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C.A. Torres
March, 2008
Geometric Characterisation of Rock Mass
Discontinuities Using Terrestrial Laser Scanner
and Ground Penetrating Radar
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Disclaimer
This document describes work undertaken as part of a programme of study at the
International Institute for Geo-information Science and Earth Observation. All views and
opinions expressed therein remain the sole responsibility of the author, and do not
necessarily represent those of the institute.
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Abstract
A main objective of the geometric characterization of rock mass discontinuities is to
establish a three dimensional model that permits to define the fabric of this
discontinuous medium. Because of the existing limitations in field surveys and dataprocessing methods it is necessary to extract as much information as possible in an
integrated and objective way in order to create a more consistent model of the rock
mass fabric while decreasing the degree of uncertainty. The use of Terrestrial Laser
Scanner (TLS) has shown to be an attractive and consistent alternative to digitally
reconstruct the exposed surface of a rock mass outcrop and acquire geometric
information through a semi-automated extraction of the geometric properties
(orientation and spacing). On the other hand, Ground Penetrating Radar (GPR)
based methods have allowed to detect and map internal discontinuities and derive a
interpretation of a rock mass internal discontinuities network. The objective of the
research is to determine whether the geometric information derived from TLS and
GPR can be integrated and used in a geometric characterization of a rock mass and
how this can improve traditional survey methods.
Traditional, TLS and GPR surveys were performed over a rock slope at a porphyry
stone quarry (Trento, North Italy). Traditional, TLS and GPR derived data were
processed separately in order to obtain geometric information; this information was
integrated while following geometric characterization. The individual results and the
integrated analysis of the geometrical information derived from Terrestrial Laser
Scanner and Ground Penetrating Radar showed a reasonable degree of correlation
with the results of the traditional approach and demonstrated to be an attractive way
of complement such information in order to reduce the degree of uncertainty about
the geometrical characteristics of the discontinuity network of a rock mass.
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Acknowledgements
I would like to express my gratitude to my supervisors Dr. Robert Hack and Dr. Mark
van der Meijde. I also grateful to all the ITC and Nuffic Organization.
I wish to acknowledge to Dr. Antonio Galgaro, Dr. Giordano Teza and Geol.
Annapaola Gradizzi from the Department of Geology, Palaeontology and
Geophysics of the University of Padova (Padova, Italy) who provided the equipment
and offer technical expertise along the field campaign.
Andrei Torres
Enschede, 2008
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Table of contents
1. Introduction ....................................................................................................................... 9
1.1.
Scope ........................................................................................................................ 9
1.2. Problem definition .................................................................................................... 10
1.3. Research question .................................................................................................. 10
1.4. Research objective .................................................................................................. 11
1.5.
Specific objectives ................................................................................................... 11
1.6. General Methodology .............................................................................................. 11
2. Modelling the geometry of a discontinuity network in a rock mass ................................. 12
2.1. Discontinuity definition ............................................................................................. 12
2.2.
Geometric properties of discontinuities ................................................................... 13
2.3.
Traditional methods to collecting discontinuity data ................................................ 14
2.3.1. Surface methods .............................................................................................. 14
2.3.2. Subsurface methods - borehole explorations ................................................... 15
2.4. Terrestrial Laser Scanner as a recent technique to derive geometric information .. 15
2.4.1.
TLS fundamentals ............................................................................................ 15
2.4.2. Data processing ............................................................................................... 15
2.5. Ground Penetrating Radar based methodologies for detect internal discontinuities 18
2.5.1.
Ground Penetrating Radar fundamentals ........................................................ 18
2.5.2. Ground Penetrating Radar as a technique to detect internal discontinuities.... 19
2.5.3. GPR data processing methodology ................................................................. 20
2.6.
Discontinuity network modelling .............................................................................. 20
2.6.1.
Discontinuity sets and homogeneous regions .................................................. 21
2.6.2. Discontinuity orientation ................................................................................... 22
2.6.3. Discontinuity spacing ....................................................................................... 24
2.6.4. Trace length and persistence ........................................................................... 25
2.7.
Discontinuity network modelling and validation ....................................................... 26
3. Methodology ................................................................................................................... 27
3.1. Study site ................................................................................................................. 28
3.2. Weather, seepage groundwater conditions ............................................................. 29
3.3.
Geometric characterization, traditional approach .................................................... 30
3.3.1. Slope Stability Probability Classification (SSPC) ............................................. 30
3.3.2. Scanline Survey ............................................................................................... 31
3.3.3. Validation and integration of the derived information ....................................... 33
4.
Geometric characterization, TLS based methods .......................................................... 35
4.1.
Data acquisition ....................................................................................................... 35
4.2. Dataset reorientation ............................................................................................... 36
4.3. Data analysis to derive orientation information ....................................................... 36
4.3.1. Surface reconstruction with 2D gridding and Delaunay triangulation ............... 36
4.3.2.
Direct segmentation with 3D Hough transformation and least squares ........... 41
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4.4. Validation of Terrestrial Laser Scanner Mehtods against Traditional Approaches .. 47
4.5. Deriving spacing information ................................................................................... 52
5. Detecting and mapping internal discontinuity network, Ground Penetrating Radar based
method ................................................................................................................................... 53
5.1. Methodology ............................................................................................................ 53
5.2.
Establishing GPR viability and GPR survey requirements ...................................... 54
5.2.1. GPR survey objective ....................................................................................... 54
5.2.2.
Rock mass characteristics ................................................................................ 54
5.2.3. GPR performance for detecting discontinuities ................................................ 55
5.2.4. Survey requirements ........................................................................................ 56
5.3. Data adqusition ........................................................................................................ 57
5.4. GPR data processing .............................................................................................. 58
5.4.1.
GPR raw data characteristics ........................................................................... 58
5.4.2. GPR data processing ....................................................................................... 59
5.5.
Results interpretation ............................................................................................... 60
5.6.
Results validation .................................................................................................... 64
6. Integration of the geometric information derived from TLS and GPR and validation
against the traditional approach ............................................................................................. 65
6.1.
TLS and GPR derived information integration ......................................................... 65
6.2.
Validation against the traditional approach .............................................................. 65
6.2.1. Discontinuity set J1 .......................................................................................... 66
6.2.2. Discontinuity set J2 .......................................................................................... 66
6.2.3. Discontinuity set J3 .......................................................................................... 67
6.2.4.
Discontinuity set J4 .......................................................................................... 67
6.2.5. Discontinuity set J5 .......................................................................................... 67
6.2.6. Discontinuity set J6 .......................................................................................... 67
6.3.
General observations .............................................................................................. 68
6.3.1.
Number of discontinuity sets ............................................................................ 68
6.3.2. Discontinuity sets orientation ............................................................................ 68
6.3.3. Normal discontinuity set spacing ...................................................................... 68
6.3.4. Discontinuity sets persistence .......................................................................... 69
7.
Conclusions .................................................................................................................... 69
7.1. Terrestrial Laser Scanner method ........................................................................... 69
7.2. Ground penetrating radar ........................................................................................ 70
References ............................................................................................................................. 71
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List of figures
Figure 1. General Methodology flowchartFigure 2. Geometric properties in a discontinuous rock mass (after (Hudson, 1989))
Figure 3. a) Rock mass scanned surface, b) Polygonal surface reconstruction
Figure 4. a) Rock mass scanned surface, b) Segmented TLS point cloud data
Figure 5. a) Rock mass scanned surface, b) Surface reconstruction and c) Equal area
hemispherical projection of all facet poles grouped using fuzzy k-means clustering (see
section 2.6.2), (Slob and van Knapen, 2006)
Figure 6. Illustration of the processing applied to GPR data a) Raw data, b) Processed data
using i) a DC removal ,ii) a zero-phase band-pass filter and iii) an AGC time equalization. (c)
Static corrections for topography and time to depth conversion were applied, d) Interpretation
of the discontinuity network (Deparis et al., 2007)
Figure 7. Stereographic projection of the pole of a plane: (a) Reference sphere, b)
Hemispherical projection, c) Stereonet representation (after (Brady and Brown, 2004)).
Figure 8. Some examples of orientation models
Figure 9. General methodology flowchart
Figure 10. Study site at Albiano (Province of Trento, North Italy) a) Porphyry quarry (Permian
Rhyolite), b) Location, c) geological map
Figure 11. Rock mass exposure at Albiano quarry (Permian Rhyolite), height 20m.
Figure 12. Scanline survey
Figure 13. Low hemisphere, equal angle stereo-plot and density of orientation data (poles)
obtained from SSPC (in red) and scanline survey (orientation data in black and kernel density
in grey scale)
Figure 14. a) Laser scanner campaign. b) Cropped TLS dataset: 1.993.314 points (displayed
by intensity value)
Figure 15. TLS data process for deriving geometric information through surface
reconstruction using 2D gridding and Delaunay triangulation
Figure 16. Original point cloud data and surface reconstruction through 2D gridding and
Delaunay triangulation (Software: Split-FX Ver.1.0)
Figure 17.Surface reconstruction through 2D gridding and Delaunay triangulation and result
of planes patterns recognition. Isolated plane patterns are displayed in blue, and excluded
areas in red. (Software: Split-FX Ver.1.0).
Figure 18. Lower hemisphere, equal area stereo-plot and density of orientation data (poles).
a) Traditional methods: SSPC (red squares), Scanline (black signs). b) Surfacereconstruction method (blue points).(Software: Dips Ver. 5.106 , Split-FX Ver.1.0).
Figure 19. TLS data process for deriving geometric information direct segmentation and least
squares estimation
Figure 20. Original point cloud data and direct segmentation results through
Figure 21. Low hemisphere, equal area stereo-plot and density of orientation data (poles). a)
Traditional methods: SSPC (red squares), Scanline (black signs). b) Direct segmentation
(black signs). (Software: Dips Ver. 5.106 )
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Figure 22. Low hemisphere, equal area stereo-plot and density of orientation data (poles). a)
Traditional methods: SSPC (red squares), Scanline (black signs), b) Surface reconstruction
and c) Direct segmentation (black signs). (Software: Dips Ver. 5.106 , Split FX Ver.1.0)
Figure 23. GPR methodology for detect and map internal discontinuity network
Figure 24. GPR survey setting
Figure 25. GPR raw data (profile H3). Data is dominated by direct air wave (A), ground wave
(B), system ringing (C), multiples (D) and diffraction hyperbolas (E).
Figure 26. GPR raw data processing scheme
Figure 27. Progressive results of applying processing scheme to a typical horizontal section
(profile H3). a) Raw data, b) Geometry specification, static correction, and background
removal, c) amplitude compensation, d) band-pass filtering, e) Running average and d) Time
to depth conversion and migration. Blues/greens and reds/violets define negative and
positive pulses and colour intensity is a function of amplitude.
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List of tables
Table 1. SSPC rock mass geometric description ( > denotes greater than the exposure size,see SSPC filed form details in appendix 1)
Table 2. Descriptive statistics of the scanline surveys results (* Fisher kconstant is not valid
if the sample size N is smaller than 10)
Table 3. Summary of geometric parameters derived from each method for each set
Table 4. Parameter values used for surface reconstruction through 2D gridding and Delaunay
triangulation (Software: Split-FX Ver.1.0)
Table 5. Parameter values used for surface reconstruction through 2D gridding and Delaunay
triangulation
Table 6. Summary of the orientation results: Traditional methods (SSPC and Scanline)
versus surface reconstruction method. (* Fisher kconstant is not valid if the sample size N is
smaller than 10)
Table 7. Kd-tree structure parameters (* Refers to the average number of points that each
kd-tree cell contain)
Table 8. Parameter values used for direct segmentation
Table 9. Summary of the orientation results: Traditional methods (SSPC and Scanline)
versus direct segmentation method. (* Fisher kconstant is not valid if the sample size N is
smaller than 10)
Table 10. Summary orientation statistics. a) Traditional methods: SSPC, Scanline, b) Surface
reconstruction and c) Direct segmentation
Table 11. Summary of normal set spacing results, comparison between traditional and TLS
(direct segmentation) method
Table 12. Summary of the geometrical and condition characteristics of the
Table 13. Properties of the acquired GPR profiles
Table 14. Comparison between geometrical information derived from the interpretation of
GPR profiles and SSPC characterization (the symbol > denotes that the persistence is lager
than the characterized exposure or larger the GPR profile length)
Table 15. Integration of geometric information derived from the remote sensing approach (the
symbol > denotes that the persistence is lager than the characterized exposure or larger the
GPR profile length).
Table 16. Integration of geometric information derived from the remote sensing approach
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1. Introduction
1.1. Scope
When dealing with discontinuous rock masses, the properties of the discontinuities
in the rock becomes of prime importance, since they will determine, to a large
extent, the mechanical behaviour of the rock mass (Bieniawski, 1989). These
properties are classified into geometric and non-geometric. The non-geometric
properties are related to mechanical behaviour of the infill material and the shear
strength of the intact rock adjacent to the discontinuity while the geometric
properties define the fabric of the discontinuous rock mass (Hack, 1998).
The main objective of the geometric characterization of the discontinuities within a
rock mass is to establish a model that permits to define the fabric of this
discontinuous medium. Discontinuities are just partially accessible at their
intersection with outcrops, boreholes and drifts from which analysis methods make
assumptions about such discontinuity network. Variation in the performed field
measurements and hence the model that is derived are constrained by the
sampling technique is used, the degree of exposure the rock mass outcrop has
and the number of observations that can be done (Priest and Hudson, 1981).
Traditional techniques for geometric characterization of rock masses include scan
line survey, cell mapping, and rapid face mapping to systematically direct the
mapping of a rock face (Hack, 1998). These surface interpretation methods can be
complemented by borehole surveys in order to achieve a better knowledge of the
discontinuity network (Wines and Lilly, 2002). However these traditional methodsare time consuming and often present some degree of error.
New techniques for geometric characterization of discontinuities based on the
interpretation of the visible surface of a rock mass outcrop include image analysis,
digital photogrammetry and total station (Kemeny, 2003; Lemy and Hadjigeorgiou,
2003; Roncella and Forlani, 2005; Zhang et al., 2004). Among these new
methods, Terrestrial Laser Scanner is a remote sensing technique which has
shown a great potential to obtain a large quantity of accurate geometric data (Slob
et al., 2004). A remarkable aspect is the possibility of reconstructing rock mass
face and extracting geometrical information of such surface by analytical methods
(Rotondaet al., 2007; Slobet al., 2004; Slob and van Knapen, 2006).
On the other hand, Ground Penetrating Radar has been used to detect and map
internal discontinuities in rock masses as an alternative to borehole exploration.
After processing and interpreting the Ground Penetrating Radar data, a
representation of the geometry of the internal discontinuities can be obtained.
Comparison between discontinuities observed on surface and those mapped
using Ground Penetrating Radar have shown reasonable correlation (Deparis and
Garambois, 2006; Grandjean and Gourry, 1996; Porsaniet al., 2006).
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1.2. Problem definition
In order to perform a geometric characterization, traditional survey techniques
have shown large disadvantages since they are time consuming, involve human
bias, and present safety, access and economic constraints (Slob et al., 2004),
however for most engineering problems the use of these techniques with a properengineering judgement are considered to be enough and useful (Hack, 1998).
Although comparison between Terrestrial Laser Scanner based and traditional
methods have shown coherent results, difficulties have been reported associated
with some unfavourable geometric configurations (i.e. angle of incidence of the
laser beam and the identification of horizontal surfaces) (Roncella and Forlani,
2005; Rotondaet al., 2007). Hence, there is still a need for engineering criteria to
provide manual intervention, spot checks and results interpretation (Cogganet al.,
2007).
On the other hand, Ground Penetrating Radar based methods to detect and map
internal discontinuities have shown a good degree of correlation with surface
observations when characterizing rock masses at quarry scale ((Grandjean and
Gourry, 1996), but they are limited to the interpretation of 2D profiles in order to
obtain a representation of the internal discontinuities and they require to be
validated by gathering additional information (i.e. the results of the interpretation of
GPR profiles must be validated with structural maps of the rock mass).
Because of the existing limitations in field surveys and data processing methods it
is necessary to extract as much information as possible in an integrated and
objective way in order to create a more consistent model of the rock mass fabric
while decreasing its degree of uncertainty.
1.3. Research questionThe assumption behind the Terrestrial Laser Scanner technique is that the
geometry of the discontinuities in the visible rock mass surface has a relation with
the geometry of the discontinuities within the rock mass. As it has been discussed
before, the geometric information is derived through an analytic process and
comparisons between these results and those derived from the traditional
approach have shown coherent results, but difficulties have been reported
associated with some unfavourable geometric configurations.
On the other hand, Ground Penetrating Radar technique has allowed detecting
and mapping internal discontinuities based on the interpretation of the
heterogeneities that can appear in two-dimensional profiles. However, whileinterpreting internal discontinuities, it is often necessary to use additional
information to correlate such features and validated the final results.
The research question that comes out when considering these facts is: Is it
possible to analyse in an integrated way the geometric information resulting from
Terrestrial Laser Scanner and Ground Penetrating Radar surveys in order to
complement such information and to obtain a more consistent model of the fabric
of a discontinuous rock mass?
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1.4. Research objective
The research objective of the research is to determine whether the geometric
information derived from Terrestrial Laser Scanner and Ground Penetrating Radar
can be integrated and used in a geometric characterization of a rock mass, how
this can improve traditional survey methods and how satisfactory is the output withcomparing with a traditional engineering method.
1.5. Specific objectives
To derive geometric information from a Terrestrial Laser Scanner survey
To derive geometric information from a Ground Penetrating Radar survey
To analyze in an integrated way Terrestrial Laser Scanner and Ground
Penetrating Radar geometric derived parameters in order to perform a
geometric characterization of a rock slope.
To determine the consistency of the results of the proposed methodology when
comparing with traditional ones such as SSPC (Hack, 1998) and scanline.
1.6. General Methodology
Figure 1. General Methodology flowchart
Figure 1 illustrates the general methodology which is followed along this research.
It consists of different elements as follows. Literature review contains an
examination of concepts related with geometric characterization of discontinuous
rock masses, traditional and recent methodologies for collecting geometric
information and antecedents with Terrestrial Laser Scanner and Ground
Penetrating Radar.
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The dataset that is used through the research was acquired at rock slope in a
porphyry stone quarry located at Albiano (South Italy). Traditional approaches
(SSPC and scan-line) to characterize the rock mass exposure and remote sensing
surveys (Ground Penetrating Radar and Terrestrial Laser Scanner) were
performed all together in single field campaign. Remote sensing equipment was
provided by the Department of Geology, Palaeontology and Geophysics of the
University of Padova (Padova, Italy).
In order to derive geometric parameters that are required in a geometric modelling
schema, the data process is performed attending the methodologies and results of
previous experiences as is established along the literature review.
Terrestrial Laser Scanner and Ground Penetrating Radar derived information is
finally integrated while following a geometric modelling schema, through the
process traditional engineering criteria and statistical tools are used to determine
whether the integrated analysis of this complemented information can improve the
knowledge about the geometric characteristics of the rock mass and if this is
consistent with traditional approach.
Discussion and conclusions provides a summary of the research in terms of
advantages, disadvantages, learned lessons, conclusions and recommendations
for further research.
2. Modelling the geometry of a discontinuitynetwork in a rock mass
2.1. Discontinu ity definition
A discontinuity is a plane or surface that marks a change in physical or chemical
characteristics in rock material (Hack, 1998). Discontinuities can be classified into
mechanicals or integrals. A mechanical discontinuity denote a plane of physical
weakness, this means that the tensile strength perpendicular to this surface or the
shear strength along it are lower than those of the surrounding material (ISRM,
1981). Contrarily, an integral discontinuity is as strong as the surrounding material.
Integral discontinuities can become mechanical due to weathering or chemical
reactions that develop a change in mechanical properties (Hack, 1998).
According to the geological process by which are discontinuities formed they can
be classified as follows:
Bedding planes: Typical of sedimentary rocks as a result of different
sedimentation cycles.
Joints: Produced by changes in stress condition due to geological processes.
By definition, no movement has taken place in geological time along a joint.
Foliation: Formed by the tendency that some minerals have to grow in a
specific orientation under the influence of stress and temperature. This occurs
in metamorphic and igneous rocks.
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Shears: Rocks deformed by folding often contain shears due to minor fault
generation. These kinds of discontinuities are more spaced than joints (from
few millimetres to as much as a meter) and are filled with soft or friable soil or
rock.
Manmade discontinuities: Caused by blasting or mechanical excavation. Theyoccur in a random manner due to breakage of intact rock blocks and generally
are not persistent.
Faults: Present relative movement on either side of the fault and often all other
discontinuities through. Faults occur mostly as an individual phenomenon.
Discontinuities show development patterns that are the result from the geological
(and sometimes man-induced) processes through which they were formed. They
can exist as single feature or as discontinuity sets. In theory, orientations and
spacing of the planes discontinuities gather around a certain number of
discontinuity sets with a distinctive orientation, spacing value and mechanical
behaviour as result of a common geological origin (Goodman, 1989; Hack 1998).
2.2. Geometric properties of discontinuit ies
The geometric properties that have engineering significance for rock mass
modelling are orientation, spacing, persistence, gap, and roughness (see figure 2).
Figure 2. Geometric properties in a discontinuous rock mass (after (Hudson, 1989))
Geometric characterization of discontinuities in a rock mass can be performed on
different scales (i.e. faults, discontinuities, joints, etc.). Two features are mainly
studied (Rafiee and Vinches, 2007):
The discontinuity network which defines the rock mass fabric, wherein each
element is considered as relatively simple (i.e. a planar discontinuity with a
given orientation, spacing and persistence) and the study is concerned with
their imbrications. This is the case of the current research. Deterministic and
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statistical methodologies have been used in order to study and model the
characteristics of such networks (Billauxet al., 1989a; Chiles, 1989; Ayalewet
al., 2002; Kulatilakeet al., 2003).
The single discontinuity, which generally does not consist of a pair of simple
parallel surfaces. Its study considers roughness characterization on small andlarge scale, gap, contact areas properties and infill material (Huang et al.,
1992; Ehlen, 2000; Yang and Di, 2001; Zillur Rahman, 2005).
The final objective of a geometric characterization is to analyze information
provided by field survey data in order to deduce geometric parameters and
construct a model of the discontinuity network.
2.3. Traditional methods to collecting discontinuit y data
Traditional methods to collecting discontinuity data include scan-line survey,
sampling window and rapid face mapping (ISRM, 1981; Kulatilakeet al., 1993; La
Pointe and Hudson, 1985; Priest, 1993; Priest and Hudson, 1981). Along thepresent research, scan-line survey and Slope Stability Probability Classification
(SSPC) system (Hack, 1998), which is based on a rapid face mapping approach,
are used to perform the geometric characterization of the rock mass.
2.3.1. Surface methods
2.3.1.1. Scanline survey
Scanline is a one dimensional discontinuity sampling technique. A line is located
on the rock face and discontinuity planes that intersect the scan line are registered
with their properties (i.e. location, orientation, trace or semi trace length,
persistency, roughness, and infill). A scan-line survey provides statistical
information for engineering design purposes; however scan-line is not a
standardized method. Additionally, the method can introduce sampling bias in
each measured parameter and corrections have to be used to compensate it as is
discussed in section 2.6 (ISRM, 1981; Kulatilake et al., 1993; La Pointe and
Hudson, 1985; Priest, 1993; Priest and Hudson, 1981).
2.3.1.2. Slope Stability Probability Classification (SSPC) system (Hack, 1998)
In most cases, it is enough to distinguish the principal discontinuity sets and then
measure their representative properties (Hack, 1998). First is necessary to identify
the most important homogeneous rock mass units and then to carry out the
discontinuity sets description for each unit separately. This method has shown to
be fast and practical and provides adequate information for most engineering
applications. Bias caused by sampling area size and relative orientation as well as
under or over-sampling of discontinuities is also avoided. However it does not
provide statistical information to determine the variability of the estimated
properties.
It requires field experience to recognise engineering units and to accurately
identify discontinuity sets, hence also human bias may be involved. However, the
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Slope Stability Probability Classification system provides a systematic approach to
perform the rock mass exposure characterization in order to minimize such bias.
2.3.2. Subsur face methods - borehole explorations
Although discussions usually refers to scanline and sampling window data,
borehole core logging also provides similar information to that gleaned from a
scanline survey (i.e. location, spacing, orientation, roughness and infill) and in fact
has shown good correlation (Wines and Lilly, 2002). However, the bias effect due
to borehole orientation and the correct identification of actual discontinuities
reduce its accurateness. On the other hand it is expensive and an invasive
technique.
2.4. Terrestrial Laser Scanner as a recent technique to derive geometricinformation
As has been stated in the introductory chapter, among other new methodologies
such as image analysis and total station, Terrestrial Laser Scanner (hereafterTLS) is a remote sensing technique which has shown a great potential to obtain a
large quantity and highly accurate discontinuity geometric information (Slob et al.,
2004).
2.4.1. TLS fundamentals
During a TLS survey, a laser beam emits repeated pulses that are reflected by the
rock face. These measurements can be translated into xyz-coordinates, using
either the two way time of flight for each received pulse or the amplitude
modulated continuous wave principle (Frhlich, 2004). This results in the
acquisition of a dense 3D point cloud of the rock surface with a high spatial
resolution (5 10 mm), which represents the surface shape at a very high detail
(see figure 3). Thexyzdata can be complemented with the intensity value of each
returned pulse and color information extracted from digital imagery (Slob and van
Knapen, 2006).
There are a number of 3D laser scanning devices on the market that use the
ranging principle, (i.e. Leica-Cyrax, Riegl, Trimble-Mensi). Their principles are the
same, but the quality attributes of the data (i.e. resolution, accuracy, precision,
scanning speed, and laser beam divergence) may vary between manufacturers
and models. Further details can be found in (Frhlich, 2004).
2.4.2. Data processing
Prior to realize the geometric analysis, TLS data must be reoriented with respect
to the true north. This can be achieved a) using control points on the rock face
with known x, yand zcoordinates, b) knowing the true orientation (respect to the
north) of at least two control surfaces on the rock face (usually control boards) or
c) knowing the true orientation of the laser scanner (Slobet al., 2005).
TLS data provide a very good visual impression of the scanned object (see figure
3). However, further analysis is required to construct a true 3D surface model; this
can be followed through two methodologies as follows:
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2.4.2.1. Pro
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Then, a
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new rand
the data
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Thr
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2.6.
me
2.5. Grdis
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tals
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omparison
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hic and
., 1995);
tructural
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GPR for
e range
ves with
r waves
energy
he radar
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19
wave in a material varies with its dielectric permittivity and attenuation increase
with increasing frequencies (therefore with increasing wavelength as well).
GPR equipment consists principally of a control unit, a transmitter and a receiver.
A computer is used for data collection. The transmitters and the antennas of
transmitter and receiver can be changed to operate the GPR at different
frequencies. The transmitter generates a single and short high voltage pulse and
transmits it into the antenna, which emits EMR of a specific frequency into the
surrounding area. The receiver collects incoming signals in samples which are a
digital representation of the amplitude and phase of the signac3ar6l in a certain
unit of time. To improve ratio between signal and noise, several samples are
recorded simultaneously and are put together to a so called stack by calculating
their mean value.
Transmitter and receiver can be placed in fixed configurations such as monostatic,
bistatic, mobile or common middle point. The selection of the configuration
depends on the specific conditions of the survey. A full theoretical basis of GPR
can be found in (Davis and Annan, 1989; Parasnis, 1997; Reynolds, 1997).
2.5.2. Ground Penetrating Radar as a technique to detect internal discon tinuit ies
When compared with other traditional subsurface exploration methods such as
borehole (see section 2.3.2), GPR has demonstrated to be a suitable geophysical
method to detect internals discontinuities in a rock mass. Depending on the survey
requirements, it can reach the required vertical and horizontal resolution and depth
penetration. Additionally it is a non destructive method and GPR surveys are
usually fast and economical (Depariset al., 2007; Grandjean and Gourry, 1996)
Literature shows that the feasibility of GPR technique is limited by a) the degree of
discontinuity detection, b) the penetration versus resolution radio and c) thecomplexity of the discontinuity network as follows (Grandjean and Gourry, 1996):
Degree of discontinuity detection
There is a minimal aperture for a discontinuity to be detected by GPR, according
to the filling material in the discontinuity, the propagating medium and the
frequency acquisition (Deparis and Garambois, 2006). Depending on the electrical
properties of the rock and the infill material (electric conductivity and dielectric
permittivity) the amount of returned energy can be high. In such way different
resolutions and penetration depths can be reached (Grandjean and Gourry, 1996).
Penetration versus resolution
It is important to note that GPR is unable to distinguish discontinuities separatedby a distance lower than a half-wavelength (Reynolds, 1997). The main difficulty in
discontinuity detection is the ambiguous relation between penetration depth and
resolution. The higher the signal frequency the better the resolution is. In the other
hand the higher the frequency, the higher the attenuation is. This is because of the
increasing attenuation of the propagating GPR wave at higher frequencies.
However, depending on the electrical properties of the rock, attenuation can be
low.
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20
Complexity of the discontinuity network
Discontinuities can be correctly detected and located on condition that they are
sufficiently opened and separated from each other; otherwise they can create a
complex reflectivity pattern and cannot be distinguished anymore. Multi-reflections
and 3D geometric effects can be also possible in discontinuities with a roughnessof strong amplitude.
Ideally, a complete determination of the discontinuities would require a set of close
parallel and perpendicular GPR profiles as well as compound processing and
interpretation methodology (Deparis et al., 2007). Finally a representation of the
discontinuity network can be obtained through the correlation of discontinuity
signatures of each profile with those from the nearest one (Grandjean and Gourry,
1996).
2.5.3. GPR data processing methodology
The objective of the processing is to enhance the reflected and diffracted signal
returned from the discontinuities. A standard processing methodology includes
amplitude compensation, filtering, migration, static correction, display and
interpretation (Reynolds, 1997). In this way the diffractors and reflectors can be
located accurately and the signal profile becomes clearer.
The processed intensity values are converted and displayed as signal voltage
versus two-way time. In one type of display the intensity is plotted as wiggle curve
with the positive area in each wiggle blacked. Other case is the variable-area
display where successive scans at points along the profile are plotted side by side.
(Reynolds, 1997). Interpretation of the obtained profiles is based on the
assumption that reflection horizons and refraction bright spots correspond to
discontinuities and cavities in the rock. Interpretation must be performed andvalidated by gathering of available information (see figure 6).
2.6. Discontinu ity network modelling
As was stated before in section 2.2, the discontinuity network modelling is
concerned with the imbrications of the different discontinuities wherein each one of
these elements is considered as relatively simple: a planar surface with a given
orientation, spacing and persistence.
Discontinuity network modelling must be tailored to end use requirements (i.e.
kinematics analysis of mechanical stability, discrete analysis of a blocky rock
mass, or statistic characterization of geometric parameters).
In general, the discontinuity network can be treated either by a deterministic model
where discontinuities are considered separately as single features (which
geometric properties are all known) or by a stochastic model (where geometric
properties of the discontinuities are statistically inferred) (Kulatilakeet al., 1993).
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21
Figure 6. Illustration of the processing applied to GPR data a) Raw data, b)Processed data using i) a DC removal ,ii) a zero-phase band-pass filter and iii) an
AGC time equalization. (c) Static corrections for topography and time to depthconversion were applied, d) Interpretation of the discontinuity network (Deparis et
al., 2007)
Since traditional survey methods provide very limited data in comparison with the
size of the model that will be simulated, deterministic modelling is often not
possible. In order to characterize a discontinuity network a useful approach is the
integration of the statistical properties of the discontinuity network such as
distribution of orientation, spacing, and persistence (Kulatilake et al., 2003;
Kulatilake et al., 1993). The final objective is to characterize the geometric
information provided by field survey data in order to deduce such required
geometric parameters and construct a model of the discontinuity network.
Survey data is usually limited to 1D and 2D domain (see section 2.3) and present
some degree of error and sampling biases. Geometric and probability techniqueshave been proposed to correct such biases and to derive 3D parameters from 1D
or 2D data (Baecher and Lanney, 1978; Priest, 1993; Sen and Kazi, 1984;
Wathugalaet al., 1990).
A discontinuity network modelling method includes specific procedures to model
each discontinuity geometric parameter. Different modelling methods have been
proposed in the literature (Rafiee and Vinches, 2007; Kulatilake et al., 1993;
Kulatilakeet al., 2003; Billauxet al., 1989b). A general approach consists of a) to
determine the number of discontinuity sets and their statistical distributions of
orientation, trace length, discontinuity size and spacing, b) to apply corrections for
sampling biases associated with orientation, trace length, size and spacing, c)
from these distributions (which describe 1D or 2D parameters) deduce the
parameters to construct the a 3D model and d) to validate the developed
stochastic 3D discontinuity network model by comparing statistical properties of
observed parameters with those predicted by the model (Kulatilake et al., 1993).
2.6.1. Discontinu ity sets and homogeneous regions
Theoretically, a discontinuity set can be statistically determined as a
homogeneous region within the rock mass. A statistically homogeneous region
presents similar distributions for orientation, spacing, size, shape, roughness
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22
intensity and constitutive properties; however as is discussed in section 2.6.2.
However, in practice only the number of discontinuity sets and its orientation
distribution are considered in determining statistically homogeneous regions
(Kulatilakeet al., 2003; Kulatilakeet al., 1993).
2.6.2. Discontinuity orientation
2.6.2.1. Data acquisition
Orientation data acquisition routines are part of traditional techniques for
geometric characterization of discontinuities based on the interpretation of the
visible surface of a rock mass outcrop include one dimensional scan line survey,
two dimensional mapping, borehole exploration and rapid face mapping using a
field form to systematically direct the mapping of a rock face (see section 2.5).
Recent remote sensing based techniques include digital image analysis (Kemeny,
2003), digital photogrammetry (Roncella and Forlani, 2005) and photo total station
(Zhanget al., 2004). As was discussed in section 2.4 terrestrial laser scanner has
shown a great potential to obtain a large quantity and highly accurate discontinuity
geometric information (Slobet al., 2004).
2.6.2.2. Discontinuity orientation representation
The graphic representation of discontinuity orientation and the recognition of
statistical homogeneous regions (discontinuity sets) are usually performed using
techniques of hemispherical projection of discontinuity poles (Priest, 1985; Priest,
1993). The hemispherical projection is a method of representing and analyzing the
three-dimensional relations between planes on a two dimensional projection plane
using a reference sphere (see figure 7). Details about the steps required to
construct a hemispherical projection using a stereonet can be found in (Brady and
Brown, 2004). Engineering applications are described in detail by (Goodman,
1989; Goodman and Shi, 1985), (Hoek and Bray, 1981), (Priest, 1985; Priest,
1993).
It becomes useful to use the representation of the planes in the form of poles
when dealing with large volumes of orientation data. This is also helpful in
identifying statistically homogeneous regions. Poles to discontinuity planes that
have a similar orientation (parallel planes) will plot as distinct clusters.
2.6.2.3. Orientation homogeneity modelling
Several techniques have been proposed in order to identify clusters of similar
discontinuity orientations using graphical analysis of the poles in a hemispherical
projection (Hoek and Bray, 1981; Priest, 1993). These clusters exhibit specific
distribution characters called orientation models. The most commonly used are:
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23
Figure 7. Stereographic projection of the pole of a plane: (a) Reference sphere, b)Hemispherical projection, c) Stereonet representation (after (Brady and Brown,
2004)).
Fisher Distribution
It is the most used for modelling orientation vectors in 3D space (Fisher, 1953). It
describes the angular distribution of orientations through two parameters: , a
mean vector orientation and k, dispersion (the dispersion is assumed to be
symmetric around the mean orientation). Clusters of poles following the Fisher
Distribution are plotted as circular patterns (figure 8). Some other parameters that
have been proposed to express the dispersion around a mean orientation are the
spherical variance and the resultant vector length (Davis, 1986; Davis, 2002).
Bingham Distribution
The Bingham Distribution typically represents the orientation of curved or wavy
discontinuity surfaces (Bingham, 1964). It forms asymmetrical elliptical patterns
(figure 8) and hence uses extra parameters to characterize the elliptical pattern of
the dispersion around the mean orientation.
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24
Figure 8. Some examples of orientation models
Other statistical methods to examine orientation data have been developed
allowing for the characterisation of more complicated situations. Numerical
methods have been extended to the analysis of variability using fuzzy set theory
and uncertainty in natural data (Bezdek, 1981) and spectral analysis (Jimenez-
Rodriguez and Sitar, 2006).
Fuzzy k-means clustering (Slob and van Knapen, 2006)
Is a supervised classification method, for which the number of clusters has to be
determined in advance based on validity indices. The method partitions the data
according to degrees of membership assigned to a set. The degree of
membership ranges from zero to one. The greater the certainty that a data point
belongs to a set, the closer its membership value is to one (Zadeh, 1965;
Harrison, 1992).
The algorithm seeks primarily for rotationally symmetric clusters (Fisher
Distribution). Non-circular clusters that are well separated and equally distributed
with respect to each other can also be isolated.
In order to assess the results of the data partitioning with fuzzy k-means
clustering, fuzzy validity indices have been developed (Xie and Beni, 1991; Gathand Geva, 989). Related to the definition of a cluster is the basic assumption that
clusters are by definition present in the data. The correctness of the data set
partitioning and the use of validity indices therefore depend on the existence, as
well as the distribution of the trends in the data.
2.6.3. Discontinuity spacing
2.6.3.1. Data acquisition
Spacing denotes the distance between adjacent discontinuities. Similarly to the
orientation case, spacing data is obtained with the methods cited on section
2.6.2.1.
2.6.3.2. Total spacing, set spacing and normal set spacing
When determining discontinuity spacing, three different types must be
distinguished (Priest, 1993):
Total spacing: Distance between a pair of adjacent discontinuities measured
along a specified line. Since the total spacing is measured along a single line,
there is no relation to the spacing of individual discontinuity sets.
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25
Set spacing: Distance between a pair of adjacent discontinuities belonging to
the same set, along a specified line. The average of all set spacings is the
mean set spacing. There is no correction for the orientation of the scanline. In
consequence, the spacing for a set that is oriented almost parallel to the
scanline is greatly over estimated.
Normal set spacing: Distance between a pair of adjacent discontinuities, from
the same set, perpendicular to the average orientation in that set. The average
of all normal set spacings is the mean normal set spacing. Normal set spacing
and mean normal set spacing are good indicators of the block shape and size
distribution in the rock mass.
2.6.3.3. Sampling bias correction
The estimation of mean spacing and frequency (1/spacing) is based on the
measurements carried out on finite length scan-lines in single and different
orientations; hence an orientation correction must be performed in order to derive
correct values for normal set spacing. Methods proposed to compensate suchbiases are proposed in (Kulatilakeet al., 1993; La Pointe and Hudson, 1985).
2.6.3.4. Discontinuity spacing and frequency modelling
Discontinuity spacing behaviour is usually treated using statistical methods based
on the central limit theorem (Priest and Hudson, 1981). The inverse of the mean
spacing is the mean frequency of intersections along the scanline and the
frequency of occurrence of the discontinuity spacing varies within a series of
spacing ranges and can be represented by some probability distribution (either for
individual discontinuity sets or for all discontinuity data). (Priest, 1985) described
and illustrated the difference between Negative exponential, Uniform and Normal
distributions of spacing. However, it has been shown that discontinuity sets canfollow a Lognormal or Fractal distribution (Hobbs, 1993). Weibull or Negative
exponential distributions can be also applicable. (Kulatilake et al., 1993) also
mentioned the Gamma distribution to describe the distribution of discontinuity
spacing.
Goodness of fit tests must to be performed to find a suitable probability distribution
as well as the best probability distribution to represent the statistical distribution of
spacing for each discontinuity set obtained from data (Kulatilake et al., 2003).
2.6.4. Trace length and persis tence
2.6.4.1. Trace length sampling
Trace length describes the prolongation of a discontinuity in a given orientation
(Priest and Hudson, 1981). Since predominantly only a single trace or a part of the
discontinuity is exposed in a rock face, to determine actual trace length of the
discontinuities in a rock mass is difficult. A fair approach is to measure or estimate
the trace length of the discontinuity along dip and along strike, in this way two
dimensional persistence can be derived (Hack, 1998). Information about trace
length is derived from traditional survey methods (section 2.3).
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26
For each discontinuity set, the semi-trace length data can be analyzed under three
categories: (a) data above (in the case of a horizontal scanline) or to the right of
scanline (in the case of a vertical scanline); (b) data below (in the case of a
horizontal scanline) or to the left of scanline (in the case of a vertical scanline);
and (c) data on both sides of the scanline (Kulatilakeet al., 2003).
2.6.4.2. Sampling bias correction
Observed trace lengths sampled on finite size exposures are subject to size
censoring and truncation biases. Effect of censoring and truncation bias causes
that the estimated trace length and its statistical distribution differs from the actual
one. Bias correction must be also performed for this reason (Kulatilake, 1985;
Priest and Hudson, 1981). Once the corrected mean trace length is estimated
from censored semi-trace lengths through this procedure, it is then possible to
establish the trace length distribution with the estimated corrected mean trace
length.
2.6.4.3. Trace length modelling
Similarly to spacing statistics, trace length is also usually treated using statistical
methods based on the central limit theorem. Goodness of fit tests to check the
suitability of exponential, gamma, lognormal and normal distributions have been
discussed by (Ang and Tang, 1975) and (Benjamin and Cornell, 1970). According
to literature usually either the lognormal or the exponential distribution are the
most suitable to describe the trace length statistical distribution. (Robertson, 1970)
concluded that the strike and dip trace lengths have about the same distribution
(implying discontinuities are equidimensional), however some studies have shown
that this is not necessarily always true (Bridges, 1975).
2.6.4.4. Persistence
In statistical terms, persistence (prolongation of the trace length of a discontinuity
in a given direction) can be defined as the probability that any discontinuity cuts a
block that lies in its path (Kalenchuket al., 2006; Einstein, 1993). This parameter
can be seen as an alternative parameter for trace length. Persistence can have a
value between 0 and 1.
For a value near to 1, there would be more discontinuities that go through other
discontinuities. For values near to 0, a given discontinuity end when intersecting
other ones. In practice the persistence value for each discontinuity set is
determined comparing the discontinuity length distribution obtained from the field
survey with the distribution resulting from the generated model.
2.7. Discontinu ity network modelling and validation
To describe the discontinuity network geometry in 3D for a homogeneous rock
mass model, it is necessary to specify the distributions that are obtained for
orientation; spacing, trace length and persistence (see section 2.6). From those
parameters, further analyses (which are out of the scope of this research) would
permit to generate a virtual discontinuity network in 3D which is used to make
predictions from a virtual scanline or a virtual sampling window. A comparison
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27
between the distributions of the geometric parameters derived from such virtual
scanline with those observed in the rock mass permit to validate the model.
Further details can be found on (Billauxet al., 1989b; Kulatilakeet al., 2003).
3. Methodology
In order to determine whether the geometric information derived from TLS and
GPR can be integrated and used to characterize the discontinuity network of a
rock mass, two approaches (traditional and remote sensing) were followed in
order to compare their performance and results.
The traditional approach involves scanline and SSPC method (see section 2.3.1),
the remote sensing approach includes TLS and GPR data (see sections 2.4 and
2.5). In both cases, the final objective is to derive the required geometric
parameters that can be used to model a discontinuity network (see section 2.7).
The figure 9 illustrates the general methodology that is followed along the
research, in broad terms it can be described as follows:
a) Traditional approach: Through the rock mass exposure characterization
provided by SSPC system (section 2.3.1.3) discontinuity sets were identified
and described by its representative geometric properties. On the other hand a
scanline survey (section 2.3.1.1) was performed and its correspondent data set
was processed in order to derive the required geometric parameters (i.e.
discontinuity sets with their orientation and spacing distribution (section 2.6).
Next step is to compare and complement the discontinuity sets
characterization obtained from both methods. Since in theory the SSPC
method avoids sampling biases for orientation and length of a scanline survey,
scanline derived information is compared and validated for each set using
SSPC characterization as reference. The geometric characterization obtained
through scanline complements the SSPC results for those cases where the set
scanline characterization agrees with the SSPC. Otherwise, because the
limitations that were present while performing the scanline survey (see section
3.2.2), SSPC information is considered as representative of the rock mass.
b) Remote sensing approach: A TLS and GPR surveys were performed and its
correspondent datasets follow an independent process in order to derive
geometric information. TLS data is processed following an automatedapproach (see section 2.4) to derive geometric information. The results are
compared and validated against those obtained following the traditional
approach.
GPR data is processed in order to detect the rock mass internal
discontinuities (see section 2.5). The resultant profiles are interpreted and
used to map and construct a model of the internal discontinuities.
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After validating geometric characterization provided by TLS method with
SSPC characterization as reference, both TLS and GPR derived geometric
information is complemented to generate a final model. This model is validated
again against the results of the traditional approach.
In all the cases validation is performed for each discontinuity set bycomparison of the derived geometric parameters and their statistical
characteristics (when possible).
Figure 9. General methodology flowchart
3.1. Study site
A single rock mass exposure located in a porphyry quarry at Albiano (Province of Trento,North Italy) was chosen to perform the field data acquisition. Porphyry stone has become
one of the most important materials for paving and facing in Europe and it is intensively
mined in several quarries at the area.
The porphyry stone correspond to a Permian rhyolite present on the so called Atesine
Porphyric Platform, a result of alternate eruptive and stable phases started 260 million
years ago. Figure 10 shows both location and geological setting of the study site. Data
acquisition was performed on 13 September, 2007.
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3.2.
Fig
Weather
At the m
level at th
are well aand no w
in the nig
probably
discontin
re 10. Study sit(Pe
, seepage
ment of the
e sites was
bove quarrater seepag
ht water m
in intact r
ity infill mat
e at Albiano (Prrmian Rhyolite),
groundwa
field camp
below the q
bottom. Ite has been
y have co
ock. Henc
erial is dam
T
vince of Trento,b) Location, c)
ter conditi
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as not beenoticed on
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, it cannot
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Stud
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Trento
North Italy) a) Peological map
ions
mass was
whereas t
raining duthe investig
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be exclud
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y Site
Alb
Albia
orphyry quarry
dry. The pe
he investiga
ing the perited exposu
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iano
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ted exposu
od of fieldwres. Howev
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ter
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nd
nd
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3.3. Geometric characterization, traditional approach
3.3.1. Slope Stabili ty Probabil ity Classif ication (SSPC)
The objective of the SSPC system (Hack, 1998) is to get generalised geometric
information for the rock mass exposure (number of sets with their orientation,
normal set spacing and persistence).
3.3.1.1. Field method
The characterization of the discontinuity sets and the measurement of the
discontinuity parameters in the SSPC method are based on the rapid face
mapping approach (section 2.3.1.3), it includes the description of the rock mass
according to Code of Practice for Site Investigations (British Standard Institution,
1999).
3.3.1.2. Limitations
Rapid face mapping based methods present human bias when determining
representative parameters (see section 2.3.1.3). On the other hand instrumenterrors can be also involved.
3.3.1.3. Results
According to the BS classification system (BS 5930; 1999) the rock can be
described as: Grey, Coarse crystalline size, Foliated large tabular, Fresh - slightly
weathered RHYOLITE. Field form and its details are presented in appendix 1.
Figure 11. Rock mass exposure at Albiano quarry (Permian Rhyolite), height 20m.
Six discontinuity sets were identified while using the SSPC system (see table 1).
The geometric characterization of such sets is based on the rapid face mapping
approach (see section 2.3.1.3).
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Set / Parameter J1 J2 J3 J4 J5 J6
Dip direction () 170 248 268 250 280 080
Dip angle () 86 80 82 52 05 55
Normal set spacing (m) 0.07 1.00 1.00 4.00 2.00 5.00
Persistence (Along Strike) > > 0.07 0.50 > 10.00
Persistence (Along Dip) > > 3.00 0.50 > 0.20
Table 1. SSPC rock mass geometric description ( > denotes greater than theexposure size, see SSPC filed form details in appendix 1)
3.3.2. Scanline Survey
Since the SSPC system gives a generalised characterization of the rock exposure,
the objective of the scanline survey is to acquire geometric data in a systematic
way in order to complement the information derived from SSPC.
3.3.2.1. Field Methods
The scanline survey was performed according to the method suggested by
(Windsor and Robertson, 1994)). Three horizontal scanline surveys were
preformed on the rock exposure (see appendix 2). A total of 19.80 m of scanline
were mapped for a total of 35 discontinuity measurements and the orientation of
the scanline relative to the orientation of the main discontinuity sets was chosen in
order to minimize sampling bias (see figure 12).
Figure 12. Scanline survey
3.3.2.2. Limitations
Similarly to the SSPC method, scanline surveys involve both human bias and error
in measurements when determining representative geometric parameters.
Additional to these facts the following drawbacks in the survey were noted in the
context of this study:
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Since SSPC method determined the presence of a sub-horizontal discontinuity
set (see table 1), it would have been necessary to perform a vertical mapping,
however, due to time constraints it was not possible to perform it.
Even though pre-splitting is used along most quarry walls, the exposure
exhibits some degree of local damage (see appendix 1). Special care had tobe taken in order to avoid recording such cracks as discontinuities, but this fact
also implies human bias while doing the survey.
According to the SSPC characterization, some of the discontinuity sets exhibit
a representative set spacing up to five meters (see table 1). (Priest and
Hudson, 1981) suggested a scanline length of at least 50 times the mean
discontinuity set spacing in order to provide an ideal representation of the
properties of each set. This condition can not be achieved for all discontinuity
sets.
Bias produced by scanline length and orientation limited the usefulness of the
scanline method. In general it was found that the sample size for each set istoo small to statistically state conclusions. Despite of this, fuzzy k-means
clustering was applied to orientation data (see section 2.6.2.4) in order to split
the data into clusters. This permitted to reach some agreement with the SSPC
observations and estimate the geometric parameters.
3.3.2.3. Results
Table 2 presents the results of the scanline survey method after orientation
correction (see computation details in appendix 2). Through hemispherical
projection of orientation data (see section 2.6.2.3) and fuzzy k-means clustering,
five discontinuity sets can be recognised (see figure 13). According to section
2.6.2 and 2.6.3, for each identified set the mean orientation, resultant vector R,Fisher k constant, spherical variance s,and normal mean spacing were calculated.
Regardless of the described limitations, the scanline and the SSPC results
correlate reasonably well. This is discussed in detail in the next section.
Cluster / Parameter 1 2 3 4 5 6
Mean dip direction () 175 254 266 255 - 81
Mean dip angle () 85 89 81 57 - 64
Sample Size N 6 10 5 10 - 4
Resultant vector R 6.00 6.01 4.99 9.87 - 4.97
Fisher kconstant 9436* 184.0338.4* 436.1
- 179.2*
Spherical variance s 0 0.399 0.002 0.013 - 0.005
Mean normal set spacing (m) 0.06 0.83 0.77 1.52 - 0.48
Std. deviation normal set spacing (m) 0.01 0.80 0.61 1.18 - 0.35
Max. normal set spacing (m) 0.08 2.48 1.80 2.81 - 0.73
Min. normal set spacing (m) 0.06 0.20 0.20 0.51 - 0.24
Table 2. Descriptive statistics of the scanline surveys results (* Fisher kconstant isnot valid if the sample size N is smaller than 10)
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3.3.3.
Set /Cluster
1
2
3
4
5
6
Consi
limitat
Validatio
Table 3
using the
methods.
Fig(p
SSPC
Dipdirection/ Dip ()
N
s
170/86
248/80
268/82
250/52
280/05
80/55
Ta
ering the r
ions that ha
Sub-v
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Since
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ure 13. Low hemles) obtained fro
ormalsetacing(m)
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0.07 >
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5 >
le 3. Summary
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isphere, equalm SSPC (in red
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f geometric par
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Scanline
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254/89
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255/57
-
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meters derived
table 3 and
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- -
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-
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od for each set
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Equally, by the moment is not possible to verify if the discontinuity observed at
285/55 correspond to an outlier or is part of an unnoticed discontinuity set.
As final conclusion, a discussion for each discontinuity set is now presented as
follows:
3.3.3.1. SSPC discontinuity set J1 / Scanline cluster 1
This sub-vertical set (SSPC: 170/86, Scanline: 175/85) was identified as a clearly
isolated set which is persistent in both strike and deep directions (persistence is
equal or greater than the mapped exposure). Its mean normal set spacing is
around 0.07 m.
3.3.3.2. SSPC discontinuity set J2 / Scanline cluster 2
This sub-vertical set (SSPC: 248/80, Scanline: 254/89) belongs to a group of sub-
vertical discontinuities that were sampled between 250-270 and 70-90 (wrapping
the stereo-plot, see figure 13). It is a persistent set in both strike and deep
directions (persistence is equal or greater than the mapped exposure, although
some scanline observations showed smaller values). Its representative normal set
spacing was defined as 1.00 m by the SSPC system and 0.83 by the scanline
method.
3.3.3.3. SSPC discontinuity set J3 / Scanline cluster 3
This sub-vertical set (SSPC: 268/82, Scanline: 266/81) also belongs to the group
of sub-vertical discontinuities that were sampled between 250 and 270 degrees
(dip direction) and 70-90 degrees (dip) (see figure 13). The derived geometric
parameters from SSPC and scanline are not consistent with each other. Taking
into account the limitations of the scanline survey SSPC parameters are
considered as representative.
3.3.3.4. SSPC discontinuity set J4 / Scanline cluster 4
This sub-vertical set (SSPC: 250/52, Scanline: 255/57) also belongs to the group
of sub-vertical discontinuities that were sampled between 250-270 and 70-90 (see
figure 13). The derived geometric parameters from SSPC and scanline are not
consistent with each other. Taking into account the limitations of the scanline
survey SSPC parameters are considered as representatives.
3.3.3.5. SSPC discontinuity set J5
This was the only sub-horizontal set (280/05) that was identified along the SSPC
characterization. Since scanline missed it, SSPC parameters are considered as
representative for it.
3.3.3.6. SSPC discontinuity set J6 / Scanline cluster 6
This sub-vertical set (SSPC: 80/55, Scanline: 81/64 - see figure 13), appears as
isolated set. It is a persistent set in both strike and deep directions (persistence is
equal or greater than the mapped exposure, although some scanline observations
showed smaller values). Mean normal set spacing derived from SSPC and
scanline are not consistent with each other. Taking into account the limitations of
the scanline survey SSPC mean normal spacing is considered as representative.
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4. Geometric characterization, TLS basedmethods
4.1. Data acquisit ion
The rock mass exposure was scanned in a single survey using a time based
Optech Ilris 3-D laser scanner. The equipment and technical expertise were
provided by the Department of Geology, Palaeontology and Geophysics of the
Universi