Rock Mechanical Analyses in Deep Underground Tunneling Projects for High Level Nuclear Waste Disposals

Shales 
Disposal of high level wastes in shales would probably involve the use of deep wells. This 
sounds a rather risky plan until one considers the absortive properties and relative 
impermeability of shale as a host for the wastes. A naturally occurring deposit of radioactive 
materials in shale is located in the African country of Gabon. The site has served as a “natural 
laboratory” where scientists have been able to observe, model and test the migration of 
radioactive materials through shale. Their findings show that migration rates are very low and 
the shale could serve as an effective barrier in a repository for high-level wastes. 
Salt Vaults 
The mining of salt domes, salt occurring in bedded layers within a marine sedimentary 
sequence, often leaves a cavity, called a vault. Salt vaults are well suited for the disposal of 
radioactive wastes for several reasons. The presence of salt implies that it has not come into 
contact with groundwater since it originally formed, otherwise the salt would have been 
dissolved and carried away in solution. Salt deforms plastically, that is, it tends to bend or 
flow rather than break of fractured. This means that any fracture would form and allow 
leaking wastes to enter the environment. Because salt is a good conductor, heat from the 
wastes would be dissipated effectively. Salt has been considered as a potential host rock for 
high-level wastes in both Canada and United States, and an operating radioactive waste 
disposal facility in Germany is sited in an old salt vault. 
Volcanic tuffs 
The disposal site that is currently favored by many scientists in the United States is Yucca 
Mountain, Nevada. It is situated in a thick sequence of volcanic tuffs. The site was chosen 
because of the thickness and lateral continuity of the rock unit; its highly impermeable, 
welded character and is location is in the unsaturated zone about 251 m above the water 
tables. The rock contains some minerals, called zeolites, that may prove to be effective 
chemical absorbers should a leak ever occur. However, proposals for siting a facility at Yucca 
Mountain are highly controversial. Much of the debate has centered on rates of groundwater 
flows, the likelihood of fracturing, the potential for volcanic activity, erosion rates, and the 
future natural resource potential of the sites. 
Crystalline rock cavities 
The preferred disposal option in Canada, Scandinavian countries and now also taken into 
serious consideration by the United States is to excavate a large vault in very deep-seated, 
stable plutonic rock bodies like the granitic rocks. These old crystalline rock units have been 
tectonically stable for very long periods. However, crystalline rocks have a tendency to 
fracture, especially when subjected to heat. The disposal of nuclear wastes in crystalline rocks 
is treated in details in the following chapters. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
High orizontal in situ stresses in crystalline bedrock is one of the most important parameters 
affecting the planning and understanding of the behavior of the rock mass around an 
underground nuclear waste repository. By opening the disposal tunnels in highly stressed 
rocks the stress state greatly redistributes and high secondary (boundary) stresses are likely to 
occur around and in the vicinity of excavated rooms in the deposition holes. The magnitudes 
of the secondary stresses might be close to the strength of the intact rock. Under these 
conditions, the occurrence of the rock failure (spalling, rock burst, etc.) might be possible. 
The objective of this section is to understand the problems that may be caused by excavating 
underground structures in high stress field. The exceeding of rock strength and intensive 
failure might exist around the tunnels based on high stress/strength relation. Besides, the 
methods to estimate and prevent failures around the excavations are studied. 
 
1.1 Rock mechanical analyses of in situ stress/strength ratio 
 
1.1.1 In situ stress/strength ratio of a rock mass  
The stress/strength ratio of a rock mass is one of the most essential rock mechanical 
parameters to determine when planning an underground excavation in a highly stressed 
medium. Both, in situ state of stress and the peak strength of rock are influenced by different 
geological factors, like discontinuities and rock types. How much effect the in situ stress has 
on the excavated room, depends on the dimension and the direction of a tunnel as well as on 
the geology and the strength of the rock. 
The rock noise, spalling and rock burst are typical phenomena that might occur in hard, 
brittle, crystalline rock in the vicinity of tunnels subjected to high in situ stress fields. These 
kinds of rocks are for example gneissic and granitic rocks, which fractures at less than 3-5% 
deformation or strain. These rock types have the capacity to store large amounts of strain 
energy before failing. This causes the failure process to act like an explosion with rock pieces 
flying from the excavation face. A very good indicator of the existence of high stresses or low 
rock strength, is core discing. It is a phenomenon where the core sample is broken into slices 
due to the high stresses oriented perpendicular to the axis of the borehole. 
1.1.2 Exceeding of rock strength in tunneling 
In an area of high in situ stresses, the tangential stresses around the excavation might be close 
or exceed the rock strength, and failure is likely to occur. The intensity of failure is dependent 
on the seismic energy stored in the rock mass. The stages when rock strength is exceeded are 
called microcracking, rock noise, spalling and rock bursting. The contributing factors, which 
control the amount of energy are local geology, strain energy, opening design and the physical 
properties for the rock mass. The redistribution of stress state in the vicinity of the excavated 
room, take place immediately after excavation, but the failure process might occur even after 
some hours or days. 
When the tangential stress exceeds the crack initiation strength of the rock microcracking 
begins. Cracking will occur perpendicularly to the surface of excavated tunnel and the 
direction of tangential stress. The zone of microcracking might vary from a few centimeters to 
several meters, depending on the magnitude of in situ state of stress, opening design, rock 
strength and excavation method. 
Rock noises are the first signs of the redistribution of stresses and the development of 
microcracking around an excavation. The sound of rock noise can be so low that it can be 
observed with seismic monitoring system. However, strong and very loud noise (like gun 
shots) appears in high stress regime. The level of sound is dependent on the energy stored in 
the rock. Rock noise is mainly occurring in hard and brittle rock. 
The spalling occurs, when the rock around an excavated room is broken by high tangential 
compressive stresses. In addition to exceeding rock strength, the thin layers of rock, the so-
called slabs, loosen off the tunnel surface and fell down. 
When the microcrack zones induced by the tangential compressive stress are large enough 
compared to the layer thickness, the layer becomes slender and will tend to buckle or burst. 
This will create a new surface and the process will be repeated. That phenomenon is called 
rock burst. The typical feature of rock burst is its sudden, violent nature and appearance. Rock 
burst might cause safety problems during construction or damage underground works. 
1.1.3 Controlling of in situ stresses in tunneling 
The methods to control in situ stresses during the planning and construction phases are 
presented in the following sections. Also, the support systems for failure prevention and some 
monitoring methods are introduced. 
• Planning phase 
In the planning phase, the depth and the orientation of excavated rooms are designed by 
taking into account the in situ stress and the geology of the surrounding rock mass. The 
utilization of the excavated room will set some requirements for the dimensions. The in situ 
conditions usually give the limitations for the design. 
The extent of exceeding rock strength might be difficult to estimate. Even the most 
sophisticated modeling programs can not predict the total stability of the rock around the 
tunnels excavated in high in situ stress regime. In complicated geological environment with 
different rock types and discontinuities, the proper parameters of the rock mass must be 
carefully selected for the design. 
When planning a tunnel in an area with in situ stresses, the rule of thumb in rock mechanics 
says that the tunnel should be oriented parallel to the direction of maximum principal stress. If 
possible, the tunnels also should be planned to be located perpendicular to the geological 
discontinuities like joints and faults. 
• Excavation planning and rock support 
In the design phase, the effect of the excavation works of the surrounding rock mass should be 
taken into account. Changing the amount or type of explosive, detonators might restrict the 
extent of the blast induced damage zone and the planning of the blasting holes. If the damage 
zone would tend to be enlarged, the loose rockmass around the tunnel should be supported. 
When considering the Norwegian experience, careful excavation works will minimize the risk 
of exceeding the rock strength. Especially, the drilling and charging of the contour holes 
should be made carefully. In Norway, some tunnels with asymmetric shape are excavated to 
avoid failure. 
The purpose of rock support planning is to generate an adequate safety against the tangential 
compressive stress and predict rock mass loosening. In the vicinity of high regime where there 
is a risk of rock failure, two main functions of a support system are used: 
- Strengthen a jointed rock mass by forming a rock arch to carry the induced stresses, 
minimize the loosening and the weakening of the rock mass. Support elements are acted in 
a stiff manner. 
- Retain the broken rock and hold the material in place by tying it back; so called the 
yielding method 
Service life, design of span, magnitude and direction of the in situ stress and geology in the 
vicinity of an opening, are important factors for the design of the support system. When 
magnitude of in situ stress and deformations will increase, the retaining or holding function of 
the reinforcement apparently becomes more critical and the reinforcing and strengthening 
function will diminishes. 
When planning the support system in burst-prone areas, the following aspects should be 
considered: 
- High initial stiffness of reinforcing elements for  strengthening the rock mass 
- Maintenance of the supporting function even under conditions of large deformations 
- Enhancement of ductility of support system 
- Maintenance of the integrity of full areal coverage 
- Strong connection between retaining and holding elements 
- Efficient integration of elements comprising from low to higher level support system  
- Support density should be at least 0.6 t/m
2 
= 60 kN/ m
2
 
In case of spalling and rock burst, the main support methods is rock bolt installed with steel 
platens. Rock bolts can be either mechanical or grouted bolts. The mechanical bolts are 
ungrouted and of end-anchored type with wedge or shell friction bolts. 
The most common used bolt type is cement or resin grouted rebar. Sometimes the rebars are 
replaced with cable bolt in case where more yielding of reinforcing action is needed. That is 
achieved with the Kiruma bolt or with the tube bolt. Kiruma bolt is a cement-grouted rebar, 
which is cross splitted at the inner end. The bolt is installed into the pregrouted drillhole and 
tensioned to about 50 kN. The tube bolt is first anchored with an expansion shell and later can 
be injected with cement.  
The galvanized mesh with or without shotcrete is also used in burst-prone ground. In some 
deep mines in very high-risk areas for rock burst, the cable or band lacing is used. The mesh 
and steel are installed using bolts and washers. 
• Destressing method 
In application of destressing methods, a yielding zone is created to decrease and redistribute 
the stresses in high stressed zone. This results in improved stability and reduces the incidence 
of rock bursts. Destressing using blasting is the most common method used in underground 
mines. Other destressing methods, like the drilling method, the cooling method, the hydraulic 
breaking and the parallel room method, are also used.  
A basic idea that underlies the blasting method is that a properly designed blast within a 
confined zone and transfers the stresses to the adjacent rock structure. Destress blasting can be 
made to prevent the occurrence of rock burst or to precondition a rock mass. In the 
preconditioning, drilling and blasting are carried out before excavation takes place. 
• Monitoring 
Seismic monitoring systems are used to record and analyze seismicity and predict the 
occurrence of rock bursts in underground mines. A major step forward of the monitoring 
method took place in the 1980’s, when multichannel microseismic equipment was developed. 
With this equipment, the location of seismic event is possible to define with surface or 
underground sensor after a few seconds.There are three types of seismic monitoring 
equipment to record and analyze seismicity: 
- Seismographs, which are used for earthquake detection, or to record the larger rock bursts 
- Macroseismic systems to investigate the seismic source parameters to rock burst. These 
are being used mainly by research organizations. 
- Microseismic systems used to detect both small and large seismic events. 
1.1.4 Methods of estimating stress/strength relations 
Stress/strength relation and failures can be estimated using analytical, empirical based or 
numerical methods. Some of the most well know and used methods and equations are 
introduced in this chapter. 
• Analytical methods 
One of the earliest solutions for the two-dimensional stress distribution around an opening in 
an elastic body was published in 1898 by Kirsch for the simplest cross-sectional shape, the 
circular hole. A full discussion one the derivation of the Kirsh equations, as they are now 
know, is given by Jaeger and Cook (1969). The final equations are presented in Egs 1-6. 
The stress component at point (r,θ) 
Radial: 
Tangential: 
Shear: 
 
Principal stresses in plane of paper at point (r,θ) 
Maximum: 
Minimum: 
Inclinations to the radial direction: 
• Empirical methods 
When predicticting the possibility of failure in underground excavations several empirical 
methods exist. The methods are based on the ratio of the uniaxial compressive strength and in 
situ stress, ratios of the tangential stress and uniaxial compressive strength, ratio of the 
maximum and minimum in situ stress and the point load index and compressive tangential 
stress. The Kirsh equations are used, when calculating the compressive tangential stresses 
around the excavation. 
Grimstad and Barton (1993) have studied the correlation of the ratio of the uniaxial 
compressive strength and in situ stress and ratio of the tangential stress and uniaxial 
compressive strength when phenomena occurred in Norway. 
Zhen-yu (1988) has studied the rock burst phenomena occurring in underground constructions 
in China. He also found a correlation between occurrence of rock burst and the ratio of the 
uniaxial compressive strength and in situ stress. 
Ortlepp and Wood (1977) study the influences of the major and minor principal stresses on 
the rockburst intensity. 
Russenes (1974) made a study of rock bursting problems in tunnels of steep hillsides in 
Norway. He divided the rock bursting activity into four classes from 0 to 3. Class 0 indicates 
no rock bursting and class 3 high or intense rock burst activity. He calculated the tangential 
stresses in the tunnel periphery using Kirsch’s equations and plotted them as a function of 
strength values obtained from diametrical point load tests. 
• Numerical methods 
Numerical methods are nowadays used in rock mechanical analyses when planning an 
excavation or in controlling the stability of underground structures. A number of suitable 2D 
and 3D programs exist today. The most common ones are FLAC, FLAC
3d
, UDEC, 3DEC. 
It has been recognized that there exist no good constitutive failure models to explain failure 
processes in rock masses. All existing constitutive equations tend to overestimate the 
maximum extent of area. By using standard failure criteria like Mohr-Coulomb in 
)2cos)341)(1()1)(1((
2
1
4
4
2
2
2
2
θσσ
r
a
r
a
k
r
a
k
vr
+−−+−+=
)2cos)31)(1()1)(1((
2
1
4
4
2
2
θσσ
θ
r
a
K
r
a
k
v
+−−++=
θστ
θ
2)321)(1((
2
1
4
4
2
2
sin
r
a
r
a
k
vr
−+−−=
22
1
4/)()(
2
1
θθθ
τσσσσσ
rrr
+−++=
22
2
4/)()(
2
1
θθθ
τσσσσσ
rrr
+−−+=
)(22tan
rr
g σστα
θθ
−=
combination with numerical models for stress analyses, it is, however, possible to estimate 
the maximum extent of failure. By changing iteratively the shape of an excavation it has been 
proven that the failure process is self-stabilizing. The existing computer codes are so far good 
tools, but they do not tell about the true mechanism of failure. 
Numerical models can be of considerable assistance to mining engineers in designing 
underground excavations, provided that they are used correctly. Anyway, the usefulness of 
numerical models is mostly limited by their applicability. 
In other words, for design purposes, the collective group of models available today is capable 
of successfully simulating almost any rock mass characteristic, from rock salt to hard, brittle 
rock. However, the simulated rock mass behavior may not correspond to reality and may not 
be applicable to a given rockmass conduction, i.e., The actual rockmass response may differ 
from that of the model. A better understanding of the rock mass behavior, particularly near to 
underground excavation, could be achieved through the observational modeling approach 
(OMA). 
• Observational Design Approach (ODA)  
Peck (1969) introduced the Observational Design Approach (ODA) with feedback from 
monitoring as a fundamental element of the design/construction process. The underlying 
logic is that a design is not complete until the design assumptions have been verified and the 
structure’s performance has been matched with performance predictions. 
During this design evaluation process which is based on in situ monitoring, the anticipated 
behavior is to be verified and the non-existence of potential, but unlikely, failure modes is to 
be demonstrated. For example, if a circular slip model determines the factor of safety of a 
slope, it must be confirmed that this or any other failure code such as wedge-type failure does 
not develop. 
The more complex the situation is the greater is the need to apply the Observational Design 
Approach since geological complexities, material variations, material non-linearity, 
progressive failure processes, large strain response (dilation), etc., cannot be properly 
predicted because of data limitations, scale effects, stress path dependencies, process 
coupling and ground/structure interaction amongst other factors. 
• Observational Modeling Approach (OMA) 
The reasoning that led to the introduction of the Observational Modeling Approach (OMA) is 
directly applicable to modeling for the design of underground excavations. Valid models 
must be selected, their applicability must be justified during the design phase, and then 
verified in an ongoing evaluation process. Therefore applications of numerical models to 
design can only be successful if their validity can be demonstrated. Consequently, the 
successful application of numerical models requires an Observational Modeling Approach 
(OMA) with four key elements: 
- Selection of the most appropriate model(s); based on experience or engineering judgment 
- Determination of material parameters and boundary conditions 
- Observations, visual (qualitative) or quantitative in nature, to verify the assumed material 
and structure or system response 
- Modification of model input, if necessary, or selection of more representative model(s). 
Hoek et al (1991) reviewed the various modeling approaches that are available to a design 
engineer and provides extremely useful guidance for non-specialists interested in selecting 
and using numerical models as tools for stress, displacement and failure analyses in rock 
surrounding underground excavations. The various modeling methods (Boundary Element 
Method, Finite Element Method or Finite Difference Method, Distinct Element Method, 
Hybrid Method) are carefully reviewed are both advantages and disadvantages are listed. 
Today, it is possible, given sufficient time and computing power, to model just about anything 
in both a deterministic or probabilistic manner (complex 3D geometry, elastic or plastic rock 
mass behavior, fracture propagation, etc.) as long as the necessary input parameters can be 
determined. For rockmasses, finding representative material parameters is, of course, often 
very difficult if not impossible. 
Even if all required input data (properties, geometry, and boundary conditions) can be 
provided, there are still two main problems to overcome 
- the constitutive models may not truly reflect the physical process observed in the field 
- the transition from continuum to discontinue my not be properly simulated (e.g., brittle 
rock failing in an unstable manner). 
Models not matching the actual physical processes in the field, anticipated or observed, 
should not be used for design unless the goal of the design is to force the structure to perform 
as simulated by the model. For example, linear elastic models may be fully justified design 
tools if the goal is to stabilize key blocks by rock reinforcements which is pretensioned to 
prevent non-elastic deformations. It is often convenient or desiderable to force the ground to 
behave like the linear elastic model, particularly for long-term installations where 
deformations and stresses must be limited. This approach is often applied for the design of 
civil engineering structures or nuclear waste disposal vaults. Consequently, if processes are to 
complex to understand, it is unlikely that sophisticated numerical models, too intricate to 
understand, are of any use. In these situations, simplistic models may have to be used to 
identify situations where really deviates from the idealized behavior. Hence, models can not 
be used effectively in isolation, they must be continuously assessed and validated by an 
observational modeling approach. The observational design approach was found to be 
beneficial for the design and construction of complex engineering structures. Similarly, the 
OMA can be of considerable assistance to mining engineers in design complex underground 
excavations. The examples discussed in this paper were chosen to illustrate four rather 
specific ingredients of OMA: 
- Feedback from field observations must be used to verify the boundary conditions of a 
model 
- Stress change observations may provide useful insight for model validation and 
calibration  
- Stress changes and their effect on the rockmass and support response must be considered 
for mining applications 
- The transition from continuum to discontinuum behavior, particularly near underground 
excavations can not yet be simulated accurately. Hence, the failure process must be 
inferred and the effects simulated. 
 
1.2 Stress Heterogeneity and geological structures 
 
Considerable advances have been made in the measurement of in situ stress over the past 25 
years; however, the interpretation of these measurements with respect to geological structures 
has received significant attention only over the past 10 years. The major limitation in the 
interpretation of the stress measurements is the paucity of measurements at any one site. An 
exception is the Underground Research Laboratory (URL), where about 350 triaxial stress 
measurements have been made in a volume of about 100m*100m*500m deep. This is more 
than twice the number of triaxial stress measurements for all other sites in the Canadian 
Shield combined. In addition to the triaxial stress measurements at the URL, other techniques 
and observations have also been used to help determine the stress state. The URL is located 
within the Lac du Bonnet granite bathlith, which is considered to be representative of many 
granitic intrusions of the Canadian Shield. 
Geological structures must be defined at the scale of the investigation. At the URL, the 
predominant structures affecting the in situ stress interpretation methods vary from the near-
grain-size scale of microcracks, through single discrete fractures and thrust faults, al the way 
up to a predominantly intact rock mass. The following sections will summarize the observed 
influence of these structures on measured stresses at the URL.  
1.2.1 Microcracks 
Brittle rocks are prone to microcracking. An extensive study on the 240 level has shown that 
stress-induced microcracks, barely visible to the eye, are found in overcore samples. The 
trend of the visible microcracks was found to align with the strike of the subvertical natural 
joints. In order to determine the secants Young’s modulus and Poisson’s ratio parallel and 
perpendicular to the plane of these microcracks, four overcored samples from a borehole-
drilled perpendicular to this plane were tested using a standard triaxial configuration. These 
tests indicated that the secant Young’s modulus in the direction perpendicular to the plane 
was approximately 30 Gpa, which were about 50% of the secant modulus in the direction 
parallel to the plane. Poisson’s ratios parallel and perpendicular to the plane were 0.25 and 
0.15 respectively. This information was used to develop a transverse isotropic model to 
interpret overcore measurements. 
The overcoring results on the 240 level were initially interpreted assuming a continuous 
homogeneous isotropic linear elastic rock. The reanalysis of the 240 level overcore results 
using transverse isotropy was successful because, although the rock contained microcracks, 
the behavior of the entire core during overcoring remained essentially elastic. At depth below 
the 240 level, this was not the case and attempts to fit an anisotropic elastic model were not 
successful. In these situations alternate stress measurements techniques were employed to 
develop the in situ stress model. 
1.2.2 Single discrete fracture 
A single discrete fracture, intersected on the 240 level, was used to investigate the 
perturbation caused to the in situ stresses near the fracture. The facture is actually a series of 
en echelon fractures comprising a fracture zone about 0.4 m thick. Both overcore testing and 
hydraulic testing were contacted to investigate this fracture. 
The difference between the stress magnitude from the overcore testing and the hydraulic 
opening pressure may be a function of the scale of the measurements, the overcore test is a 
point of measurement, whereas the hydraulic injection test influences a much larger area.  
 
1.2.3 Thrust fault 
Excavations of the URL shaft intersected two major thrust faults that dip about 25 to 30º 
southeast. These faults are referred as to Fracture Zone 3 and Fracture Zone 2 and their splays 
as Fracture zones 2.5 and 1.9. The fracture zones divide the rock mass into distintic stress 
domains: one from the surface to Fracture Zone 2, where the maximum horizontal stress is 
oriented parallel to the major subvertical joint set; and the second extending below Fracture 
Zone 2, where the maximum horizontal stress has rotated about 90º and is aligned with the dip 
direction of Fracture Zone 2. The maximum principal stress direction in the second domain is 
coincident with the direction of the major compression noted by Herget for this area of the 
Canadian Shield. 
The rotation of the maximum horizontal stress across the domain boundary can be examined 
using a simple mechanical model. Fracture Zone 2 tends to follow the weaker xenolitic layers 
within the Lac du Bonnet batholitic. Considerable reverse slip has occurred across Fracture 
Zone 2 and this movement may have led to stress relief in the deep direction of the overlying 
rock. 
A numerical model was used to illustrate the mechanism of stress rotation across the fracture 
zone. At the URL, the horizontal stress at depth is in the dip direction of Fracture Zone 2 and 
the ratio between the maximum and the minimum horizontal stress is about 1.2. This basic 
information was input into a UDEC plane strain model. The model was compressed in the 
horizontal direction and the fracture Zones 2, 2.5 and 3 allowed slipping. As in the case at the 
URL, the maximum horizontal stress direction rotates from the dip direction below the 
fracture zone to the strike direction above the fracture zone. This type of stress release and 
associated stress rotation is commonly observed in modeling with constant-displacement 
boundary conditions where the block of rock above the fault has lost its original load because 
of displacements above the fault. Two other points are also worth noting from the results of 
this simple model. First, the magnitudes of the maximum stress above Fracture Zone 2 are 
considerable less than the stress magnitudes below Fracture Zone 2. In the UDEC model no 
allowance is made for subvertical fracturing in the proximity of Fracture Zones 2.5 and 3, 
which would tend to reduce the horizontal stresses even more and bring the model stresses 
closer to those measured. Second, the stress magnitudes below the Fracture Zone 2 are fairly 
constant with depth (the model has a depth of 1.5 km). Although stress magnitudes at the 
URL have only been measured to a depth of 512 m, measurements and construction 
observations suggest that the maximum horizontal stress from Fracture Zone 2 to 512 m is 
fairly constant at about 55 Mpa. 
The vertical stress magnitudes sampled from around the shaft at the URL were compiled from 
triaxial overcore results, from idraulic fracturing conducted in horizontal boreholes and from 
subhorizontal hydraulic fractures in near-vertical boreholes. 
1.2.4 URL Rock mass 
Within the Canadian Shield the major and intermediate principal stresses tend to be aligned in 
the horizontal plane. Thus the maximum horizontal stress is commonly equivalent to s
1 
and 
the vertical stress is commonly equivalent to σ. Herget and Arjan have compiled in situ 
stresses in the Canadian Shield. Their data set of 133 stress tensors were obtained from the 
overcore results at mining location primarily in Ontario and Quebec. Most of the sites are 
located in the Superior and Southern Tectonic Provinces of the Canadian Shield, which 
consist of Archean and Proterozoic rocks. The youngest orogenic deformations occurred 
during the Grenville Orogeny. 
Many authors have documented the influences of discontinuities and deformation modulus on 
stress magnitudes. At the URL the jointed granite has a deformation modulus of about 30 to 
40 Gpa, whereas the massive granite below the fracture Zone 2.5 has a deformation modulus 
of about 60 Gpa. To the authors’ knowledge, this high a deformation modulus is seldom 
reported at such shallow depths. The significant increase of the deformation modulus below a 
depth of about 200-m, coupled with the close proximity to Fracture Zone 2, is a probable 
cause for the very high stress magnitudes found at the URL at such a shallow depths. The 
changes of deformation modulus of a jointed granite with depth is mainly controlled by the 
stiffness and spacing of the joints. Because the gray granite below the Fracture Zone 2 is 
essentially unjointed, the deformation modulus of about 60 Gpa represents an upper-bound 
modulus. Thus, the high stress magnitudes at the URL are more typical of magnitudes that 
would be found in a jointed rock mass at greater depths in the Canadian Shield. Therefore, it 
seems possible that at greater depths at the URL the horizontal stress magnitudes may not 
increase significantly over those already measured and may actually start to approach the 
average condictions found elsewhere in the Canadian Shield. The in situ stress measurements 
at the Underground Research Laboratory serve to show that even in a large relatively 
homogeneous pluton, such as the Lac du Bonnet batholith, in situ stress magnitudes and 
orientations are highly variable. This is particularly true near geological structures where 
recent findings show that stress magnitudes can increase and/or decrease significantly, and 
stress orientation can rotate as much as 90º when these geological structures are crossed. In all 
cases considered, knowledge of geological structures is required to correctly interpret the 
stress measurements. In some situations, such as with overcoring, the geological structures 
(i.e., microcracks) also dictate the type of analytical solution required interpreting the 
measured strains. The results also show that mechanistic elastics models developed from 
geological information can generally explain the stress magnitudes at the Underground 
Research Laboratory. 
 1.3 Rockmass Relaxation 
 
The stress relaxation can greatly affect the performance of the rockmass near large 
excavations in terms of critical span or demand of support; rockmass relaxation, in fact, may 
often dominate stability of an excavation. 
The practical implications of the analyses of this section are that tunnel advance should be 
sequenced to prevent or minimize stress relaxation. 
1.3.1 Stress relaxation 
In most engineering designs, particularly when limit equilibrium methods are applied, the 
support capacity is compared to the demand placed on this support in order to establish a 
measure of safety, i.e., a factor of safety. This section deals with the stability of excavations, 
as it is the failing rock that places a demand on the support.  
• Rockmass relation: is used here to describe conduction where the stresses in the tangential 
direction to the excavation wall (the major and/or intermediate principal stress) are reduced 
in the rockmass, often to values far below those predict by linear elastic models, because 
the rockmass has been allowed to deform at some distance from the excavation. Rockmass 
relaxation therefore refers mostly to stress reductions parallel to the excavation wall and 
not to stress reductions in the radial direction or a reduction in confinement. In practice, 
such conditions are encountered, for example, when a large underground excavation is 
constructed near a tunnel. In the principal stress space, relaxation if therefore reflected in a 
stress path that points downward or toward the origin. Instability occurs when the 
rockmass has reached a critical relaxation threshold at which gravity-driven failure modes 
or slip along weakness planes are encountered. Full relaxation-causing zero or even tensile 
stress condition is not required to cause failure. 
When single openings are advanced, stress arching normally occurs in the direction of the 
shortest span and if the arch is stable, the excavation can remain unsupported. However, if the 
abutments of the arch are allowed to move, the stresses relax and instability may occur. At 
tunnel intersections, due to the geometry of the excavation, later deformations are permitted to 
occur in the direction of preferred arch formation and this leads to rockmass relaxation rather 
than arching in the back of intersections. It is for this reason that intersections are less stable 
than single drifts of similar size. 
1.3.2 Modes of failure 
The rockmass behavior or the failure mode of underground excavations depends upon the 
magnitude of the in situ stress relative to the rockmass strength and the characteristics of the 
rockmass, which is strongly influenced by the degree of jointing and joint persistence. Six 
distinctly different behavior modes, ranging from the elastic behavior of essentially intact 
rock in a low stress environment to plastic behavior of a highly jointed rockmass under high 
stresses can be identified. 
• Failure in low to moderately stressed ground 
In low to moderately stressed rock, underground excavations are either stable or the failure 
modes are largely controlled by the rockmass structures consisting of joints, laminations, 
bedding and other weakness planes. Wedge-types failures, peeling of laminations, or 
unraveling due to the gradual removal of keyblocks are most dominant failure modes in this 
environment. These modes of failure are very sensitive to stress changes and thus relaxation 
in the back of an excavation. 
• Failure in highly stressed ground 
In highly stressed ground, the rockmass strength is exceeded near the excavation wall and the 
rock deforms inelastically. In ductile rocks, such as clayshales or friable sandstones, this 
failure process can be described as yielding and can be simulated reasonable well by the 
application of conventional failure criteria (e.g., Mohr-Coulomb or Heak and Brown). 
However, in hard, brittle rock, the rockmass failure process involves the creation of new 
fractures and their propagation, leading eventually to the disintegration of the rockmass with a 
gradual transition from continuum to discontinuum behavior. This process of stress-induced 
fracturing near excavations is associated with substantial rockmass dilation resulting from two 
sources: dilation due shear at fracture boundaries or joints, and more importantly, dilation due 
to geometric incompatibilities when blocks of rock created by the fractures are forced into the 
excavation. This dilation process, called rockmass bulking, produces large volume increases. 
However, after the rockmass has been fractured, the stability of an excavation is again very 
sensitive to stress relaxation because even minor extension straining will allow the rockmass 
to unravel. Hence, the threshold when support is required (called the no-support limit) or the 
amount of support required (the support demand) depends on the amount of stress relaxation. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
  
 
Rockbursts are a hazard in underground operations in numerous countries. In this context 
rockbursts are defined as the damage caused as a result of a seismic event, or which is directly 
associated with a seismic event. Whatever the mechanisms, the manifestation in the damage 
location is the violent ejection of a volume of rock. In tunnels it has been observed that 
commonly approximately a meter thickness of rock may be ejected from the surface. Ortlepp 
has considered the ground velocities associated with rockburst damage and interpreted that 
velocities up to 50 m/s may occur. For design purpose, however, it was suggested that a 
velocity in the range of 5 to 10 m/s would be appropriate. The energy released in the event, 
which is dependent on the mass of rock ejected and the velocity of ejection, is the important 
consideration. Ortlepp has given an indication of the typical magnitude of energy that may be 
involved in a significant rockburst event, and showed that this energy is approximately 20 
times the energy absorbing capability of rockbolts commonly used in mines. To achieve safer 
conditions in a tunnel subjected to rockbursts, the support installed in the tunnel must be 
capable of absorbing the energy generated during this event. To achieve that it is essential for 
support to be capable of yielding and, in so doing, to absorb energy. Support systems for 
severe rockburst conditions must therefore be designed on an energy basis rather than on a 
conventional factor of safety approach. The behavior of the rockmass around the excavated 
rooms depends mostly on the stress/strength ratio at depths. When designing underground 
openings, the orientation of the tunnel play an important role in high stress regime with large 
stress differences and deviatoric stresses. If it is not possible to locate the tunnels with 
favorable orientation they can be stabilized by the use of rockbolts and meshes. The type of 
support is dependent on the strength and structure of the rock mass. The four main strength 
states of the rock mass around the presented (see 1.1.2) 
• Elastic state: Whiting the elastic limit, no support is required 
• Stable crack growth. The dilation begins and invisible microcracking occurs 
Initiation of microcraks is invisible and the rock mass is stable and an increase in load is 
required to cause further cracking. In that stage, the need for support is dependent only on the 
structure of the rockmass, e.g. single joints and foliation 
• Unstable crack growth. The long term stability of the rock is reached and spalling occurs  
with time The unstable crack growth will lose the rock around the opening and spalling of 
rock is just a matter of time. Rebar bolts with steel plates and mesh or cables are 
recommended. The density of bolting is dependent on the structure of the rock and the 
intensity of rock failure 
• Immediate shear failure. Spalling or violent rockburst occurs 
When phenomena such as rockburst and loud rock noises occur, immediate shear failure is 
evident. Often supports are possible to install only after the deformation has stopped and the 
equilibrium is obtained. Instant support as cable or friction bolts and mesh installed with 
plates is recommended. Also stripes can be used.  
Basic rules concerning the supporting of the deposition rooms should be that bolts and meshes 
are installed at the roof of the deposition tunnel if unstable crack growth or immediate shear 
failure exists. The need for spot bolting at the wall of the tunnels is dependent on the structure 
of the rockmass. Concerning the deposition hole, no support is required. The failed pieces of 
rock from the hole walls drop to the bottom and should be removed. If the deposition hole is 
largely broken, it should be abandoned. 
2.1 Rockbolt anchors for high convergence or rock burst condition 
 
In the deeper hard rock mines of Canada, the rockmass and stress conditions can lead to 
extensive rockfracturing and dilatation resulting in high ground convergence around mine 
opening and drifts. In some cases, the convergence occurs violently and rapidly in the form of 
rockbursts. As these mines proceed to greater depths, the ground control problems will 
become worse and new rock support systems must be developed and used. 
Conventional rockbolts such as resin-grouted rebars and mechanical, end-anchored rockbolts 
have proved highly effective under most ground conditions, even for drifts in highly fractured 
and stresses ground where moderate ground convergence occurs. However, when these 
rockbolts are used in tunnels or mine drifts that experience large ground convergence or 
rockbursts, their limited ability to yield often results in their failure. Within economic and 
practical limits, ground support can not be used to prevent movement and rock fracturing. 
Under these conditions, the primary support design philosophy is not to enhance the stiffness 
and strength of the rockbolts to resist or prevent the ground movement. Instead, the rockbolts 
must be designed to yield or slide with the ground movements while simultaneously 
providing a substantial resistive force, thereby helping to control rock displacements and 
minimizing damage to the excavation. 
The need for yielding tendons or rockbolts for use in highly stressed and rockburst-prone 
drifts has long been recognized in the deep gold mines of South Africa (Ortlepp, 1983). This 
has lead to the development of recommended performance requirements for yielding rock 
tendons and the development and testing of yielding rockbolts. A yielding rockbolt based on a 
fully grouted deformed bar with a sliding nut near the plate has been developed for use in 
burst-prone ground. This sliding support nut concept was also adapted for squeezing ground 
and openings subject to high convergence. Tannat and Kaiser (1995) discussed the use of 
Swellex bolts to provide frictional anchorage of wire rope or cables. If the overlap between 
the rope and the Swellex bolt is kept below a critical length (about 1.5 to 2 m) then when the 
rope is loaded it can slide past the Swellex bolt without breaking. 
The fracturing and dilatation of the rockmass during tunnel convergence and the ejection of 
rock during a rockburst generally cause axial loading of rockbolts. Tests in which the rockbolt 
is simply pulled out of the ground are used to represent these types of loading conditions. 
2.1.1 Pull test 
In situ pull out tests were conducted at INCO Limited Creighton mine over a two year period to 
measure the load-displacement characteristics of grouted bolts, some of which were designed to 
yield by anchor slip. These tests were aimed at determining the most appropriate bolt for use in 
highly converging and burst-prone ground. Five types of bolts were tested and the peak load 
capacity and the displacement at peak were tabulated. 
• Bolt types tested 
The following bolt types were tested: 
- Conventional resin-grouted rebars to provide a baseline for comparison with the other 
tests 
- Rebars installed in boreholes containing a fast setting resin at the toe of hole with the 
remainder of the bolt grouted in a very slow setting cement 
- Cement-grouted smooth-walled tubular bolts 
- Cement-grouted cone bolts 
- Resin-grouted cone bolts 
 
 
All bolts were 1.8 m long and they were installed in 32 mm diameter, 1.8 m long boreholes 
that were drilled into granitic rock. The rebars were made froem 20M or #7 reinforcing bars 
that had threads machined onto one end. The rebars were made from steel with a yield 
strength of 400 MPa and an ultimate strength of 550 MPa. Cutting off the anchor portion of 
tubular rockbolts made the smooth-walled bolts. The resulting bolt consists of a high strength, 
low alloy, tubular shaft was that was roll-threaded on one end. These bolts were made from 
steel with a minimum tensile strength of 758 MPa resulting in a bolt with a minimum-
breaking load of 133 kN. The cone bolt, originated from South Africa, consists of a 16 mm 
diameter steel bar with a wax coated smooth shank and a flattened conical flaring forged to 
the “anchor” end of the bolt. The wax coating is designed to minimize the friction and 
cohesion resistance along the bolt shank while the cone creates a pull-out resistance as it 
shears through the grout column. The cone bolts were 1.8 m long and had a minimum yield 
load of 90 to 100 kN and a minimum ultimate load of 120 to 135 kN. The yielding 
mechanism of the cone bolt is based on the shear strength of the grout and the geometry of the 
cone and as such differs from a grouted smooth bar, which relies on friction. Cone bolts were 
deigned to be grouted in cement. However, as there is a need for an immediate holding action 
in mining situations, cone bolts were also installed in quick setting, resin-grouted holes for 
comparative purposes. 
2.1.2 Discussion 
• Bolts in highly converging ground: in highly stressed rock, fracturing and inward ground 
motion can occur. In these situations the displacement capacity of rockbolts is important. The 
displacement and load capacity of fully grouted bolts can be affected by straining that is 
localized around joints or rock fractures that separate and by shear displacements at joints or 
fractures. Bolts that are designed to yield by anchor slip or shear can result in displacements 
greater than 10 times larger than those possible with conventional grouted bolts. Cone bolts 
could accommodate roughly 10 times more displacement than rebars before failing. The peak 
load in the cone bolts before failure was about 160 kN. This is slightly less than the 170 kN 
peak load in the rebars but is understandable given the smaller shank diameter on the cone bolts. 
Cone bolts may work well in areas experiencing significant ground convergence if their pull-out 
performance could made more reliable. There are important quality control issues related to the 
use of two-part resin grouts with cone bolts. The small conical section of the bolt during 
installation must perform the mixing. The cone bolt does not have the advantage of the ribbed 
surface texture and the larger diameter of the rebar to aid in mixing the resin. Very little mixing 
occurs if the cone bolt is pushed into the borehole too quickly or without adequate rotation. In 
addition, the small shank on the cone bolt does not displace the resin as well as the rebar. The 
latter problem may be overcome by manufacturing cone bolts with a larger shank diameter. The 
cone bolt was originally designed to yield by shearing of the conical section through the cement 
annulus around the bolt at loads less than the yield load (90 to 100 kN) of steel shank. A 
cemented-grouted smooth bolt may provide a yielding anchorage through frictional slip. 
However, to optimize the pull-out response of a grouted smooth bolt, the length of bolt the in 
contact with the grout must be selected to allow the bolt to slide from the grout column without 
breaking, while also ensuring that sufficient frictional resistance is mobilized to generate pull-
out capacities that are near the yield load of the bolt. The pull-out force and hence, the optimal 
contact length between a bolt and the grout will depend on the grout properties, borehole 
conditions (stiffness and stress), and the shape and surface properties of the bolt. Cement grout 
properties such as compressive and tensile strengths are sensitive to water: cement ratio and 
curing conditions. Therefore, if cement-grouted smooth bars are used as yielding rockbolts, then 
very careful quality control of the grout properties is needed to ensure consistent pull-out 
behavior. The sensitivity of the pull-out behavior of the smooth bar to the installation conditions 
may prohibit the use of grouted smooth bolts in practice. The use of a two-stage grout for 
installing rebars temporarily creates a debonded length of bolt between the collar and the resin-
grouted section of the bolt. Debonding a length of bolt can increase the displacement capacity of 
the bolt. Unfortunately, the elastic elongation of the steel up to the yield load can only 
contribute about 2 mm of elongation per meter of free bolt length. Therefore, increasing the free 
length of the bolt to increase the elastic bolt elongation will only marginally improve the bolt’s 
ability to handle rock convergence. During the pull-out tests on the rebars, most of the measured