geophysical and geomechanical investigations applied to the rock mass characterisation for distinct...

Rock Mech. Rock Engng. (2007) 40 (6), 603–622

DOI 10.1007/s00603-006-0092-9

Printed in The Netherlands

Geophysical and Geomechanical InvestigationsApplied to the Rock Mass Characterisation

for Distinct Element Modelling

By

A. M. Ferrero1, A. Godio2, L. Sambuelli2, and I. H. Voyat3

1 University of Parma, Parma, Italy2 Dipartimento di Ingegneria del Territorio, dell’Ambiente e delle Geotecnologie,

Politecnico di Torino, Torino, Italy3 Dipartimento di Geotecnica e Ingegneria Strutturale, Politecnico di Torino, Torino, Italy

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

Summary

The paper describes the experience gathered in an underground quarry of crystalline marble wherethe rock mass structure has been characterised by a joint approach using geomechanical mappingand geophysical investigations with a high resolution radar system. Standard geomechanical sur-veys have been coupled and integrated by radar acquisition performed on a selected pillar of thequarry to improve the rock mass description. The fracture pattern has been computed on the basisof the deterministic model on the rock faces of the pillar and taking into account both thestatistical approach to describe the extent within the rock mass and the fracture pattern describedby 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 orna-

mental stone exploitation, the best modelling approach is often based on a discontin-

uous 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.

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 distribu-

tion 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 dis-

continuity locations can be determined by measuring their traces on an excavation

surface, even though the persistence within the rock mass is more difficult to deter-

mine. 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.

604 A. M. Ferrero et al.

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 mea-

surements 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 accord-

ing to the procedure reported in Table 1 where indications on the mapped disconti-

nuity 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

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

location (Cravero et al., 2002)

Geophysical and Geomechanical Investigation 605

Table

1.

Ex

amp

leo

fst

ruct

ura

lsu

rvey

wit

hd

isco

nti

nu

ity

loca

lisa

tio

no

nth

ero

ckw

all

Zo

ne

of

inves

tig

atio

nw

all

A

Ref

eren

cep

oin

t:x

(lo

cal)

y(l

oca

l)z

Fra

ctu

reN

�d

ip(�

)d

d(�

)ty

pe

thic

kn

ess

(cm

)ap

ertu

re(c

m)

mo

rph

olo

gy

end

1(m

)en

d2

(m)

no

te

s.sc

ale

b.s

cale

x1

y1

type

x2

y2

type

17

01

20

dia

c0

.1–

smP

1.2

03

.2L

2.4

60

.00

L2

77

11

8d

iac

0.2

–sm

P3

.15

3.2

L4

.00

0.0

0L

38

59

dia

c0

.1–

rP

6.4

01

.15

L6

.50

3.2

L4

74

11

2d

iac

0.1

–0

.2–

rP

10

.91

3.2

L1

1.2

70

.00

LW

56

51

95

dia

c0

.1–

0.2

–r

U1

7.5

13

.2L

18

.10

0.0

0L

W6

76

20

2d

iac

<0

.1–

rP

21

.90

3.2

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2.9

01

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L

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dia

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pre

sen

ceo

fw

ater

Mo

rph

olo

gy

:r

rou

gh

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smo

oth

,Sl

slic

ken

sid

ed,S

step

ped

,U

un

du

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ng

,P

pla

nar

Ty

pe:

sst

op

ped

,L

lon

ely,

ttr

un

cate

d


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).

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

Fig. 2. Rock wall exposure and relative survey digitalization


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 classifica-

tions methods. The Rock Mass Rating (Bieniawski, 1989) and the Geological Strength

Index (Hoek, 1994) have been computed. The rock mass was classified with

RMR¼ 72 and GSI¼ 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 re-

flection. 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:

v ¼ 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�"

2

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ �

!"

� �2r

þ 1

s � when� �

!"

�¼ 1 ! v ¼ cffiffiffiffi

"rp :

The wavelength � [m] is given by:

� ¼ 2�

!

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�"

2

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ �

!"

� �2r

þ 1

s � ¼ 2�v

!;

Table 2. Orientation values used in the Resoblok model where K is the Fisherdistribution coefficient

Dip dd k Variabilitylimit 68.27%

Confidencelimit 68.27%

Family 1 71�

201� 62 11.1� 2.5�

Family 2 72�

115� 210 6� 1.4�

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

Carrara Family 1 Family 2

Log – normal distribution �¼ 8, �¼ 7 �¼ 8, �¼ 6.8


with:

� ¼ �0�r [H=m], the magnetic permeability of the rock mass, where �0 ¼ 4��10�7 [H=m] is the vacuum magnetic permeability and �r½�� is the relative magnetic

permeability of the rock;

" ¼ "0"r [F=m], the electric permittivity of the rock mass, where "0 ¼ 10�9=36�[F=m] is the vacuum electric permittivity and "r½�� is the relative electric permittivity

of the rock;

c ¼ 1=ffiffiffiffiffiffiffiffiffi"0�0

p[m=s], the velocity of the electromagnetic pulse in vacuum;

� [S=m] is the conductivity of the rock;

! ¼ 2�f [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 accord-

ing to e��r. The attenuation coefficient � [neper=m] depends on the electromagnetic

characteristics of the rock mass according to:

� ¼ !

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�"

2

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 þ

� �

!"

�2r

� 1

s �:

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 number¼ 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]:

Z ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

i!�

ð�þ i!"Þ

s;

where, as usual, i ¼ffiffiffiffiffiffiffi�1

p; it is partly reflected and partly refracted.

Fig. 4. Representation of the a single trace of radar signal in time domain (a) with the pulse at thetransmitter and the reflected signal due to a fracture; on the right (b) the amplitude spectrum of the radarsignal. 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


The electromagnetic characteristics of the materials involved in the pulse propa-

gation 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 (d�5�), 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:

R12 ¼ Z2 � Z1

Z2 þ Z1

; T12 ¼ 2Z2

Z2 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 R12ð1 � eibÞ1 � R2

12eib

where b ¼ 4�M�1

with �1 the wavelength in medium 1.

If moreover M��1 then a better expression would be:

R00 � �R12ib

1 � R212

:

Table 4. Value of electromagnetic parameters involved in radar investigation in Stazzema quarry at frequencyof 500 MHz and 900 MHz

� [S=m] "r [–] �r [–] v [m=ns] � [m] 1=� [m] Z [Ohm]

Frequency 500 MHz

Marble 0.002 7.5 1 0.11 0.22 7.25 137.7þ i 0.661Air 0.000001� 1 1 0.30 0.60 5� 103 377þ i 0.007Water 0.03 65 1 0.04 0.07 1.42 46.7þ i 0.388

Frequency 900 MHz

Marble 0.002 7.5 1 0.11 0.12 7.25 137.7þ i 0.367Air 0.000001� 1 1 0.30 0.33 5� 103 377þ i 0.004Water 0.03 65 1 0.04 0.04 1.42 46.7þ i 0.216

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

Table 5. Reflection coefficients for different couples of materials

R12 R0 R00

Frequency 500 MHz

Marble–air 0.465� i 0.001 5.73� 10�3 � i 0.068 �2.96� 10�4 � i 0.068Marble–water �0.493� i 0.003 �6.27� 10�3 � i 0.074 7.26� 10�4 þ i 0.075

Frequency 900 MHz

Marble–air 0.465� i 0.001 0.02� i 0.12 �4.26� 10�4 � i 0.123Marble–water �0.493þ i 0.001 �0.02þ i 0.13 3.30� 10�4 � i 0.134


The R0 coefficient would then be suitable when there are ‘‘thin layers’’, the R00 co-

efficient 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 param-

eters 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 10�5.

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 geo-

radar 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 propagat-

ing 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 aseparation 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


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 even-

tually 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 frequencyof 900 MHz (top) and instantaneous amplitude response (bottom)


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 hor-

izontal 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. Migra-

tion 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 com-

pared 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 (diffrac-

tion 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.

Dat

ap

roce

ssin

go

fra

dar

imag

esac

qu

ired

alo

ng

face

Cat

am

ain

freq

uen

cyo

f5

00

MH

z.L

eft:

raw

rad

arim

ages

.C

ente

r:af

ter

ho

rizo

nta

lb

ack

gro

un

dn

ois

ere

moval

,b

and

-pas

sfi

lter

ing

and

dif

frac

tio

nst

ack

mig

rati

on

.R

igh

t:in

stan

tan

eou

sam

pli

tud

eo

fth

em

igra

ted

imag

e.T

he

refl

ecti

on

on

the

bo

tto

mo

fth

eim

ages

refe

rsto

the

stro

ng

refl

ecte

dsi

gnal

of

the

mar

ble

-air

inte

rfac

eat

the

opposi

tesi

de

of

the

pil

lar

(sid

eA

)


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 perpen-

dicular to the plane of the antennas could be resolved only under favourable condi-

tions, 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 with900 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 renderingof the fracture planes within the pillar as seen from south-east


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 persis-

tence 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 under-

ground 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 relation-

ships 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 pre-

existing 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 medi-

um 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


sets are automatically generated in a statistic way on the basis of the surveyed dis-

continuities, 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 orienta-

tion, mean spacing and persistence.

The persistence of the joints is performed by generating a hierarchy of the prob-

abilistic 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 Ele-

ment 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

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


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 repre-

sentative 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)


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, conse-

quently, 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, simulat-

ing 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

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


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 reconstruc-

tion 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 activ-

ity 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 inte-grated computed aided design and planning methodology for underground marble quarries’’CAD-PUMA BE97-5005 Brite Euram III and by the Italian Minister of Research, COFIN2001 ‘‘Mechanised excavation of tunnels’’. In situ measurements and laboratory tests have beencarried out by CNR-FIRGET Torino.


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Authors’ address: Dr. A. M. Ferrero, Dipartimento di Ingegneria Civile, Universita di Parma,Parco delle Scienze 1, 43 100 Parma, Italy; e-mail: [email protected]

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