Geophysical and Geomechanical Investigations Applied to the Rock ...

Rock Mech. Rock Engng. (2007) 40 (6), 603–622 DOI 10.1007/s00603-006-0092-9 Printed in The Netherlands

Geophysical and Geomechanical Investigations Applied to the Rock Mass Characterisation for Distinct Element Modelling By 1

2

A. M. Ferrero , A. Godio , L. Sambuelli2 , and I. H. Voyat3 1

University of Parma, Parma, Italy Dipartimento di Ingegneria del Territorio, dell’Ambiente e delle Geotecnologie, Politecnico di Torino, Torino, Italy 3 Dipartimento di Geotecnica e Ingegneria Strutturale, Politecnico di Torino, Torino, Italy 2

Received February 11, 2004; accepted March 7, 2006 Published online May 22, 2006 # Springer-Verlag 2006

Summary The paper describes the experience gathered in an underground quarry of crystalline marble where the rock mass structure has been characterised by a joint approach using geomechanical mapping and geophysical investigations with a high resolution radar system. Standard geomechanical surveys have been coupled and integrated by radar acquisition performed on a selected pillar of the quarry to improve the rock mass description. The fracture pattern has been computed on the basis of the deterministic model on the rock faces of the pillar and taking into account both the statistical approach to describe the extent within the rock mass and the fracture pattern described by radar survey. Keywords: Discrete rock mass modelling, geophysical measurements.

1. Introduction The evaluation of the stability conditions of an underground excavation requires a tool that is able to forecast the stress and deformation response of the rock mass. For this purpose the medium can be represented by different mathematical models to analyse the geomechanical behaviour of the rock mass (Barla et al., 2001; Jing, 2003). For a rock mass characterised by a low fracturing degree, such as those required for ornamental stone exploitation, the best modelling approach is often based on a discontinuous scheme that is able to consider the rock mass as a blocky system. The modelling procedure is performed in two phases: geometric modelling, to reconstruct the blocky system, and mechanical modelling, to reproduce the stress strain behaviour of the interacting blocks.

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The reliability of a simulation of the mechanical behaviour of a blocky system is affected by the precision in the definition of the geometry of the rock mass. The joint sets can be generated simply by using the mean orientation and spacing. These models do not necessarily reproduce the structure of the outcropping rock mass in a particular situation but determine an equivalent configuration that is given by a statistic distribution of the discontinuities. Consequently, the local rock block geometry might not correspond to the existing configuration discovered during the excavation. For a punctual reconstruction of an existing fractured rock mass, deterministic models, that are able to consider the real position of the discontinuities detected on the site, have to be developed. The discontinuity locations can be determined by measuring their traces on an excavation surface, even though the persistence within the rock mass is more difficult to determine. However, fully persistent discontinuities are often assumed in a cautelative way, although in cases this may be not realistic. Detailed geophysical investigations allow the discontinuity conditions within the rock mass to be estimated and further information to be supplied for the rock mass reconstruction in the modelling phase. In order to show this, an experiment was carried out with the following main objectives: to detect the fracture patterns of a marble pillar; to perform the stability analysis of the rock mass using deterministic and statistic models; to evaluate the reliability of high resolution radar imaging of the fractures as a useful tool to integrate the results of the structural survey; to obtain information toward a rational planning of the exploitation activity of the quarry.

2. The Experimental Site The quarry is located in Stazzema (Lucca), Italy, where dimensioned blocks for ornamental stone are exploited. The quarry is exploited with the room and pillar method. The experimental stope is excavated in virgin areas where the influence of the existing voids is limited. Four rooms are excavated perpendicularly to each other to isolate a central pillar. The final room size has been reached by two different subsequent excavation phases. In the first phase prismatic rooms of 9 3 m2 in section and 33 m in length have been excavated. During the second excavation phase, the rooms have been widened up to 20 3 m2 in section and 55 m in length. The final pillar size has been reached at the end of the second excavation phase and is 10 10 3 m2 (Fig. 1). Since the stress and strain distribution are modified by the excavations, monitoring instruments have been installed as shown in Fig. 1. Two Borehole-Stressmeters and two MultiPoint Borehole-Extensometers (MPBX) were installed for the monitoring during the first quarrying phase. One of the two stressmeters was located in the centre of the future pillar, while the other one was located in the opposite rock wall in a symmetrical position to the crown line of the drift that had to be excavated and subsequently enlarged. As far as the two MPBXs are concerned, one was located in the roof crown line of a drift and at half pillar width while the other one was located in the roof at the midpoint of the line of intersection between two consecutive drifts.

Geophysical and Geomechanical Investigation

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Fig. 1. General layout of the experimental panel: first phase exploitation (continuous line) second phase exploitation and floor deepening (dashed line); a), c) MPBX location and anchors depth; b), d) stressmeter location (Cravero et al., 2002)

When the second phase was started, which involves the widening of the drifts around the pillar, the number of measuring devices was increased by two MPBXs in each monitoring station (Cravero et al., 2001; Deangeli et al., 1999).

2.1 Rock Mass Characterisation The rock mass characterisation in the investigated quarry included both in situ measurements and laboratory testing. Detailed geostructural surveys have been carried out on every accessible rock face with different orientations. In particular six rock exposures have been mapped according to the procedure reported in Table 1 where indications on the mapped discontinuity dip and dip direction are coupled by the precise localization in an orthogonal reference system (end 1 and end 2 in the Table). Figure 2 shows the comparison between the photo showing the discontinuities exposed on a rock face and the image constructed by the survey interpretation. Discontinuity aperture, morphology at different scales and water presence are also monitored. Particular attention has been given to the different discontinuity ending types: within the rock mass, against another discontinuity or outside the visible rock

70 77 85 74 65 76

dip ( )

120 118 9 112 195 202

dd ( )

x (local)

diac diac diac diac diac diac

type

0.1 0.2 0.1 0.1–0.2 0.1–0.2 < 0.1

thickness (cm)

y (local)

– – – – – –

aperture (cm)

sm sm r r r r

P P P P U P

1.20 3.15 6.40 10.91 17.51 21.90

x1

s.scale

b.scale

end1 (m)

morphology

z

diac diaclase, W presence of water Morphology: r rough, sm smooth, Sl slickensided, S stepped, U undulating, P planar Type: s stopped, L lonely, t truncated

1 2 3 4 5 6

Fracture N

Reference point:

Zone of investigation wall A

3.2 3.2 1.15 3.2 3.2 3.2

y1

L L L L L L

type

Table 1. Example of structural survey with discontinuity localisation on the rock wall

2.46 4.00 6.50 11.27 18.10 22.90

x2

end2 (m)

0.00 0.00 3.2 0.00 0.00 1.00

y2

L L L L L L

type

W W

note

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Fig. 2. Rock wall exposure and relative survey digitalization

Fig. 3. Equal area projection of the discontinuity poles of the quarry

window. This information is very important for the rock hierarchical definition reported in a following chapter. Figure 3 shows equal-area projections of the discontinuities mapped in the site under study. Geostructural data show the presence of two main joint sets. Orientation data have been analysed taking Terzaghi correction into account. Spacing has been analysed at LAEGO laboratory (Nancy) with different statistical distribution laws with the code STAFF and verified with a classical 2 test. The modelling steps allow the spacing distribution to be modelled using different laws of density of probability (Laplace-Gauss normal, exponential, Log-normal, uniform). Every statistical simulation has also been checked by comparing observed rock walls with simulated ones. Values have been calibrated until a good correspondence has been reached. Table 2 reports the obtained results. A log-normal distribution has been chosen since it has been found as the most consistent with the experimental data (Table 3).

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A. M. Ferrero et al. Table 2. Orientation values used in the Resoblok model where K is the Fisher distribution coefficient Dip

dd

k

Variability limit 68.27%

Confidence limit 68.27%

11.1

2.5

6

1.4

Family 1 71 Family 2 72

201

62

115

210

Table 3. Spacing values utilized in the Resoblok model where and are the log-normal distribution coefficients Carrara

Family 1

Family 2

Log – normal distribution

¼ 8, ¼ 7

¼ 8, ¼ 6.8

Strength and deformability properties of the rock material and discontinuities have been assessed by laboratory tests. The material is characterised by a compressive strength (c) of 60 MPa, a tensile strength (t) of 6 MPa and a Young modulus 70 GPa. Rock mass features at large scale have been analysed by rock mass classifications methods. The Rock Mass Rating (Bieniawski, 1989) and the Geological Strength Index (Hoek, 1994) have been computed. The rock mass was classified with RMR ¼ 72 and GSI ¼ 75, respectively.

3. The Geophysical Survey 3.1 The Georadar Method The georadar (GPR) has been widely used to detect rock fractures and discontinuities both from the ground surface and from boreholes (Annan et al., 1988; Dubois, 1995, Pipan, 2003; Tillard, 1994). Experiments of 3D acquisition are also reported by Grasmueck (1996). The principles of GPR are quite similar to those of seismic reflection. The electromagnetic pulse (with centre frequency ranging from 0.1 to 1.5 GHz) radiated by a transmitter antenna propagates into the rock mass with a velocity v [m=s], given by: 1 c ffi v ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1 ! v ¼ pffiffiffiffi : when r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !" "r 2 " þ1 1þ 2 !" The wavelength [m] is given by: 2 v ffi ¼ 2 ; ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! " 2 ! þ1 1þ 2 !"


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Fig. 4. Representation of the a single trace of radar signal in time domain (a) with the pulse at the transmitter and the reflected signal due to a fracture; on the right (b) the amplitude spectrum of the radar signal. The amplitude of the reflected signal depends on the reflection coefficient and on signal attenuation. A frequency dispersion with respect to the nominal frequency of the source pulse can be observed in electrical conductive medium

with: ¼ 0 r [H=m], the magnetic permeability of the rock mass, where 0 ¼ 4 107 [H=m] is the vacuum magnetic permeability and r ½ is the relative magnetic permeability of the rock; " ¼ "0 "r [F=m], the electric permittivity of the rock mass, where "0 ¼ 109 =36 [F=m] is the vacuum electric permittivity and "r ½ is the relative electric permittivity of the rock; pffiffiffiffiffiffiffiffiffi c ¼ 1= "0 0 [m=s], the velocity of the electromagnetic pulse in vacuum; [S=m] is the conductivity of the rock; ! ¼ 2f [rad=s] is the angular frequency. The pulse amplitude is attenuated both for geometrical spreading and dissipation phenomena (Fig. 4). The geometrical spreading attenuates the pulse amplitude roughly as 1=r (being r the travel path length) and the dissipation phenomena according to er . The attenuation coefficient [neper=m] depends on the electromagnetic characteristics of the rock mass according to: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 " ¼! 1 : 1þ 2 !" The quantity 1= is referred to as ‘‘skin depth’’, that is the distance from the source where the pulse amplitude is 1=e (where e is the Neper number ¼ 2.71. . .) times its amplitude at the source; the skin depth can be related to the penetration depth of the radar signal. Every time the pulse impinges an interface between two media with different intrinsic impedance Z [Ohm]: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i! ; Z¼ ð þ i!"Þ pffiffiffiffiffiffiffi where, as usual, i ¼ 1; it is partly reflected and partly refracted.

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Table 4. Value of electromagnetic parameters involved in radar investigation in Stazzema quarry at frequency of 500 MHz and 900 MHz [S=m]

"r [–]

r [–]

v [m=ns]

[m]

1= [m]

Z [Ohm]

7.5 1 65

1 1 1

0.11 0.30 0.04

0.22 0.60 0.07

7.25 5 103 1.42

137.7 þ i 0.661 377 þ i 0.007 46.7 þ i 0.388

7.5 1 65

1 1 1

0.11 0.30 0.04

0.12 0.33 0.04

7.25 5 103 1.42

137.7 þ i 0.367 377 þ i 0.004 46.7 þ i 0.216

Frequency 500 MHz Marble Air Water

0.002 0.000001 0.03

Frequency 900 MHz Marble Air Water

0.002 0.000001 0.03

This value is not measurable (air in the rock fractures), the datum in the table is indicative for a very low conductivity

The electromagnetic characteristics of the materials involved in the pulse propagation in the experiments in Stazzema quarry are shown in Table 4 (Vaccaneo et al., 2004); air and water are the materials filling the marble fractures. At distance from the source greater than some wavelength (d5), a plane wave propagation can be assumed. Supposing a normal incidence of the plane wave on a plane interface, the amplitude coefficient for reflection R and transmission T are given by the Fresnel equations: Z2 Z1 2Z2 R12 ¼ ; T12 ¼ : Z2 þ Z1 Z 2 þ Z1 The formula above holds when the interface separates two half-spaces: Z1 is the intrinsic impedance of the medium 1 of the incoming wave and Z2 is the intrinsic impedance of the medium 2 of the outgoing wave. If the outgoing wave travels into an embedded layer with thickness M comparable to in medium 1, a more appropriate expression for the reflection coefficient is: R0 ¼

R12 ð1 eib Þ 1 R212 eib

where b ¼ 4M 1 with 1 the wavelength in medium 1. If moreover M1 then a better expression would be: R12 ib R00 : 1 R212 Table 5. Reflection coefficients for different couples of materials R12

R0

R00

0.465 i 0.001 0.493 i 0.003

5.73 103 i 0.068 6.27 103 i 0.074

2.96 104 i 0.068 7.26 104 þ i 0.075

0.465 i 0.001 0.493 þ i 0.001

0.02 i 0.12 0.02 þ i 0.13

4.26 104 i 0.123 3.30 104 i 0.134

Frequency 500 MHz Marble–air Marble–water Frequency 900 MHz Marble–air Marble–water


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The R0 coefficient would then be suitable when there are ‘‘thin layers’’, the R00 coefficient would be suitable when the layers ‘‘close’’ to fractures. In Table 5 the values of the reflection coefficients are given as calculated from the electromagnetic parameters of the materials encountered by the radar pulse in the pillar. At least theoretically, according to the radar performances, there is the chance of getting a signal back even from a fracture as open as 2 mm (see Table 5) filled by water; commercial radar systems have performance of approximately 100 dB, that means a capability of detecting signal of 1 mV for a pulse amplitude of 100 V, with a ratio between incident and reflected amplitude of 105 . The values of R00 also ensure that a high percent of energy passes through the fracture and is disposable to detect a following fracture on the pulse path. However, as far as the possibility of detecting two parallel fractures separated by a distance d, the ‘‘vertical resolution’’ (i.e. the resolution along the propagation direction) of the georadar must be defined. The most common approximation of the vertical resolution r is in the range from 1=4 to 1=2 of the wavelength , mainly depending on the noise level. A simulation with a finite difference code (REFLEXTM) leads to the results shown in Fig. 5. Within this simulation the radar traces of a 500 MHz pulse propagating in marble (wavelength was 0.21 m) have been calculated and the response of two parallel fractures at different distances from each other (350, 280, 210, 140, 70 mm) have been simulated; the distance between the antennas and the nearest fracture was 1 m, and the assumption of plan wave propagation is therefore satisfied. As shown in Fig. 5, the possibility of clearly identifying two reflections as coming from two different planes holds only for a separation greater than about 140 mm. The reflection event for a separation distance of 70 mm could be attributed, in some more slightly noisy conditions, to a single interface.

Fig. 5. Simulation of the 1D radar response of two parallel fractures separated by different distances; for a separation between the fractures of 30 mm the radar events can not be distinguished. The simulation has been carried out with an antenna central frequency of 900 MHz and supposing air filled fractures in marble

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The radar theory and the numerical simulations allow then to proceed with the field test and to help in data interpretation. The GPR pulse that has been sent into the rock mass is then reflected and eventually diffracted and comes back to the surface and is usually captured by another antenna thus forming the radar signal. This process is very fast so that many signals (some tens of thousands per second) are stacked to give a single radar trace. About 50 traces each second can be easily acquired with georadar so that if the two antennas (transmitting and receiving) move at a speed of 1 m=s about one trace every two

Fig. 6. Example of reflection of an inclined fracture in the pillar using a radar pulse with a central frequency of 900 MHz (top) and instantaneous amplitude response (bottom)


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centimetres can be acquired. The traces, plotted together, form the raw radargram (Fig. 6) that can be referred to the diffractions and reflections of the electromagnetic pulse within the rock mass.

3.2 Georadar Measurements and Processing Radar data acquisition was performed using a SIR2TM GSSI radar with 500 MHz and 900 MHz antennas on the four sides of the pillar along horizontal profiles at different elevation. The data processing, performed with REFLEXTM package, involved horizontal normalisation, bandpass filtering, migration and attribute computation (Godio et al., 2003). The horizontal normalisation regularises the separation distance between two adjacent radar traces adjusting for the non uniform speed of the antenna along the profile (it is an horizontal interpolation of the whole data set of radar traces). The band pass filtering decreases the amplitude of certain unwanted frequencies in the reflected signal. Usually unwanted low frequencies are associated with the system noise while high frequencies can be associated to the background electromagnetic noise. Migration is a procedure that permits to reduce the effect of wavefield artefacts (diffraction hyperbolas), collapsing all the energy in a single point.

3.3 Geophysical Results The results of the georadar survey are described taking into account the penetration depth and the resolution obtained at different frequencies, moreover they are compared with the preliminary reconstruction obtained by the geomechanical mapping. The acquisition on the pillar at low frequency (Fig. 7) permitted a penetration depth of more than 10 meters with a very low degradation of information also in presence of several reflection events. Intense diffraction effects were evident in each acquisition when the 500 MHz antennas were used. The main diffraction patterns were caused by discontinuities on the pillar faces (steps on the wall surface, remains of cutting trace on the pillar). While it was expected that the diffraction pattern would have disappeared after few meters, considering that in theory the antenna has a rather narrow radiation beam, with a maximum radiated power centred to an angle of 20 from the normal to the dipole, the experiment evidenced strong diffracted signals for angles wider than 45 . In such a context the migration procedures were used for filtering the radar image and reduce the effect of diffraction hyperbolas, representing in a more realistic image the ‘‘true’’ position of the reflectors (steep layers). A simple time migration (diffraction stack) of the radar zero-offset profiles using a constant velocity was performed. The diffraction stack was performed in the x–t range. A selected example of the reliability of the diffraction stacks is depicted in Fig. 7. The acquisition using high frequency antenna therefore confirmed the capability of the system to detect the main (close) fractures up to a distance of 4–5 meters from the wall of the pillar. The resolving power degrades more because of attenuation due to reflection and diffraction events and because of geometrical spreading than because of dissipation phenomena.

Fig. 7. Data processing of radar images acquired along face C at a main frequency of 500 MHz. Left: raw radar images. Center: after horizontal background noise removal, band-pass filtering and diffraction stack migration. Right: instantaneous amplitude of the migrated image. The reflection on the bottom of the images refers to the strong reflected signal of the marble-air interface at the opposite side of the pillar (side A)

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The investigation limited to a single face of the pillar shows that the system is well able to detect discontinuities and fractures parallel or gently inclined with respect to the pillar face where the antennas move. On the contrary, the discontinuities perpendicular to the plane of the antennas could be resolved only under favourable conditions, where the tortuosity of the fracture planes determine localised diffraction hyperbolas. The investigation on the two opposite sides of the pillar increases the reliability of the detection of sub-parallel fractures but does not always provide a good estimate of the discontinuities located perpendicularly to the pillar face. A better result in terms of rock mass quality evaluation is obtained from the analysis of the investigation per-

Fig. 8. Improvement in detection of fractures according to the free surface of the pillar (acquisition with 900 MHz antenna). Left: composition of the radar images acquired along two adjacent faces of the pillar (faces A and D). Right: composition of the radar images acquired along three adjacent faces of the pillar (faces A, D and C)

Fig. 9. Left: Cad reconstruction of the main fractures from georadar data interpretation; right: 3D rendering of the fracture planes within the pillar as seen from south-east

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formed on two pillar faces perpendicular to each other (Fig. 8). This condition is a realistic approximation of many cases that can be encountered during the exploitation activities. The optimum results can be achieved when three different walls of the pillar are accessible for the radar survey, as pointed out in Fig. 8. A 3D reconstruction of the persistence of the main fractures can be obtained by interpolating the reflections events acquired at different levels along the pillar face (Fig. 9). The comparison of the (partial) reconstruction of the geometry and persistence of the main joints and fractures with the preliminary computed structural model shows the limitations of this model in modelling the fracture pattern within the pillar and the need to compute a new model starting form the information obtained by the georadar survey.

4. Rock Mass Modelling Rock engineering design for the assessment of the stability condition of an underground excavation needs a tool able to forecast the stress and deformation responses of the rock mass. Fractured rock masses are often geometrically complex and can be regarded as an assemblage of many individual polyhedral blocks. When such a rock mass is subjected to mechanical disturbance, through, for example, the excavation of an underground opening, the blocks of the rock mass will displace and rotate. Displacements and rotations can be very large, and the contacts between the individual blocks may change as the blocks move. Consequently, the mechanical response of a rock mass can be properly determined through the use of computational methods that are designed to account for large block displacements and rotations, and block detachment and re-attachment (Bray, 1975). The modelling of the rock mass considered as a blocky system is performed in two phases: the geometrical modelling and the mechanical modelling

4.1 Geometrical Modelling The geometrical discretisation of a rock mass into blocks is based on an ideal, perfect discontinuous medium. In order to describe a rock mass as a blocky system, it is necessary to consider the relationships between the joint sets. These relationships can be ruled by the interruption of some joints in correspondence to joints that belong to another set or by relative displacements between blocks. The relationships between the joint sets are the results of successive failures. The natural state of fracture of a rock mass is the result of its geological and structural history. Its history is made up of a succession of events each with different stress states. The early events generally generate one or two joint sets. The later events usually affect preexisting fractures. The chronology of the various events determines the hierarchy of the fractures. The software code utilised in this work is Resoblok (Heliot, 1988a, b) which has been implemented to follow the tectonic history of the formation; a continuous medium is transformed into a blocky system. Joints can be introduced in a deterministic way, as in the case of faults or major discontinuities directly detected on site; the joint


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Fig. 10. a Example of in situ survey of the rock mass on the pillar face C, b deterministic reconstruction of the same pillar rock face, c RESOBLOK complete rock mass model reconstruction

sets are automatically generated in a statistic way on the basis of the surveyed discontinuities, by means of statistical distribution. The deterministic analysis is based on the orientation, position and persistence of the fractures; a single discontinuity can be considered either completely persistent, and therefore crossing the overall model, or not completely persistent. The joint sets (derived from statistic analysis) are represented on the basis of the principal orientation, mean spacing and persistence. The persistence of the joints is performed by generating a hierarchy of the probabilistic distribution of the discontinuities by taking into account the relationships between the joint sets and considering the geophysical radar results. Figure 10a shows the fracturing state observed on the quarry rock wall while Fig. 10b and c depict a section performed by Resoblok with the deterministic model along a vertical section. A comparison between the measured discontinuities and the modelled ones gives a good correspondence for the accessible face and with the rock pattern reconstruction obtained by the georadar method.

4.2 Mechanical Modelling The mechanical behaviour of the blocky rock mass is modelled by the Distinct Element Method (DEM). Over recent years, the DEM has emerged as one of the principal computational methods for such problems (Lemos et al., 1985; Cundall, 1971; Cundall et al., 1985). According to this method, the problem domain under investigation is

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regarded as a discontinuous medium, composed of an assembly of discrete blocks (the distinct elements), which may be rigid or deformable, and which interact with one another through deformable boundaries of definable stiffness. In the DEM, the contact between two elements results in the generation of inter-element forces. Since an element may simultaneously be in contact with a number of adjacent elements, there is usually a number of these forces applied to each element. According to DEM, a block geometry is defined using the spacing, orientation and the persistence of the joint sets which characterise the rock mass under study. Large displacements and rotation, detachment and re-attachment are allowed for a single block, each of which may be assumed as a rigid or deformable body. The stress and strain in the blocks can also be computed and the response of a discontinuous medium (jointed rock mass) subject to either static or dynamic loading can be simulated. The method can be applied to compute the mechanical behaviour of a blocky system and the stability condition of the excavation since the blocks that can fall or slide from the roof of the room or within the pillar can be determined, and the induced stresses can be evaluated. The 3DEC code (ITASCA, 1999) has been used to analyse the mechanical behaviour of a blocky system in the three dimensional space. A 3 dimensional model has been set up for this site. The rock mass as simulated by means of the Resoblok schematisation is shown in Fig. 11. The size of the model is: 150 50 150 m and it includes 3252 blocks and 3762 contacts. For each modelled excavation step the stresses and the displacements are computed and compared with the available measurements. The displacements computed by the 3DEC code are shown in Fig. 12 in a representative section of the model. A rock block that is about to fall from the roof of the excavation is visible in this section showing the remarkable influence of the location and the persistence of the discontinuities on both the stress distribution and the induced displacements. The comparison (Cravero et al., 2002; Deangeli et al., 2002) between computed and measured stress and displacements shows a good correspondence, indicating the

Fig. 11. Rock mass modelled with the codes Resoblok and 3DEC (after Thoraval, 2002)


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Fig. 12. a Computed principal stresses at the center of the pillar. b Computed displacements in the rock mass showing a falling block at the roof of the excavation

reliability of the modelling work an overall stable condition of the stope although possible falling of limited size blocks con occur.

5. Concluding Remarks The evaluation of a rock mass discontinuity distribution is of relevant importance for the planning of a quarry exploitation; the evaluation of the spatial density and of persistence of a fracture may affect the adopted exploitation method and, consequently, the obtainable extraction rate. For this reason a deep knowledge of the rock mass structure is important and for this purpose a combination of the classical and the geophysical survey methods has been explored. Particularly, radar measurements have been performed to obtain an estimate of the morphology of the main fractures within the rock mass. The effectiveness of the georadar method was analysed according to the following steps: – the information derived from the radar survey on a single face was taken into account; – the improvement of the information on the rock mass quality through a joint analysis of the results on two opposite faces was verified; – finally, the improvement of the information on the rock mass quality through the combined analysis of the results on two perpendicular faces was analysed, simulating the investigation on the butt of the quarry. The performance of a radar system in marble material has been analysed in detail with respect to the penetration depth and the depth resolution at different frequencies. The

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reconstruction of 2D and 3D images of the main fractures allows the information of the geostructural survey to be integrated. The accuracy and the reliability of the georadar interpretation has been confirmed through a comparison between the results and the traces of the joints and fractures that are visible on the different pillar walls. The shortcomings of the radar investigation have been outlined considering the penetration depth and the vertical and horizontal resolving capabilities. These drawbacks pointed out the importance of performing an investigation along two adjacent walls of the quarry in order to obtain a more accurate reconstruction of the persistence and geometry of the fractures. Determining the density of the discontinuities is a difficult task in areas of high density with inter-spacing between the fractures of less than 0.2–0.3 metres. The feasibility of operating along profiles at different elevations on the faces permits a realistic visualisation of the main fractures using 3D rendering techniques. In the selected case the presence of vertical discontinuity planes makes the rendering easy and reliable. The 2D and 3D reconstruction of the fractures permits a more accurate deterministic evaluation of the 3D structural model. The final comparison between the radar images and the reconstruction performed by the Resoblok code allowed to verify the pitfalls of the deterministic reconstruction based only on the analysis of the visible traces of joints and fractures on the pillar faces, allowing the optimising of the reconstruction of the pillar fracturing system. Finally, the geophysical results have been integrated in the study of the mechanical behaviour of the marble rock mass and the mechanical behaviour has been analysed using both probabilistic and deterministic geometrical models of the rock mass. As far as the radar acquisition and data processing are concerned the low costs of single fold data acquisition (near zero offset) and the good quality of the results justified the validity of the simplified approach. Technical improvements in horizontal resolution could be obtained using more sophisticated acquisition schemes (optimum offset and CMP acquisition). Borehole investigations would increase the effectiveness of the radar survey, permitting accurate investigation surveys in complex logistical conditions of the quarry; in many cases the number and the position of boreholes have to be well planned in order to avoid damage to the integer zone of the quarry. On the other hand, an increase in the unitary costs of the survey using a more complicated approach could make an extensive investigation during the mining activity unrealistic. The methodology is particularly interesting for a low degree fractured rock mass where the discontinuities rule the mechanical behaviour of the rock mass and where the proposed geophysical techniques can be more reliable.

Ackowledgement This work has been funded by the European Union with project ‘‘Development of an integrated computed aided design and planning methodology for underground marble quarries’’ CAD-PUMA BE97-5005 Brite Euram III and by the Italian Minister of Research, COFIN 2001 ‘‘Mechanised excavation of tunnels’’. In situ measurements and laboratory tests have been carried out by CNR-FIRGET Torino.


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