A New Model for the Dilation of Brittle Rocks Based on Laboratory Compression Test Data with Separate Treatment of Dilatancy Mobilization and Decay

In this study, a new model is presented for the dilation angle of rocks which deform through brittle mechanisms in laboratory compression tests. This model, which is defined by a smaller number of independent parameters than similar models, is shown to fit laboratory test data for a wide variety of rocks (sedimentary rocks, diabase, marble, granites, and quartzite). A detailed investigation of each model parameter is performed, and potential links to geological and geotechnical properties are made. A mechanistic interpretation of the observed dilation angle data is also presented, in the context of the new model. Model parameters for the rock types studied are presented, and recommendations for parameter determination/estimation are made. The key strength of the model is shown to be its flexibility to accommodate a data-poor or data-rich analysis, as well as a simplified or comprehensive implementation. Practical guidance for model modifications is provided.

[1]  R. Hill The mathematical theory of plasticity , 1950 .

[2]  John H. Schmertmann,et al.  An Experimental Study of the Development of Cohesion and Friction with Axial Strain in Saturated Cohesive Soils , 1960 .

[3]  Kiyoo Mogi,et al.  Pressure Dependence of Rock Strength and Transition from Brittle Fracture to Ductile Flow. , 1966 .

[4]  C. Scholz,et al.  Dilatancy in the fracture of crystalline rocks , 1966 .

[5]  Z. Bieniawski Fracture dynamics of rock , 1968 .

[6]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[7]  N. Cook An experiment proving that dilatancy is a pervasive volumetric property of brittle rock loaded to failure , 1970 .

[8]  Steven L. Crouch,et al.  Experimental determination of volumetric strains in failed rock , 1970 .

[9]  P. R. Sheorey Discussion of Z.T. Bieniawski's paper The effect of specimen size on compressive strength of coal☆ , 1970 .

[10]  K. Roscoe THE INFLUENCE OF STRAINS IN SOIL MECHANICS , 1970 .

[11]  P. W. Rowe Theoretical meaning and observed values of deformation parameters for soil , 1972 .

[12]  Paul Tapponnier,et al.  Development of stress-induced microcracks in Westerly Granite , 1976 .

[13]  Stein Sture,et al.  Strain‐softening of brittle geologic materials , 1978 .

[14]  I. W. Farmer,et al.  Application of yield models to rock , 1979 .

[15]  Ian W. Farmer,et al.  Engineering Behaviour of Rocks , 1983 .

[16]  R. Borst,et al.  Non-Associated Plasticity for Soils, Concrete and Rock , 1984 .

[17]  G. A. Hegemier,et al.  Strain softening of rock, soil and concrete — a review article , 1984 .

[18]  L. S. Costin,et al.  Damage mechanics in the post-failure regime , 1985 .

[19]  H. W. Chandler,et al.  A plasticity theory without drucker's postulate, suitable for granular materials , 1985 .

[20]  Emmanuel M Detournay,et al.  Elastoplastic model of a deep tunnel for a rock with variable dilatancy , 1986 .

[21]  Yasuaki Ichikawa,et al.  Deformation and fracturing behaviour of discontinuous rock mass and damage mechanics theory , 1988 .

[22]  Michael F. Ashby,et al.  The damage mechanics of brittle solids in compression , 1990 .

[23]  Joseph F. Labuz,et al.  Class I vs Class II stability: a demonstration of size effect , 1991 .

[24]  N. A. Chandler,et al.  The progressive fracture of Lac du Bonnet granite , 1994 .

[25]  I. Vardoulakis,et al.  Bifurcation Analysis in Geomechanics , 1995 .

[26]  C. Martin,et al.  Seventeenth Canadian Geotechnical Colloquium: The effect of cohesion loss and stress path on brittle rock strength , 1997 .

[27]  E. Z. Lajtai Microscopic Fracture Processes in a Granite , 1998 .

[28]  Mark S. Diederichs,et al.  Instability of hard rockmasses, the role of tensile damage and relaxation , 2000 .

[29]  Diederichs,et al.  Underground Works In Hard Rock Tunnelling And Mining , 2000 .

[30]  V. Hajiabdolmajid,et al.  Modelling brittle failure of rock , 2002 .

[31]  Mark S. Diederichs,et al.  Manuel Rocha Medal Recipient Rock Fracture and Collapse Under Low Confinement Conditions , 2003 .

[32]  J. Rudnicki,et al.  Chapter 5 Localization: Shear bands and compaction bands , 2004 .

[33]  M. S. Diederichsa,et al.  Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation , 2004 .

[34]  Yves Guéguen,et al.  Mechanics of fluid-saturated rocks , 2004 .

[35]  E. Alonso,et al.  Considerations of the dilatancy angle in rocks and rock masses , 2005 .

[36]  J. Riedel,et al.  Propagation of a shear band in sandstone , 2007 .

[37]  Mark S. Diederichs,et al.  The 2003 Canadian Geotechnical Colloquium: Mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling , 2007 .

[38]  Diederichs,et al.  Application of modified Hoek-Brown transition relationships for assessing strength and post yield behaviour at both ends of the rock competence scale , 2008 .

[39]  Catrin Edelbro,et al.  Numerical modelling of observed fallouts in hard rock masses using an instantaneous cohesion-softening friction-hardening model , 2009 .

[40]  C. Martin,et al.  Measurement of spalling parameters from laboratory testing , 2010 .

[41]  M. Cai,et al.  Considerations of rock dilation on modeling failure and deformation of hard rocks—a case study of the mine-by test tunnel in Canada , 2010 .

[42]  Vincent Labiouse,et al.  Rock Mechanics in Civil and Environmental Engineering , 2010 .

[43]  Ming Cai,et al.  A mobilized dilation angle model for rocks , 2010 .

[44]  Yingxin Zhou,et al.  Harmonising Rock Engineering and the Environment , 2011 .

[45]  M. Kwaśniewski,et al.  Study on the Dilatancy Angle of Rocks in the Pre-Failure Domain , 2011 .

[46]  N. Chandler Quantifying long-term strength and rock damage properties from plots of shear strain versus volume strain , 2013 .

[47]  Leandro R. Alejano,et al.  Dilation in granite during servo-controlled triaxial strength tests , 2013 .

[48]  Leandro R. Alejano,et al.  Strength and dilation of jointed granite specimens in servo-controlled triaxial tests , 2014 .

[49]  G. Walton,et al.  A Detailed Look at Pre-Peak Dilatancy in a Granite – Determining “Plastic” Strains from Laboratory Test Data , 2014 .

[50]  M. Diederichs,et al.  A Review of the Tensile Strength of Rock: Concepts and Testing , 2014, Geotechnical and Geological Engineering.

[51]  Mark S. Diederichs,et al.  Dilation and Post-peak Behaviour Inputs for Practical Engineering Analysis , 2015, Geotechnical and Geological Engineering.

[52]  Mark S. Diederichs,et al.  A Laboratory-Testing-Based Study on the Strength, Deformability, and Dilatancy of Carbonate Rocks at Low Confinement , 2015, Rock Mechanics and Rock Engineering.

[53]  J. Hutchinson,et al.  PLASTICITY THEORY , 2008, How to Love Everyone and Almost Get Away with It.