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The 50 Principles of Rock Mechanics
for Rock Engineering
1. Rock is a natural material: its properties cannot be specified as with a fabricated material; the properties have to be measured on site. The geological history of a rock mass will determine several key characteristics. These include the inhomogeneity (different properties at different locations), the anisotropy (different properties in different directions), the presence and mechanical characteristics of the discontinuities (pre-existing fractures), and the hydraulic properties.

2. The nature of the intact rock will depend on its geological type and the degree of weathering to which it has been subjected. Rock mechanics started with detailed studies of the deformation and failure of intact rock. The engineering properties of intact rock are functions of the rock microstructure which in turn is a function of the geological formation and history.

3. Using a stiff or servo-controlled testing machine, the complete stress-strain curve for intact rock in uniaxial compression can be obtained. The test is conducted with axial strain as the independent variable (the controlled variable) and axial stress as the dependent variable (the measured variable). The complete stress-strain curve represents the structural collapse of the rock microstructure from initial loading to complete disintegration. The most widely-used characteristics of the complete stress-strain curve are the modulus (measured at 50% maximum stress) and the compressive strength ( the maximum stress sustained).

4. The complete stress-strain curve for intact rock depends on the specimen geometry and loading conditions of the test and the environmental conditions. In fact, neither the compressive strength nor the tensile strength is a material property – because they both depend on the specimen geometry and the loading conditions of the test. A material property does not depend on these factors.

5. When a confining pressure is also applied during a compression test on intact rock, the rock will exhibit either brittle or ductile behavior. In brittle behavior, the stress decreases after the compressive strength has been reached. In ductile behavior, the stress continues to increase. The confining pressure associated with the brittle-ductile transition is, for example, 0 MPa for rock salt, 20-100 MPa for limestone, and more than 100 MPa for sandstone and granite.

6. The most widely used failure criteria for intact rock are the Mohr-Coulomb, Griffith, and Hock-Brown failure criteria. The Mohr-Coulomb criterion considers the cohesion and angle of friction associated with shear failure. The Griffith criterion considers the energy required by a propagating crack in terms of an initial crack length. The Hoek-Brown criterion is an empirical criterion using two parameters which can be estimated from the rock description. Many other failure criteria for intact rock have been developed.

7. In most cases, the properties and engineering behaviour of rock masses are governed by the discontinuities. The discontinuities are any breaks in the mechanical rock continuum - which can occur at a variety of scales, from faults to bedding planes to joints to fissures and micro-fissures. The most important discontinuities for engineering are faults or other shear features, but joints - which have been created by normal tensile stresses - can be very significant as well. Discontinuities have little or zero tensile strength.

8. Ten main characteristics are used to describe discontinuities: spacing; orientation; persistence; roughness; aperture; number of sets; block size; filling; wall strength; and seepage.

9. The most widely used parameter to describe discontinuity occurrence is the Rock Quality Designation (RQD). This is the percentage of pieces in a borebole core or lengths along a seanline that are greater than l0 mm or 4 inches. The RQD can be related to the discontinuity frequency if the nature of the discontinuity spacing histogram is known.

10. Because discontinuities tend to occur in sets (of parallel or sub-parallel discontinuities), the discontinuity frequency value is different along lines in different directions through a rock mass. It follows that the RQD will also be different in different directions through the rock mass.

11. The persistence, or extent of a discontinuity, is an important characteristic for many engineering characteristics, such as the modulus of deformation of the rock, the degree to which rock blocks are formed, and the hydraulic connectivity of the discontinuity network. The roughness, aperture and filling of the discontinuities are also important for the mechanical and hydrological characteristics.

12. The main mechanical properties of a discontinuity for engineering are the stiffness and strength. The stiffness should be considered as the normal stiffness and the two shear stiffnesses; the strength is specified by the shear strength, i.e. the angle of friction (remembering that the discontinuity has essentially no tensile strength, and is also assumed to have little or no cohesion). The angle of friction is a complex combination of the basic friction angle, the strength of the asperites and the discontinuity roughness.

13. A rock mass will contain a pre-existing natural stress state, the in situ stress, which is caused by geological processes, mainly tectonic. The quantity ‘stress’ is not a scalar or vector quantity but a tensor quantity which has to be characterized by six independent values----usually the magnitudes and directions of the three principal stresses. These rock stresses are mainly caused by tectonic activity but old, residual stresses can also be present.

14. There are four main methods of measuring the in situ stress: the flat jack, hydraulic fracturing, the USBM overcoring torpedo, and the CSIRO overcoring gauge. The CSIRO gauge is the most reliable and hydraulic fracturing is the only method, that can be used a significant distance from 'man-access'. It is the rule rather than the exception that the maximum horizontal stress component is greater than the vertical stress component. Because discontinuities have a significant effect on the local principal stress magnitudes and directions, measured stresses are expected to vary at the project location.

15. Water can be present in the pores of the intact rock and in the discontinuities. The water pressure is subtracted from the normal stress components of the stress tensor to give effective stresses.

16. Strain is a tensor quantity like stress. Assuming the rock is behaving elastically, the six components of the strain tensor can be related to the six components of the stress tensor by the elastic compliance matrix. For isotropy, two elastic constants are needed: Young's modulus and Poisson's ratio. For transverse isotropy, five elastic constants are needed: two Young's moduli, two Poisson's ratios and a shear modulus. For orthotropy, nine elastic constants are required: three Young's moduli, three Poisson's ratios and three shear moduli. For complete anisotropy, the 21 independent constants of the elastic compliance matrix are required.

17. The 'ideal' rock mass is a CHILE material: Continuous, Homogeneous, Isotropic, and Linearly Elastic. The actual rock mass is a DIANE material: Discontinuous, Inhomogeneous, Anisotropic, and Not Elastic. Rock masses are discontinuous because they contain discontinuities. They are inhomogeneous and anisotropic because they are composed of different geological strata and different discontinuity geometries at different locations and which have different properties in different directions. They are not elastic because the energy given to the rock mass during deformation cannot generally be recovered completely.

18. The deformability of a rock mass results from deformation of both the intact rock and the discontinuities. Because the intact rock can be anisotropic and because the discontinuities occur in sets causing the discontinuity contributions to be anisotropic, the deformation modulus of the rock mass will be different in different directions.

19. The strength of a rock mass will depend on whether failure occurs through the intact rock or along one or more discontinuities.

20. The ease with which water flows through a rock mass is expressed by the permeability. Like stress and strain, permeability is a second order tensor with six independent components - usually characterized by the magnitudes and directions of the principal permeabilities. The permeability of fractured rock masses can vary greatly.

21. The Representative Elemental Volume (REV) is an important concept for the permeability of rock mass. In a rock mass sample, the number of discontinuities present is a function of the sample size, stabilizing in average properties when the sample size is large enough. The REV is the rock mass sample size below which the permeability can vary significantly and at and above which the permeability is essentially constant. This REV concept also applies to all properties governed wholly or partly by the discontinuities.

22. In order to establish the properties of rocks, testing techniques are used. These testing techniques can be standardized. However, different properties are required for different projects. Because there are many different rock engineering objectives, even though the testing techniques themselves can be standardized, there can be no standardized site investigation.

23. Because the REV size is generally of the order of tens of meters, it is generally not possible to conduct meaningful tests directly on the rock mass. Tests are conducted on the intact rock and the discontinuities separately and their significance for the rock mass properties evaluated. The main organizations publishing test methods are the ISRM and the ASTM.

24. The concepts of accuracy, bias, precision and resolution are useful when considering rock tests on intact rock and discontinuities. Accuracy is when the correct answer is obtained on the average, the bias is the difference between the sample mean and the actual mean, precision is when the results are closely spaced (whether they are accurate or not), and resolution is the number of decimal places to which the value is obtained.

25. One of the most popular methods of combining the intact rock and discontinuity properties for assessing rock mass properties is through the use of rock mass classification schemes. The two most popular schemes are the Rock Mass Rating (RMR) developed by Bieniawski and the Q rating developed by Barton. The RMR system uses one property of the intact rock, three properties of the discontinuities, the ground water conditions and the orientation of the discontinuities relative to the engineered structure. The Q system uses four properties of the discontinuities, the water flow and the stress condition. These systems have been successfully and widely used in practice to design tunnel supports and to estimate rock mass properties.

26. It is very important in rock engineering design to establish the objectives of the project and the objectives of the supporting analysis. Once the objectives have been established, the physical variables and their interactions can be established using the Rock Engineering Systems approach. The main variables are listed along the leading diagonal of an interaction matrix with the interaction between each pair of variables established for each position in the matrix. This defines the rock engineering system and, from the matrix, an audit of the information required for design, the variables that are most significant, the critical mechanisms and hence the optimal form of site investigation, numerical codes and the hazards that may arise can all be established.

27. When rock is excavated for an engineering project, it is necessary to break the rock being removed and avoid breaking the remaining rock. The created rock surface (e.g. the slope face or tunnel surface) is thus a critical interface between the excavation and support objectives.

28. The excavation process consists of changing the in sim block size distribution to the fragment size distribution after excavation.

29. There are only two main methods of excavation. One is blasting in which large mounts of energy are applied to the rock in seconds with quiescent periods of several hours in between. The other is by mechanized excavation where a much smaller level of energy is continuously input to the rock (except when the machine is not operating).

30. Optimizing rock breakage by explosives consists of optimizing the separate effects of the explosive's stress wave and gas pressure and their interactions with the free face. Optimizing meehanised excavation consists of optimizing the transfer of energy from the tunnel boring machine cutters to the rock. This involves mechanical engineering considerations, the configuration of the cutters, steering the machine, reducing vibrations, minimizing down time etc.

31. After the rock is excavated the stability of the resultant rock surfaces must considered. The three primary effects of excavation are as follows.
a. Displacements occur because rock resistance has been removed.
b. There are no normal and shear stresses on an unsupported excavation surface and hence it becomes a principal stress plane---involving a change of the pre-existing stress field.
c. At the boundary of the excavation open to the atmosphere, water pressure is reduced to atmospheric pressure causing the excavation to act as a sink with water flowing into it.

32. To stabilise an excavation, either no support, rock reinforcement (i.e. rock bolts) or rock support (e.g. a cast concrete roof) may be necessary. The reinforcement strategy is to bolt the rock blocks together so that they behave more like a rock continuum. The support strategy is to maintain the rock displacements to tolerable levels.

33. The ground response curve, in which the support pressure is plotted against the boundary displacement, is a useful conceptual framework for considering the stability requirements in continuous and discontinuous rock, and to illustrate the effect of rock damage that might be caused by the excavation process.

34. A method of rapidly assessing the potential of an excavation to initiate slip on discontinuities or laminations in rock is theφj theory in which the direction of the stress at the excavation surface is considered in relation to the orientation of the discontinuities and their angle of friction.

35. Slope instability can be caused by failure occurring through weak intact rock or along pre-existing discontinuities in harder rock. This indicates four main types of rock slope instability: circular slip; plane sliding; wedge sliding; and toppling. A great deal can be achieved quickly in assessing the potential for instability by using simple solutions for circular slip potential and considering the slope and discontinuity dip and dip directions for failure initiated along pre-existing discontinuities.

36. The same applies for foundations where considerations of, for example, the Boussinesq solution for the point load of a half space (and how this might be modified by anisotropic rock and slip on pre-existing discontinuities), are helpful.

37. When designing surface slopes, there should always be an initial kinematic analysis of slope instability, i.e. given the geometry of the slope and the discontinuities, is it physically possible for the rock to slide? Because the discontinuities tend to occur in sets, there always needs to be consideration of designing the excavation in harmony with the rock structure. For example, a surface excavation which is circular in plan never provides optimal protection; an excavation which is elliptical in plan is always better.

38. Because of uncertainty in the input data in such design considerations, it is helpful to conduct a sensitivity analysis using probalisfic methods, fuzzy maths etc.

39. Certain directions and cross-sectional shapes of tunnels and other underground excavations will always be better than others - because the discontinuities do not occur at random orientations. Preliminary considerations using methods such as hemispherical projection and block theory to identify the ustable blocks are most helpful.

40. The excavation must also be designed against failure induced by stresses. The process of excavation not only makes the excavation surface a principal stress plane, it also increases the stress component in one direction and decrease it in another. It is necessary to assess the regions of high stress and whether failure will occur, and the consequences of such failure. Simple considerations of the stress can be most helpful in this regard. The load in the region of an excavation is conserved before and after excavation so the redistribution of the load can be considered, and solutions for circular and elliptical excavations can be used to estimates stress concentrations.

41. Sophisticated numerical codes are now available for assessing the effect of excavation on block movements, stresses and water flow within rock masses. Most of the trends predicted by these programmes can be established from the principles already presented. Therefore, these programmes come into their own when specific values are required, high speed sensitivity studies are needed, etc. These numerical codes are a revolution in rock mechanics analysis capability.

42. A useful concept when dealing with closely spaced excavations is the 'zone of influence'. The disturbance caused to the rock mass by excavation is evaluated and then the engineering zone of influence is studied, i.e. the volumetric extent of the rock where the stress for example is affected by more than say 5% of its original value. The zone can be estimated via the simple methods already mentioned and is of help not only in deciding how far away from each other proximate excavations should be but also the best sequence of excavation.

43. The design life of the project is important because the rock mechanisms are time dependent. An open-pit coal mine can have a life as low as five years, an open pit or underground metal mine can have a life of around 30 years, a civil engineering tunnel 120 years, and a radioactive waste repository 10,000 years.

44. The principles in this list apply to all rock engineering projects because they are based on the fundamental geometry, properties and mechanics of rock masses. The principles apply to foundations, slopes, shafts, tunnels, caverns, mining, geothermal energy, radioactive waste disposal, etc.

45. The two subjects which are most useful for rock engineering design are stress analysis and steo-graphic projection. All rock engineers must understand the essence of these two subjects.

46. The process of analysis, design and site investigation continues during construction when the rock properties are more apparent and the effects of construction clearer. Remember that measured engineering performance parameters, such as tunnel convergence, can provide the best information for design and that successful back analysis may be required for a fuller understanding of the observed mechanisms.

47. Each rock mass and each rock engineering project are unique.

48. The principles of structural mechanics and soil mechanics should be used for rock only with extreme caution, checking that the assumptions on which the principles were developed do indeed apply to rock (in some cases they will, and in most cases they will not).

49. In the case of a new project (in which there is no precedent practice), the design considerations will rely entirely on the rock mechanics principles and numerical codes, backed by in situ feedback at early stages of construction.

50. There is no standardized method for designing structures in rock. It is, however, essential to understand and apply all the fifty principles to any rock engineering project. The application of these principles does not guarantee success, but it certainly reduces the possibility of failure - and it is your responsibility to do everything that you can to ensure that these principles are applied on any rock engineering project with which you are involved.