Skip to main content

Advertisement

SpringerLink
Log in

Geostatistical analyses of exfoliation and tectonic joint set spacing in alpine granites (Aar Valley, Switzerland)

  • Original Paper
  • Published:
Bulletin of Engineering Geology and the Environment Aims and scope Submit manuscript

Abstract

Joint set spacing is a fundamental parameter in the determination of rock mass quality and can be measured in situ by means of, e.g., scanline surveys and/or by remote sensing techniques, such as photogrammetric analyses. In many Alpine areas, rock mass outcrops are not easily accessible, and geomechanical propexrties can be measured only in a few unevenly distributed locations, which are often separated by large distances (in the order of hundreds of meters). Geostatistical techniques have been explored to achieve a reliable estimate of rock mass properties in unreachable zones. This work aims to estimate joint set spacing of outcropping rock masses and the associated uncertainty, using photogrammetric models and geostatistical modeling, in an area of about 30 km2, located in the Aar Massif of the Swiss Central Alps. Since the joint set spacing is strongly related to fracture genesis, joints were subdivided according to their type and age into three younger exfoliation joint sets and older tectonic joint sets. Each fracture set spacing was analyzed by variography and its spatial distribution was estimated using Sequential Gaussian Simulations. The present research proves that photogrammetric techniques combined with geostatistical modeling can be satisfactorily applied to develop predictive maps of joint spacing, providing that the geological processes governing the formation of joints are taken into account. Moreover, predictive maps must be associated with the corresponding uncertainty maps. Finally, in mountainous area, whenever a full three-dimensional approach is not feasible due to the absence of subsurface data, at least the ground altitude, besides latitude and longitude, has to be included in the geostatistical modeling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • 3G Software & Measurement (2007) ShapeMetrix3D User Manual 2.0

  • Abrecht J (1994) Geologic units of the Aarmassif and their pre-alpine rock associations: a critical review. Schweiz Mineral Petrogr Mitt 74:5–27

    Google Scholar 

  • Asghari O, Soltni F, Amnieh HB (2009) The comparison between sequential gaussian simulation (SGS) of Choghart ore deposit and geostatistical estimation through ordinary kriging. Aust J Basic Appl Sci 3(1):330–341

    Google Scholar 

  • Ayalew L, Reik G, Busch W (2002) Characterizing weathered rock masses — a geostatistical approach. Int J Rock Mech Min 39(1):105–114

    Article  Google Scholar 

  • Bachmaier M, Backes M (2011) Variogram or Semivariogram? Variance or Semivariance? Allan variance or introducing a new term? Math Geosci 43(6):735–740

    Article  Google Scholar 

  • Bahat D (1991) Tectonofractography. Springer, Berlin

    Book  Google Scholar 

  • Barla G, Scavia C, Antonellis M, Guarascio M (1987) Characterization of rock mass by geostatistical analysis at the Masua Mine. Proceedings of 6th ISRM Congress, Montreal, pp 777–786

  • Barnes RJ (1991) The variogram sill and the sample variance. Math Geol 23(4):673–678

    Article  Google Scholar 

  • Barton N, Lien R, Lunde J (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mech 6(4):189–236

    Article  Google Scholar 

  • Baumberger R (2015) Quantification of lineaments: Link between internal 3D structure and surface evolution of the Hasli valley (Aar massif, Central Alps, Switzerland). Doctoral dissertation, University of Bern

  • Bieniawski ZT (1989) Engineering rock mass classifications: a complete manual for engineers and geologists in mining, civil, and petroleum engineering. John Wiley & Sons, New York

    Google Scholar 

  • Billaux D, Chilès JP, Hestir K, Long J (1989) Three-dimensional statistical modelling of a fractured rock mass — an example from the Fanay-Augères mine. Int J Rock Mech Min 26(3–4):281–299

    Article  Google Scholar 

  • Bolay S (2013) Quantitative Measurements of Exfoliation Joint Spacing in the Central Aar Granites of the Grimsel Area (Central Swiss Alps). Master Thesis, ETH of Zurich

  • Brunner F, Scheidegger A (1973) Exfoliation. Rock Mech Rock Eng 5(1):43–62

    Article  Google Scholar 

  • Caers J (2005) Petroleum Geostatistics. Society of Petroleum Engineers, Richardson

    Google Scholar 

  • Caers J, Zhang T (2004) Multiple-point geostatistics: a quantitative vehicle for integrating geologic analogs into multiple reservoir models. AAPG Memoir: Integration of outcrop and modern analogs in reservoir modelling, pp 383–394

  • Carlsson A (1979) Characteristic features of a superficial rock mass in southern central Sweden: horizontal and subhorizontal fractures and filling material. Striae 11:1–79

    Google Scholar 

  • Challandes N, Marquer D, Villa IM (2008) P-T-t modelling, fluid circulation, and 39Ar-40Ar and Rb-Sr mica ages in the Aar massif shear zones (Swiss alps). Swiss J Geosci 101:269–288

    Article  Google Scholar 

  • Chilès JP (1988) Fractal and geostatistical method for modelling a fracture network. Math Geol 20(6):631–654

    Article  Google Scholar 

  • Chiles JP, Delfiner P (1999) Geostatistics: modeling spatial uncertainty. Wiley & Sons, New York

    Book  Google Scholar 

  • Choukroune P, Gapais D (1983) Strain pattern in the Aar granite (central alps): orthogneiss developed by bulk inhomogeneous flattening. J Struct Geol 5:411–418

    Article  Google Scholar 

  • Ciotoli G, Finoia MG (2005) Dalla statistica alla geostatistica, Introduzione all’analisi dei dati geologici e ambientali. Aracne Ed, Roma

    Google Scholar 

  • Dale TN (1923) The commercial granites of New England. Government Printing Office, Washington

    Google Scholar 

  • David M. (2012) Geostatistical ore reserve estimation. Elsevier

  • Deere DU (1963) Technical description of rock cores for engineering purposes. Felsmechanik Ingenieurgeologie 1(1):16–22

    Google Scholar 

  • Deutsch CV, Journel AG (1998) GSLIB — geostatistical software library and User’s guide. Oxford University Press, New York

    Google Scholar 

  • Dowd PA, Xu C, Mardia KV, Fowell RJ (2007) A comparison of methods for the stochastic simulation of rock fractures. Math Geol 39(7):697–714

    Article  Google Scholar 

  • Egaña M, Ortiz JM (2013) Assessment of RMR and its uncertainty by using geostatistical simulation in a mining project. J GeoEng 8(3):83–90

    Google Scholar 

  • Eggenschwiler P (2016) Erosion controlled by crosscuttings between faults and exfoliation joints leading to rockfalls in the plutonites in Haslital (BE). Master thesis, Institute of Geological Sciences, University of Bern

  • Einstein HH (2003) Uncertainty in rock mechanics and rock engineering — then and now. Proceedings of 10th Congress of ISRM, Technology roadmap for Rock Mechanics, Pretoria, pp 281–293

  • Ellefmo SL, Eidsvik J (2009) Local and spatial joint frequency uncertainty and its application to rock mass characterisation. Rock Mech Rock Eng 2(4):667–688

    Article  Google Scholar 

  • Escuder Viruete J, Carbonell R, Jurado MJ, Martí D, Pérez-Estaún A (2001) Two-dimensional geostatistical modeling and prediction of the fracture system in the Albala granitic pluton, SW Iberian massif, Spain. J Struct Geol 23:2011–2023

    Article  Google Scholar 

  • Escuder Viruete J, Carbonell R, Martí D, Jurado MJ, Pérez-Estaún A (2003a) Architecture of fault zones determined from outcrop, cores, 3-D seismic tomography and geostatistical modeling: example from the Albalá granitic pluton, SW Iberian Variscan massif. Tectonophysics 361:97–120

    Article  Google Scholar 

  • Escuder Viruete J, Carbonell R, Martí D, Pérez-Estaún A (2003b) 3-D stochastic modeling and simulation of fault zones in the Albalá granitic pluton, SW Iberian Variscan massif. J Struct Geol 25:1487–1506

    Article  Google Scholar 

  • Esfahani NM, Asghari O (2013) Fault detection in 3D by sequential Gaussian simulation of rock quality designation (RQD). Case study: Gazestan phospate ore despoit, Central Iran. Arab J Geosci 6:3737–3747

    Article  Google Scholar 

  • Ferrari F (2014) Rock mass characterization and spatial estimation of geomechanical properties through geostatistical techniques. Doctoral dissertation, Università degli Studi di Milano

  • Ferrari F, Apuani T, Giani GP (2011) Geomechanical surveys and geostatistical analyses in Valchiavenna (Italian Central Alps). Proceedings of the 8th International Symposium on Field Measurement in GeoMechanics, Berlin

  • Ferrari F, Apuani T, Giani GP (2012) Analisi spaziale e previsionale delle proprietà geomeccaniche degli ammassi rocciosi della Valle San Giacomo (SO), mediante tecniche geostatistiche. GEAM 39(1):21–30

    Google Scholar 

  • Ferrari F, Apuani T, Giani GP (2014) Rock mass rating spatial estimation by geostatistical analysis. Int J Rock Mech Min 70:162–176

    Article  Google Scholar 

  • Giani GP (1992) Rock slope stability analysis. Balkema, Rotterdam

    Google Scholar 

  • Goodman RE, Taylor RL, Brekke TL (1968) A model for the mechanics of jointed rocks. J Soil Mech Found Div

  • Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New York

    Google Scholar 

  • Goovaerts P (1999) Impact of the simulation algorithm, magnitude of ergodic fluctuations and number of realizations on the spaces of uncertainty of flow properties. Stoch Env Res Risk A 13(3):161–182

    Article  Google Scholar 

  • Goovaerts P (2001) Geostatistical modelling of uncertainty in soil science. Geoderma 103(1):3–26

    Article  Google Scholar 

  • Grigarten E (1996) 3-D geometric description of fractured reservoir. Math Geol 28(7):881–893

    Article  Google Scholar 

  • Grigarten E, Deutsch CV (2001) Variogram Interpretation and Modelling. Math Geol 33(4):507–534

    Article  Google Scholar 

  • Hoek E, Brown ET (1997) Practical estimates of rock mass strength. Int J Rock Mech Min 34(8):1165–1186

    Article  Google Scholar 

  • Honarkhah M, Caers J (2012) Direct pattern-based simulation of non-stationary geostatistical models. Math Geosci 44(6):651–672

    Article  Google Scholar 

  • International Society for Rock Mechanics (ISRM) 1975) Commission on Terminology, Symbols and Graphic Representation.: Terminology. Int. Soc. Rock Mech. secretary, Lisbon

  • Isaaks EH, Srivastava RM (1989) An introduction to applied Geostatistics. Oxford University press, New York

    Google Scholar 

  • Jahns RH (1943) Sheet structure in granites: its origin and use as a measure of glacial erosion in New England. J Geol 51:71–98

    Article  Google Scholar 

  • Johnson AM (1970) Physical processes in geology: a method for interpretation of natural phenomena; intrusions in igneous rocks, fractures, and folds, flow of debris and ice. Freeman, Cooper

    Google Scholar 

  • Journel AG (1974) Geostatistics for conditional simulation of ore bodies. Econ Geol 69(5):673–687

    Article  Google Scholar 

  • Keusen HR, Ganguin J, Schuler P, Buletti M (1989) Grimsel Test Site. Geology. Technical Report NTB 87-14E. Nagra, Baden

  • Kieslinger A (1968) Spannungen und Entspannungen im Steinbruchbetrieb. Berg- Hüttenmänn Monatsh 113(8):298–304

    Google Scholar 

  • Koike K, Ichikawa Y (2006) Spatial correlation structures of fracture systems for deriving a scaling law and modeling fracture distributions. Comput Geosci 32:1079–1095

    Article  Google Scholar 

  • Koike K, Komorida K, Ichikawa Y (2001) Fracture-distribution modelling in rock mass using borehole data and geostatistical simulation. Proceedings of the International Association for Mathematical Geology Conference, Cancun

  • Koike K, Liu C, Sanga T (2012) Incorporation of fracture directions into 3D geostatistical methods for a rock fracture system. Environ Earth Sci 66(5):1403–1414

    Article  Google Scholar 

  • Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J South Africa Inst Min Metall 52(6):119–139

    Google Scholar 

  • Krige DG (1996) A practical analysis of the effects of spatial structure and of data available and accessed, on conditional biases in ordinary kriging. Geostatistics Wollongong 96:799–810

    Google Scholar 

  • La Pointe PR (1980) Analysis of the spatial variation in rock mass properties through geostatistics. Proceedings of the XXI Symposium on Rock Mechanics, Rolla, pp 570–580

  • La Pointe PR, Hudson JA (1985) Characterization and interpretation of rock mass joint patterns. Geol Soc Am Spec Pap 199:1–38

    Google Scholar 

  • Labhart TP (1977) Aarmassiv und Gotthardmassiv. Bornträger, Berlin

    Google Scholar 

  • Laubach SE, Lamarche J, Gauthier BDM, Dunne WM, Sanderson DJ (2017) Spatial arrangement of faults and opening-mode fractures. J Struct Geol. https://doi.org/10.1016/j.jsg.2017.08.008

  • Leith K, Moore J, Amann F, Loew S (2014) Subglacial extensional fracture development and implications for Alpine Valley evolution. J Geophys Res: Earth Surf 119:62–81

    Article  Google Scholar 

  • Li X, Li P, Zhu H (2013) Coal seam surface modeling and updating with multi-source data integration using Bayesian Geostatistics. Eng Geol 164:208–221

    Article  Google Scholar 

  • Lilliefors HW (1967) On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J Am Stat Assoc 62(318):399–402

    Article  Google Scholar 

  • Long JCS, Billaux DM (1987) From field data to fracture network modeling: an example incorporating spatial structure. Water Resour Res 23(7):1201–1216

    Article  Google Scholar 

  • Ma YZ, Jones TA (2001) Teacher's aide: modeling hole-effect variograms of lithology-indicator variables. Math Geol 33(5):631–648

    Article  Google Scholar 

  • Marinoni O (2003) Improving geological models using a combined ordinary–indicator kriging approach. Eng Geol 69(1):37–45

    Article  Google Scholar 

  • Marinos V, Marinos P, Hoek E (2005) The geological strength index: applications and limitations. Bull Eng Geol Environ 64(1):55–65

    Article  Google Scholar 

  • Marrett R, Gale JFW, Gomez L, Laubach SE (2017) Correlation analysis of fracture arrangement in space. J Struct Geol. https://doi.org/10.1016/j.jsg.2017.06.012

  • Martel SJ (2006) Effect of topographic curvature on near-surface stresses and application to sheeting joints. Geophys Res Lett 33(1):L01308

    Article  Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266

    Article  Google Scholar 

  • Matheron G (1971) The theory of regionalized variables and its applications. Ecole de Mines, Fontainebleau

    Google Scholar 

  • Meyer T, Einstein HH (2002) Geologic stochastic modelling and connectivity assessment of fracture Systems in the Boston Area. Rock Mech Rock Eng 35(1):23–44

    Article  Google Scholar 

  • Miller SM (1979) Geostatistical analysis for evaluating spatial dependence in fracture set characteristics. Proceedings of the 16th International Symposium on Applications of Computers and Operational Research in the Mineral Industry, Tucson, pp 537–545

  • Miller DJ, Dunne T (1996) Topographic perturbations of regional stresses and consequent bedrock fracturing. J Geophys Res 101(B11):25523–25536

    Article  Google Scholar 

  • Minder W (1932) Beiträge zur Petrographie des mittlern Aarmassivs: tektonischpetrographische Studien im Zentralgranit des obern Haslitales. Schweiz Mineral Petrogr Mitt 12:353–422

    Google Scholar 

  • Mullis J (1996) P–T–t path of quartz formation in extensional veins of the central alps. Schweiz Mineral Petrogr Mitt 26:159–164

    Google Scholar 

  • Olson JE (1993) Joint pattern development: effects of subcritical crack growth and mechanical crack interaction. J Geophys Res Solid 98(B7):12251–12265

    Article  Google Scholar 

  • Ortega OJ, Marrett R, Laubach SE (2006) A scale-independent approach to fracture intensity and average fracture spacing. AAPG Bull 90(2):193–208

    Article  Google Scholar 

  • Ozturk CA, Nasuf E (2002) Geostatistical assessment of rock zones for tunnelling. Tunn Undergr Space Technol 17:275–285

    Article  Google Scholar 

  • Ozturk CA, Simdi E (2014) Geostatistical investigation of geotechnical and constructional properties in Kadikoy–Kartal subway, Turkey. Tunn Undergr Space Technol 41:35–45

    Article  Google Scholar 

  • Palmstrom A (1982) The volumetric joint count – A useful and simple measure of the degree of rock mass jointing. IAEG Congress, New Delhi, V.221–V.228

  • Pollard DD, Aydin A (1988) Progress in understanding jointing over the past century. Geol Soc Am Bull 100(8):1181–1204

    Article  Google Scholar 

  • Priest SD (1993) Discontinuity analysis for rock engineering. Springer Science & Business Media

  • Priest SD, Hudson JA (1976) Discontinuity spacing in rock. Int J Rock Mech Min 13:135–148

    Article  Google Scholar 

  • Rafiee A, Vinches M (2008) Application of geostatistical characteristics of rock mass fracture system in 3D model generation. Int J Rock Mech Min 45:644–652

    Article  Google Scholar 

  • Remy N, Boucher A, Wu J (2008) Applied Geostatistics with SGeMS. A user’s guide. Cambridge University Press, New York

    Google Scholar 

  • Rolland Y, Cox SF, Corsini M (2009) Constraining deformation stages in brittle–ductile shear zones from combined field-mapping and 40Ar/39Ar dating: the structural evolution of the Grimsel pass area (Aar massif, Swiss alps). J Struct Geol 31:1377–1394

    Article  Google Scholar 

  • Romana M (1993) A geomechanical classification for slopes: slope mass rating. In: Hudson JA, Brown ET, Fairhurst C, Hoek E (eds) Comprehensive rock engineering: principles, practice and projects. Pergamon Press, Oxford, pp 575–599

    Google Scholar 

  • Savage WZ, Swolfs HS (1986) Tectonic and gravitational stress in long symmetric ridges and valleys. J Geophys Res 91(B3):3677–3685

    Article  Google Scholar 

  • Schlüchter C (2004) The Swiss glacial record — a schematic summary. In: Ehlers J, Gibbard PL (eds) Quaternary glaciations — extent and chronology. Part 1: Europe. Developments in quaternary science, 2. Elsevier, Amsterdam, pp 413–418

    Chapter  Google Scholar 

  • Şen Z (2014) Rock quality designation-fracture intensity index method for geomechanical classification. Arab J Geosci 7(7):2915–2922

    Article  Google Scholar 

  • Srivastava RM (2013) Geostatistics: a toolkit for data analysis, spatial prediction and risk management in the coal industry. Int J Coal Geol 112:2–13

    Article  Google Scholar 

  • Stalder HA (1964) Petrographische und mineralogische Untersuchungen im Grimselgebiet (Mittleres Aarmassiv). Schweiz Mineral Petrogr Mitt 44:187–398

    Google Scholar 

  • Sutter B (2008) Kluftmuster und Kluftgenese am Grimselpass. Geologisch-geotechnische Eigenschaften und Tiefenwirkung der Trennflächensysteme. Master Thesis, ETH of Zurich

  • Tavchandjian O, Rouleau A, Archambault G, Daigneault R, Marcotte D (1997) Geostatistical analysis of fractures in shear zones in the Chibougamau area: applications to structural geology. Tectonophysics 269:51–63

    Article  Google Scholar 

  • Terzaghi RD (1965) Sources of error in joint surveys. Geotechnique 15(3):287–304

    Article  Google Scholar 

  • Vatcher J, McKinnon SD, Sjöberg J (2016) Developing 3-D mine-scale geomechanical models in complex geological environments, as applied to the Kiirunavaara mine. Eng Geol 203:140–150

    Article  Google Scholar 

  • Villaescusa E, Brown ET (1992) Maximum likelihood estimation of joint size. Rock Mech Rock Eng 25:67–87

    Article  Google Scholar 

  • Voight B (1966) Beziehung zwischen grossen horizontalen Spannungen im Gebirge und der Tektonik und der Abtragung. Proceedings of the First Congress of the International Society of Rock Mechanics. Laboratório Nacional de Engenharia Civil, Lisbon, pp 51–56

  • Yu YF, Mostyn GR (1993) Spatial correlation of rock joints. Probabilistic methods in geotechnical engineering. Balkema, Rotterdam, pp 241–255

    Google Scholar 

  • Zangerl C, Loew S, Eberhardt E (2006) Structure, geometry and formation of brittle discontinuities in anisotropic crystalline rocks of the central Gotthard massif, Switzerland. Eclogae Geol Helv 99:271–290

    Article  Google Scholar 

  • Ziegler M, Loew S, Amann F (2016) Near-surface rock stress orientations in alpine topography derived from exfoliation fracture surface markings and 3D numerical modelling. Int J Rock Mech Min 85:129–151

    Article  Google Scholar 

  • Ziegler M, Loew S, Bahat D (2014) Growth of exfoliation joints and near-surface stress orientations inferred from fractographic markings observed in the upper Aar valley (Swiss alps). Tectonophysics 626:1–20

    Article  Google Scholar 

  • Ziegler M, Loew S, Moore JR (2013) Distribution and inferred age of exfoliation joints in the Aar granite of the central Swiss alps and relationship to quaternary landscape evolution. Geomorphology 201:344–362

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank Stephen Bolay (ETH) for the realization of photogrammetric models.

This paper is dedicated to the memory of Prof. Gian Paolo Giani, whose expertise in rock mechanics, as well as his congeniality, will be deeply missed within the scientific community.

Author information

Authors and Affiliations

  1. Dipartimento di Scienze della Terra “Ardito Desio”, Università degli Studi di Milano, via Mangiagalli 34, 20133, Milan, Italy

    Federica Ferrari & Tiziana Apuani

  2. Department of Earth Sciences, ETH Zurich, Sonneggstrasse 5, 8092, Zurich, Switzerland

    Martin Ziegler & Simon Loew

Authors
  1. Federica Ferrari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Martin Ziegler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tiziana Apuani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Simon Loew
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federica Ferrari.

Appendix

Appendix

Table 3 Summary table of all models with outcrop location (coordinates: CH1903), outcrop dimensions, average photogrammetric distance, tectonic joint set (J1–J4) and exfoliation joint generations (JlP: lower Pleistocene; JmP: middle Pleistocene; and JuP; upper Pleistocene) with relative mean joint set orientation (in terms of dip direction/dip), average trace length and joint set spacing
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferrari, F., Ziegler, M., Apuani, T. et al. Geostatistical analyses of exfoliation and tectonic joint set spacing in alpine granites (Aar Valley, Switzerland). Bull Eng Geol Environ 78, 1645–1668 (2019). https://doi.org/10.1007/s10064-018-1251-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10064-018-1251-4

Keywords

Search

Navigation