The stochastic assessment of strength and deformability characteristics for a pyroclastic rock mass

Abstract A practical procedure is described for implementing probabilistic determination of rock mass strength and deformability properties of a pyroclastic rock medium. In order to carry out this procedure, the discontinuity properties of rock mass are collected in the field and laboratory studies are conducted on the intact rock samples. The appropriate statistical distributions are fitted on the available data by using the chi-square goodness of fit technique. For the estimation of strength and deformability of rock mass, input parameters of the generalized Hoek–Brown empirical equations are replaced by previously defined probability density functions. After running Monte Carlo simulations, potential ranges of the strength and deformability values of the investigated rock mass are accomplished. The simulation results suggest that it is promising to represent the random characters of rock mass mechanical properties when used with proper empirical or analytical relationships.

[1]  W. Weibull.  A statistical theory of the strength of materials , 1939 .

[2]  F. Innocenti,et al.  The Neogene calcalkaline volcanism of Central Anatolia: geochronological data on Kayseri—Nigde area , 1975, Geological Magazine.

[3]  Brian D. Ripley,et al.  Stochastic Simulation , 2005 .

[4]  A. J. Hendron,et al.  Design Of Surface And Near-Surface Construction In Rock , 1966 .

[5]  P. Kulatilake,et al.  Stochastic fracture geometry modeling in 3-D including validations for a part of Arrowhead East Tunnel, California, USA , 2003 .

[6]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[7]  T. Topal,et al.  Engineering geological properties and durability assessment of the Cappadocian tuff , 1997 .

[8]  Hyuck-Jin Park,et al.  Risk analysis of rock slope stability and stochastic properties of discontinuity parameters in western North Carolina , 1999 .

[9]  Gregory B. Baecher,et al.  Probabilistic and statistical methods in engineering geology , 1983 .

[10]  Gregory B. Baecher,et al.  The effect of discontinuity persistence on rock slope stability , 1983 .

[11]  Z. Bieniawski.  Engineering rock mass classifications , 1989 .

[12]  A. Gürer,et al.  Geoelectromagnetic and geothermic investigations in the Ihlara Valley geothermal field , 1997 .

[13]  W. W. Daniel.  Applied Nonparametric Statistics , 1979 .

[14]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[15]  G. Walker,et al.  Lateral variations in the taupo ignimbrite , 1983 .

[16]  Z. T. Bieniawski,et al.  Engineering classification of jointed rock masses , 1973 .

[17]  Mehmet Sarı,et al.  Kızılkaya ignimbiritlerinde görülen süreksizliklerin incelenmesi ve kaya kütlesinin tanımlanması , 2007 .

[18]  G. Baecher.  Statistical analysis of rock mass fracturing , 1983 .

[19]  Z. Sen,et al.  Discontinuity spacing and RQD estimates from finite length scanlines , 1984 .

[20]  M. Mahtab,et al.  A Proposed Model For Statistical Representation Of Mechanical Properties Of Rock , 1983 .

[21]  A. Rouleau,et al.  Statistical characterization of the fracture system in the Stripa granite, Sweden , 1985 .

[22]  Z. Bieniawski.  Determining rock mass deformability: experience from case histories , 1978 .

[23]  Celal Karpuz,et al.  Rock variability and establishing confining pressure levels for triaxial tests on rocks , 2006 .

[24]  Jean-Luc Froger,et al.  Neogene ignimbrites of the Nevsehir plateau (Central Turkey): stratigraphy, distribution and source constraints , 1994 .

[25]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[26]  H. S. B. Duzgun,et al.  A Methodology for Reliability-Based Design of Rock Slopes , 2003 .

[27]  R. F. Wallis,et al.  Discontinuity spacings in a crystalline rock , 1980 .

[28]  V. Toprak,et al.  Tectonic control on the development of the Neogene-Quaternary Central Anatolian Volcanic Province, Turkey , 1993 .

[29]  Bjørn Nilsen,et al.  Probabilistic rock slope stability analysis for Himalayan conditions , 2004 .

[30]  E. T. Brown,et al.  Underground excavations in rock , 1980 .

[31]  G. Walker.  Ignimbrite types and ignimbrite problems , 1983 .

[32]  E. T. Brown.  Rock characterization, testing & monitoring: ISRM suggested methods , 1981 .

[33]  John A. Hudson,et al.  Discontinuity frequency in rock masses , 1983 .

[34]  E. Hoek.  Reliability of Hoek-Brown estimates of rock mass properties and their impact on design , 1998 .

[35]  D. Vose.  Risk Analysis: A Quantitative Guide , 2000 .

[36]  Hyuck-Jin Park,et al.  Development of a probabilistic approach for rock wedge failure , 2001 .

[37]  Ove Stephansson,et al.  Joint network modelling with a validation exercise in Stripa mine, Sweden , 1993 .

[38]  A E Ades,et al.  Correlations Between Parameters in Risk Models: Estimation and Propagation of Uncertainty by Markov Chain Monte Carlo , 2003, Risk analysis : an official publication of the Society for Risk Analysis.

[39]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[40]  Sung-Chi Hsu,et al.  Characterization of Eagle Ford Shale , 2002 .

[41]  Hyuck-Jin Park,et al.  Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA , 2005 .

[42]  John A. Hudson,et al.  Discontinuity spacings in rock , 1976 .

[43]  M. Evans.  Statistical Distributions , 2000 .

[44]  Alain Gourgaud,et al.  Ignimbrites of Cappadocia (Central Anatolia, Turkey): petrology and geochemistry , 1998 .

[45]  H. Gao,et al.  Probabilistic approaches to estimating variation in the mechanical properties of rock masses , 1995 .

[46]  Milton E. Harr,et al.  Reliability-Based Design in Civil Engineering , 1987 .

[47]  P. Grasso,et al.  Problems and promises of index testing of rocks , 1992 .

[48]  Evert Hoek,et al.  Practical estimates of rock mass strength , 1997 .