ARTIGOS ENGENHARIA REVISTA PINI

Prévia do material em texto

Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
1 
1. INTRODUCTION 
The topographic conditions in Norway are 
favorable for the development of hydropower 
and more than 99% of annual production of 
electrical power in Norway is generated from 
hydro. Underground powerhouses and unlined 
tunnels have been constructed starting from the 
end of World War I in 1919. High-pressure 
unlined tunnels and shafts have been the 
preferred best solution for cost and time 
effective construction of hydropower. Thus the 
expensive lining with steel penstock and 
concrete embedment is avoided. From the 
valuable experience gained through the design, 
construction and operation of tunnels in the past 
100 years in Norway, unlined pressure tunnels 
have been developed reaching 1046m 
hydrostatic head for Nye-Tyin Hydropower 
Project being a world record for its high 
hydrostatic head as exceeds 1,000 m in 
unsupported unlined pressure tunnel. Figure 1 
shows the development of high head unlined 
tunnels and shafts in Norway. 
The concept of constructing unlined pressure 
tunnel and shaft is based on the principle that 
the rock itself shall resist the water pressure 
during water transfer. It is essential that the 
minimum principal rock stress in the rock mass 
should be higher than the water pressure with 
regard to safety against hydraulic fracturing and 
uplift. A safe construction is highly dependent 
upon the design based on adequate vertical rock 
cover and side-cover near side valleys with 
regard to the rock mass quality. 
At the very beginning when unlined high-
pressure shafts and tunnels were introduced, an 
evaluation based on a simple equilibrium state 
of stress was used. The principle for this was 
that the weight of the rock cover above the 
tunnel should exceed the water pressure induced 
inside throughout the tunnel or shaft in-order to 
avoid hydraulic jacking and uplift. 
The Norwegian rule of thumb design 
approach method has been widely applied for 
common case in which a tunnel is near to the 
side of valley. It considers both the overburden 
and side-cover to avoid the risk of hydraulic 
fracturing. 
Snowy mountain design creation was also 
introduced in Australia as a consequence of that 
the side cover was found less effective 
compared to the vertical rock cover to secure 
that the tunnel or shaft has the required 
confinement. 
Parallel to the revision of the rule of thumb, a 
new better simulation model was presented with 
the established standard design chart tools based 
on a finite element model (FEM) and the 
concept was that no-where along the unlined 
pressure tunnel and shaft should the internal 
water pressure exceed the minor principal stress 
in the surrounding rock mass. 
Analysis using numerical models is one of the 
modern design approaches, which in use widely 
at present to carry out qualitative, stability and 
Pressure design in unlined tunnels and shafts 
Dawit Tadesse B. 
NTNU, Trondheim, Norway 
Eivind Grøv 
SINTEF/NTNU, Trondheim, Norway 
 
 ABSTRACT: Unlined tunnels and underground powerhouses have been constructed in Norway 
starting from the end of World War I in 1919. From the valuable experience gained through the 
design, construction and operation of tunnels in the past 100 years in Norway, unlined pressure 
tunnels have been developed reaching 1046 m hydrostatic head for Nye-Tyin hydropower project 
being a world record at present. 
In this paper, the possibility to develop high pressure unlined tunnel and shaft with even higher 
static heads has been looked at being exemplified with the Nye-Tyin hydroelectric project. In this 
regard, different design principles and approaches have been applied being based on empirical, 
deterministic, numerical analyses as well as using other sources of design principles to ensure safety 
against hydraulic fracturing and uplift. 
 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
2 
support analysis in addition to its vital use in the 
verification of the above deterministic design 
approaches. This paper evaluates the possibility 
to develop ultrahigh head in unlined tunnels in 
general and particularly for the exemplified 
project for higher hydrostatic head based on the 
outcome of the empirical, deterministic and 
numerical analysis and recommendations have 
been proposed for further conclusions on this 
thesis. 
The Nye-Tyin Hydropower project is located 
in Årdal, Norway. It has a hydrostatic head of 
1047 m and operates at an installed capacity 
of 380 MW and discharges 2 times 20 m3/s with 
an average annual production of 1398 GWh. 
 
Figure 1. Development of Norwegian unlined high-
pressure tunnels and shafts 
2. DESIGN APPROACHES & PRINCIPLES 
2.1 The “First Design Criteria” 
Summarizing the experience from early unlined 
pressure shafts, Vogt (1922) states that the first 
and foremost requirement for a pressure tunnels 
was that leakages have to be avoided and it was 
understood that an unlined tunnel is safe when 
the weight of the rock overburden is greater 
than the water pressure. According to Vogt 
(1922), the main risk of unlined pressure tunnels 
and shafts is bad rock masses with weathered 
zone, joints etc. Hence, the best solution of 
avoiding leakage is to place the tunnel as deep 
into the rock mass as possible. In Norway, 
before the rule of thumb method was 
introduced, the general design rule for the 
required overburden thickness was expressed as 
follows by the Equation 1: 
 
h > C . H, (1) 
 
For the inclination of the unlined shaft/tunnel 
varies between 310 and 470, with 450 at the most 
common. 
For every point of the tunnel where h is 
vertical depth of the point studied (in m), H is 
static water head (in m) at the point of studied 
and C is a constant, which was 0.6 for valley 
side inclinations up to 350 and increased to 1.0 
for valley side inclination of 600. The results of 
this method of analysis are presented in section 
3. 
2.2 The Norwegian Rule of Thumb 
 
The Norwegian rule of thumb method 
developed some forty years ago by prof. 
Selmer-Olsen (1970), has been widely applied 
in common case for the tunnels or shafts sited in 
valley sides. It considers both vertical cover 
and the steepness of the slope of the adjacent 
valley side and assumes that, the minimum in-
situ principal stress should exceed the water 
pressure at any point to avoid the risk of 
hydraulic fracturing. The method accounts for 
gravitational rock stresses only, but in many 
cases considerable tectonic and residual stresses 
also exist. In Norway the design criteria for high 
pressure water tunnels and shafts have been 
revised and improved continuously as more 
experience has been gained from completed 
projects and hence this method of criterion for 
confinement is still in use in prefeasibility 
studies. The rule was expressed as shown in 
Figure 2 and the Equation 2: 
L > γw.H
γ r.cosα
.F , (2) 
 
Where, γw is density of water, γr is density of 
rock-mass, α is the inclination of the shaft h is 
vertical depth of the rock cover to the study 
Figure 2. Norwegian rule of thumb criterion for 
confinement 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
3 
point, H is static water head at the point studied 
and F is factor of safety. 
Following some failures of unlined tunnels 
near the valley side, a new rule of thumb was 
introduced by Bergh and Dannevig (1987), 
which directly take in to account the inclination 
of the valley side. 
 
L > γw.H
γ r.cosβ
.F , (3) 
Where L is shortest distance between the 
surface and the point studied (m), β is average 
inclination of valleyside and H, F, γw, γr are as 
earlier (shown in figure 2) 
 
Limit equilibrium between the rock weight 
and water pressure defined using the following 
simple equation for a potential displacement 
towards a free surface as defined below in 
Figure 3 indicates necessary rock cover: 
 
L
H ≥
1
γ r.cosβ
 , (4) 
Where L is shortest distance between the 
surface and the point studied (m), H is static 
water head at the point studied, β is average 
inclination of valley side and γr is density of 
rock-mass. 
Bergh-Christensen and Dannevig (1971) 
described the possibility to comprehend the 
agreement with the imperial data by plotting 
L/H-ratios for unlined pressure shaft against 
inclination of valley side and the limit curve as 
presented in Figure 4. The probability of 
leakage problem will arise when the project falls 
below the limit. Filled points indicate tunnels or 
shafts where leakage has been observed. 
In Nye Tyin HEP the highest water pressure 
is 10.47 MPa. For the analysis of hydraulic 
fracturing, three study points has been chosen 
along the tunnel alignment. These are located at 
positions bearing potential risk where hydraulic 
fracturing will occur such as where there is 
small rock cover, weakness or fault zones and 
the highest water pressure available. The chosen 
studied points for the exemplified project for 
Nye-Tyin HEP is presented below in Figure 5. 
2.3 The Snowy Mountain criterion 
 
Unlined tunnels and shafts were located for 
many years by ensuring that the static head or 
water pressure inside the tunnel was at least 
equal to the weight of the rock mass cover 
vertically from the pressure waterway adding an 
adequate factor of safety. It was simplified to 
provide rock cover at least half of the head 
considering the density of rock is normally at 
least twice that of water (Benson, 1887). This 
criterion was found not sufficient while it comes 
to waterways in valley side and it was 
recognized during the development of the 
Figure 3. Limit equilibrium condition. 
Study point at Power 
station 11 + 750 
Study point 
9 + 782 
Study point 
 8 + 076 
Figure 5. Location of study points chosen along the 
tunnel/shaft alignment 
Figure 4. Unlined pressure shaft/tunnel in valley side 
with various inclinations, β 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
4 
Snowy Mountains project in Australia. The side 
cover is found less effective compared to the 
vertical rock cover to secure that the tunnel or 
shaft has the required confinement Brekke 
(1987). The Snowy mountain criterion for the 
confinement is defined by the following 
equations: 
 
h ≥ γw.H
γ r
, (5) 
Lh = 2h, (6) 
 
Where, h is vertical rock cover (m), Lh is 
horizontal rock cover (m), γw is unit weight of 
water, γr is unit weight of the rock mass and H is 
static water head at the point studied (m). 
Figure 6. Snowy Mountains Criterion for confinement 
2.4 Design Charts based on FEM 
 
Hence, the rule of thumb and snowy mountain 
creations represent gross oversimplification, to 
compensate for this; a better simulation model 
was produced. It was a set of two-dimensional 
standard design charts based on the use of a 
numerical finite element model (FEM). It 
represents a useful tool at the feasibility stage of 
a project and makes it possible to find a 
preliminary location of the pressure tunnel or 
shaft, a location that in many cases turns out to 
be the final one. 
 The basic principle of the finite element 
method for this purpose is to find the location, 
which for all parts of the shaft fulfills the 
Equation 7 Nilsen (1993): 
 
σ3 > H. γw, (7) 
 
Where σ3 is minor principal stress, γw is unit 
weight of water mass and H is static water head 
at the point studied (m). 
Design charts of the same type presented by 
Broch (1985) were produced and the diagrams 
cover valley side inclinations between 140 and 
750, and a variety of rock stress configurations 
and rock mass properties. However, in case very 
high water head or complex geology, FEM-
analysis more exactly adjusted to the actual 
topography and the rock mass conditions are 
suggested and often applied (Broch, 1985). The 
required rock cover is estimated by transferring 
the scheme to topographical models adapted to 
local actual conditions. However, special 
attention has to be paid any significant 
geological factors that may be presented during 
in determining the final siting of scheme. 
When it comes to the exemplified project Nye 
Tyin HEP, the design charts may only be 
suitable for the representative study point 
selected at the location of the power station, 
which directly considers the valley side 
inclination. In his thesis, Belayneh (2013) 
suggested that using this analysis method will 
lead to errors as the in-situ actual topography 
with the inclination of the valley side 170 
befitted very simplified and idealize with regard 
to the topography condition used in the model. 
It is also known that the design chart obtained 
with the finite element method is based on the 
assumption that the rock mass type like 
bedding, foliation, or jointing on in-situ stress 
distribution and magnitude is usually not taken 
in to account. A factor of safety 1.3 is used and 
the result of this analysis is presented in detail in 
the following section 3. 
Figure 7. Standard design chart based on FEM for 
static head of 1047 m study point at power station	
  
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
5 
2.5 Numerical Analysis 
 
A comprehensive 2-dimensional finite element 
(Phase2) calculation has been performed and the 
aim was to analyses the minimum principal rock 
mass stress situation in the vicinity of the 
pressure tunnel and to compare it with the water 
pressure of the exemplified project of the Nye 
Tyin Hydropower project. It is also performed 
for verification and comparison of the analysis 
done by the analytical, theoretical and empirical 
design principles and approaches used in the 
previous sections. For this purpose, three 
representative study points have been chosen 
along the tunnel alignment as shown in Figure 
5. These are located where it is assumed to be 
the most likely places that hydraulic fracturing 
will occur such as small rock cover, weakness 
and fault zones and highest water pressure to be 
intended in side the tunnel or shaft. The input 
parameters for the evaluation of hydraulic 
fracturing along the tunnel are found from 
laboratory test results and in-situ measured 
stresses of the exemplified project. The 
generalized Hoek-Brown failure criterion 
(Hoek, 2012) has been used to estimate the 
required input data. It has been necessary to 
introduce a horizontal in-situ stress field, which 
the horizontal stress consists of a tectonic 
component in addition to the gravity stress 
induced by gravity alone. The input data and 
parameters used for the analysis are presented in 
Table 1 and Table 2 respectively. 
	
  
Table 1. Input parameters used for the model 
simulation 
Description Sym. Value 
Measured in-situ 
Magnitude of rock stresses 
 
 
Orientation of major 
principal- stress 
 σ1 σ2 σ3 
Dir. 
Inc. 
 
 
31.2MPa 
25.8 MPa 
19.9 MPa 
N110W 
N870E 
Laboratory tested: 
Uniaxial Compressive 
Strength 
Young’s Modulus (lab.) 
Poisson’s ratio 
Estimated/assumed: 
Horiz. by Vertical stress ratio 
Young’s Modulus (rock mass) 
Rock mass unit weight 
 
σci 
 
E 
ν 
 
σh/ σv 
Erm 
ϒ 
 
92.6 MPa 
 
31400 MPa 
0.203 
 
0.5 
15700 MPa 
0.0279MN/m3 
*In-situ stresses measured by 3D overcoring 
 
Table 2. Estimated input parameters used for the 
model 
DescriptionValue 
Filed Stress type: 
Total Stress Ratio (in plane) 
Total Stress Ratio (out-of- plane) 
Locked-in hor. stress (in-plane) (MPa, 
Comp+) 
Locked-in hor. stress (out-of-plane) 
(MPa, Comp+) 
Estimated for rock mass based on Hoek-
Brown Failure Criterion: 
Geological Strength index (GSI) 
Constants (s) from RocLab 
Constants (a) (RocLab) 
Material Constant (mb(peak)) 
 
0.55 
0.59 
 
0 
 
0 
 
 
79 
0.096 
0.5 
13.22 
 
The numerical approach of analysis 
compensates the completely neglected effects of 
stress due to the topographic and tectonic stress 
unlike the deterministic design approaches used 
in evaluation of hydraulic fracturing. The effect 
of topography is very dominant in the stress 
regime in the lower part of the unlined pressure 
tunnel of the project that was analyzed. This 
result revealed when the modes were built. 
Figure 8 shows the effect of the topography on 
the stress regime. 
 
The analysis by numerical modeling revealed 
a conservative result for up to hydrostatic head 
up to 1100 m with a factor of safety 1.3 against 
hydraulic fracturing. Moreover, the result of 
numerical analysis shows fairly good degree of 
correlation between the simulation results and 
what was actually found in the existing project 
unlined tunnel and shaft. Figure 9 shows the 
minimum principal stress (σ3) of the mode and 
the water pressure (γw.H) for the study point at 
location of chainage 11+750 (power house). 
Figure 8. Effect of topography is very dominant 
on the stress regime. 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
6 
 
Increasing the static head on the Nye Tyin 
HEP will increase the water pressure inside the 
tunnel and consequently large rock mass cover 
will be required. The geological restrictions are 
the main challenges in the development unlined 
high-pressure tunnels and shafts. It is essential 
to understand the geologic conditions along the 
tunnel alignment, relative to the hydraulic forces 
that will be applied during operation. 
With respect to the geology condition at Nye 
Tyin Hydroelectric project, increasing head will 
have a challenge in related to the existing minor 
weakness zone on the top of the mountain 
plateau above the power station location even 
though it does not intersect the underground 
powerhouse as well as the tunnel (Lilleland, 
2002). Figure 10 shows the result of the model 
considering the effect of the joint near to the 
power station. 
 
 
3. RESULTS, COMPARISONS AND 
DISCUSSIONS 
The first and foremost requirement for a 
pressure tunnel or shaft is that leakages have to 
be avoided by providing adequate overburden 
which has a weight greater than the water 
pressure. This method was used In Norway 
before the rule of thumb method was introduced 
and in this paper, the method gives surprisingly 
a conservative result of the possibility to 
develop ultrahigh head in unlined tunnels/shafts 
up to static head of 1137 m with a factor of 
safety 1.3 for the exemplified project Nye Tyin 
HEP. In fact, this method does not consider side 
valley cover requirement for confinement, the 
topographic effect on stress, and the existence 
of considerable tectonic stresses. 
The Norwegian rule of thumb has been 
widely applied in cases for tunnels and shafts 
sited in valley sides. It considers both vertical 
cover and the steepness of the slope of the 
adjacent valley side. The method assumes that, 
the minimum in-situ principal stress should 
exceed the water pressure at any point to avoid 
the risk of hydraulic fracturing. The analysis of 
this method indicated a static head of more than 
1427 m with a factor of safety 1.3 being feasible 
to develop for the Nye Tyin HEP. The method 
accounts for gravitational rock stresses only but 
in many cases considerable tectonic and residual 
stresses also exist. Hence the effect of required 
increased confinement should be disregarded 
where the valley is undergoing tectonic 
extensions. This method of criteria for 
confinement is still used in prefeasibility 
studies. 
The Snowy Mountains for confinement 
requirement was recognized during the 
development of the Snowy Mountains project in 
Australia. The side cover is found less effective 
compared to the vertical rock cover to secure 
that the tunnel/shaft has the required 
confinement. This method has fairly similar 
results as the Norwegian rule of thumb method 
with some more conservative result on the side 
cover. Maximum water pressure of 16.77 MPa 
can be safe against hydraulic fracturing based 
on this method of analysis for the Nye Tyin, 
which is hydrostatic head of 1677 m with 1.3-
safety factor. Both methods, Snowy Mountain 
and Norwegian rue of thumb reinforce that the 
pressurized water tunnel and shaft for Nye Tyin 
HEP is placed deep enough laterally and 
vertically. Hence, neither methods are actually 
considering the effect of tectonic horizontal 
stresses and topographic conditions on the stress 
regime. The comparison of depth of minimum 
cover specified by vertical, Snowy Mountain 
and Norwegian rule of thumb are in good 
agreement with the results, while the vertical 
criterion is not to the safe side relative to the 
Figure 9. 	
  σ3 and water pressure for the study point at 
location of powerhouse 
Figure 10. σ3 considering the weakness zone and 
joints near to the study point at chainage 11+873 	
  
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
7 
numerical analysis. For preliminarily layout in 
terms of minimum requirements, it appears that 
the Norwegian and Snowy Mountain criteria are 
very useful tools. 
Two-dimensional standard design charts 
based on the use of a numerical finite element 
model (FEM) has given a solution to 
compensate the completely neglected effect of 
tectonic horizontal stresses and topographic 
conditions on the above deterministic 
approaches. The basic principle of the finite 
element method for this purpose is to find the 
location, which for all parts of the shaft ensure 
that no-where along the unlined pressure tunnel 
or shaft should the internal water pressure 
exceed the in-situ minor principal stress in the 
surrounding rock mass. This method is a useful 
tool at the feasibility stage of the project and it 
makes it possible to find a preliminary location 
of the pressure tunnels and shafts; a location 
that in many case turns out to be the final one. 
The analysis based on this method indicated that 
the existing unlined pressure tunnel and shaft at 
Nye Tyin could handle a maximum static head 
of 1140 m with a factor of safety 1.3, which is a 
conservative result with respect to the above 
deterministic approaches. However, The result 
tends to be mesh-dependent and error can arise 
when selecting the boundary conditions of the 
domain of interest. Besides, using this analysis 
method will lead to errors, as the in-situ 
topography is very simplified and idealize with 
regard to the topography condition used in the 
model. 
Finally, comprehensive 2-dimensional finite 
element calculation using Phase2 has been 
performed and the aim was to analyze the 
minimum principal rock mass stress situation in 
the vicinity of the pressure tunnel and to 
compare it with the induced water pressure 
inside the tunnel and shaft. The maximum static 
head that can be utilized for the existing unlined 
high-pressure tunnel and shaft at Nye Tyin 
hydropower project is 1097 m with 1.3 factors 
of safety. The analysis shows fairly good degree 
of correlation between the simulation results 
and the in-situ situation of the existing unlined 
tunnel. The author believes that the use of 
numerical analysis with profound knowledge of 
the geological conditionof the area will give 
best result in the design of ultrahigh head of 
unlined tunnels and shafts while having 
shortcomings of that it requires rock mass 
parameters such as in-situ stress ratios that will 
be a problem to obtain, especially at the design 
stage when there is no in-situ measured rock 
mass stresses. The advantage of this analysis is 
that the influence to stress distribution of the 
valley side inclination, of major continuities, 
and rock with different properties can be as 
certain. Table 3 shows the summarized results 
of the different design approaches for their 
maximum static head that can be developed 
with safety of factor above 1.3 against hydraulic 
fracturing and uplift. 
 
Table 3. Comparisons and results of analysis 
*A 1.3 factor of safety used and the actual project static 
Head is 1047 m 
 
 
4. CONCLUSION 
The geological restrictions are the main 
challenges in the development ultrahigh head in 
unlined tunnels and shafts. It is essential to 
understand the geologic conditions along the 
tunnel alignment, relative to the hydraulic forces 
that will be applied during operation. Generally 
the rock should be sound and massive with a 
high intact tensile strength and low permeability 
in order to use unlined high-pressure tunnels 
and shafts. 
Development of the design criteria for 
unlined pressure tunnels and shafts has proved 
the need for more rational and comprehensive 
design approach. Empirical and deterministic 
analyses have been established, and design 
charts prepared for use of preliminary feasibility 
studies. A numerical design approach has been 
developed for qualitative thorough design 
analysis. 
Based on the outcome of these design 
approaches, the development of ultrahigh head 
of unlined tunnel and shaft is possible even for 
higher static head for Nye Tyin HEP as well as 
in general. All unlined sections should satisfy 
confinement criteria in order to avoid hydraulic 
jacking, unless the consequences of the 
hydraulic jacking have been reckoned 
acceptable. The unlined sections should be 
Design approaches 
Max. Possible 
static head, (m) 
First Design criteria 1137 
Norwegian rule of thumb 1427 
Snowy Mountain Creation 1677 
Design Charts based on FEM 1140 
Others 1197 
Numerical Analysis 1097 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
8 
located only in rock masses, which are 
sufficiently durable and sound so as to satisfy 
long term requirements. 
It needs to be emphasized that this paper 
covers only the confinement requirements in 
general to develop safe ultrahigh head unlined 
tunnels and shafts against hydraulic fracturing 
of the main failure mode uplift of the ground 
surface for the exemplifying Nye Tyin 
hydroelectric Project. Even though various 
design approaches has been successfully done 
for an overall assessment of the possibility to 
develop ultrahigh head unlined tunnels, detail 
analysis including local fractures effect has not 
been assessed with respect to other fundamental 
mode of failures. These could be such as 
hydraulic jacking of joints or discontinuities, 
hydraulic shearing of joints and local crushing 
or blasting effects on the wall of the tunnel or 
shaft, as the water head becomes ultra high. 
 
REFERENCES 
 
Berdal and Palmstrom A., 1987. Norwegian Design and 
Construction Experience of Unlined Pressure Shaft 
and Tunnels. (Published in International Conference 
on Hydropower. Oslo, Norway,): p. 10. 
Bergh-Christensen, 1971. Engineering Geological 
Considerations for an unlined pressure shaft at 
Mauranger Hydro Power Station. 1987. 
Brekke, T.L.a.R., B.D.,, Design Guidelines for Pressure 
Tunnels and Shafts.: The Institute. 
Broch, E., 1985. Unlined high pressure tunnels in areas 
of complex topography.: Tapir. 
Broch, E., Hydropower '92: 1992. Proceedings of the.: 
A.A. Balkema. Broch,	
  E.,	
  1986.	
  Development	
  of	
  Unlined	
  Pressure	
  
Shafts	
   	
   and	
  Tunnels	
   in	
  Norway..	
   International	
  Water	
  
Power	
   &	
   Dam	
   Construction.	
   1975:	
   IPC	
   Electrical-­‐Electronic	
  Press. 
Broch, E. and Lysne, D.K., Hydropower '97: 1997. 
Proceedings of the 3rd International Conference on 
Hydropower : Trondheim/Norway/30 June-2 July, 
1997: A.A. Balkema. 
Belayneh D.T, 2013. MSc thesis, High pressure unlined 
tunnels and shafts exemplified with Nye-tyin HEP, 
Norwgian University of Science and Technology 
(NTNU). 
Grøv E., Bruland, Nilsen, Krishna Panthi, Ming Lu, 2011. 
Developing future 20 000MW hydro rlrctric power in 
Norway - Possible concepts and need of resources, , 
SINTEF Building and Infrastructure. 
Hoek, E., 2000. Practical Rock Engineering. 
J. Bergh-Christensen, 1982. Design of Unlined Pressure 
Shaft at Mauranger Power Plant. ISRM Symposium: 
p. 6. 
Lilleland, O., 2002. Under Pressure at Tyin. Tunnel and 
Tunnelling, 34 London: Lomax, Erskine and Co. 
Finnes også som: T & T. 
Lu M., 2011. Numerical Analysis for Rock Engineering, 
in Rock Engineering AC. p. 29P. 
Murthy, V.R.K., 1964. Design of Lined and Unlined 
Pressure Tunnels Incuding [sic] Water-hammer 
Effects.: University of Florida. 
Myrvang, A., 1991. Rock Stress and Rock Stress 
Problems in Norway. Hudson, J.A.: "Comprehensive 
Rock Engineering", Pergamon Press. 
Nilsen, B., Palmstrøm A., Engineering Geology and Rock 
Engineering.: Norwegian Group for Rock Mechanics. 
Nilsen, B.and Palmstrøm A., Investigation and Tests 
Engineering Geology and Rock Engineering. 02 NBG-
Handbook: p. 24. 
Nilsen, B. and Palmstrøm A., 1993. Rock Engineering.: 
Norwegian Institute of Technology, Division of 
Hydraulic Engineering. 
R. Benson, Design of unlined and lined pressure tunnels. 
1987/1988 Tunnelling Association of Canada Annual 
Publication. 
Reidar S. K., Bergh-Christensen J. and Torbjørn Yri, 
1998. The New Tyin Hydropower system Engineering 
Geology Report, NORSKHYDRO ASA. 
Ripley, B.D., 1987. Design and Performance of Lined 
and Unlined Pressure Tunnels and Shafts.: University 
of California, Berkeley. 
Norwegian Soil Rock Engineering Association, 1985. 
Norwegian Hydropower Tunnelling.: Tapir Publishers, 
University of Trondheim. 
Lu Ming and Brown E. T., 1988. Designing unlined 
pressure tunnel in jointed rock. International water & 
dam construction, 40 (11): p. 5. 
Tunderbridge, G.L., 1986. Hydraulic fracturing - a simple 
tool for controlling the safety of unlined high pressure 
shafts and headrace tunnels. Proceedings of the 
Intemational Symposium on Rock Stress and Rock 
Stress MeasurementsiStockholm/1-3: p. 7. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Proceedings of the World Tunnel Congress 2014 – Tunnels for a better Life. Foz do Iguaçu, Brazil. 
9