im_9 - the contribution of geostatistics to the characterisation of some bimrock properties.pdf
TRANSCRIPT
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
1/12
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/256699583
The contribution of geostatistics to thecharacterisation of some bimrock properties
ARTICLE in ENGINEERING GEOLOGY · SEPTEMBER 2012
Impact Factor: 1.74 · DOI: 10.1016/j.enggeo.2012.03.015
CITATIONS
7
READS
43
4 AUTHORS:
Niccolò Coli
9 PUBLICATIONS 63 CITATIONS
SEE PROFILE
Paolo Berry
University of Bologna
23 PUBLICATIONS 73 CITATIONS
SEE PROFILE
Daniela Boldini
University of Bologna
58 PUBLICATIONS 220 CITATIONS
SEE PROFILE
Roberto Bruno
Ministero degli Affari Esteri e della Coopera…
30 PUBLICATIONS 41 CITATIONS
SEE PROFILE
Available from: Roberto Bruno
Retrieved on: 07 April 2016
https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/profile/Niccolo_Coli?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Niccolo_Coli?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_5https://www.researchgate.net/?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_1https://www.researchgate.net/profile/Roberto_Bruno2?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/profile/Roberto_Bruno2?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Roberto_Bruno2?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/institution/University_of_Bologna?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_6https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Daniela_Boldini?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Paolo_Berry?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/institution/University_of_Bologna?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_6https://www.researchgate.net/profile/Paolo_Berry?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Paolo_Berry?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_4https://www.researchgate.net/profile/Niccolo_Coli?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_7https://www.researchgate.net/profile/Niccolo_Coli?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_5https://www.researchgate.net/profile/Niccolo_Coli?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_4https://www.researchgate.net/?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_1https://www.researchgate.net/publication/256699583_The_contribution_of_geostatistics_to_the_characterisation_of_some_bimrock_properties?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_3https://www.researchgate.net/publication/256699583_The_contribution_of_geostatistics_to_the_characterisation_of_some_bimrock_properties?enrichId=rgreq-2a809b68-b59c-4569-8d42-4692431736e5&enrichSource=Y292ZXJQYWdlOzI1NjY5OTU4MztBUzoyMzU4ODAxMjQyNTIxNjBAMTQzMzI0OTYxMjIzNg%3D%3D&el=1_x_2
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
2/12
The contribution of geostatistics to the characterisation of some bimrock properties
N. Coli, P. Berry, D. Boldini ⁎, R. Bruno
Department of Civil, Environmental and Material Engineering (DICAM), University of Bologna, Via Terracini 28, 40131, Bologna, Italy
a b s t r a c ta r t i c l e i n f o
Article history:
Received 15 October 2010
Received in revised form 28 December 2011
Accepted 24 March 2012
Available online 1 April 2012
Keywords:
Bimrock
Image analysisGeostatistical analysis
Variogram
Correlation
Santa Barbara mine
This paper introduces a geostatistical approach for characterising the morphological and spatial variability of rock inclusions in bimrocks and for attempting their direct mechanical characterization through an indirect
description deduced by image analysis of outcrop images.
The study was carried out on the Shale–
Limestone Chaotic Complex (SLCC) bimrock, which is affected byseveral slope stability problems in the disused Santa Barbara open-pit mine (Tuscany, Italy). Due to itscomplex heterogeneity, the mechanical characterization of SLCC was based on a limited number of non-
conventional shear tests (BimTests).Due to the relevant inuence of rock inclusions on bimrock strength, the study focused on identifying the
possible image parameters characterising content and variability of rock inclusions in each sampled picture.A two-step analysis was carried out for: a) identication of an image parameter (centimetric scale) that isable to grasp some property of rock fragment shape and size spatial distribution; b) veri cation of the
correlation at the outcrop scale (multimetric scale) between the bimrock strength parameters and the new
regionalised variables (ReV) describing image properties related to rock fragment distribution. Ageostatistical approach was adopted for both steps, but applied to two different problems, at two differentscales, with different variables.
An extensive sampling of outcrop pictures was carried out and a variogram analysis was performed on the
“rock fragment indicator variable”, I B ( x, y), dened at the image scale, and obtained through the digital
segmentation of the collected pictures. A very good link was observed between the geostatistical modelparameters and the content, size and spatial variability of rock fragments shown in every picture.
The values of the total sill of the block indicator variograms were then assumed as a new ReV, C tot ( x, y),dened all over the SLLC outcrop. A cross-covariance was computed between the variogram total sill and thefriction angle, φ ( x, y) and cohesion c ( x, y), at the scale of the whole outcrop area and a preliminary analysis
showed a likely correlation.© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Bimrocks (Medley, 1994; Medley and Lindquist, 1995; Medley,2002, 2007) are complex formations characterised by competent rockinclusions oating in a weaker matrix. Due to their complex structure,they always represent a challenging engineering problem: the
mechanical behaviour of bimrocks, in fact, is governed by theinteraction and the geometrical properties of rock inclusions(Lindquist, 1994; Lindquist and Goodman, 1994; Goodman andAhlgren, 2000; Kim et al., 2004; Sonmez et al., 2004a, 2006a). For
this reason, the mechanical characterisation of bimrocks must bepreceded by the investigation of the morphological and spatialvariability of rock fragments.
Several methods can be employed for this purpose, from theinterpretation of scanlines and boreholes to the analysis of digital
images and physical sieving.1D method, based on the interpretation of scanlines and
boreholes, although being one of the most used techniques, allowsinvestigating mainly the volumetric percentage of rock inclusions, by
assuming it to be stereologically equivalent to its cumulative linearproportion. As a consequence, this approach is heavily affected by theamount of available sampling data (Haneberg, 2004).
3D sieving can be easily performed at the laboratory scale, but for
larger volumes it becomes cumbersome and very expensive. More-over, this technique only investigates the volumetric content and thegrain-size distribution of rock inclusions, but not their morphological
and spatial variability.On the other hand, the use of 2D digital image processing for
characterising rock masses and ornamental stones is well known toprovide satisfactory results. This technique, in fact, ensures a
relatively fast, non-destructive and inexpensive way for studying avariety of morphological properties, which can be described and
Engineering Geology 137–138 (2012) 53–63
⁎ Corresponding author. Tel.: +39 0512090233; fax: +39 051 2090247.
E-mail address: [email protected] (D. Boldini).
0013-7952/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.enggeo.2012.03.015
Contents lists available at SciVerse ScienceDirect
Engineering Geology
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g g e o
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://dx.doi.org/10.1016/j.enggeo.2012.03.015http://dx.doi.org/10.1016/j.enggeo.2012.03.015http://dx.doi.org/10.1016/j.enggeo.2012.03.015http://dx.doi.org/10.1016/j.enggeo.2012.03.015http://dx.doi.org/10.1016/j.enggeo.2012.03.015mailto:[email protected]://dx.doi.org/10.1016/j.enggeo.2012.03.015http://www.sciencedirect.com/science/journal/00137952http://www.sciencedirect.com/science/journal/00137952http://localhost/var/www/apps/conversion/tmp/scratch_5/Unlabelled%20imagehttp://dx.doi.org/10.1016/j.enggeo.2012.03.015http://localhost/var/www/apps/conversion/tmp/scratch_5/Unlabelled%20imagemailto:[email protected]://dx.doi.org/10.1016/j.enggeo.2012.03.015http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
3/12
quantied through synthetic indexes. These indexes, when correlatedwith the results of laboratory or in-situ mechanical tests, can be veryhelpful for an indirect and quick estimation of specic rock massmechanical properties (Hagerman et al., 1980; Dougherty and Pelz,
1991; Horgan, 1998; Persson, 1998; Coster and Chermant, 2001; Yueet al., 2003; Chen et al., 2004; Lebourg et al., 2004; Bruno andFocaccia, 2009).
The present study was carried out on the Shale–Limestone Chaotic
Complex (SLCC) bimrock, outcropping over a wide slope in thedisused Santa Barbara (SB) open-pit mine (Tuscany, Italy). Theinvestigated domain is a surface S encompassing the SLCC outcrop
exposure at the SB mine, for a total extension of 345,000 m2.The mechanical characterization of SLCC was previously carried
out by a few in situ shear tests (BimTests).Subsequently, a photographic “sampling” of 2 m×2 m outcrop
pictures was carried out with the aim of extracting one or moresynthetic indexes to be correlated with strength experimentalvalues. Such potential correlation is possible only by a geostatisticalspatial cross-covariance analysis, due to the fact that the variables
are not referred to the same location on the outcrop, i.e. are notisotopic.
Through image analysis it is possible to investigate severalproperties of rock inclusions, for instance: statistical distribution of
the maximum observable dimensions (dmod) (Medley, 1994), statis-
tical shape distribution, and spatial variability of useful parameters.The present research rst introduces a geostatistical approach for
the characterization of the 2D spatial distribution of SLCC rock
fragments at the scale of the 4 m2 image, by studying the regionalized
variable “indicator” of the presence/absence of fragments, I B ( x, y),derived by digital processing of outcrop pictures. The 2D spatialvariability of rock inclusions was characterised and modelled, and avalue of a specic synthetic parameter deduced by the geostatistical
model, C tot, was assigned to each picture.
In the second geostatistical study the synthetic parameter wasconsidered a ReV over the SLCC eld, C tot ( x, y), and its spatialcorrelation with the SLCC strength parameters was studied.
In the following, a rst attempt to quantify and validate the
possible correlations between the scarce direct information from thein situ shear test data, and the large indirect information from thesynthetic image parameters is also presented.
2. The SLCC and the Santa Barbara open-pit mine
The SLCC is a mélange of the Northern Apennine orogenic chain.Its genesis is commonly associated with a gravitational accumulationof material derived from dismembered formations, and originatedfrom huge submarine mass movements (olistostromes) that took
place during the Oligo-Miocene era (Castellucci and Cornaggia, 1980;Abbate et al., 1981; Boccaletti et al., 1996). Recent advances in thegeological comprehension of the Northern Apennines mountainchain, however, interpret the SLCC as a tectonic mélange (i.e.
tectonosome), that originated from the in-place dismemberment of pre-existing formations due to the overthrusting of tectonic nappesduring the Apennine orogenetic phases (Boccaletti et al., 1996;
Bonini, 1999).The SLCC is characterised by a mixture of a highly tectonised dark
grey clayey matrix with calcareous fragment inclusions of varioussizes. The clayey matrix, a typically structured over-consolidated clay,
is subdivided into centimetre and millimetre thin lens-like laminaealong pervasive and polished ssility planes (Pini, 1999). Thecalcarenite and calcilutite fragments are distributed throughout the
clayey matrix without any apparent preferred orientation in a typicalblock-in-matrix fabric (Figure 1).
The exhausted SB mine, owned and operated by ENEL S.p.A until1994, is located in Tuscany, Italy, on the Western side of the Valdarno
Superiore Basin, approximately 30 air km South-East of the city of
Firenze. The mine, which encompasses an area of 15 km2, is currentlyundergoing a full reclamation programme. The mining of the lignite
produced a wide slope in the SLCC, with a maximum height of about180 m. During mining, the slope underwent several mass movementsand rotational landslides, which are in part still active today ( D'Eliaet al., 1984, 1986, 1988; Esu and D'Elia, 1990; D'Elia, 1993; D'Elia
et al., 1993).
3. The bimrocks
The term “bimrock” was introduced by Medley (1994) in order to
describe, from a geomechanical point of view, structurally complexformations made up of a mixture of competent and multi-size rock
fragments embedded in a weaker matrix. The term bimrock has nogenetic signicance and it refers to a wide variety of geologicalformations like mélanges, fault gouges, debris and glacial tills
(Medley, 2002; Medley and Wakabayashi, 2004).
3.1. Block/matrix threshold
The possible inuence of a rock fragment of size r on the overallmechanical behaviour of a bimrock is strictly controlled by the scaleof the engineering problem under investigation. Given a scale of
interest, some rock fragments, in fact, can be so small compared to thescale of the investigated problem that they have no practical
inuence on the strength of the bimrock, and they can be consideredas part of the matrix itself.
The threshold below which rock fragments are assumed to havenegligible inuence on the overall bimrock strength is dened as the“block/matrix threshold” (B/M) (Medley, 1994, 2001, 2002).
Medley (1994, 2002) and Medley and Lindquist (1995) proposed
to estimate the B/M as 5% of Lc, where Lc is a linear dimensioncorresponding to a characteristic dimension of the engineering
problem under investigation. Lc can be the average thickness of asliding body (Medley and Sanz Rehermann, 2004), the extension of adam foundation (Goodman and Ahlgren, 2000), the dimension of anin-situ test specimen (Xu et al., 2007) or a fraction of a tunnel
diameter (Button et al., 2004).It is important to keep in mind that in the present paper the term
rock inclusions and rock fragments are used to indicate all the
Fig. 1. Typical aspect of the SLCC bimrock. The light-grey calcareous blocks areembedded in the clayey matrix according to a matrix-supported fabric.
54 N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
4/12
calcareous fragments regardless of their size, while blocks indicatesonly the rock fragments above the B/M.
At the scale of the 2 m×2 m image window adopted in the rstpart of the present study. The rule of 5% Lc yields a B/M of 0.1 m (5% of
2 m edge size), while it yields a B/M of 0.01 m at the scale of theBimTests performed in the SB mine, and briey described later inSection 6.1 (Coli et al., 2011).
In the present study, however, the geostatistical analysis at the
scale of images was performed on the whole population of rockfragments visible on the sampling picture and, therefore, the resultsare not affected by the choice of different B/Ms.
3.2. Properties of rock inclusions
Several studies on Franciscan complex mélanges (California)indicated that the size distribution of the maximum observabledimension of rock fragments (dmod) follows a negative power lawgiven by Eq. (1) (Medley, 1994; Medley and Lindquist, 1995;
Riedmuller et al., 2001; Medley, 2002):
N ¼ r −D
ð1Þ
where N is the relative frequency of fragments with a lineardimension greater than r and the exponent D is the fractal dimension(Mandelbrot, 1983; Turcotte, 1997). The latter is equal to 1.2 for the
Franciscan Mélange (Medley, 1994).One of the most important properties of a power law distribution
is self similarity, i.e. the invariance of fractal dimension D regardlessof the scale of observation.
However, it is important to remark that for the size distribution of natural objects there are lower and upper limits to the validity of scale independency (Turcotte, 1986, 1997). In recent studies, in fact,some authors indicate that a power law distribution may not be valid
across the entire range of particle sizes (Filgueira et al., 2006), and
that, within the same grain size distribution, multiple scale domainsmay exist with different fractal dimensions (Millan et al., 2003).
The dmod size distribution for the SLCC rock inclusions, at the 4 m2
scale of the sampling window, also resulted in following a negativepower-law distribution with an average fractal dimension D of 1.55
(Figure 2) (Coli et al., 2008, 2009).Studies carried out on outcrop pictures of the same SLCC
formation, but in different locations in the Northern Apennines,indicated that, at the scale range of 2–9 m, the spatial arrangement of
rock fragments was well described by a positional dependant power-law, based on the cantor and the Sierpinsky fractal models, with afractal dimension DH varying between 1.737 and 1.745 (Catani andFanti, 1996; Catani, 1999).
4. The use of image analysis for bimrock characterisation
The 2D image analysis of bimrock inclusions, although notaccurate, is widely used in the geoengineering practice.
Medley (1994) and Medley and Lindquist (1995), in order tocalculate the dmod size distribution of rock fragments, used simplemethods of manual contouring on a variety of two-dimensional
sources (images of bimrock outcrop exposures, geological maps).
Sonmez et al. (2004a,b, 2006a,b), in order to investigate thevolumetric proportions of andesite inclusions in the Ankara Agglomerateperformed image classications and node counting on greyscale and
colour pictures of outcrop exposures. They used a supervised imageclassication procedure consisting in a training stage, where thepixel intensity rangeof each lithotype wasdetermined,followedby aclassication stage where the pixels were categorized into the
constituents. They also used the node-point-counting technique,where a regular square mesh was overlaid on the pictures and theunderlying material at each node was then visually classiedaccording to its lithotype. The percentage of each constituent was
then determined by dividing the number of nodes belonging to eachconstituent by the total number of intersections of the mesh. Thevolumetric proportion obtained from the two methods resulted invery similar estimations.
Yue et al. (2004) developed a specic digital image processingtechnique for the analysis of material inhomogeneities aiming atmodelling inhomogeneous rock failures through numerical codes.These methods estimate the structures of geomaterials by applying a
multi-threshold algorithm based on edge detection lters. The sameprocedure, through contrast enhancement, edge detection andthreshold ltering, was used by Xu et al. (2007) in order to isolatethe blocks above the B/M on cross-section pictures of a soil–rock
mixture in the Leaping Tiger Gorge (China).Catani and co-workers performed the fractal analysis of the rock
fragment indicator variable from binary images of SLCC outcropsthrough a box-counting procedure implemented in the GIS ArcInfo©
software (Catani and Fanti, 1996; Catani, 1999).However, the use of 2D images to estimate bimrock 3D
geometrical properties of rock fragments inevitably introduces anoutcrop sampling bias (Haneberg, 2004). The shape and orientation
of the rock inclusions relative to the outcrop exposure, in fact,determine whether the analysis of the 2D image underestimates oroverestimates the real 3D geometrical parameters.
Nevertheless, this issue is not relevant to our study, which onlyaims at verifying whether or not some parameters deduced by imageanalysis show a statistically meaningful correlation with the physicaland strength rock properties as measured by the in-situ shear tests.
5. Identication of image parameters related to rock fragments
spatial variability
The dmod approach and the image analysis methods previouslydescribed are very effective in investigating equivalent size-distribution and volumetric proportion of rock fragments, but theydisregard information such as shape and spatial variability. Thespatial information is, instead, taken properly into account by the
position-dependant Cantor and Sierpinsky fractal models by assum-ing as a descriptive index the Hausdorff –Besicovitch fractal dimen-sion DH (Catani and Fanti, 1996; Catani, 1999).
In this study, a variographic analysis of the rock fragment indicator
variable I B ( x, y) was performed with the purpose of describing andquantifying the 2D morphological and spatial variability of the rockinclusions. The block indicator, I B, was obtained through the digitalsegmentation of the sampled pictures, and it expresses the presence
or absence of the calcareous lithology in the two-dimensional domain
of the image.Fig. 2. dmod size distribution of the SLCC bimrock at the 4 m2
scale of investigation.
55N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B2%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
5/12
The stationary indicator variable I ( x, y) of a random set A isexpressed as (Matheron, 1973; Journel and Huijbregts, 1978; Chilèsand Delner, 1999):
I x; yð Þ ¼ 0 if x∈ A
1 if x∈ A :
ð2Þ
For our purpose, set A represents the calcareous lithology, i.e. thepresence of calcareous rock fragments in the investigated bimrock.
In a binary image each pixel can only assume the values of 0 (black) or 255 (white). The pixel value is a regionalized variable,which is used to dene an indicator variable, i ( x, y), assumed as therealisation of a random function I B ( x, y). The I B ( x, y) is here denedon a punctual support (i.e. the image pixels).
The working scale of this rst geostatistical analysis is the 4 m2
image area. The area is comparable with the size of the specimenssubjected to a series of non-conventional in situ shear tests (0.8 m by0.8 m by 0.5 m), which had previously been performed by the authors
at the SB mine (further description of the test is given in Section 6.1).A 2 m×2 m sampling window was considered a good compromisebetween the necessity to encompass the area representative of the insitu shearspecimen and at the same time to account for a slight larger
surface in order to avoid edge-biases and to ensure an easy shootingof the pictures from the ground.
5.1. Sampling technique
The rst step of the study was the selection of an appropriatephotographic sampling methodology of the SLCC outcrop surface S . In
general, the best sampling technique is the regular mesh sampling,but, due to the impossibility of physically reaching some areas of theinvestigated domain, the stratied sampling technique (SST) wasadopted. In fact, for a given number of samples, the SST represents the
best approximation of the regular mesh (optimal) sampling. The SSTworks by subdividing the investigated domain into several non-overlapping subsets (strata), and by random choosing the sample
location inside each stratum.The investigated domain was subdivided into 68 square cells, each
encompassing an area of 5000 m2, which represents about 1.5% of theoutcrop surface s. Inside each cell, a picture encompassing an area of 4 m2 of the SLCC outcrop was taken at a random position (Figure 3).
Only 40 of the 68 cells were sampled, because 18 cells were
discarded due to the inaccessibility of the area or excessive vegetationcover.
The pictures were shot by using a Sony DSC-800 digital reexcamera with 8 megapixel resolution, which ensures a high image
resolution and a quick transfer of pictures from camera to PC for theimage processing.
In order to account for lens and angular distortion, an aluminiumsquare frame of 2 m×2 m was assembled, placed on the ground and
centred in the camera's eld of view. Pictures were taken asperpendicularly as possible to the exposed surfaces and then digitallyrectied and cropped to the 2 m×2 m frame in order to restore theexact angular and linear proportions (Figure 4).
5.2. Digital image processing
The term digital image processing (DIP) refers to the modica-
tions that can be made to a digital image (DI) using a computer. A DIcan be expressed as a discrete two-dimensional function f ( x, y) where
x and y are spatial coordinates and the value of f at any pair of
coordinates ( x, y) is the light intensity at that point. For amonochromatic grey-scale image, the intensity values are integerswhich dene the grey level for each pixel by assuming integer values
between 0≤ f ( x, y)≤255.
Fig. 3. Simplied geological map of the investigated area at the SB mine. The map
shows the strati
ed sampling grid, the location of pictures and of the BimTests.
Fig. 4. Cropped and orthorectied picture of an SLCC outcrop exposure.
56 N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B4%80http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B3%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
6/12
Since the main difference between calcareous fragments and theclayey matrix is related to variations of grey levels (Figure 5), theSLCC pictures were converted to monochrome 8-bit greyscale imagesand processed through contrast enhancement lters (histogram
equalization and histogram stretching).An image segmentation procedure was then used in order to
obtain binary images where calcareous fragments (foreground) areisolated from the matrix (background).
Segmentation is performed by studying the variations of greyintensity in the input image and by applying a threshold (T ) to theimage histogram: all pixels with an intensity lower than thethreshold are set at 255 (white) while the others at 0 (black)
(Sahoo et al., 1988; Glasbey, 1993; Nikhil and Sankar, 1993; Costerand Chermant, 2001; Gonzalez and Woods, 2001):
g x; yð Þ ¼ 0 f x; yð Þ≥T ⇒ x; yð Þ∉ A255 f x; yð ÞbT ⇒ x; yð Þ∉ A
: ð3Þ
As a consequence, the binary image can be interpreted as arealisation of an indicator variable describing the presence or absenceof calcareous fragments constituting set A: I B( x, y) (Figure 6).
A supervised maximum entropy threshold algorithm was used for
the image segmentation (Kapur et al., 1985; Sahoo et al., 1988). Thealgorithm performs the histogram thresholding on the basis of
entropy considerations: the optimal threshold T is dened as the
grey level which maximizes the sum of the entropies of the two sets U and V :
T ¼ ArgMaxT ∈ 0;255½
H U ð Þ þ H V ð Þf g
¼ ArgMax −XT i¼0
piP T
ln piP T
!þ þ
X255 j¼1þT
p jP T
ln p jP T
0@
1A
8<:
9=; ð4Þ
where H (U ) and H (V ) are the entropy equations associated with eachdistribution, p is the probability distribution of grey levels, T the
threshold value and P T ¼PT i¼0
pi.
This method is very effective on randomly distributed objects overa rather uniform background.
Some artefacts introduced by segmentation were successivelyremoved by applying mathematical morphology lters (Serra, 1982)
to remove isolated pixels and lling holes.The open-source software ImageJ (NIH, 2004) was used for the
entire digital image processing.
5.3. Structural analysis of block indicator
In order to investigate the spatial variability of the I B ( x, y),experimental variograms were calculated on the binary images along
the directions of 0° and 90°, assuming lags (h) ranging between0.005 m and 1 m (Figure 7). The open-source GIS software ILWIS(©NorthPole) was used for the calculation of experimentalvariograms.
The experimental variograms were tted by nested structuremodels by means of a Visual Basic macro library of DICAM, developedfor Microsoft™ Of ce®. The nested models take into account both anomnidirectional component of spatial variability and/or a geometrical
anisotropy, when they assume different ranges along differentdirections maintaining a constant sill.
The tted structures of Fig. 8, for example, show a cleargeometrical anisotropy: the N–S component (90°) has a larger range
compared to the E–W one (0°) and, in fact, the black features of thebinary image are elongated towards the direction between 45° and
70°. In Fig. 9, instead, a substantial isotropy can be observed.
Fig. 5. Linear plot of grey intensity values (a) along the A–B scanline of the image (b).
The high intensity contrast at the edges of the block produces abrupt variations of grey
levels.
Fig. 6. Binary image representing the fragment indicator variable I B ( x, y).
57N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B6%80http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B5%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
7/12
Variogram models are described by the sum of several elementarystructures, each one being identied by a different function type andby specic parameters (sill, range, period).
The I B ( x, y) variograms show a very interesting feature: everyvariogram is always characterised by three common elementary
structures, with constant range a and variable sill C (Figure 10):
1. A spherical model at a small scale, always isotropic, with a constantrange of about 8 mm;
2. A rst exponential model for medium scale variability, always
isotropic, with a range between 11 and 15 mm;3. A second exponential model for large scale variability, with a range
between 30 and 300 mm. This model sometimes shows ageometric anisotropy.
Moreover, some of the nested variograms also show a slightperiodicity, which, when relevant, was modelled with a hole effect ora periodical model.
The characteristic parameters of the elementary models for all
analysed images are listed in Table 1.
5.4. Signi cance of geostatistical indexes
The properties of the elementary models describing the variability
of I B ( x, y) can be referred to the spatial and morphological propertiesof rock fragments.
Given the initial denition of the block indicator variable, I B ( x, y),it follows that:
• the range a is correlated with the average size of fragments;
• the sill C is linked to the percentage of calcareous lithology on theimage, being the variance of the indicator: σ I
2= p(1− p);• the variogram geometrical anisotropy is correlated with the
anisotropy of the iso-oriented shape of fragments;
• the periodicity T is a function of the average local distance betweenthe fragments and, therefore, it is only evident when, at the scale of investigation, the inclusions are arranged according to a regularpattern of spatial distribution.
Due to these properties, the three elementary models of theindicator variable, I B ( x, y), can be interpreted as follows (Figure 11,
Table 1):
• the spherical model takes into account the shape and spatialvariability of the very small calcareous fragments (set 1); it
expresses more than one-quarter of the total variability (total sill);
Fig. 7. a) Example of a binary SLCC image which can be interpreted as the realisation of the indicator variable I B ( x, y) (black features: calcareous fragments, white background:
matrix); b) experimental variograms calculated along the directions of 0° and 90°.
Fig. 8. a) Binary image I B ( x, y); b) experimental and model indicator variograms withnested structures along the directions of 0° and 90°.
58 N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B8%80http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B7%80http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
8/12
• the 1st exponential model refers to the variability of smallinclusions, with an average size of about 1 cm (set 2); it takes intoaccount about one-quarter of the total variability;
• the 2nd exponential model expresses the variability of medium tolarge fragments, with an average size between 3 cm and 30 cm (set3); it represents almost one-half of the total variability.
The presence of geometrical anisotropy is only highlighted formedium–large fragments (2nd exponential model), while it is not
visible for the small ones. The isotropic behaviour of the small-scaleelementary models (spherical and 1st exponential), however, does
not necessarily imply an isotropic shape of the small elements, butrather that the resolution of the actual working scale doesn't allow forproperly taking into account the shape variability of tiny elements.
The periodical/hole model is seldom observed and it usually has a
low impact given that its sill contributes only 4% to the totalvariability. No evidences from eld surveys and geological literature(cfr Section 2) suggest that this periodicity might be somehow relatedto a recurrent systematic internal zonation of the SLCC formation. The
periodical model is more likely to be due to a local arrangement of thefragments at the scale of the 4 m2 sampling window with no lateralcontinuity. Nonetheless, further multi-scale studies are required in
order to investigate the possible presence of structures representing
internal zonation of the bimrock at the scale of the entire outcrop.
6. Spatial correlation between strength and image parameters
6.1. Strength data by in situ tests
BimTests (Xu et al., 2007; Coli et al., 2011) are non-conventional insitu shear tests performed by the authors at the SB mine. The testing
procedure (Figure 12), in fact,signi
cantly differs from the classical insitu direct shear test (ISRM, 2007), i.e. the shear surface is not forcedto develop along a pre-dened horizontal plane, but rather it is free togrow in a tortuous way along the rock-matrix contact boundaries. In
addition, no vertical load is applied to the specimen.The tested specimen has a volume of 0.3 m3 and a size of 0.8 m
wide by 0.8 m long by 0.5 m high.Five BimTests were performed at the SB mine in order to
investigate the SLCC strength properties and to correlate them withthe volumetric block content (VBC) inside each specimen. The frictionangle was found to have a good positive correlation with VBC, whilecohesion showed a slight negative correlation with a sudden drop
above a critical VBC threshold of 20–25% (Figure 13).Strength parameters also depend on the BimTest location on the
outcrop surface, that is they are ReV, c ( x, y), φ ( x, y), dened on asupport of 0.3 m3 (the volume of tested specimens).
6.2. The auxiliary variable: total sill
Given the costs and the technical dif culties in performing the insitu tests, it is of signicant interest attempting to correlate thestrength parameters with some parameters characterising each one
of the 4 m2 sampling windows.The previous geostatistical analysis identied the parameters (i.e.
a, C ) of the nested elementary structures of block indicatorvariograms, which quantitatively highlight the spatial variability of
rock fragments at the scale of 4 m2.The values of range a are constant all over the eld S , while other
parameters vary among the pictures differently located over the
Fig. 9. a) Binary image I B ( x, y); b) experimental and model indicator variograms with
nested structures along the directions of 0° and 90°.
Fig. 10. a) I B ( x, y) experimental and nested variograms and b) elementary models.
59N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B0http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B9%80http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
9/12
outcrop surface. This is the case of the sills, which can be consideredas ReVs, C tot ( x, y). Moreover, since the total sill, i.e. the sum of sills of
elementary structures, is a function of the 2D fragment content, C tot( x, y) = p(1− p), a rst attempt was carried out to verify if theparameter C tot is correlated with the strength parameters.
For this reason, a new geostatistical study at the outcrop scale was
performed by calculating the spatial variability of a synthetic
parameter dened on each image: the total sill C tot ( x, y). Theworking scale of this second step of the geostatistical study is thewhole investigated domain of the outcrop surface S , and the support
of the new variable C tot ( x, y) is a surface of 4 m2.
A correlation study usually takes into account variables measuredon the same samples. This would have required pictures to be takenon the same spots where the BimTest had been performed.
Nevertheless, at the time the SLCC pictures were collected, theBimTests were already done and, therefore, pictures were only takenon nearby SLCC outcrops. As a consequence, the samples of the twovariables, strength data and image total sill, are non-isotopic
(samples are not taken at the same locations) and, therefore, anyattempt to study their possible correlation cannot be performed usingthe standard statistical and probabilistic techniques (i.e. covariance,
index of correlation, standard regression).
The spatial cross-covariance (C ⁎12), instead, is a geostatistical toolthat, in principle, makes it possible to study the correlation of twonon-isotopic variables. If we consider two ReVs, z 1( x) and z 2( x),as the
realisation of two StRF, Z 1( x) and Z 2( x), their spatial cross-covariance,
Table 1
Parameters of the elementary models.
Picture Spherical Exp I Exp II Periodical/
hole
C a
(mm)C a
(mm)C amax
(mm)Dir
anis.
(°)
amin(mm)
C T
(mm)
1 3000 8 1800 11 4200 142 88 125
2 1500 8 1850 11 700 40 30 100
3 3000 8 3800 11 3350 75 65 40
4 1500 8 2500 18 3900 90 90 80
5 4000 8 2400 11 3400 70 70 50
6 1000 8 2100 28 1200 35 24 1207 1500 8 2700 13 4800 180 70 100
8 3000 8 2800 11 5500 65 80 50
9 3000 8 1800 11 3700 30 85 25
10 2400 8 1600 11 1600 130 85 80
11 3000 8 4000 11 3300 100 85 70
12 300 8 1200 11 8600 70 80 50 2500 770
13 2600 8 3000 11 3400 160 80 120
14 1500 8 2400 11 3000 120 80 80
15 2500 8 1000 11 2500 90 85 75
16 2400 8 1100 11 3000 90 80 75
17 1900 8 1400 11 3000 110 80 70
18 2400 8 1600 11 1600 130 85 80
19 1400 8 2500 11 2900 80 85 55
20 2000 8 2500 11 4100 110 85 8021 2000 8 2200 11 4900 65 85 5522 2200 8 1200 11 4400 80 85 60
23 3000 8 4000 11 3300 100 85 70
24 2200 8 2000 11 2200 85 5 70
25 2200 8 1850 11 5300 130 85 90 100 180
26 1700 8 800 11 2100 55 85 45
27 1800 8 1000 11 2500 55 85 50
28 1000 8 1100 11 2100 45 85 40 200 520
29 1800 8 800 11 1850 45 85 35
30 1500 8 900 11 5000 125 80 70 2200 1300
31 2500 8 2000 11 3700 80 80 50 200 350
32 2100 8 2250 11 7300 120 80 85 200 350
33 2400 8 2200 11 3200 120 80 70 2700 350
34 2000 8 3100 12 6100 250 80 200
35 3000 8 2900 13 4950 100 80 9536 2100 8 2500 11 8000 220 80 150 6500 350
37 1800 8 2000 11 7800 85 80 80 7800 35038 1800 8 2000 11 2900 120 80 100
39 3100 8 2000 11 6000 140 80 120
40 3000 8 2400 12 4000 85 80 80
Fig. 11. Each of the elementary variograms in b) describes the spatial variability of a
specic dimensional range of the rock fragments in a).
Fig. 12. BimTest scheme. 1) Specimen, 2) frontal steel plate, 3) LVDT transducer, 4) load
cell, 5) hydraulic jack, 6) support plate and holder for the hydraulic jack, and 7) failure
surface.
60 N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B2http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B1
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
10/12
C 12(h), expressed by Eq. (5a), can be experimentally computed by
Eq. (5b),
C 12 hð Þ ¼ E Z 1 x þ hð Þ Z 2 xð Þ½ −m1m2 ð5aÞ
C 12 hð Þ ¼
Pnc hð Þi¼1
z 1 xi þ hð Þ z 2 xið Þð Þ
nc hð Þ −m
1m
2 ð5bÞ
where m1, m⁎1 and m2, m⁎2 are, respectively, the mean theoretical
and experimental values of the variables.The spatial cross-covariance for h→0 coincides with the classical
covariance between two random variables, C 12(0)=σ 12, which canbe roughly inferred by extrapolating C ⁎12 at the origin even in case of
non-isotopic variables:
C 12 h→0ð Þ≅C 12 0ð Þ ¼ E Z 1 xð Þ Z 2 xð Þ½ −m
1m
2 ¼ σ 12: ð6Þ
For the purpose of the present study, the BimTest strengthparameters (i.e. cohesion c and friction angle φ dened on a support
equal to the BimTest sample volume) represent the rst ReV, c ( x, y),φ ( x, y), while the variogram total sill of the block indicator of eachimage represents the second ReV, C tot ( x, y).
Due to the low cost and relative simplicity, the number of
collected images (40) was larger than the number of performedBimTests (5), thus allowing computing experimental spatial correla-tions even if a rigorous correlation study would have also required
more data of the rst variable.
A correct cross-covariance modelling requires the strict stationar-ity of both variables, therefore it is necessary to examine theirvariograms γ 1⁎(h) and γ 2⁎(h) at the working scale of the investigateddomain S .
The variogram γ ⁎2(h) of Fig. 14 shows the spatial autocorrelationof C tot at the scale of the investigated domain S . Beside a markednugget effect, the behaviour of variography calls for a spherical model
with a range of 250 m and a sill coherent with the experimental
variance. The stationarity is thus veri
ed at the multi-metric scale. Itis well known that the meaning of the nugget effect can be explainedby several causes, among which a spatial micro-variability, that is a
spatial autocorrelation at a scale smaller than the multi-metric one.Due to the lack of suf cient c and φ experimental data, the spatial
auto-correlation of the strength parameters, γ ⁎1(h), could not beinferred. However, the omnidirectional spatial cross-covariance C ⁎12(h)
was anyway calculatedthanks to thehigher number of image data (40).
6.3. Cross-correlograms
Cross-correlograms ρ12(h) were introduced in order to facilitatethe interpretation of the spatial cross-correlation. Cross-correlogramsare dened as the spatial cross-covariance C 12(h) of the reduced
variables Y ( x)= [ Z ( x)−(m/σ )]. They represent a dimensionless mea-sure of the spatial cross-correlation, variable in the interval [+1, −1],and, therefore, they are much easier to interpret than C 12(h).
Experimentally they can be calculated as:
ρ12 hð Þ ¼
Pnc hð Þi¼1
z 1 xiþhð Þ z 2 x ið Þð Þ
nc hð Þ −m1m
2
σ 1σ 2
: ð7Þ
Due to the limited number of BimTests, and to the elongatedshape
of the sampled area (Figure 4), the omnidirectional cross-covarianceswere computed, by a-priori assuming the isotropy of the spatial
structures; which requires the ρ12(h) to be an even function.Before calculating the cross-correlograms, it is of fundamental
importance to verify if there are some anomalous values in the inputvariables that might fake the true ρ⁎12 behaviour. One BimTestsample shows very different strength parameters compared to theother test results (Figure 15).
According to Coli et al. (2011) these values are in agreement withthe mechanical behaviour of the bimrock and, in principle, they shouldbe included. However, in order to verify the stability of the correlation,the experimental cross-correlograms ρ⁎12 were calculated by both
including and excluding these suspected anomalous strength values,which proved to have no inuence on the resulting ρ⁎12. Also, severallags h were tested in order to nd a good compromise between thenecessity to study the small distances (smaller lags) and to work on a
statistically meaningful number of z 1( x+h), z 2( x) pairs (larger lags): abase lag h of 30 m, with a tolerance of ±15 m, was found to be the bestcompromise.
The ρ⁎12 relative to φ −C tot (Figure 16) shows a clear positive
correlation when h→0 ( ρ⁎12=0.3 for h=30), while for c −C tot(Figure 17) the correlation is negative ( ρ⁎12=−0.38 for h=30).These are very interesting results, because they are in agreement withwhat was expected given the relationships between the strength
parameters and the physical VBC (Coli et al., 2011). Due to theinsuf cient amount of data, the cross-covariance between strengthand image parameters could not be fully modelled on the basis of theexperimental ρ⁎12 only. Nevertheless, the likely existence of a
positive/negative correlation, probably at a scale b100 m, betweenthe total sill of the block indicator and the in-situ strength parameters
is quite evident.
Fig. 13. Correlation of friction angle and cohesion with VBC.
Fig.14. Experimental omnidirectional variogram and model variogram of C tot
calculated over the investigated domain S .
61N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.14http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B3http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
11/12
7. Conclusions
In the present work a propaedeutic analysis was carried out aimedat improving the morphological and mechanical characterization of a
bimrock by exploiting the information made available by imagesampling of the outcrop surface.
The study was developed in two stages; a rst geostatisticalanalysis on binary images was performed to identify parameters
which are able to describe some properties of spatial and morpho-logical variability of rock fragments. A second geostatistical analysiswas then performed to study the possible correlation between theexperimental in-situ strength data and the index “total sill”
previously identied on the images.The following conclusions can be drafted:
• the geostatistical analysis of the images well characterises the
spatial distribution of bimrock rock fragments. The variogrammodels of the rock fragment indicator I B allowed identifying a
number of indexes (range a, sill C , period T ) that quantitatively andsynthetically express some essential properties of the morpholog-ical and spatial variability of fragments. Moreover, the proposed
approach appears to be of general interest for the 2D investigation
of bimrocks;• one of the geostatistical parameter identied on the images, i.e. the
total sill C tot of the block indicator, is eligible to be considered a ReV,
expressing rock fragment meaningful properties all over theinvestigated eld. As a consequence, a geostatistical correlationstudy with the strength values obtained by in-situ shear tests (e.g.BimTests) was carried out. A preliminary cross-covariance analysis,
possible also in case of non-isotopic variables (the strength
parameters and the C tot) highlighted the likely presence of ameaningful correlation at the multi-metric scale;
• this study and its preliminary results justify the pursuit of the
research aimed at improving the direct geotechnical characteriza-tion of bimrocks by auxiliary variables deduced by image analysis, acheaper and faster tool compared to an extensive campaign of in
situ mechanical testing. An immediate possible improvement forthe correlation study might be the integration of the cross-covariance analysis with a consistent number of new imagestaken in the proximity of the BimTest locations. The new data will
conrm the existence of a good correlation at the short scale bystudying their spatial cross-correlogram. This work is a rst steptowards the further investigation required to get a condent andoperational tool and procedure for improving the geotechnical
characterization of bimrocks by simple image sampling.
Acknowledgements
The authors would like to thank Dr. Edmund Medley for hissupport provided during the development of the present researchand the revision of the manuscript. The authors are also veryappreciative of the reviewer Dr. Bill Haneberg and of the second
anonymous reviewer for their contributions.
References
Abbate, E., Sagri, M., Bortolotti, V., 1981. Excursion no.5: olistostromes in the OligoceneMacigno Formation (Florence area). Introduction: an Approach to OlistostromesInterpretation: International Association of Sedimentologists, 2nd EuropeanRegional Mettine, Excursion Guidebook, Bologna, pp. 165–185.
Boccaletti, M., Bonini, M., Moratti, G., Sani, F., 1996. Tectono-sedimentary evolution of the post-nappe basin in the Northern Apennines. Proceedings of the InterimColloquium R.C.M.N.S. “Relations tectono-sédimentaries dans les basins Néogenèsde la Méditerranéè Occidentale”, Rabat, 7–8 April 1994. Notes et MémoriesServices Géologique Maroc 387, 177–193.
Bonini, M., 1999. Basement-controlled Neogene polyphase cover thrusting and basindevelopment along the Chianti Mountains ridge (Northern Apennines, Italy).Geological Magazine 136, 133–152.
Bruno, R., Focaccia, S., 2009. Formazione avanzata nel settore delle rocce ornamentali edelle geoelaborazioni / /Formaçao avançada no Sector das Rochas Ornamentais edo Geoprocessamento. DICMA, Università di Bologna, Rete Alfa-Faro, 293 pp.
Button, E., Riedmüller, G., Schubert, W., Klima, K., Medley, E., 2004. Tunnelling inTectonic Melanges: Accommodating the Impacts of Geomechanical Complexitiesand Anisotropic Rock Mass Fabrics. Bulletin of Engineering Geology and theEnvironment. March 2004.
Castellucci, P., Cornaggia, F., 1980. Gli olistostromi nel Macigno dei monti del chianti:analisi stratigraco-strutturale. Memorie Società Geologica Italiana 21, 171–180
(In Italian).
Fig. 15. Correlation between the c and φ strength parameters obtained through theBimTests.
Fig. 16. φ −C tot omnidirectional cross-correlogram, the base lag h is 30 m. For h→0
ρ⁎12 shows a clearly positive correlation ( ρ
⁎12≥0.3).
Fig. 17. c −C tot omnidirectional cross-correlogram, the base lag h is 30 m. For h→0
ρ⁎12 shows a clearly negative correlation ( ρ⁎12≤−0.38).
62 N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B7http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B6http://localhost/var/www/apps/conversion/tmp/scratch_5/image%20of%20Fig.%E0%B1%B5
-
8/18/2019 IM_9 - The contribution of geostatistics to the characterisation of some bimrock properties.pdf
12/12
Catani, F., 1999. Fractal properties of the “Chaotic Complex”: methods and applicationsin Tuscany (Italy). In: Nardi, G., Vigliotti, M. (Eds.), GIAST 1999. Sansepolcro,Arezzo (Italy), 14–16 September 1999, 1. De Frede, Napoli, pp. 237–252.
Catani, F., Fanti, R., 1996. Verica delle caratteristiche frattali nella distribuzionegranulometrica di un af oramento del Complesso Caotico (Toscana settentrio-nale). Proceedings of V Convegno Giovani Ricercatori Gruppo Nazionale GeologiaApplicata. Cagliari, 8–11 October 1996. Università degli Studi di Cagliari, pp. 42–49(In Italian).
Chen, S., Yue, Z.Q., Tham, L.G., 2004. Digital image-based numerical modeling methodfor prediction of inhomogeneous rock failure. International Journal of RockMechanics and Mining Science 41, 939–957.
Chilès, J.P., Delner, P., 1999. Geostatistics: Modeling Spatial Uncertainty. Wiley, NewYork.Coli, N., Berry, P., Boldini, D., Castellucci, P., 2008. Analysis of the block-size distribution
in the Shale–Limestone Chaotic Complex (Tuscany, Italy). ARMA 2008 – AmericanRock Mechanics Association, 42nd U.S. Rock Mechanics Symposium, San Francisco(USA), 28 Giugno–5 Luglio 2008, ARMA 08–233. 7 pp.
Coli, N., Berry, P., Boldini, D., Bruno, R., 2009. Investigation of block geometricalproperties of the Shale–Limestone Chaotic Complex bimrock of the Santa Barbaraopen pit mine (Italy). Rock Engineering in Dif cult Conditions, 3rd Canada–USRock Mechanics Symposium, Toronto (CA), 9–14 Maggio 2009. 8 pp.
Coli, N., Berry, P., Boldini, D., 2011. In situ non conventional shear tests for themechanical characterisation of a bimrock (BimTest). International Journal of RockMechanics and Mining Science 48, 95–102.
Coster, M., Chermant, J.L., 2001. Image analysis and mathematical morphology for civilengineering materials. Cement and Concrete Composites 23, 133–151.
D'Elia, B., 1993. Fronti di scavo della miniera di Santa Barbara nelle argille scagliose(Mine slopes of the Santa Barbara open-pit mine). GEAM, Memorie e Note 30,133–139.
D'Elia, B., Di Stefano, D., Federico, G., Oliva, S., 1984. Full-scale study of a high cut in a
structurally complex formation. Proceedings of the 4th International Symposiumon Landslides, Toronto, Canada, 16–21 September 1984, volume 2. University of Toronto Press, pp. 57–62.
D'Elia, B., Di Stefano, D., Esu,F., Federico, G., 1986. Slope movements in structurally complexformations. Proceedings of the International Symposium on Engineering in ComplexFormations, 3–7 November 1986, Beijing, China, XIV. Science Press, pp. 430–436.
D'Elia, B., Di Stefano, D., Esu, F., Federico, G., 1988. Deformations and stability of highcuts in a structurally complex formation: analysis and prediction. Proceedings of the 5th International Symposium on Landslides, Lausanne, 10–15 July 1988, vol. 1,pp. 599–604.
D'Elia, B., Di Stefano, D., Esu, F., Federico, G., 1993. Problematiche geotecniche nellacoltivazione a cielo aperto della miniera di S.Barbara. GEAM, Memorie e Note 30,121–125 (In Italian).
Dougherty, E.R., Pelz, B.J., 1991. Morphological granulometric analysis of electropho-tographic images - size distribution statistics for process control. OpticalEngineering 30 (4), 438–445.
Esu, F., D'Elia, B., 1990. Ricerche e studi geotecnici per la coltivazione della miniera dilignite a cielo aperto di Santa Barbara. Università degli Studi “La Sapienza”. Roma.Dip. Di Idraulica, Trasporti e Strade, Dip. Di Ingegneria Strutturale e Geotecnica,unpublished Technical Report. In Italian.
Filgueira, R.R., Fournier, L.L., Cerisola, C.I., Gelati, P., García, M.G., 2006. Particle-sizedistribution in soils: a critical study of the fractal model validation. Geoderma 134,327–334.
Glasbey, C.A., 1993. An analysis of histogram-based thresholding algorithms. CVGIP,Graphical Models and Image Processing 55 (6), 532–537.
Gonzalez, R.C., Woods, R.E., 2001. Digital Image Processing, Second Edition. PrenticeHall. 793 pp.
Goodman, R.E., Ahlgren, C.S., 2000. Evaluating the safety of a concrete gravity dam onweak rock—Scott Dam. Journal of Geotechnical and Geoenvironmental Engineering126, 429–442.
Hagerman, T., Balck, K., Lilliesköld, M., 1980. Shape and surface of mineral grainsautomatically determined for mortar and concrete purposes through imageanalysis. Swedish Council for Building Research D26, pp. 63.
Haneberg, W.C., 2004. Simulation of 3D block populations to characterize outcropsampling bias in bimrocks. Felsbau Rock and Soil Engineering— Journal forEngineering Geology, Geomechanics and Tunneling 22 (5), 19–26.
Horgan, G.W., 1998. Mathematical morphology for analysing soil structure from
images. European Journal of Soil Science 49, 161–
173.ISRM, 2007. Suggested method for in situ determination of direct shear strength. In:
Ulusay, R., Hudson, J.A. (Eds.), The Complete ISRM Suggested Methods for RockCharacterization Testing and Monitoring: 1974–2006. AA Balkema, Rotterdam,pp. 167–176.
Journel, A.G., Huijbregts, C.J., 1978. Mining Geostatistics. Academic Press, London.Kapur, J.N., Sahoo, P.K., Wong, A.K.C., 1985. A new method for gray-level thresholding
using the entropy of the histogram. Computer Vision, Graphics, and ImageProcessing 29, 273–285.
Kim, C., Snell, C., Medley, E., 2004. Shear strength of Franciscan Complex Melange ascalculated from back-analysis of a landslide. Proceedings of the Fifth International
Conference on Case Histories in Geotechnical Engineering, New York, pp. 1–8.Paper 2–33.
Lebourg, T., Riss, J., Pirard, E., 2004. Inuence of morphological characteristics of heterogeneous moraine formation on their mechanical behavior using image andstatistical analysis. Engineering Geology 73, 37–50.
Lindquist, E., 1994. The Strength and Deformation Properties of Melange. Ph.D.dissertation, Department of Civil Engineering, University of California, Berkeley.
Lindquist, E.S., Goodman, R.E., 1994. Strength deformation properties of a physicalmodel melange. Proceedings 1st North American Rock Mech. Symp., Austin, Texas,pp. 843–850.
Mandelbrot, B.B., 1983. The Fractal Geometry of Nature. W.H. Freeman and Co., New
York. 468 pp.Matheron, G., 1973. The intrinsic random functions and their applications. Advances inApplied Probability 5, 439–468.
Medley, E., 1994. The engineering characterization of melanges and similar block-in-matrix rocks (bimrocks). Dept of Civil Engineering, University of California,Berkley, California, PhD diss., UMI Diss. Svc., Ann Arbor, NI.
Medley, E., 2001. Orderly characterization of chaotic Franciscan Melanges. FelsbauRock and Soil Engineering— Journal for Engineering Geology, Geomechanics andTunneling 19, 420–421.
Medley, E., 2002. Estimating block size distributions of melanges and similar block-inmatrix rocks (bimrocks). Proceedings of 5th North American Rock MechanicsSymposium (NARMS), Toronto, July 2002, pp. 509–606.
Medley, E., 2007. Bimrocks article part 1: “introduction”. Newsletter of HSSMGE 7,17–21.
Medley, E., Lindquist, E.S., 1995. The engineering signicance of the scale-independence of some Franciscan melanges in California, USA. Proceedings of the35th US Rock Mechanics Symposium, Reno, pp. 907–914.
Medley, E., Sanz Rehermann, P.F., 2004. Characterization of bimrocks (rock/soilmixtures) with application to slope stability problems. Proceedings Eurock 2004
& 53rd Geomechanics Colloquium Salzburg, Austria October 2004.Medley, E., Wakabayashi, J., 2004. Geological characterization of melanges for
practitioners. Felsbau Rock and Soil Engineering— Journal for Engineering Geology,Geomechanics and Tunneling 22 (5), 10–18.
Millan, H., Gonzalez-Posada, M., Aguilar, M., Domınguez, J., Cespedes, L., 2003. On thefractal scaling of soil data. Particle-size distributions. Geoderma 117, 117–128.
NIH, 2004. ImageJ, Image Processing and Analysis software in Java. http://rsbweb.nih.gov/ij/2004.
Nikhil, R.P., Sankar, K.P., 1993. A review on image segmentation techniques. PatternRecognition 26 (9), 1277–1294.
Persson, A.L., 1998. Image analysis of shape and size of ne aggregates. EngineeringGeology 50, 177–186.
Pini, G.A., 1999. Tectonosomes and olistostromes in the argille scagliose of theNorthern Apennines, Italy. Geological Society of America, Special Paper 335, 1–69.
Riedmuller, G., Brosch, F.J., Klima, K., Medley, E., 2001. Engineering geologicalcharacterization of brittle faults and classication of fault rocks. Felsbau Rock andSoil Engineering— Journal for Engineering Geology, Geomechanics and Tunneling19 (4), 13–19.
Sahoo, P.K., Soltani, S., Wong, A.K.C., 1988. A survey of thresholding techniques.Computer Vision, Graphics, and Image Processing 41 (2), 233–260.
Serra, J., 1982. Image Analysis and Mathematical Morphology. Academic Press, London.Sonmez, H., Gokceoglu, C., Tuncany, E., Medley, E., Nefeslioglu, H.A., 2004a. Relation-
ships between volumetric block proportions and overall UCS of a volcanic bimrock.Felsbau Rock and Soil Engineering— Journal for Engineering Geology, Geomecha-nics and Tunneling 22 (5), 27–32.
Sonmez, H., Tuncay, E., Gokceoglu, C., 2004b. Models to predict the uniaxialcompressive strength and the modulus of elasticity for Ankara Agglomerate.International Journal of Rock Mechanics and Mining Sciences 41, 717–729.
Sonmez, H., Altinsoy, H., Gokceoglu, C., Medley, E., 2006a. Considerations in developingan empirical strength criterion for bimrocks. Proceedings 4th Asian RockMechanics Symposium (ARMS 2006), November 6–10, Singapore.
Sonmez, H., Gokceoglu, C., Medley, E., Tuncay, E., Nefeslioglu, H.A., 2006b. Estimatingthe uniaxial compressive strength of a volcanic bimrock. Int. J. Rock Mech. Min. Sci.43, 554–561.
Turcotte, D.L., 1986. Fractals and fragmentation. Journal of Geophysical Research 91(B2), 1921–1926.
Turcotte, D.L., 1997. Fractals and Chaos in Geology and Geophysics, Second Edition.
Cambridge University Press. 398 pp.Xu, W., Hu, R., Tan, R., 2007. Some geomechanical properties of soil–rock mixtures in
the Hutiao Gorge area, China. Geotechnique 57 (3), 255–264.Yue, Z.Q., Chen, S., Tham, L.G., 2003. Finite element modeling of geomaterials using
digital image processing. Computers and Geotechnics 30, 375–397.Yue, Z.Q., Chen, S., Tham, L.G., 2004. Digital image-based numerical modeling method
for prediction of inhomogeneous rock failure. International Journal of RockMechanics and Mining Sciences 41, 939–957.
63N. Coli et al. / Engineering Geology 137 –138 (2012) 53–63
http://rsbweb.nih.gov/ij/http://rsbweb.nih.gov/ij/http://rsbweb.nih.gov/ij/http://rsbweb.nih.gov/ij/