http://mech.spbstu.ru/images/b/bd/Potyondy_Cundall_2004_A_bonded-particle_model_for_rock.pdf

A bonded-particle model for rock

http://www.geoplanning.it/test/wp-content/uploads/2012/02/Practical-estimates-of-rock-mass-strength.pdf

Practical estimates of rock mass strength

The goal of this article is to revise several aspects of the well-known classification of landslides, developed by Varnes (1978). The primary recommendation is to modify the definition of landslide-forming materials, to provide compatibility with accepted geotechnical and geological terminology of rocks and soils. Other, less important modifications of the classification system are suggested, resulting from recent developments of the landslide science. The modified Varnes classification of landslides has 32 landslide types, each of which is backed by a formal definition. The definitions should facilitate backward compatibility of the system as well as possible translation to other languages. Complex landslides are not included as a separate category type, but composite types can be constructed by the user of the classification by combining two or more type names, if advantageous.

The Varnes classification of landslide types, an update

The Hoek-Brown failure criterion for rock masses is widely accepted and has been applied in a large number of projects around the world. While, in general, it has been found to be satisfactory, there are some uncertainties and inaccuracies that have made the criterion inconvenient to apply and to incorporate into numerical models and limit equilibrium programs. In particular, the difficulty of finding an acceptable equivalent friction angle and cohesive strength for a given rock mass has been a problem since the publication of the criterion in 1980. This paper resolves all these issues and sets out a recommended sequence of calculations for applying the criterion. An associated Windows program called "RocLab" has been developed to provide a convenient means of solving and plotting the equations presented in this paper.

/pdf/hoek-brown-failure-criterion-2002-edition-1jol1a5awf.pdf

Hoek-brown failure criterion - 2002 edition

Volume changes of a granite, a marble, and an aplite were measured during deformation in triaxial compression at confining pressure of as much as 8 kb. Stress-volumetric strain behavior is qualitatively the same for these rocks and a wide variety of other rocks and concrete studied elsewhere. Volume changes are purely elastic at low stress. As the maximum stress becomes one-third to two-thirds the fracture stress at a given pressure, the rocks become dilatant; that is, volume increases relative to elastic changes. The magnitude of the dilatancy, with a few exceptions, ranges from 0.2 to 2.0 times the elastic volume changes that would have occurred were the rock simply elastic. The magnitude of the dilatancy is not markedly affected by pressure, for the range of conditions studied here.

For granite, the stress at which dilatancy was first detected was strongly time dependent; the higher the loading rate the higher the stress. Dilatancy, which represents an increase in porosity, was traced in the granite to open cracks which form parallel with the direction of maximum compression.

Dilatancy in the Fracture of Crystalline Rocks

Progressive spalling in massive brittle rock

Predicting tunnel squeezing problems in weak heterogeneous rock masses

Tunnels of 10 to 16 m span are frequently constructed for hydroelectric or transportation projects, and many of these tunnels are excavated in rock masses of very poor quality. When the ratio of rock mass strength to in situ stress falls below 0.2, squeezing of the rock mass becomes a problem that can cause instability of both the tunnel and the face. A method for predicting squeezing conditions is presented and the practical options for prereinforcing the face and supporting the tunnel to deal with these problems are discussed. Two case histories are included to illustrate how these prereinforcement and support measures can be incorporated into a tunnel design. Brief discussions are also given on water problems in tunneling, the use of tunnel boring machines (TBMs) in squeezing ground, and the construction costs for large tunnels in varying ground conditions.

Big Tunnels in Bad Rock

The Hoek-Brown failure criterion-a 1988 update

The original Geological Strength Index chart was developed on the assumption that observations of the rock mass would be made by qualified and experienced geologists or engineering geologists. With the ever increasing use of the GSI chart as the basis for the selection of input parameters for numerical analysis, often by individuals without the strong geologic understanding of rock mass variability necessary to interpret the graphical GSI chart properly, some uniformity and quantification of the chart seems necessary. This paper presents a proposed quantification of the GSI chart on the basis of two well-established parameters Joint Condition and RQD. Recommendations for future development of more robust scales are presented. 2. CONSTRUCTION OF THE BASIC GSI CHART The GSI chart published by Hoek and Marinos (2000) [1] is reproduced in Figure 2. Scale A has been added to represent the 5 divisions of surface quality with a range of 45 points, defined by the approximate intersection of the GSI = 45 line on the axis. Scale B represents the 5 divisions of the block interlocking scale with a range of 40 points in the zone in which quantification is applied. Figure 2: The basic structure of the Hoek and Marinos (2000) GSI chart and possibilities for quantification. At each intersection of the A and B scales the value of GSI has been estimated from the GSI lines on the chart. These values are shown as the upper italicized number at the intersection point. At the same intersection points the lower italicized number equals the sum of the A and B values. The two numbers at each intersection point are then plotted against each other in Figure 3. This plot demonstrates that there is a high potential for quantifying GSI by means of two linear scales representing the discontinuity surface conditions (scale A) and the interlocking of the rock blocks defined by these intersecting discontinuities (scale B). Figure 3: Plot of GSI estimated from the basic GSI chart against the sum of the A and B values. Figure 3 also shows that there is a systematic trend in each group of plotted points and, from an examination of the chart in Figure 2, it is obvious that this trend is due to the fact that the original GSI lines, which were hand drawn, are neither parallel nor equally spaced. With a modest correction to the original GSI lines to make them parallel and equally spaced, the error trends in Figure 3 can be eliminated completely. This correction has been applied to Figure 5. Note that the correction of the GSI lines and the addition of the A and B scales do not change the chart’s original function of estimating GSI from field observations of blockiness and joint condition, characterized in terms of the descriptive axis title blocks. Hence the chart shown in Figure 5 has the potential for satisfying both the descriptive and quantitative user camps. Before proceeding any further with this discussion it is necessary to define a number of conditions and limitations of the proposed quantitative GSI chart. 1. The addition of quantitative scales to the GSI chart should not limit the use for which it was originally designed – the estimation of GSI values from direct visual observations of the rock conditions in the field. 2. A fundamental assumption of the Hoek-Brown criterion for the estimation of the mechanical properties of rock masses is that the deformation and the peak strength are controlled by sliding and rotation of intact blocks of rock defined by intersecting discontinuity systems. It is assumed that there are several discontinuity sets and that they are sufficiently closely spaced, relative to the size of the structure under consideration, that the rock mass can be considered homogeneous and isotropic. These concepts are illustrated diagrammatically in Figure 4. Figure 4: Limitations on the use of GSI depending on scale. 3. For intact massive or very sparsely joined rock, the GSI chart should not be used for input into the HoekBrown criterion as shown in Figure 1. This is because there are insufficient pre-existing joints to satisfy the conditions of homogeneity and isotropy described above. Hence, in order to avoid confusion, the upper row of the chart shown in Figure 2 has been removed in the development of the quantified GSI chart. Brittle failure processes such as rockbursts and spalling are specifically excluded from the section of the quantified GSI chart since these processes do not involve the rotation and translation of interlocking blocks of rock as defined in 2 above. Similarly, structurally controlled failure in sparsely jointed rock does not fall within the definition of homogeneity inherent in the definition of GSI. 4. The lower row of the original 2000 GSI chart has also been removed since this represents previously sheared or transported or heavily altered materials to which the conditions defined in item 2 above also do not apply. A second GSI chart for heterogeneous, pre-sheared materials such as flysch has been published by Marinos and Hoek (2002) [2] and Marinos et al (2007) [3]. Where applicable this flysch chart could be used or a similar site specific chart could be developed for rock masses that fall below the last row of the chart given in Figure 5. Some approaches for tackling both ends of the rockmass competency scale addressed in paragraphs (3) and (4) are suggested by Carter et al, 2008, [4]. 5. In order to quantify GSI using the chart, the quantities used to construct the A and B scales have to be practical ratings that are familiar to engineering geologists and geotechnical engineers operating in the field. They should also be well established in the literature as reliable indices for characterizing rock masses intersecting discontinuity systems. It is assumed that there are a sufficient number of discontinuities and that they are sufficiently closely spaced, relative to the size of the structure under consideration, that the rock mass can be considered homogeneous and isotropic. 3. ESTIMATION OF GSI IN TERMS OF RQD AND JOINT CONDITION Scale A in Figure 2 represents discontinuity surface conditions while Scale B represents the blockiness of the rock mass. Prime candidates for these scales are the Joint Condition (JCond89) rating defined by Bieniawski (1989) [5] and the Rock Quality Designation (RQD) defined by Deere (1963) [6]. These ratings are given in Appendix 1. The JCond89 rating corresponds well with the surface conditions defined in the text boxes of the x axis of the GSI chart in Figure 5. This rating parameter has been in use for many years and users have found it to be both simple and reliable to apply in the field. The RQD rating has been in use for 50 years and some users have defined it as boringly reliable. Hence these two ratings appear to be ideal for use as the A and B scales for the quantification of GSI. Figure 5 shows a chart in which the A scale is defined by 1.5 JCond89 while the B scale is defined as RQD/2. The value of GSI is given by the sum of these scales which results in the relationship: GSI = 1.5 JCond89 + RQD/2 (1) 4. CHECK OF QUANTIFIED GSI AGAINST MAPPED GSI In order to check whether or not the proposed quantification of GSI works it is necessary to check the values of GSI predicted from equation 1 against field mapped GSI values. At the time of writing only one set of reliable field data, from a drill and blast tunnel, is available to the authors. The GSI values calculated from JCond89 and RQD are plotted against mapped GSI values in Figure 6. This plot shows that the correlation between the calculated and mapped GSI values is reasonably close to the ideal 1:1 relationship for a perfect fit. This suggests that, once additional field data are obtained, the application of this quantification of GSI may justify the transition from proposed to recommended. It is possible that some adjustments in the positions of the JCond89 and RQD scales in Figure 5 may be required as more mapped GSI data becomes available and as experience is gained in using this quantification. Figure 5: Quantification of GSI by Joint Condition and RQD. Figure 6: Comparison between mapped GSI and GSI predicted from JCond89 and RQD. 5. ALTERNATIVE JOINT CONDITION SCALE In recognition of the fact that values of JCond89 are not always available in data from field mapping, the authors have examined two options for alternative scales for the surface quality axis in Figure 5. The first candidate is the version of Joint Condition rating (JCond76) included in the paper by Bieniawski (1976) [7] (see Appendix 1). Regression analysis of a plot of individual values assigned to JCond76 and JCond89 gives JCond89 = 1.3 JCond76 which, when substituted into equation 1, gives GSI = 2 JCond76 + RQD/2 (2) A second candidate is the quotient Jr/Ja, included in the Tunnelling Quality Index (Q) of Barton et al (1974) [8]. This quotient (Jr/Ja) represents the roughness and frictional characteristics of the joint walls or fillings. Comparing the ratings for JCond89 with those allocated to Jr and Ja by Barton et al (1974) [7] (see Appendix 1) gives the relationship JCond89 = 35 Jr/Ja/(1 + Jr/Ja). Substitution of this relationship into equation 1 yields: For the same data set used in the preparation of Figure 6, the predicted values of GSI are plotted against field mapped values of GSI in Figure 7. While the results for a linear regression analysis are not as good as those obtained for equation 1, the fit is an acceptable approximation for engineering applications. Figure 7: Comparison between mapped GSI and GSI predicted from Jr/Ja and RQD. 6. RQD DETERMINED FROM FACE MAPS When no core is available and RQD has to be determined from the mapping of tunnel faces, tunnel walls or slope faces, three methods are available. The first involves a simple physical measuring rod or tape held against or in front of the face. The length of intact rock segments greater than 10cm falling between natural fractures intersecting the rod or tape 

Evert Hoek

Papers

Progressive spalling in massive brittle rock

Predicting tunnel squeezing problems in weak heterogeneous rock masses

Big Tunnels in Bad Rock

The Hoek-Brown failure criterion-a 1988 update

Quantification of the Geological Strength Index Chart