at coordinate $x = 6.5$ m and the eastern end of Galerie Est at $x = 31$ m. These reflections are observed between coordinates 15.5 and 21.5 m indicated by arrows.</figcaption></figure>

Zinszner et al. (2002) performed ultrasound measurements on polyhedral samples of Toarcian claystone from Tournemire and obtained velocities of $v_p = 4200–4300 \text{ m s}^{-1}$, $v_{SH} = 2500 \text{ m s}^{-1}$ and $v_{SV} = 1800 \text{ m s}^{-1}$ in the plane of isotropy and $v_p = 3300 \text{ m s}^{-1}$ and $v_s = 1800 \text{ m s}^{-1}$ in symmetry axis direction (fig. 6 of Zinszner et al. 2002). The ultrasonic velocities showed little variation with uniaxial stress between 0 and 20 MPa. The *in situ* stress at Tournemire has been measured in two experiments of which the first gave a quasi-isotropic stress distribution of about 4 MPa and the second an anisotropic stress field with the principal stresses between 2 and 4 MPa (Rejeb & Tijani 2003). Valès et al. (2004) obtained ultrasonic *qP*-wave velocities of 4000 m s⁻¹ in the plane of isotropy and values above 3500 m s⁻¹ in other directions for 90 per cent *in situ* water saturation of the pore space. All ultrasonic velocities are 500–700 m s⁻¹ higher than the seismic and logging velocities. Zinszner et al. (2002) failed to explain the difference as a frequency dependent viscoelastic effect. Biot’s poroelastic theory leads to frequency dependent wave propagation velocities caused by the global fluid flow in the pore space (see e.g. Bourbié et al. 1987). Wave propagation velocities are frequency independent for frequencies much lower than the critical frequency $\omega_c = \frac{g\phi}{K}$ where g is gravitational acceleration, $\phi$ is porosity and K hydraulic conductivity. Boisson et al. (2001) measured $K \approx 10^{-14} \frac{m}{s}$ for Toarcian claystone which gives a critical frequency of about $\frac{\omega_c}{2\pi} \approx 10^{14} \text{ Hz}$. Both seismic and ultrasonic measurements use much lower frequencies, so that the observed velocity dispersion is not explained by Biot’s theory. Winkler (1986) and Mavko & Jizba (1991) discussed grain-scale local (squirt) flow where for high frequencies ‘regions of unequilibrated pore pressures are effectively isolated with respect to fluid flow’ (Mukerji & Mavko 1994) and the rock is stiffer than for low frequencies. For a rock with pores and microcracks the critical frequency is smaller than for Biot’s theory and depends on the aspect ratio of the cracks (Le Ravalec et al. 1996; Schubnel 2003). In tri-axial compression tests of Toarcian claystone Niandou et al. (1997) observed a crack closure phase with beginning axial loading for three different orientations of the samples. He concluded that there are randomly distributed microfractures in the claystone. Another hypothesis is that the samples selected for the ultrasonic measurements represent the intact claystone on a centimetre scale while seismic and logging velocities characterize the rock on a larger scale [see

also Jones & Wang (1981)]. In the vicinity of the fault zones F1 and F2 the claystone is damaged. Fractures were found in drill cores of a horizontal borehole west of the tunnel near fault zone F2 but not in the borehole east of the tunnel and a difference in *qP* wave logging velocities of about 5 per cent was measured (Zinszner et al. 2002). One might speculate that the damaged area near fault zones F1 and F2 is larger and that all seismic measurements were affected.

The dynamic elastic constants differ from static constants obtained by compression tests on samples where much higher strain appears (Niandou 1994; Niandou et al. 1997; Rejeb 2003; Valès et al. 2004; Ben Ouanas 2010; Masri 2010). There is no unique set of static constants for Toarcian claystone which describes the elastic part of the deformation under loading.

Seismic measurements in underground galleries with short geophone or shot spacing of less than 1 m can be used to detect fracture zones. It is advantageous to analyse the complete wave field: Fracture zones lead to traveltime variations of the first arriving *qP* wave. The *qSV* wave and the Rayleigh wave have the shortest wavelengths and show the strongest reflection signals. The same type of experiment can be used to investigate the thickness of the excavation zone. An analysis of the variations in thickness of the EDZ needs a model of a fractured anisotropic medium which explains the low velocities in the EDZ.

## ACKNOWLEDGEMENTS

This work was performed with support by grants 2008–2DD and 2010–2E from the research project GNR TRASSE IRSN-CNRS/PACEN. The authors thank Pierre-Daniel Matthey and Laurent Rihouey (IPGS) for technical support and Elise Vi Nhu Ba (Mines ParisTech) for support during the field measurement in 2013. We also thank LIAG (Hannover) for information and technical advice regarding the borehole geophone.

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